Manual de calcule CYPE CYPECAD
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CYPECAD - Calculations manual
Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
1.7.3. Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
1.8. Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
1. Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
1.8.1. Ultimate limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
1.1. Description of problems to resolve . . . . . . . . . . . . . . . . . . . . .9
1.9. Data entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
1.2. Description of the analysis undertaken by the program . . . . . . .9
1.9.1. General data of the job . . . . .
. . . . . . . . . . . . . . . . . . . . . .35
1.3. Discretisation of the structure . . . . . . . . . . . . . . . . . . . . . . . .10
1.9.2. Loads. Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
1.3.1. Node sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
1.9.3. Wind loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
1.3.2. Force envelopes at supports . . . . . . . . . . . . . . . . . . . . . .14
1.9.4. Seismic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
1.4. Analysis options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
1.9.5. Fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
1.4.1. Redistributions considered by the program . . . . . . . . . . .16
1.9.6. Additional loadcases (special loads) . . . . . . . . . . . . . . . .38
1.4.2. Stiffnesses considered by the program . . . . . . . . . . . . . . .17
1.9.7
. Limit states (combinations) . . . . . . . . . . . . . . . . . . . . . . .38
1.4.3. Torsional stiffness coefficients . . . . . . . . . . . . . . . . . . . . .18
1.4.4. Axial stiffness coefficient . . . . . . . . . . . . . . . . . . . . . . . . .18
1.9.8. General data of floor/groups, columns,
column starts and shear walls (Column Definition tab) . . . . . . . .38
1.4.6. Other options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
1.9.10. Loads. Sloped beams. Diagonal bracing . . . . . . . . . . . .48
1.4.5. Minimum moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
1.9.9. Floor slab data (Column Definition tab) . . . . . . . . . . . . . .40
1.5. Loads to consider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
1.9.11. Stairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48
1.5.1. Vertical loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
1.10. Analysis of the struc
ture . . . . . . . . . . . . . . . . . . . . . . . . . . .49
1.6. Materials used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
1.11.1. Consulting on screen . . . . . . . . . . . . . . . . . . . . . . . . . . .50
1.5.2. Horizontal loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
1.11. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
1.6.1. Concrete for foundations, slabs, columns and walls . . . . .32
1.11.2. Printed reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
1.6.2. Bar steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
1.11.3. Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
1.6.3. Steel for steel columns, beams and baseplates . . . . . . . .33
1.12. Design and check of elements . . . . . . . . . . . . . . . . . . . . . . .55
1.7. Weighting factors . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . .33
1.12.2. Sloped beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
1.6.4. Integrated 3D structures materials . . . . . . . . . . . . . . . . . .33
1.12.1. Horizontal and inclined panel beams . . . . . . . . . . . . . . .56
1.7.1. Analysis method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
1.12.3. Steel beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
1.7.2. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
1.12.4. Columns, shear walls and reinforced concrete walls . . . .61
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1.12.5. Joist floor slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
3. Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
1.12.7. Hollow core slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
3.1.1. Masonry wall properties . . . . . . . . . . . . . . . . . . . . . . . . .88
1.12.6. Composite slabs .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
3.1. Masonry walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
1.12.8. Flat slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
3.1.2. Masonry wall introduction . . . . . . . . . . . . . . . . . . . . . . . .89
1.12.9. Waffle slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
3.1.3. Correct use of masonry walls . . . . . . . . . . . . . . . . . . . . . .89
1.13. Beam deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
3.2. Reinforced concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . .92
1.14.1. One-way spanning slabs . . . . . . . . . . . . . . . . . . . . . . . .69
3.2.2. Load bearing walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95
1.14. Slab deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
3.2.1. Reinforced concrete basement walls . . . . . . .
. . . . . . . . .93
1.14.2. Composite slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
3.2.3. Correct use of reinforced concrete walls . . . . . . . . . . . . . .96
1.14.3. Flat and waffle slabs . . . . . . . . . . . . . . . . . . . . . . . . . . .69
3.2.4. Wall design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97
1.14.4. Deflection between 2 points . . . . . . . . . . . . . . . . . . . . . .69
3.2.5. Foundation design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98
1.14.5. Foundation elements . . . . . . . . . . . . . . . . . . . . . . . . . . .77
3.3. Practical advice for reinforced concrete wall in buildings . . . .98
2.1. Discretisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
4. Footings and pile caps . . . . . . . . . . . . . . . . . . . .102
2.3. Design options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
4.2. Advanced design of surface foundations
. . . . . . . . . . . . . . .103
3.3.1. Revision of the analysis results of the wall . . . . . . . . . . . .99
2. Mat foundations and foundation beams . . . . . . .78
2.2. Subgrade modulus for mat foundations and foundation beams78
4.1. Footings and pile caps . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
2.4. Loads to consider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
4.3. Pad footings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104
2.5. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
4.3.1. Bearing pressures on the soil . . . . . . . . . . . . . . . . . . . . .104
2.6. Checks and combinations . . . . . . . . . . . . . . . . . . . . . . . . . . .81
4.3.2. Equilibrium states . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
4.3.3. Concrete states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
2.7. Design of mat foundations and foundation b
eams . . . . . . . . .82
2.8. Analysis results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
4.4. Strip footings below walls . . . . . . . . . . . . . . . . . . . . . . . . . .107
2.9.1. Foundation beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
4.6. Tie beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108
4.5. Strap beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
2.9. Element design and check . . . . . . . . . . . . . . . . . . . . . . . . . . .86
4.7. Pile caps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
2.9.2. Mat foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
2.10. General recommendations . . . . . . . . . . . . . . . . . . . . . . . . .87
4.7.1. Design criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
4.7.2. Sign criteria . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . .110
2.10.1. Mat foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
4.7.3. Design and geometry considerations . . . . . . . . . . . . . . .110
2.10.2. Foundation beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
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6.6. Comments on the use of joist floor slabs . . . . . . . . . . . . . . .121
4.8. Baseplates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112
4.9. Mass concrete footings . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
7. Sloped floor slabs . . . . . . . . . . . . . . . . . . . . . . . .124
4.9.1. Design of footings as rigid solids . . . . . . . . . . . . . . . . . .114
7.1. Element design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126
4.9.2. Design of footings as mass concrete structures . . . . . . .114
4.9.3. Design report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115
8. Composite beams . .
. . . . . . . . . . . . . . . . . . . . . .127
4.11. Footings with non-rectangular limits . . . . . . . . . . . . . . . . .117
10. Stairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131
4.10. Specific checks due to the code that has been considered (footings, beams and pile caps) . . . . . . . . . . . . . . . . . . . . . . . . . . . .117
9. Composite slabs . . . . . . . . . . . . . . . . . . . . . . . . .128
10.1. Common data of the staircase . . . . . . . . . . . . . . . . . . . . . .131
5. Corbels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118
10.1.1. Geometrical properties . . . . . . . . . . . . . . . . . . . . . . . .131
6. Joist floor slabs . . . . . . . . . . . . . . . . . . . . . . . . .119
10.1.2. Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132
6.1. Concrete joists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
10.2. Staircase flight data . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .132
6.1.2. Stiffness considered . . . . . . . . . . . . . . . . . . . . . . . . . . .119
10.3.1. View staircase reinforcement details . . . . . . . . . . . . . .133
6.1.1. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
10.3. Results, reports and drawings of the Stairs module . . . . . .133
6.1.3. Estimating the deflection . . . . . . . . . . . . . . . . . . . . . . . .119
10.3.2. View forces and displacements using contour maps . . .133
6.2. Reinforced/Prestressed joists . . . . . . . . . . . . . . . . . . . . . . .119
10.3.3. Staircase design . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
6.3. In-situ joist floor slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
10.3.4. Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
10.3.5. Stair drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
6.3.1. Geometry . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .120
6.3.2. Stiffnesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
11. Integrated 3D structures . . . . . . . . . . . . . . . . . .135
6.3.3. Estimating the deflection . . . . . . . . . . . . . . . . . . . . . . . .120
6.3.4. Design for bending . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
12. Rigid Diaphragm . . . . . . . . . . . . . . . . . . . . . . . .136
6.4. Steel joists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
12.2 Rigid diaphragm in reinforced concrete walls,
masonry walls and reinforced concrete block walls . . . . . . . . . . .136
12.1 Rigid diaphragm in exempt beams . . . . . . . . . . . . . . . . . . .136
6.3.5. Design for shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
6.4.1. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
12.1. Load codes . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . .137
6.5. Open-web joists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
12.2. Material codes
6.5.1. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138
12.3. Combinations codes . . . . . . . . . . . . . . . . . . . . . . . . . . . .139
6.5.2. Considered stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . .121
6.5.3. Joist design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
13. Code implementation . . . . . . . . . . . . . . . . . . . .137
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14. Interaction of the structure with
the construction elements . . . . . . . . . . . . . . . . . . .140
14.1. Model used to analyse the effect
of the non-structural elements . . . . . . . . . . . . . . . . . . . . . . . . . .145
14.2. Cracked or fissured states . . . . . . . . . . . . . . . . . . . . . . . . .145
14.3. Analysis example . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .147
14.3.1. Description of the structure . . . . . . . . . . . . . . . . . . . . .147
14.3.2. Construction elements . . . . . . . . . . . . . . . . . . . . . . . . .148
14.3.3. Seismic action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148
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Presentation
CYPECAD is the software for reinforced concrete and steel buildings which provides the spatial analysis, structural element design, reinforcement and section edition, and construction drawings of the structure.
It carries out the analysis of three dimensional structures composed of supports and floor slabs, including their foundations, and the automatic design of reinforced concrete and steel elements.
If the user has acquired Metal 3D, integrated Metal 3D structures (steel and timber sections) can be
included with 6 degrees of freedom per node, with the design and optimisation of sections.
With CYPECAD, the engineer holds a precise and e
fficient tool to resolve all the aspects related to
the analysis of the structure of any type of concrete as well as being adapted to the latest international Codes.
The user will always have complete control of the project, without risks.
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1. Calculations
1.1. Description of problems to resolve
The deformation compatibility is established at all nodes,
taking into account 6 degrees of freedom and the hypothesis that each floor of the structure cannot be deformed, preventing any relative displacements between nodes of the
floor (rigid diaphragm). Therefore, each floor will only be
able to rotate and suffer displacements as a whole (3 degrees of freedom).
CYPECAD has been conceived to carry out the force
analysis and design of reinforced concrete and steel structures supporting joist floor slabs (generic, reinforced, prestressed, in-situ, steel and open web joists), hollow core
plate slabs, composite slabs, waffle slabs and f
lat slabs in
buildings exposed to vertical and horizontal loading. The
beams supporting the slabs can be reinforced concrete,
steel or composite (steel and concrete) beams. The supports can consist of reinforced concrete or steel columns,
reinforced concrete shear walls, reinforced concrete walls,
with or without lateral pressures or masonry walls (generic
or concrete block walls). The foundations can be composed of footings or pile caps, or alternatively by use of
mat foundations. The foundations can be designed individually with respect to the rest of the structure by simply introducing the column starts. Reinforced concrete stairs, supported by the floor slabs can be also be introduced.
The rigid diaphragm state for each independent zone is
maintained even if only beams and no floor slabs have
been introduced in the floor, , except for the case of exempt
beams which the user disconnects from the rigid diaphragm and walls that are not in contact with floor slabs
(as of the 2012.a ve
rsion) (please refer to chapter 12. Rigid
diaphragm of this manual).
When independent zones exist on a single floor, each one
will be taken as a different section when regarding the deformations of the zone and the influence of the other zone
will not be taken into account. Therefore, each floor will behave as independent non-deformable planes. A column
which is not connected to an element is considered as an
independent zone.
Using the program, the technical drawings of the structure
can be obtained which include the dimensions and reinforcement of beams, columns, shear walls and walls via
plotter, printer and/or DXF/DWG or PDF files, as well as the
analysis reports and results. If the Metal 3D license has
been acquired, Integrated 3D structures can be introduced using steel, timber and aluminium bars.
A static analysis is carried out for all load states (except
when dynamic loading is considered due to seismic loading, in which case a modal spectral analysis is used). A linear beha
viour of the materials is assumed and therefore, a
first order analysis in obtaining displacements and forces.
1.2. Description of the analysis undertaken by
the program
When analysing Integrated 3D structures, 6 degrees of
freedom will always be used.
The analysis of the forces is carried out by means of a spatial 3D analysis using stiffness matrices forming all the elements defining the structure: columns, RC shear walls,
beams and floor slabs.
Stairs also have 6 degrees of freedom, are resolved independently and their reactions are transmitted to the structure.
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1.3. Discretisation of the structure
inciding with the discretisation nodes along the wall
support, which considerably increases its stiffness
(x100). It can be interpreted as behaving as an extremely rigid supported beam with very short spans. The
types of supports are:
The structure is discretised as bar elements, bar and node
meshes, and triangular finite elements as follows:
• Columns
-
Th
ese are vertical bars between floors, with an initial
node at the foundations or on another element such as
a beam or slab, and other nodes at floor intersections,
its axis being the cross section of the element. Eccentricities due to dimension variations with increasing
height at each floor are considered.
-
The length of the bar is the height or free distance to
the surface of other elements between its initial and final floors.
Fixed. Displacements and rotations prevented in all
directions
Pinned. Prevented displacements but free rotation.
Pinned with free horizontal displacement. No
vertical displacement permitted but has free horizontal displacement and rotation.
The effects these types of supports have on the remaining elements if the structure should be taken into account. If vertical movement of the structure has been
prevented, all the structural elements supported by or
connected to them will also have their vertical movement prevented. This is important if columns with e
xternal fixity are being used and are in contact with these
types of supports; their load will be ‘absorbed’ by the
support and will not be transmitted to the foundations.
This may even cause negative reactions to arise, which
represent the weight of the column or part of its weight
‘hanging’ at the wall support.
• Beams
These are defined on the floor layout by fixing nodes at
intersections with the surfaces of support elements (columns, shear walls or walls), as well as at intersection
points with floor slab elements and beams. This way
nodes are created along the axis and at the ends, at
the ends of overhanging beams, free ends or at contact
points with other floor slab elements. They possess, by
default, 3 degrees of freedom, maintaining the rigid diaphragm hypothesis between all the elements located
on the floor. For example, a continuous beam supported by various columns will conserve the rigid diaphragm theory even though no floor slabs are present.
Exempt beams can b
e disconnected from the rigid diaphragm. Please refer to chapter 12. Rigid diaphragm.
Especially in the case of a pinned connection with displacement, when a beam is connected to the end of a
wall support a fixed effect is obtained due to the beam
being taken as an extension of the crown beam of the
wall support. This can be observed in the force envelopes whereby negative moments are present at the
end. In reality, it must be verified whether or not these
conditions will actually be met on site as they must be
complied with when it is executed.
Reinforced concrete, steel and composite beams are
available. Beams are discretised as bars whose axis
coincides with the mid plane passing through the vertical web, and at the height of its centre of gravity.
If the beam is not a straight extension of the wall support
but deviated from its axis, a hinged effect is produced.
Wall support simulation. Three types of beams (external fixity beam) are available which simulate a wall
support whic
h is discretised as a series of supports co-
If the beam is a straight extension of the wall support,
but the user does not wish for the connection to behave
as a fixed connection, the connection should be pinned.
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These may be analysed based on their construction
process in an approximate manner by modifying their
edge fixities using a simplified method.
It is not possible to obtain the reactions on this type of
support.
Foundation beams. These are ‘floating’ beams supported by elastic soil. They are discretised into nodes
and bars, where the nodes are assigned a spring constant which, in turn, is defined by the subgrade modulus (see Mat foundations and foundation beams
chapter).
• Flat slabs
Flat slabs are discretised as meshes of bar type elements
possessing a maximum size of 25 cm. A static condensation is carried out (exact method) of all the degrees of
freedom. Deformation due to shear is considered and the
rigid diaphragm hypothesi
s is maintained. The torsional
stiffness of the elements is taken into account.
• Sloped beams
These are bars spanning between two points, which
can be at the same elevation or floor, or at different
floors and which create two nodes at these intersections. When a sloped beam joins two independent
zones the non-deformable effect of the plane with rigid
behaviour is not produced, as they possess six degrees of freedom without restrictions.
• Composite slabs
These are joist floor slabs discretised by bars every
40cm. They are made up of a flat slab and a ribbed
deck which acts as formwork for the slab. The deck can
be used so it behaves in the following ways: as lost
formwork (Form deck) and contributing deck (Composite deck). For more information, please consult the
Composite slabs chapter.
• Corbels
Please consult the Corbels chapter of this manual.
• Joist floor slabs
• Mat foundations
Joists are bars defined within slabs between beams or
walls which create nodes at
the face intersections and
corresponding axis of the beam they intersect. Double
or triple joists can also be defined. The geometry of the
joist section with which each joist is simulated in the
program is defined in the corresponding data file of the
slab. Please consult the chapter on Joist floor slabs
of this manual for more details.
These are ‘floating’ solid slabs whose discretisation is
identical to that of flat slabs used at floor levels and
whose spring constant is defined based on the assigned subgrade modulus. Each slab is permitted to
have different coefficients. (see Mat foundations and
foundation beams chapter)
• Waffle slabs
Waffle slabs are discretised into bar type element
meshes whose bar size is one third of the rib spacing
defined in the data window of the slab. Their moment
inertia (for both solid and lightweight zones) is half of
the solid zone and the torsional inertia is double that of
the moment inertia.
• Hollow core slabs
These are joist floor sl
abs discretised by bars every
40cm. The geometrical and resistance properties are
defined in a slab properties sheet, which may be introduced by the user and hence create a library of hollow
core slabs.
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The dimensions of the mesh are kept constant for both solid and lightweight zones, adopting the previously indicated
mean inertias at each zone. Deformation due to shear is
considered and the rigid diaphragm hypothesis is maintained. The torsional stiffness of the elements is taken into
account.
of each side can be different at each floor and their
thickness can be reduced at each floor.
For walls, one of the transverse dimensions of each
side must be at least five times greater than the other
dimension. If this condition is not verified, their discretisation as a finite elements is not adequate and can be
considered as being columns and treated as linear elements.
• Shear walls
Both beams and slabs can be connected to the sides
of the walls at any position
or direction. All nodes that
are generated correspond to one of the nodes of the triangular finite element mesh of the wall.
These are vertical elements with any transverse section
composed of multiple rectangles between each floor
and defined by an initial and final floor. The dimensions
of each side are constant in height, however their thicknesses may be modified.
The discretisation is undergone by finite elements
whereby the wall resembles a thick three dimensional
sheet, which takes into account deformations due to
shear. They are composed of six nodes, at the vertices
and at the mid-points of the sides, each with six degrees of freedom. The wall is discretised into a triangular mesh adjusted to the dimensions of the wall, its
geometry, openings and with a more refined mesh in
critical zones, which reduces the size of the elements at
angles, edges and singularities.
For shear walls, one of the transverse dimensions of
each side must be at least five times greater than the
othe
r dimension. If this condition is not verified, its discretisation as a finite element is not adequate and can
be considered as being a column and treated as a linear element.
Both beams and slabs can be connected to the sides
of the walls at any position or direction, by means of a
beam with a width of the thickness of the span and a
constant depth of 25cm. The nodes do not coincide
with the nodes of the beam.
Walls which are not in contact with any floor slabs are
not considered as rigid diaphragms at that floor level.
Please consult chapter 12. Rigid diaphragm.
• Stairs
Stairs are discretised using triangular thick shell finite
elements, for both sloping and horizontal spans. The
start and end supports are discretised as a floor slab simulation by means of a beam with elevated stiffness,
and the intermediate supports by means of elastic supports simulating real masonry walls or ties. The loadcases considered are only those corresponding to gravitational loads; dead and live lo
ads.
Fig. 1.1 Shear wall examples
• Reinforced concrete walls, masonry walls and reinforced concrete block walls
These are vertical elements with any transverse section
composed of multiple rectangles between each floor
and defined by an initial and final floor. The dimensions
Once the reactions have been established after a design process (carried out independently), they are inteCYPE
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grated at the supports and represented as line loads,
which are applied to the structure at its connection
points and then included in the analysis of the complete structure. Their design has not been integrated in
the analysis procedure due to the great impact of horizontal loads on them.
1.3.1. Node sizing
A group of general nodes with finite dimensions is created
at column axes and at intersections of slab elements with
beam axes. Each general node has one or several associated nodes. The associated nodes are formed at intersections of slab elements with beam f
aces and column faces,
and at intersections of beam axes with column faces.
Fig. 1.2 Discretisation of the structure
δz1, θx1, θy1 are considered as being the displacements of
column 1 and δz2, θx2, θy2 are considered as being the displacements of point 2, which represents the intersection of
the beam axis with the face of the column. Ax and Ay are
the coordinates of point 2 relative to point 1.
Given that they are related due to their deformation compatibility with the assumed flat deformation, the general
stiffness matrix and associated matrices can be resolved
and hence obtain the displacements and forces in all the
elements.
The following conditions are met:
As an example, the discretisation would be carried out as
shown in the diagram below. Each finite dimension node
can have several or no associated nodes, but there will always be one general node.
Given that the program does take into account the size of
the column, and supposing a linear behaviour within the
support
, with flat deformation and infinite stiffness, the deformation compatibility is considered.
The size of the beams is taken into account in the same
way, considering their deformation to be flat.
The bars defined between the axis of column 1 and its
faces are considered as being infinitely rigid.
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In the overall analysis of frames, when lef is less than the
distance between axes of columns the dimensions of the
joints should be taken into account by introducing rigid elements between the centroidal axis of the column and the
end section of the beam.”
Generally, the reaction at the support is eccentric due to
the presence of an axial force and a moment being transmitted to the support, the size of the nodes is considered
when rigid elements have been introduced between the axis of the support and the end of the beam. This is reflected
in the considerations detailed below.
Fig. 1.3
The structural model defined by the program responds to the
data introduced
by the user, therefore special attention must be
paid that the geometry defined for the elements is compatible
with the type of chosen element and that its use is adequate in
real situations.
A linear reply is assumed within the support representing
the reaction of the loads transmitted by the lintel and those
applied at the node which have been transmitted by the
rest of the structure.
Particular attention is brought to those elements which are considered as being linear in the program (columns, beams, joist)
when they may not be in real life, resulting in elements with two
dimensional or three dimensional behaviour whereby the analysis criteria and reinforcement provided by the program will not
be adjusted to the real design of these elements.
Examples of where this may occur include: corbels, wall-beams
and plates, situations which may occur in beams, slabs which
are really beams, or columns or short shear walls not complying
with the geometric limits between their transverse and
longitudinal dimensions. For these cases, the user must carry out the necessary manual corrections after the analysis so the results of
the theoretical model are adapted to their physical reality.
It is known that:
1.3.2. Force envelopes at supports
The 1990 CEB-FIP Model Code, which inspired the Eurocodes, is considered. When quoting the design effective
span, article 5.2.3.2. indicates the following:
Fig. 1.4
The moment equations reflect, generally, a cubic parabolic
curve with the format:
“Usually, the span l has to be introduced as the distance
between adjacent support axes. When reactions are located significantly away from the axis of support, the effective
span has to be calculated taking into account the real position of the support section.
The shear force is the corresponding differential equation:
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By assuming the following conditions:
x=0
Eurocode 2 allows for moments to be reduced at the supports;
the reduction depending on t
he support reaction and width:
Q = Q1 = c
x=0
M = M1 = d
x=1
M = M2 = al3 + bl2 + cl + d
x=1
Q = Q2 = 3al2 + 2bl + c
If it is to be executed as a single element between supports, the design moment can be taken as that of the support face and no less than 65% of the support moment, assuming a perfect fixed connection at the faces of the rigid
supports.
a system of four equations with four unknown variables,
which can easily be resolved, is obtained.
The force diagrams are as follows:
In this sense, it is worth mentioning the Argentinean codes:
C.I.R.S.O.C. which are based on the German D.I.N. codes
which allow for the parabolic rounding of the force diagrams depending on the size of the supports.
Within the support, the depth of the beams is considered to
increase in a linear manner, in accordance with a 1:3 slope,
up to the axis of the support. By considering the size of the
nodes, the parabolic rounding of the force diagrams and the
increase of depth within the support, a m
ore economic longitudinal reinforcement solution is obtained for bending in
beams; as the maximum steel area occurs between the face
and axis of the support, the most usual case being at the
face depending on the geometry that has been introduced.
Bending moment diagram Shear force diagram
Fig. 1.5
These assumptions were taken on by several authors
(Branson, 1977) and are related with the debate on the design span and free span and the way in which it is contemplated in various codes, as well as whether the design moment is calculated taking the distance between support axes or support faces.
In the case of a beam supported by a long element such as
a wall or shear wall, the moment diagrams will be extended
at the support as of the face of the support for a length
equivalent to that of the depth of the beam, designing the
reinforcement up to this length and not extending it past
the point where it is not required. Even if the beam has a
greater width than the support, the beam and i
ts reinforcement are interrupted once it has penetrated a distance of
one depth into the shear wall or wall.
The structure is being idealised into linear elements, with a
length to be determined by the real geometry of the structure. In this sense, the size of the columns should be taken
into account.
It should not be forgotten that, to consider an element as
being linear, the beam or column is to have a span or element length greater than a third of its mean depth and
greater than four times its mean width.
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1.4. Analysis options
at their faces, i.e. the free span is affected. The new moment values within the support are calculated using the moments redistributed at the face and taking into account the
rounding of the force diagrams indicated in the previous
section.
An ample series of structural parameters of great importance for obtaining forces and for the design of elements
can be defined. Given the vast amount of options available,
it is recommended th
e help explanations of the options be
consulted.
Additionally for beams and floor slabs, besides the moment
redistributions, the user can define the minimum positive
and negative moments specified by the code in use.
The general options for beams, floor slabs, joints are located in the Beam Definition tab > Job. The reinforcement
tables and specific options for each element can be found
in General data > By position icon (situated to the right
of Steel: Bars). The most significant of these are mentioned
below.
Fixity coefficient at the last floor
The negative moments at the connection between the top
of the last span of a column with the end of the corresponding beam can optionally be redistributed. This value varies
between 0 (pinned) and 1 (fixed), even though 0.3 is
recommended as an intermediate value (default value).
1.4.1. Redistributions considered by the program
Negative moment redistribution coefficients
The program undertakes a linear interpolation between the
stiffness
of bars fixed at either end and those with one end
fixed and the other pinned, which affect the EI/L terms of
the matrices of the last span of the column:
A negative moment redistribution of up to 30% is accepted
in beams in joists. This parameter can be optionally established by the user, however it is recommended it be set at
15% for beams and 25% for joists (default values). This redistribution is carried out after the analysis.
By considering a moment redistribution, the resulting reinforcement is more expensive but is safer and easier to execute on site. However, it must be noted that an excessive
redistribution produces deflections and cracking which are
incompatible with the internal partitions.
Where α is the value of the introduced coefficient.
Fixity coefficient at the top and bottom of columns, at
slab, beam and wall surfaces; pinning of beam ends
A fixity coefficient can also be defined for each column
span at its start and/or end (0 = pinned; 1 = fixed) (default
valu
e). The coefficients corresponding to the top of the column at its final span are multiplied by these. This plastic
joint is physically considered at the connection point of the
top or bottom of the column with the beam or flat/waffle
slab reaching the node.
A redistribution of 15% in beams produces generally acceptable results and can be considered as the optimum
value. In slabs it is recommended a redistribution factor of
25% be used, which is equivalent to approximately equalising the positive and negative moments.
The moment redistribution is carried out using the moments at support surfaces, which in the case of columns, is
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column and shear wall contact edges where the connection
is always taken as fixed. A rigid bar is defined between the
support and the axis, and so there is always a moment
present at the axis produced by the shear at the edge due
to its distance to the axis. This moment becomes a torsional moment if the reinforcement is n
ot continuous with that of
adjacent slabs. This option should be used with special
care because if the edge of a panel is pinned at the intersecting surface with its perimeter beam and the beam’s torsional stiffness is reduced, without it becoming a mechanism, ridiculous deflection results may be obtained of the
panel at its edge and therefore, also of the design forces.
Fig. 1.6
It may occur that absurd results, even mechanisms, be obtained at beam ends and at tops of columns when very
small coefficients are used due to the presence of two
hinges being connected by rigid spans.
Fig. 1.8
Pinned connections can also be defined at beam ends.
They are physically present at the support surface, be it a
column, wall, shear wall or wall support.
Fig. 1.7
A fixity coefficient can be defined when using flat slabs,
joist floor slabs and waffle slabs at their supported edges.
The value may oscillate between 0 and 1 (default value).
These redistributions are taken into account in the ana
lysis
and therefore affect the final displacements and forces that
are obtained.
A fixity coefficient whose value may vary between 0 and 1
(default value) may be defined at beam edges, in a similar
way as for slabs only here for one or several edges, due to
it being specified using a beam.
1.4.2. Stiffnesses considered by the program
To obtain the terms of the stiffness matrix, the gross section
of all concrete elements are considered.
When fixity coefficients are defined simultaneously at beam
and slab edges, these are multiplied by one another to obtain the resulting coefficient to apply at each edge.
When obtaining the terms of the stiffness matrix, the following values have been distinguished:
EI/L: Bending stiffness
GJ/L: Torsional stiffness
EA/L: Axial stiffness
The defined plastic joint is created at the edges of slabs
and at the edge of beams and walls, and is not effective at
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1.4.4. Axial stiffness coefficient
And the coefficients indicated in t
he following table have
been applied:
Element
(Ely)
(Elz)
(GJ)
Columns
G.S.
G.S.
G.S. · x
Sloped beams
G.S.
G.S.
G.S. · x
Steel or concrete beams
G.S.
Joists
G.S.
∞
∞
G.S. · 10-15
∞
G.S. · 102
Shear walls and walls
Flat and waffle slabs
Limit beam
Wall support
(external fixity beam)
Hollow core plates
and composite slabs
The shortening of reinforced concrete columns, walls and
shear walls due to axial forces is taken into account by the
program. This is affected by an axial stiffness variable between 1 and 99.99 which enables to simulate the construction process of the structure and its influence on the final
forces and displacements. The recommended value lies
between 2 and 3, where 2 is provided as the default value.
(EA)
G.S. · axial
stiffness coeff.
G.S.
∞
G.S. · x
∞
G.S. · x
G.S. · x
∞
G.S. · x
∞
G.S.
G.S.
F.E.
G.S.
∞
G.S. · x
G.S.
∞
G.S. · x
1.4.5. Minimum moments
∞
A minimum moment represented as a fr
action of that of a
simply supported element (wl 2 /8) may be covered by
beams. This minimum moment can be defined for both
negative and positive moments with a wl2/x format, where x
is a whole number greater than 8. The default value is 0, i.e.
they are not applied.
G.S. · axial
stiffness coeff.
∞
It is recommended that reinforcement capable of resisting a
negative moment of wl2/32 and a positive moment of wl2/20
be placed. This minimum moment requirement can be applied to the whole structure or only part of it, and may also
be different for each beam. Each code usually indicates the
minimum values to apply.
∞
G.S.: Concrete gross section
∞: not considered due to the relative non-deformable
shape of the floor
x: Torsional stiffness reduction coefficient
F.E.: Flat finite element
Similarly, minimum moments can be defined for joist floor
slabs and hollow core plates. They can be defined for the
entire job or for individual panels and/or different values. A
value of ½ of t
he static moment (=wl2/16 for a uniform
load) is reasonable for positive and negative moments. It is
recommended the user consult the Options.
1.4.3. Torsional stiffness coefficients
An option exists whereby a torsional stiffness reduction coefficient can be defined (x). This option is not applicable to
steel sections. When the dimension of the element is less
than or equal to the value defined for short bars, the value
defined within the options will be taken. The gross section
(G.S.) will be considered for torsion GJ, and for when it is
required to achieve equilibrium of the structure.
The bending moment envelopes will be displaced so that
these minimum moments are met, followed by the negative
moment redistribution that is to be applied.
The equivalent value of the applied line load is:
Consult Job > General options > Torsional stiffness
reduction coefficients for default values.
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If a minimum moment (+) has been considered, it must be
verif
ied that
intermediate overlaps at floor level eliminated until the
indicated length is reached without exceeding it. The
process is applied starting at the top pf the column and
working its way down, as long as the reinforcement is
identical.
The overlap at each floor level, in the case of disconnected columns, can be ignored and hence provide reinforcement without overlaps until the next floor or overlapping at all floors, even though no beams reach the
columns at that floor, as long as the reinforcement is
identical.
If the applied minimum moment is less than the design moment, the greatest of the two is taken.
• Cutting of starter bars at the last span (top of column). This option cuts the starter bars at the top of the
column’s last span. Only drawings and reinforcement
take-off values are affected by this option. The process
is not analysed and so care must be taken. It is recommended the fixity coefficient at the last floor be reduced
to its minimum value as well as activ
ating the reduction
of anchorage lengths at the last floor. It may arise, however, that even by applying these options, if the bars
have large diameters, they may have to be bent at their
ends. This is cancelled by this option.
Fig. 1.9
Note that these considerations work correctly with line
loads and approximately with point loads.
1.4.6. Other options
• Reduction of anchorage lengths in columns. The
reduction of anchorage lengths at start level at intermediate floors (default option = deactivated) and at the
last floor (default option = activated) can be activated
or deactivated, reducing, in accordance with the ratio of
the real stress in the reinforcement to the maximum
stress. In this case those columns containing reinforcement of the same diameter will result in having starter
bars of a different length as a result of the analysis and
therefore cannot be matched. If this is to be so, deactivate the option, even though slightly greater starter bars
will be obtained at the la
st span.
Below are options that have not yet been mentioned which
influence the analysis.
Columns
• Vertical reinforcement layout (maximum lengths,
connection of short spans, intermediate overlaps). The
maximum length of a bar (default value of 8m), makes it
compulsory for reinforcement overlaps to used if a
span exceeds this value.
The maximum connection length for short spans (default value of 4m) is activated when the elevation difference between floors is small. The spans are joined and
• Reinforcement symmetry criteria. The reinforcement
layout can be defined in the reinforcement tables. They
may be the same or different for sides X and Y of the
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• Transitions due to dimension variation. When the
change in section of a column from one floor to the next
is large, the vertical reinforcement must be bent. The
angle at which the reinforcement is bent is limited. If
these geometric conditions are exceeded, the reinforcement must be cut and anchored in
the bottom span
and new starter bars placed corresponding to the reinforcement of the span above. The bending angle depends on the depth of the slab or beam the column
reaches.
column section. During the analysis, the program runs
through the reinforcement table and selects the first reinforcement distribution which complies for all the design force combinations as well as consisting of a symmetrical layout in its four sides. If the total reinforcement
area is compared for both cases and the percentage
difference obtained, the layout complying with that
marked in the % difference box of the option (default
value of 0%, i.e. not symmetrical) shall be selected. If
the column section reinforcement is to be symmetrical,
introduce a high value, e.g. 300.
• Rounding of bar lengths. Bars are commonly cut so
their lengths are a multiple of a value (default value
5cm) so to ease work on site and fabrication.
• Bar continuity criteria. Columns are analysed by
span starting at the top and
moving downwards whereby, in usual circumstances, their reinforcement increases in diameter as the column descends. However this
does not always occur due to the results provided by
the program being those obtained from analysing the
forces acting on the column and its dimensions. Using
this option, one can force the program to maintain the
reinforcement; the bar diameter at the corners and
faces, as well as the number of bars and apply it from
the last or penultimate floor to the first span. This provides results with less discontinuity in the reinforcement.
• Hatching of columns and shear walls. These are
symbols which graphically represent if a column starts,
continues to another floor or ends. The user may
choose which to apply.
• Reinforcement splices at central span zones. For
seismic zones, the reinforcement overlaps are moved
to the central part of the span, far from the areas submitted to the maximum forces. The default setting of
this option is set as deactivated, howeve
r it is recommended it be activated where high seismic activity is
present.
The program applies continuity criteria applicable to
corner bar diameters as of the penultimate floor.
• Overlaps in walls and shear walls. Verifies that the
overlap is in compression or in tension, applying an amplification coefficient to the splice length which depends
on the bar separation.
• Geometric cover. Distance between the external surface to the first reinforcement element; the stirrups (the
default value depends on the selected code).
• Required compliance factor for walls and shear
walls. The reinforcement of a wall or shear wall span
may contain peak stresses which penalise the reinforcement if the user intends for the wall to pass with a
100% compliance factor. Using this option, a smaller %
compliance can be checked or alternatively, the reinforcement may be modified and check its compliance
factor. During the analysis, the reinforcement is designed in such a way that a compliance fac
tor is at least
• Steel column layout. The user can opt to reduce the
size of the introduced section, if possible, or maintain
and check it. It is important to bear in mind that the
force analysis is undertaken using the section that has
been introduced. If this is modified and the change in
dimensions is large, it is recommended the structure
be reanalysed to take into account this change. During
the analysis, the program locates the most economic
section.
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• Concrete cover in beams (top, bottom and lateral)
the default value of 90%. It is convenient that this value
be checked and if less than 100% see at which points
the reinforcement fails and if local reinforcement is necessary.
• Concrete cover in foundation beams (top, bottom and
lateral)
• Properties of precast beams*
• Stirrup layout. It is convenient stirrups be placed at intersections with slabs or beams (the default setting of
this option is set as activated), also at the to
p and bottom of columns at an established height and with a
smaller separation than in the rest of the column (default setting = deactivated). It is recommended it be
activated for structures in seismic zones.
• Prestressed beam library
• Error evaluation
• Frame ordering criteria
• Beam numbering criteria
• Assembly reinforcement
• Joining of assembly reinforcement in overhangs
• Column start options
• Shear envelopes (continuous or discontinuous)*
• Minimum ratios
• Shear reinforcement (provision of skin reinforcement,
section for shear check)*
• Corbel options
• Stirrup selection*
• Cracking*
Beams
• Minimum foundation beam ratios
• Beam reinforcement within walls and crown beams
Below are options relative to beams.
• Symmetrical top reinforcement in single span beams
Flat slabs, composite slabs and waffle slabs
• Percentage difference for symmetrical top reinforcement
• Flat slab and waffle slab reinforcement
• Hook layout cr
iteria
• Minimum steel areas
• Hooks at ends of alignment
• Mechanical steel area reduction
• Minimum stirrup length
• Torsion reinforcement
• Symmetry in stirrup reinforcement
• Minimum reinforcement bar lengths
• Stirrups of different diameters in a beam
• Flat slab cover
• Anchorage length in stirrup closure
• Waffle slab cover
• Bend hooks in U
• Multiple stirrup layout
• Detail base reinforcement in drawings (default option =
deactivated). It is not drawn or measured if deactivated.
• Prestressed beam stirrups
• Hooks in flat slabs
• Prefabricated beam reinforcement
• Rounding of bar lengths
• Beam detailing for seismic design
• Order and numbering criteria in flat slabs
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• Active deflection and total long term deflection
– Constructive process
• Rectangular flat slab reinforcement
• Cover in foundations
• Shear in in-situ joist floor slabs
• Cover in joist floor slabs, hollow core sl
abs and composite slabs
• Buckling coefficients for sloped beams
• Buckling coefficients for diagonal braces
Stairs
• Match reinforcements
Footings and pile caps
• Reinforcement layout
• General and specific options
• Starter bars at start and dowel bars at end
• Geometric cover
• Anchorage length in slab
Strap and tie beams
• Depth of foundation
• General and specific options
Beam and slab general options
• General drawing options*
Drawing
• Maximum bar cut off length*
• Layer, text size and pen thickness configuration for
drawings*
• Minimum steel areas for top reinforcement in joist floor
slabs
• Minimum steel areas for top reinforcement in hollow
core plates
There are options which are saved and conserved with the
job. Others (*) are general options and may therefore vary
from job to job.
• Reinforcement in usual slabs
• Reinforcement in hollow core plate slabs
To recover the default options, an ‘empty’ installation must
b
e completed, without the existence of the USR directory.
This way all the default options and tables will be installed.
Some options contain a button offering to install the default
settings which allows for them to be recovered directly without having to execute the ‘empty’ installation.
• Minimum moments to cover with reinforcement in slabs
and beams
• Girder (beam) reinforcement
• Torsional stiffness reduction coefficient in joist floor
slabs
• Consideration of torsional reinforcement in beams
• Options for steel beams and joists
• Deflection limits in beams, joists, hollow core plates
and composite slabs
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1.5. Loads to consider
Additional loadcases (special loads)
1.5.1. Vertical loads
As indicated, CYPECAD generates automatic loadcases,
such as Permanent loads (composed of the self weight of
the construction elements and the dead loads introduced
on each group on all floors), the Live load (defined for
each group for all
the surface of the floor), the Wind load
(generated automatically for each X, Y direction depending
on the selected code and the defined structure dimensions), and the Seismic load which depends on the selected code.
Permanent loads
Self weight of reinforced concrete elements, calculated
using its volume based on its gross section and multiplied
by 2.5 (specific weight of concrete) for columns, shear
walls, walls, beams and slabs.
The self weight of a slab is defined by the user upon
choosing the type of slab, which can be different for each
floor or panel, depending on the selected type. For flat
slabs, it will be calculated by multiplying its depth by 2.5,
the same is applicable to drop panels of waffle slabs. For
lightweight zones of waffle slabs and joists floor slabs, the
value indicated by the user in the data sheet of the selected
slab will be taken. In the case of joist floor slabs, the value
of the weight per square metre is multiplied by the rib spacing resulting in a line
load applied to each joist. In flat and
waffle slabs, the product of the weight by the tributary area
of each node is applied to each node.
Additional loadcases may be added to those generated automatically, which in previous version were referred to as
Special loads, and may be established as Dead loads or
Live loads regardless of whether they are point, line or surface loads.
So, additional loadcases of a different nature may be created (dead load, live load, wind, earthquake and snow) and
combine them with those that have been previously created
automatically and amongst themselves (this is not compatible with wind and seismic loads).
Additional loadcases associated to Lateral soil pressures
and Accidental loads can also be defined.
Dead loads
These are estimated as being uniformly distributed on the
floor. These are elements such as flooring and partitions
(even though this last element could be considered as being
a variable load if its position or presence varies with time).
Different load distributions can be created for each loadcase, creating groups which can be combined establishing
whether they can act simultaneously by assigning them as
compatible, incompatible or simultaneous.
The self weight of the structural elements plus the dead
loads make up the Permanent loads. These are automatically applied to the bars of the structure.
When additional loadcases are created, the user can define
whether or not they are compatible with each other.
Once all the loadcases have been defined, along with the
load distribution, simultaneity and combination modes (in
accordance with the selected codes, materials used and
use category of the building), the combinations for all the
Variable loads (live load)
The applied live load is considered as being uniformly distributed on the floor. It is applied automatically to the bars
of the structure making up the floors of each floor.
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1.5.2. Horizontal loads
Limit States are generated automati
cally, from material failure, bearing pressures to node displacements. A fire check
can also be carried out.
Wind loads
The program automatically generates the horizontal loads
to be applied at each floor, in accordance with the selected
code, in two orthogonal directions X, Y, or in a single direction, and for the two cases (+X, -X, +Y, -Y). A load coefficient can be defined for each wind direction and case. If a
building is isolated the pressure will act on the windward
face of the building and the suction on the leeward side. It
is usually estimated that the pressure is 2/3 = 0.66 and the
suction 1/3 = 0.33 of the total pressure. Therefore for an
isolated building, the load coefficient is 1 (2/3 + 1/3 = 1)
for each direction. If the building is protected on its left side
because of an adjacent building in the X direction, the wind
coefficients may be modified to reflect the situation. In this
case +X = 0.33 as there is only suction in the leeward direction and –X = 0.66 as there
is only pressure in the windward direction:
All this is configured in the Loads section of the General
Data dialogue box. The same can be applied to the Integrated 3D structures.
Vertical loads on columns
Loads (N, Mx, My, Qx, Qy, T) can be defined acting at the
top of any column. These are in reference to the general
axes and can be defined for any loadcase, additional to
those obtained from the analysis. The diagram below indicates the positive direction of the loads:
Fig. 1.10
Columns or starts with the applied loads can be introduced
on mat foundations or foundation beams so to simplify an
analysis.
Fig. 1.11
Horizontal loads on columns
The tributary width is defined as the façade length perpendicular to the direction of the wind. A different value can be introduced for each floor. When the wind acts in the X direction, the
y length of the building is to be provided and when it acts in
the Y direction, the x length of the building is to be provided.
Point loads and uniform
loads along the whole height of
the column can be applied. They can be applied in reference to the local axes of the column or to the general axes
of the structure.
When there are independent areas on the same floor, the
load is distributed proportionally to the width of each zone
with respect to the total width B defined for that floor.
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B is the tributary width defined when the wind acts in the Y
direction. b 1 and b 2 are calculated geometrically by
CYPECAD in accordance with the coordinates of the edge
columns of each zone. Therefore the tributary widths applied to each zone will be:
As a generic method for obtaining the wind loads in an automatic manner, select the Generic code option.
Having defined the directions in which the wind acts, the
load coefficients and tributary widths per floor, the pressure
curve must be selected. A library of pressure curves exists
which allows for existing pressure curves to be selected and
create new ones.
These curves display the total pressure as
a function of the building’s height. These values are interpolated for intermediate heights, which is necessary to calculate the pressure at the height of each floor of the building.
The Shape factor is a coefficient which is applied to the
building to correct the wind load depending on the shape of
the building. This may be due to the shape of its floors being
rectangular, circular, etc. and because of its slenderness.
Fig. 1.12
Once the tributary width of one floor is known, and the
heights to the floor above and the floor below, if the half
sum of these two heights is multiplied by the tributary
width, the surface exposed to wind on that floor is obtained. If this is then multiplied by the total pressure calculated at that height and by the load coefficient, the wind
load for that floor and in that direction will be obtained.
A Gust factor can also be defined. This is a coefficient
which amplifies the wind load so to take into account
the
geographical position of the building in exposed locations
such as valleys, hill-sides etc. These situations produce
greater wind speeds and so should be taken into account.
The total wind load applied to each floor is obtained by multiplying the pressure at its height by the exposed surface,
shape and gust factors. The application point of the load at
each floor is at the geometric centre of the floor, determined
by the perimeter of the floor. The value of the wind load applied at each floor can be consulted and displayed in a report.
If there are guardrails (or a solid perimeter wall) on the roof,
it can be taken into account by proportionally modifying the
band width b and using b’.
For each defined code, the pressure is calculated automatically, once the initial data has been introduced which can
be consulted within the code to be used.
In the case of Integrated 3D structures, wind loads are not
generated automatically. They must be introduced manually
on the nodes and ba
rs. If additional loadcases are defined, a
combination can be created with the automatic loads.
Fig. 1.13
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It is important the loadcase combinations be checked as well as
their compatibilities when a Metal 3D job is imported as an integrated structure, especially, if the wind loads of the job had already been generated previously using the Portal Frame Generator.
Cxi, Cyi: Seismic coefficient for each direction at floor i, also
known as “Seismic action in X or Y” in the data entry part of
the dialogue box. The seismic mass of each floor is multiplied by this coefficient to obtain the static force applied at
each floor.
Seismic loads
The displacements of the floor with respect to the general
axis are:
Two types of general analysis methods can be used for
seismic loads: static analysis and dynamic analysis.
It is possible to apply both general methods or the specific
methods indicated in the code or the application regulations depending on the location of
the building.
and the applied forces:
Static analysis. Seismic loads using coefficients. Seismic loads can be introduced as a system of static forces
equivalent to the dynamic loads, generating horizontal
loads in two orthogonal directions X and Y, applied at each
floor level, at their centre of gravity.
As a general method, the seismic loads can be applied by
floor coefficients.
The second order effects may be considered if the user
wishes for them to be so.
Within the integrated 3D structures, if the static earthquake
loadcase is activated as loads on nodes and bars, it cannot
be combined with seismic loads by coefficients or with dynamic seismic loading.
Similarly, if a static analysis using floor coefficients is to be
carried out in CYPECAD, it cannot be carried out for the integrated 3D structures, hence, the structure cannot be analysed. It may be analysed if a joint dynamic analysis is undertaken. An additional static seismic force loadcase could
be activated, but the auto
matic loadcases would have to be
deactivated.
Fig. 1.14
The static forces to apply in each direction, per floor, are:
Sx = (Gi + A · Qi) · Cxi
Sy = (Gi + A · Qi) · Cyi
Where:
Gi: The permanent loads of floor i
Qi: The variable loads of floor i
A: Live load, snow load or quasi-permanent load simultaneity coefficient
Dynamic analysis. Modal spectral analysis. The dynamic analysis method which is generally considered by
the program is the modal spectral analysis, for which the
following parameters must be indicated:
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dom, with which the modal decomposition shall be undertaken. The program carries out a static and dynamic condensation, whereby the dynamic condensation is attained
by means of the simplified classic method, and only by
means of the dynamic degrees of freedom will the forces of
inertia appear.
• Design acceleration with respect to g (acceleration due
to gravity) = ac
• Ductility of the structure = µ
• Number of modes to a
nalyse
• Live load quasi-permanent coefficient = A
• Design acceleration spectrum
The dynamic degrees of freedom that are worked with consist of three per floor of the building: two displacements in
the horizontal plane and the corresponding rotation of the
plane. This simplified model corresponds to that recommended by the vast majority of earthquake codes. Hence
when defining the number of modes, the user is recommended to define three for each floor of the building.
These are to be completed and the corresponding spectrum selected from the default library provided with the program or using another created by the user. Each spectrum
is defined by coordinates (X: period T; Y: spectral ordinate
α (T)) therefore allowing to view the generated graph. For
the definition of the normalised elastic response spectrum,
the user must know the factors that influence it (type of
earthquake, type soil, damping, etc.). These factors must
be included in the spectral ordinate, also known as t
he amplification factor and referred to the period, T.
At this point in the analysis the stiffness and mass matrices,
both reduced and with the same number or rows/columns,
have been obtained. Each of them represent one of the
previously described dynamic degrees of freedom. The
next step consists of the modal decomposition which the
program resolves by means of an iterative method and
whose results are the autovalues and autovectors corresponding to the diagonalising of the stiffness matrix with
the mass matrix.
When any type of dynamic earthquake loadcase is specified for a building, the program carries out, as well as the
normal static design for gravitational loads and wind, a
modal spectral analysis of the structure. The design spectrums depend on the earthquake code and the parameters
of the code that have been chosen. In the case of the
modal spectral analysis, the user directly indicated the design spectrum.
The system equations to be resolved are as follows:
K: Stiffness ma
trix
M: Mass matrix
To carry out the dynamic analysis, the program creates the
mass and stiffness matrices for each element of the structure. The mass matrix is created based on the self weight
loadcase and the corresponding live loads multiplied by
the quasi-permanent coefficient. CYPECAD works with
concentrated mass matrices, resulting to be diagonal.
ω2: Autovalues of the system
ω: Natural frequencies of the dynamic system
The following step consists in condensing (simultaneous
with the element assembly) of the complete stiffness and
mass matrices of the structure, to obtain other reduced
matrices which only contain the dynamic degrees of free-
φ: Autovectors of the system or condensed vibration modes
From the first equation, a maximum number of solutions
can be obtained (values of ω) equal to the assumed numCYPE
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ber of dynamic degrees of freedom. For each of these solutions (autovalues), the corresponding autovector (vibration mode) is obtained. Nonethel
ess, it is rare that the maximum number of solutions of the system be required and
only the most representative of the number indicated by
the user as vibration modes intervene in the analysis. Upon
indicating this number, the program selects the most representative solutions of the system, which are those displaced by the mass and correspond to the natural frequencies of the greater vibrations.
These values are calculated in the following way:
aij = φij · τi · aci
i: Each vibration mode
j: Each dynamic degree of freedom
aci: Design acceleration for vibration mode i
The maximum displacements of the structure, for each i vibration mode and j degree of freedom in accordance with
the equivalent linear model, are obtained as follows:
The condensed vibration modes that are obtained (also
called shape coefficient vectors) are the result of a homogenous (the vector of independent terms is null) and undetermined (ω2 has been calculated so the determinant of the
coefficient matrix be n
ull).
Therefore, for each dynamic degree of freedom, a maximum displacement value is obtained for each vibration
mode. This is equivalent to an imposed displacement problem, which is resolved for the remaining degrees of freedom (not dynamic), by means of modal expansion or
‘backward’ substitution of the previously condensed degrees of freedom.
Therefore, this vector represents a direction or deformation
mode, and not specific values of the solutions.
Based on the vibration modes, the program obtains the
participation coefficient for each direction (τi) in the following way:
Finally, a displacement and force distribution over the whole
structure is obtained for each vibration mode and for each
dynamic loadcase, with which the modal spectral analysis
is concluded.
The program uses de CQC method (complete quadratic
combination) to attain the maximum values of a force, displacement etc, whereby a modal coefficient dependent on
the ratio between the vibration periods to combine is
calculated. The formula of the method is as follows:
Where [J] is a vector which indicates the direction of the
earthquake load. For example, for an earthquake load acting in the X direction:
[J] = [100100100…100]
Once the natural vibration frequencies have been found,
these are introduced in the selected design spectrum,
along with the ductility, damping, etc parameters, and the
design acceleration for each vibration mode and dynamic
degree of freedom is obtained.
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where:
ω: Angular frequency = 2π/T
µ : Ductility
Effects of torsion
ζ : Buckling coefficient, uniform for all vibration modes and
with a value of 0.05
x: Resultant force or displacement
xi, xj: Forces or displacements corresponding to the modes
to combine
When a dynamic analysis is undertaken, the total moment
and shear force is obtained due to the earthquake loads on
the building. By dividing them, the eccentricity with respect
to the centre of gravity is obtained. Dependi
ng on the selected earthquake code of each country, it is compared
with the minimum eccentricity specified in each code and if
less, the rotational mode is amplified, in such a way that at
least the minimum eccentricity is obtained.
For those cases in which the evaluation of the concomitant
forces is required, CYPECAD undertakes a linear superposition of the various vibration modes in such a way that for
a given dynamic loadcase, n groups of forces are really
obtained, where n is the number of concomitant forces that
are required. For example, during the design of concrete
columns, three forces are being dealt with simultaneously:
axial force, bending in the xy plane and bending in the xz
plane. In this case, upon requesting the combination with a
dynamic loadcase, the program will provide three different
combination versions: one for maximum axial force, another for maximum bending in the xy plane and the other for
maximum bending in the xz plane. Additionally, the created
combinatio
ns are multiplied by ±1, as the earthquake
loads can act in either of the two directions.
If the earthquake loads on the structure are analysed in a
generic manner (Modal spectral analysis), the minimum eccentricity the program takes into account is 0.05.
This is important especially in the case of symmetrical
structures.
Base shear
When the base shear due to dynamic seismic loading is
less than 80% of the static base shear, the proportion will
be increased so not to be smaller than it.
The second order effects can be considered, if the user
wishes for them to be so, by activating the option, as the
program does not consider them automatically.
∆
Consideration of 2nd order effects (P∆)
Upon carrying out the analysis, the user may consult, for
each mode, the period, the participation coefficient in each
design direction X, Y and what is referred to as the seismic
coefficient, which is the displacement spectrum obtained
as Sd:
The user may optionally choose to consider, when
defining
wind or seismic loadcases, to amplify the forces due to the
presence of these horizontal loads. It is recommended this
option be activated in the analysis.
The method is based on the P-delta effect of the displacements produced by the horizontal loads, taking into account, in a simple manner, the second order effects based
on a first order analysis and a linear behaviour of the mate-
α (T) : Spectral ordinate
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rials with mechanical properties bases on the gross sections of the materials and secant elastic modulus.
The following coefficient:
A horizontal load Hi acts at each floor i. The structure deforms and displacements, ∆ij, occur at each column level.
At each column j, and at floor level, a load with value Pij
acts for each gravitational loadcase, transmitted by the
slab to column j at floor i.
represents the stability index for each gravitational loadcase and for each direction of the horizontal force. If it is
calculated, an amplification
coefficient to be applied to applied loadcase safety factor can be obtained for all the
combinations in which horizontal forces act. This value is
referred to as γz and is calculated using the following formula:
An overturning moment MH due to the horizontal forces is
defined, acting at elevation zi with respect to elevation 0.00
or elevation without horizontal displacements, for each direction of action:
i: Number of floors
j: Number of columns
where:
γfgi: Safety coefficient for permanent loads of loadcase i
γfqi: Safety coefficient for variable loads of loadcase j
γz: Global stability coefficient
It must be recalled when calculating the displacements due
to each horizontal load loadcase, that an first order analysis
was carried out using the gross sections of the elements. If
forces for ultimate limit state design are being calculated, it
is logical that if a thorough calculation of the displacements
is to be obtained, it be done using the fissured and homogenised sections
of the elements which may result to
be very laborious, as that implies linear simplification of the
materials, geometry and load states. This causes it to be an
unpractical solution using the analysis methods available.
Therefore a simplified method must be established consisting of supposing a reduction in the stiffness of the sections,
which implies an increase in the displacements, as they are
inversely proportional. The program requires the increase
or ‘multiplication factor of the displacements’ to take this
stiffness reduction into account.
Fig. 1.15 Wind action
In the same way a moment due to P-delta effects, MP∆ is
defined, due to the loads transmitted by the slabs to the
columns Pij for each of the defined gravitational loadcases
(k), because of the displacements due to the horizontal
load ∆i.
where:
k: For each gravitational loadcase (self weight, live load…)
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tio can be established for the global stability if the floor are
very similar:
At this point there is no single criteria, therefore it is for the
user to decide which value to introduce depending on the
type of structure, estimated fissure grade, other stiffening
elements, nuclei, stairs etc, which in reality may reduce the
calculated displacements.
γz: Global stability coefficient = 1 / (1-Q)
Regarding the limits establishing whether the floor corresponds to a non-sway fame system, or what in this case
would be the limit as to whether it is to be considered or
not, it may be taken as Q = 0.05, i.e. 1 / 0.95 = 1.05.
In Brazil, it is common to consider a reduction coefficient of
the longitudinal elasticity modulus of 0.09 and assume a
reduction coefficient of the fissured inertia with respect to
the gross inertia of 0.70. Therefore, the stiffness is reduced
by these factors:
For this case, it is to be calculated and always taken into
account if the value is exceeded, which results in always
having to consider the calculation and amplify the fo
rces
using this method.
Reduced stiffness = 0.90 · 0.70 · Gross stiffness =
=0.63 · Gross stiffness
Regarding the displacement multiplication coefficient, it is
indicated that given that the horizontal loads are temporary
and act during a short period, a reduction of approximately
70% of the inertia can be considered, and as the elasticity
modulus is smaller (15100 / 19000 = 0.8), in other words, a
displacement amplification coefficient of 1 / (0.7 · 0.8) =
1.78, which according to the global stability coefficient,
does not exceed 1.35 would be a reasonable value.
Due to displacements being the inverse of the stiffness, the
multiplying factor of the displacements will be
1 / 0.63= 1.59. This value will be introduced into the program. As a general rule, if γz > 1.20, the structure’s stiffness should be increased in that direction, as the structure
can deform easily and has little stability in that direction. If
γz < 1.1, its effect is small and practically negligible.
In the
new NB-1/2000 code, in a simplified manner, it is recommended the displacements be amplified by
1/0.7 = 1.43 and limit the value of γz to 1.3.
It may be appreciated that the model code criteria would be
recommendable and easy to remember for all its application cases:
In the 1990 CEB-FIP model code, a moment amplification
method is applied which recommends, unless a more precise analysis is undertaken, the stiffnesses be reduced to
50% or similarly, apply a displacement amplification coefficient equal to 1 / 0.50 =2.00. For this assumption, it may
be considered that if γz > 1.50, the structure’s stiffness in
that direction must be increased, as the structure can deform easily and has little stability in that direction. 2nd order
effects do not have to be considered if γz < 1.1, however it
is recommended they always be activated.
Displacement multiplication coefficient = 2
Limit for global stability coefficient = 1.5
It is true, on the other hand, that stiffening elements are
always present in buildings: façades, stairs, load bearing
walls, etc., which assure that a smaller displacement be
present against horizontal loads than those calculated. Because of this, the program leaves the value of the displacement multiplication coefficient at 1.00. It is left to the user’s
criteria as to what the value should be modified to, given
that not all the elements can be discretised in the structure.
The ACI-318-95 code refers to a stability index Q per floor,
not for the global stability of the building, even though a ra-
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Once the analysis has concluded, the calculated values for
each of the combinations can be checked at the following
option: General data > Wind and Earthquake options
> Second order effects button > Amplification factors button. Here, the maximum value of the global stability coefficient can be seen in each direction. A report can
also be printed within the Job reports section.
al second order eccentricity of the isolate
d bar will always
be calculated together with the P-delta amplification effect
of the considered method. This way, reasonable results are
obtained within the slenderness field established by each
code.
It is left to the user’s choice, given that it is an alternative
method. In this case, the user can opt for the rigorous application of the corresponding code.
The case may arise where the structure is unstable, in
which case an error message is emitted before the analysis
has concluded warning a global instability phenomenon is
present. This will occur when the value of γz tends to infinity
or, which is the same in the formula, becomes negative or
zero because:
1.6. Materials used
All the materials are selected from lists within the program.
The material’s properties are defined within a file. The data
to be specified for each case is:
1.6.1. Concrete for foundations, slabs, columns and
walls
It may be studied for wind and/or earthquake loads and is
always recommended it be c
alculated, as an alternative
calculation method to second order effects, especially for
sway-frame structures or presenting some sway, as occurs
in most buildings.
A file exists containing a list of concrete types defined by
their design resistance, reduction coefficient, secant elastic
modulus and Poisson coefficient ν = 0.2 defined in the
code.
Recall that all of the live load loadcase is considered and
given that the program does not carry out any automatic
live load reduction, it may be convenient to repeat the
analysis previously reducing the live load, which would only
provide valid results for the columns.
The concrete used can be different for each element. Additionally, in the case of columns, can be different for each
floor. These values correspond to those most frequently admitted in the code.
Regarding the ACI 318 code, once the stability of the building has been studied, the reduction of the column stiffness
for their design is carried out by applying a formula indica
ted in the code appendix of the program.
1.6.2. Bar steel
A file exists which contains a list of the steel types defined
by their elastic limit, reduction coefficient and elasticity
modulus defined in accordance with the code.
In that case and given the difficulty of calculating the buckling coefficients by determining the bar stiffnesses at each
column end, it is sufficiently safe to assume buckling coefficients with a value = 1, with which the fictitious or addition-
It is always considered due to its position and type of element.
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type of steel is defined for the plates and stiffeners, as well
as the type of steel to use for the anchorage bolts. The
available steel types and diameters are predefined within
the program and may not be modified.
The steel may be different depending on whether it be for:
Columns, walls, shear walls and corbels
• Bars (vertical and horizontal)
The materials to be used in Integrated 3D structures are to
be de
fined per bar be it timber or steel.
• Stirrups
Floor beams and foundation beams
1.6.4. Integrated 3D structures materials
• Bottom reinforcement
The materials to be used in Integrated 3D structures (steel,
timber, aluminium, concrete or generic) are to be defined in
Job > General data.
• Top reinforcement
• Assembly reinforcement
• Skin reinforcement
• Stirrups
1.7. Weighting factors
Floor slabs and mat foundations
The weighting factors are established in accordance with
the properties of the materials to use, the loads acting on
the structure and the analysis method to be used used
which specified in the selected design code.
• Punching shear
• Mat foundation top reinforcement
• Mat foundation bottom reinforcement
• Waffle and joist floor slab top reinforcement
• Waffle slab bottom reinforcement
1.7.1. Analysis method
To calculate the weighting factors the Limit states method
is used or the corresponding method to apply for each selected code.
F
ootings and Pile caps
1.6.3. Steel for steel columns, beams and baseplates
1.7.2. Materials
CYPECAD allows for steel beams and columns to be used,
in which case the type of steel to be used must be indicated. A library containing steel types which can be selected
by the user is available. This library is saved as a file and
cannot be modified by the user. The file contains information such as the elastic modulus, elastic limit, Poisson coefficient and all the parameters required for the analysis.
Rolled, welded and cold formed steel sections are available. In the case of baseplates at steel column starts, the
The reduction coefficients to be applied to the materials
used are defined for each code. The corresponding articles
of the code may be consulted.
Upon selecting the material, the execution control level on
site (if it exists for the selected code) must be indicated and
therefore, the predefined weighting coefficient, which is predefined in a file associated with the selected
design code.
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1.7.3. Loads
• U.L.S. for failure. Rolled and welded steel. Section design.
• U.L.S. for failure. Cold formed steel. Section design.
The weighting coefficients will be applied depending on the
execution control level and on the foreseeable damage that
may occur within the project and on site, as well as its construction method.
• U.L.S. for failure. Timber. Section design.
Therefore, combination groups can be defined and activate
the limit states which are to be checked for the selected
code, and the weighting coefficients to be used. It is common practice for each country to establish the states detailed below.
It should be taken into account whether the effect of the
loads is favourable or unfavourable, as well as the origin of
the load. The values may vary.
These values will have to be established for each combination. To do so, the weighting and simultaneity factors defined in the corresponding combination file will be read, dependin
g on the number of loadcases of each of the simple
loadcases in accordance with its origin. This file cannot be
edited or modified by the user, although he/she can define
his/her own combinations.
1.8.1. Ultimate limit states
These are defined to check and design the sections. The
previously mentioned combination groups for concrete,
rolled steel, welded steel, cold-formed steel, timber and
aluminium are usually indicated. They are not contemplated
by codes which use allowable stresses.
1.8. Combinations
Once the basic simple loadcases that intervene in the
analysis have been defined, and in accordance with the
code to apply, a group of element states must be checked
which may require an equilibrium, tensile, fracture, fissure,
deformation, etc check to be undertaken. All this is summarised in the limit states analysis, which may, additionally,
be obtained depending on the material to be used. A group
of combinations is defined for each of these limit states,
with their correspondi
ng weighting coefficients, which the
program generates automatically and has to be selected
for the analysis. The following states are checked:
1.8.1.1. Project situations
The load combinations will be defined in accordance with
the following criteria for the various project situations:
Non-seismic situations
• With combination coefficients
• Without combination coefficients
• U.L.S. for failure. Concrete. Section design.
• U.L.S. for failure. Foundation concrete. Section design.
• Soil pressures. Check for pressures acting on soil.
• Displacements. To obtain the maximum displacements
of the structure.
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Seismic situations
2. Job description (2 lines).
3. Concrete for floor slabs
• With combination coefficients
4. Concrete for foundations, foundation data
5. Concrete for columns and shear walls. May be different
for each floor.
6. Concrete for walls. May be different for each floor.
• Without combination coefficients
6.1
. Generic masonry wall properties:
Modulus of elasticity E
Shear modulus G
Unit weight
Design compressive strength
Design tensile stress
Consider shear stiffness
In the case of block walls, the mortar and block
resistance is selected and horizontal joint reinforcement steel.
7. Steel for concrete reinforcement
where:
Gk: Permanent load
Qk: Variable load
AE: Seismic load
γG: Partial safety factor for permanent loads
γQ1: Partial safety factor for main variable loads
γQi: Partial safety factor for accompanying permanent loads
7.1. For columns, shear walls and corbels
Vertical bars
Stirrups
(i > 1) for non-seismic situations
(i ≥ 1) for seismic situations
γA: Partial safety factor for seismic loads
The program contains two tabs; one for floor slabs and
the other for foundations
ψp1: Combination coefficient of the main variable load
ψa1: Combination coefficient of the accompanying variable loads
7.2. For beams:
Top reinforcement (bottom additional reinf. for
foundation
beams)
Bottom reinforcement (top reinf. for foundation
beams)
Assembly reinforcement (bottom reinf. for founda
tion beams)
Skin reinforcement
Stirrups
7.3. For floor slabs:
Shear and punching shear reinforcement
Flat slab and mat foundation top reinforcement
Flat slab and mat foundation bottom reinforce
ment
(i>1) for non-seismic situations
(i ≥ 1) for seismic situations
1.9. Data entry
The data to be introduced for the analysis of a job includes:
1.9.1. General data of the job
The data included in points 3 to 6 is selected from a list of
materials.
1. Design codes for concrete, steel (cold-formed and
rolled), aluminium, timber, block walls and composite
slabs.
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Waffle slab, drop panel and joist floor slab top
reinforcement
Waffle slab, drop panel and in-situ joist floor slab
bottom reinforcement
8. Steel for steel beam and column sections
8.1. Cold formed steel
8.2. Hot rolled steel
9. Wind loads
10. Seismic loads
11. Fire resistance check
Fig. 1.16
12. Additional loadcases (special loads)
When a column is disconnected in both directions for several consecutive floors, the column is designed for each
span or floor, therefore when it comes to calculating the
slenderness and effective length l0, the program takes the
maximum value amongst all the consecutive disconnected
spans, multiplying it by its total length = sum of all the
lengths.
13. Limit states (combinations)
13.1. Concrete
13.2. Foundations
13.3. Cold formed steel
13.4. Rolled steel
13.5. Timber
13.6. Aluminium
13.7. Ground bearing pressures
13.8. Displacements
14. Buckling coefficients for each floor in each direction
14.1. Concrete columns
14.2. Steel columns
Now, l0 = α · l (for both X and Y local directions of the column, with its corresponding value).
These coefficients can be defined per floor or for each independent column. The program assumes a default value
of α = 1 (also called β), whereby the user has to vary this
value if he/she considers it to be so
due to the type of
structure and connections of the column with beams and
slabs in both directions.
When a column is disconnected in a single direction for
several consecutive floors, the program will take, for each
floor i, l0 = α1 · li, not acknowledging it not being connected. Therefore, if it is to be effective, in the direction where it
is not connected, the value of each αi must be obtained, in
such a way that:
Observe the following case (Fig 1.16), whereby the buckling coefficients of a column which is not braced in various
floors are analysed. Here, it can be seen that it may buckle
along the whole of its height:
This the value corresponding to completely exempt span, l.
The value of each span, i, will be:
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the various codes only indicate how these values are exactly determined for frames, and given that the spatial behaviour of the structure does not correspond to the buckling of
a frame, it is preferable not to provide the value
s in an inexact manner.
Nell’esempio corrente
1.9.2. Loads. Groups
Therefore, when the program calculates the buckling length
of floor 3, it will calculate:
In this section, the user indicates whether or not to consider
horizontal, wind and/or seismic loads and the code which is
to be applied for each case. The program chooses the
combination for each limit state internally.
Likewise, the weighting factors are validated depending on
the materials used and the intervening loads. The additional
loads are also selected and are assigned to each loadcase.
which coincides with that indicated for the complete unconnected span, even though the calculation is carried out
for each floor, which is correct, but it will always take the
length as α· l.
The user can also modify the global dead and live loads for
each floor group. The self weight of the floor slab is indicated in the file containing its description.
The height which is considered for buckling design is the
free height of t
he column, i.e. the height of the floor minus
the height of the beam or slab, whichever has the greatest
depth) which reaches the column.
1.9.3. Wind loading
The code to apply is to be selected. Please consult the section of the corresponding code.
1.9.4. Seismic loading
If earthquake loads are present, the data to introduce will
be in accordance with the selected code. Please consult
the section of the corresponding code.
Fig. 1.17
The final value of α of a column is the product of the α of
the floor by the α of the span.
Note: Loads associated to wind and/or earthquake loadcases
can be defined in the additional loadcases section, if they are
not automatically previously generated.
It is left to the user’s opinion as to the values to be introduced in each direction of the local axes of the columns, as
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1.9.5. Fire resistance
1.9.7. Limit states (combinations)
The coating (if present) of each structural element and
group is defined, as is the required
resistance and whether
the floor slab fulfils its compartmentation duty.
The group corresponding to each state to calculate is selected.
• Concrete
• Foundations
• Cold formed steel
1.9.6. Additional loadcases (special loads)
• Rolled steel
Additional loadcases (special loads) can be defined automatically, and are different to general loads:
• Timber
• Aluminium
• Permanent loads (self weight of floor slabs + dead
loads) = (permanent loads)
• Ground bearing pressures
• Displacements
• Live load defined within group data (live load)
• Wind in accordance with the selected code (Wind)
1.9.8. General data of floor/groups, columns, column starts and shear walls (Column Definition tab)
• Seismic load in accordance with the selected code
(Earthquake)
1.9.8.1. Floors/groups
If the user wishes to define loads (point, line or surface
loads) which are to belong to these loadcases, these must
first be created. The permanent loads and live loads are always de
fined by default.
Here, the data to introduce includes:
• Name of the groups, live and dead loads
• Elevation of the foundation plane, name of the floor and
height between floors.
If alternating live loads are to be created, i.e. loads that do
not act simultaneously for a combination, additional loadcases must be defined; the number of which is to correspond with the number of independent loads that are to be
considered. The load disposition option within each loadcase can also be used.
Upon indicating the heights (h) of the floors, the difference
between the top floor slab surface is defined (or mean top
reference plane). The elevations are calculated by the program based on the indicated data.
The combinations are generated automatically based on
the defined loadcases and their combinability.
Upon introducing these special loads, be they line, point or
surface loads, the loadcase associated to the load i.e. the
loadcase to which it belongs, must be selected.
Fig. 1.18
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1.9.8.2. Columns
The first defined vertex is the insertion fixed point even
though its position may be varied. When defining a shear
wall, the following parameters are selected:
Their cross sectional and elevation geometry is to be defined, indicating:
• Shear wall type
1. The type of column (concrete or steel)
• Reference
2. Cross section at each floor level
• Angle
3. Reference
4. Rotation angle
5. Start at foundation (with external fixity) or whether it
starts elsewhere (without external fixity) and up to which
floor it reaches. If the column starts on a beam or mat
foundation, it must be defined without external fixity.
The shear walls possess the same geometry on plan,
whereby only their thickness can be varied. They may not
start on columns, and columns cannot start on them. They
are of constant geometry and brought about to brace the
building horizontally.
7. Buckling coefficients at each floor and in both local directions; x
and y (see text for Job general data).
1.9.8.5. Horizontal loads on columns
6. Fixity coefficients at top and bottom of the column
The type of load, loadcase and application point are defined.
8. If the column is a steel column, the type and series of
the steel section selected from the library is indicated.
9. Support elevation change and depth, if present, so to
include the details in the job drawings.
Horizontal loads on columns can be defined with the following properties:
1.9.8.3. Column starts
It is possible to only define the start of a column (i.e. column with zero height), so that foundation elements may be
designed by simply defining the applied loads as loads
acting at the top of the column.
• Type of load: point, uniform load or strip load
• Loadcase: those defined in the job (self weight, live
load, wind earthquake)
• Application point: at any column elevation
• Direction: in local or general axes, in X or Y.
1.9.8.4. Reinforced concrete shear walls
Fi
rst of all, a shear wall series is defined, indicating:
1.9.8.6. Vertical loads on columns
• Name
Loads (N, Mx, My, Qx, Qy, T) can be defined acting at the
top of the last span (where it ends) of any column. These
are in reference to the general axes, for any loadcase, added to those obtained from the analysis and in accordance
with the following sign criteria:
• Initial and final group
• Sides and vertices
• Thicknesses at each floor to the left and right of the axis of the side
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A Fixity coefficient can be defined at beam edges. Its value
varies between 0 (pinned) and 1 (fixed). Any slab panel
joining that edge of the beam will be affected by that coefficient.
Hinges can be introduced at the ends of any beam span, at
connection points with beams, shear walls or other beams.
Fig. 1.19
If the beam introduced is a foundation beam, the subgrade
modulus and allowable bearing pressure are required.
There is other data that can be consulted and modifi
ed
such as the support conditions, fixity and buckling coefficients.
If a composite beam is going to be introduced, please consult section 8. Composite beams.
1.9.9.2. Walls
1.9.9. Floor slab data (Column Definition tab)
Two types of walls can be defined:
The geometry of the beams is defined graphically on the
floor plan for each group of the structure. The columns and
shear walls are visible for each group. The logical order in
which the data is to be entered is as follows:
Reinforced concrete walls. These are reinforced concrete walls, which may or may not receive lateral pressures
from the soil.
Masonry walls. These are brick or concrete block walls,
which receive and transmit loads but no lateral pressures.
1.9.9.1. Beams, external wall supports and foundation
beams
The following data is to be indicated:
• Start floor
The type of beam is selected and its dimensions defined.
• End floor
• Mean thicknesses at each floor (to the left and to the
right)
• Soil latera
l pressures (only for reinforced concrete walls)
indicating:
- Loadcase of the pressure
- Apparent unit weight
- Submerged unit weight
- Slope angle
- Internal friction angle
- Loads on fill (if present)
Fig. 1.20
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• The reinforced and prestressed joists can be of the following types:
• Beam or foundation support
- Foundation beam (without external fixity)
- Strip footing (without external fixity)
- With external fixity (with or without a footing)
- Beam without external fixity
-
When required, the data of the footing is to be indicated:
• Allowable bearing pressure of the soil
-
• Soil subgrade modulus. A high default value is provided = 100,000 kN/m3, because if there are columns
present, differing settlements on the ground can occur,
which will not really occur if an analysis is carried out
later on with pad footings below the columns. If all the
foundation plane consisted of elements without external
fixity (floating), a subgrade mo
dulus corresponding to
the type of soil and dimensions of the foundations
would be introduced. Generally speaking, it is not recommended elements with external fixity and elements
without external fixity be used simultaneously. The program will emit a warning if this occurs.
Manufacturer: data provided by a manufacturer. It
cannot be edited.
Library: contains joists defined by manufacturers
and by users using a specific program “The floor
slab file editor” provided by CYPE, which any user
can use.
Geometrical properties, provided by the user whereby all the data can be edited. Regarding the deflection calculation, it may be designed as a reinforced or prestressed beam.
• By joist type: This depends on the resisted moment of
the joist whereby the type of joist may be visualised instead of the bending moments, The value is indicated in
dNm, per metre width, per joist with the applied safety
factor.
Each panel may consist of a different type of floor slab, and
its position may be
perpendicular to beams, parallel to
beams or defined by two pass-through points.
1.9.9.3. Type of floor slab
The existence or non-existence of continuity between joists
of adjacent panels can be achieved (except in the case of
steel and open web joists, which are always simply supported). By copying panels, continuity is obtained from one
to the next. By varying the insertion point, so joists in adjacent panels are not aligned, the continuity is eliminated.
This is achieved as long as the distance between the ends
of the joists of adjacent panels is greater than the short
bar length (default value of 0.20m, which can be varied using the option Reduction coefficient of flexural stiffness
of joist floor slab. The same continuity effect is produced
if a beam is located at the end of a joist and works as an
extension of the joist, where the separation of their axes is
less than the short bar length.
The floor slab is defined by giving it a name and introducing a series of data:
1.9.9.3
.1. Joist floor slabs
Several types of joist floor slabs are available:
• Concrete joists (generic geometry)
• Reinforced joists
• Prestressed joists
• In-situ joists
• Steel joists
• Open web joists
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The data contained in the properties sheet can be taken from
the use authorisations of the manufacturers, or introduce the
values of a specific plate or slab to be built in-situ. There is
some data which is required and should be clarified:
Having defined a group, one of the previously defined
groups can be copied and then carry out the required
modifications.
Elevation changes can be defined between panels. These
changes are reflected in the drawings and reinforcement
layout of slabs and beams affecting the heights of the supports which intersect the elevation change beam. This must
be used with caution, as the program does not calculate
the transverse bending of the beam. It is, therefore, recommended that the construction details be consulted and
the
stirrups and anchorage lengths of the transverse reinforcement of the beam be checked manually.
• Reference. To identify the properties sheet.
• Description. The name of the plate.
• Total slab depth. The total depth of the plate and the
compression layer thickness (if present)
• Plate width. The width of the plate.
• Compression layer thickness. The compression layer thickness if present.
• Minimum plate width. Is the smallest value that may
be obtained from a longitudinal cut of a typical plate, as
a consequence of the panel dimensions upon reaching
the edge of the panel, where a special plate with a
smaller width is placed instead. The width of the last
plate varies between the typical width of the plate and
this minimum value.
The minimum negative and positive moments for joists can
be consulted and modified. It is important they be consulted and assigned correctly.
Double, triple…joists can be introduced. In this case the
program will take the defined weigh
t, which is limited to a
triple joist. In this situation, a bar or joist parallel is introduced at a distance equal to the width of the joist defined
in the properties sheet of the slab.
• Maximum and minimum bearing. When the plate is
slanted with respect to the normal of the support, the
bearing at each edge of the plate is different, varying
between the maximum and minimum values. If the maximum value is exceeded, the plate is bevelled.
A fixity coefficient can be defined at joist edges or ends (0
= pinned, 1 = fixed which is the default value) for each
panel.
• Lateral bearing. This is the value the plate may overlap
laterally with a parallel or slightly sloped support with respect to the longitudinal direction of the plate.
1.9.9.3.2. Composite slabs
• Self weight. This is the weight per square metre of the
complete slab.
Please consult section 9. Composite slabs of this Calculations manual.
• Concrete volume. This is the concrete volume in
opening infills, joints b
etween plates and compression
layer, if present. The program adopts the value corresponding to the compression layer by default.
1.9.9.3.3. Hollow core slabs
To define a hollow core plate, its geometric data and mechanical properties must be introduced.
• Plate concrete. This is information data to display
which materials were used to calculate the resistance
data of the section.
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• Layer and joint concrete. Same as above.
The decompression moment is that corresponding to class
II, and so the positive service moment is compared with
that in the table, choosing the corresponding column.
• Top reinforcement steel. Same as above.
The resistance data of the section are described below:
2. Slab negative flexure
1. Slab positive flexure. The data of the plate with joint
infill concrete and compression layer, if present.
• Diameter / Diameter / Spacing: Two columns of diameters are indicated, which allow the combination of two
different di
ameters at a given spacing. With such reinforcement distributed in the zone of negative moments,
the mechanical properties of the section are indicated
in each row.
• Ultimate moment. The maximum resisted moment
(ultimate)
• Cracking moment. To calculate the deflection using
the Branson method.
• Total stiffness, of the concrete-plate composite section, used to generate the stiffness matrix of the
bars into which the slab is discretised.
• Cracked stiffness. To calculate the deflection using
the Branson method.
• Service moment. Resisted moment depending on
the type of prestressed concrete, which is not he
same as the environment. The equivalence is:
Environment I = Class III (Structures in building interiors or exterior areas of low humidity)
Environment II = Class II (Structures in normal or
non-aggressive exteriors, or in contact with normal
waters or ordinary soil)
Environment III = Class I (Structures in aggressive
industrial or marine environment, or in contact with
ag
gressive soils, salt or slightly acidic waters)
The program compares, according to the environment defined for the plate, the service moment from
the analysis with that from the sheet and, if it is
smaller, the plate is acceptable. Otherwise, the program looks in the table for a plate that does not fail,
and if one is not found, a message appears after
the analysis.
• Ultimate shear. Ultimate shear resisted by the total
section. It is displayed in two columns depending
on whether it is greater than the decompression
moment (Mg)
• Ultimate moment of the typical section. This is the negative moment resisted by the section for a given reinforcement.
• Cracking moment. To calculate the deflection using the
Branson method.
• Total stiffness. To calculate the deflection using the
Branson method.
• Cracked stiffness. To calculate the deflection using the
Branson method.
• Ultimate shear. Shear resisted by the section for a given
reinforcement.
Based on the calculated reinforcem
ent, the value of the
shear resisted by the plate is known, which is compared
with the design shear.
If it fails, the program issues a message at the end of the
analysis, and 'Insuf.' is indicated on the plate, on screen
and in the drawing. If there are no values in the sheet, shear
is not checked.
Design process used
Once the maximum design positive moment Md is known,
the program searches in the positive slab flexure column,
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elastic analysis subject to the total load = permanent load
+ live load. This is equivalent to building the floor on
shoring, and upon their removal, the floor is subject to this
total load.
ULT. M., for a value greater than that obtained in the analysis. At the same time, and depending on the environment
defined for the panel, the program looks in the SER. M. (1,
2, or 3) column for a value that meets the analysis service
moment (obtained with the deflection combinations). A
plate is chosen that meets both conditions. If this is not
p
ossible, a message is emitted warning that it is outside
table range.
In this analysis, the negative moments are generally greater
than the positive moments.
B. Unshored
In the same way, and for the plate selected for flexure and
environment, the program checks in the shear column, of
positive and negative slab flexure, whether the design
shear is less than that resisted by the slab. If it fails, a warning is emitted.
The precast hollow core plate floors are generally constructed without shoring, such that the final load state is
comprised of two states:
1. The plate is subject to the self-weight of the slab w, which
follows the typical moment equation for a simply supported
element (M=wl2/8).
The lengths of the bars are established depending on the
bending moment envelope, and the minimum lengths defined in the options.
2. The floor in its continuity is subject to an additional load,
after the erection of the slab, comprised of the dead loads
and live loads.
The envelopes are ob
tained according to the acting forces,
considered redistribution and minimum applied moments.
This check is not carried out when data has not been defined for deflection, environment or shear analysis.
The superposition of the two stages leads to a load state
which produces greater positive moments than negative
moments, in the majority of cases.
Within the Panel manager option, the environment can be
selected, as well as the fixity coefficient at edges and minimum moments for each type of span: end, intermediate,
isolated or overhanging.
In the current version of the program, the analysis is not
carried out in two stages. If the floor is constructed without
shoring (case B), reasonably approximate results that concur with what is expected are obtained. This is done by
modifying the fixity coefficients in the continuous panels.
Construction process
As a guide, the value of the fixity coefficient to assign to
panels depends on the relationship between the self-weight
of the floor a
nd the total load, assuming a state of uniform
loads.
The analysis can be carried out as a shored or unshored
construction.
A. Shored
The value of the fixity coefficient would be:
The analysis that is carried out by the program when continuity is considered, with a fixity coefficient value =1, is an
fix.coeff. = 1 - (floor slf.wt. / total load)
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For example, consider the case of a floor weighing
400 kg/m2, with paving weighing 100 kg/m2 and a live load
of 500 kg/m2:
floor slab self weight = 400
total load = 400+100+500 = 1000
Fig. 1.21
fix.coeff = 1-(400/1000) = 1-0.4 = 0.6
A base reinforcement mesh, spanning in both directions, top
and/or bottom can be defined, which is considered in the
analysis and has its diameter designed during the process.
A fixity coefficient of 0.6 would be assigned to continuous
slabs. The program assigns this value automatically to
each panel of hollow core slabs when the unshored option
has been activated.
In
any case, it is recommended that the user consult with
the manufacturer on the construction process and ask for
advice for the design, verifying that the plate in its first
phase, subject to its self weight and a construction live
load (generally 100 kg/m2) can withstand the construction
phase.
Fig. 1.22
Very important: If a base reinforcement is considered, the
option Job > General data > By position > Floor slabs
tab > Options for flat, waffle and one-ways slabs > Detail base reinforcement in drawings must be activated,
otherwise it will not be visible on screen. Therefore it will not
be measured in the takeoff reports or bar schedules in drawings. Special attention must also be paid when printing drawings so to ensure that it does exist, has been considered in
the analysis and therefore must be placed on site. The drawings should be checked and the necessary details added to
indicate the overlap lengths and areas where these can occur.
As for obtaining the deflection, it is calcu
lated based on the
mechanical properties indicated in the slab properties
sheet or those defined by the user, and with the moment
envelopes for the final state. These values can be consulted as a function of the established deflection limits in the
hollow core plate options.
1.9.9.3.4. Flat slabs
The depth of the panel and reinforcement direction are defined. Each panel may have a different depth. A fixity coefficient may be applied for any type of flat slab at its edges
when connecting with the beams supporting it. The value
may vary between 0 (pinned) and 1 (fixed), as well as any
other value between these limits. Elevation changes may
be defined between panels, with the same applied observations as indicated with joist floor slabs.
If this option is activated, the base reinforcement can be
seen as any other reinforcement and can be edited and
modified. The bottom base reinforcement is always continuous, and overlaps in areas with maximum negative bending. The top reinforcement is
not continuous and is only
placed where necessary. In the case of mat foundations,
the positions are inverted. The reinforcement is measured
in the takeoff reports and is drawn on drawings as additional reinforcement.
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The direction in which the reinforcement is placed can also
be indicated.
Mat foundations can also be used. In this case, the depth of
the slab is to be indicated, as well as the subgrade modulus
and allowable bearing pressure. The base reinforcement in
mat foundations is determined automatically depending on
the minimum steel ratio defined in the slab options.
1.9.9.3.5. Waffle slabs
Waffle slabs are formed by panels in which two zones are
present: a lightweight zone and a solid zone.
Fig. 1.23
The lightweight zone is the first to be defined and is done so
by selecting it from an editable program library or using the
user’s own definition. The lightweight zone can consist of removable or lost forms. Once the type of form is selected, the
c
orresponding data must be filled in (Figs. 1.23 and 1.24):
•
•
•
•
Reference
Total depth
Compression layer thickness
Number of elements making up the lightweight form
(for lost form only)
• Geometry of the transverse section: rib spacing, which
can be the same or different in X and Y and the rib
width (which can be variable in the case of removable
forms).
• Concrete volume/m2
• Self weight of the slab (approximate, depending on the
material making up the lightweight zone)
Fig. 1.24
Having defined this data, the pass-through point, which
may vary, of the rib mesh is indicated on the panel. The ribs
can span in any direction. Elevation changes between panels can be defined, obeying the same rules as for joist floor
slabs.
A base reinforcement mesh, spanning in both directions,
top and/or bottom can be defined, which is considered in
the design of the reinforcement.
Remember: when introducing data, an estimate of the total
weight is carried out, as the program initiall
y displays the volume
and approximate weight of the infilled zones, compression layer
and the selected default material (concrete). If this is not the case, the value may be modified. In the case of removable forms,
only the value of the infilled concrete is estimated.
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with a 40º angle of vision. If no other column is ‘seen’ (for
example in the case of edge columns) the same value as
was taken in the opposite sense of the same direction is
used. The drop panel limits are set at 2.5 – 5 times the
depth. An option is included in the program (Slabs > Drop
panels > Configuration of drop panel generation in
the Beam Definition tab) which allows for these design
parameters to be modified.
Very important: If a base reinforcement is considered, the
option Job > General data > By position > Floor
slabs tab > Options for flat, waffle and one-ways
slabs > Detail base reinforcement in drawings must
be activated, otherwise it will not be visible on scre
en. Therefore
it will not be measured in the takeoff reports or bar schedules in
drawings. Special attention must also be paid when printing
drawings so to ensure that it does exist, has been considered in
the analysis and therefore must be placed on site. The drawings
should be checked and the necessary details added to indicate
the overlap lengths and areas where these can occur.
If these are generated manually, solid zones may be introduced, always adjusting them to the lightweight zone. These
are not to be used to simulate beams. In that case introduce beams. Also, always do so at free edges. Drop panels
always have a base reinforcement between ribs which is
considered and deducts additional rib reinforcement in the
analysis. It is not measured and cannot be indicated, therefore drawings must be checked, its presence indicated and
construction details provided for construction on site.
If this option is activated, the base reinforcement can be
seen as any other reinforcement and
can be edited and
modified. The bottom base reinforcement is always continuous, and overlaps in areas with maximum negative bending. The top reinforcement is not continuous and is only
placed where necessary. In the case of mat foundations,
the positions are inverted. The reinforcement is measured
in the takeoff reports and is drawn on drawings as additional reinforcement.
When printing out the floor plan layout drawings, the program always places an information box indicating the base
reinforcement of the ribs and drop panels, even though the
bars are not displayed or detailed.
The floor slab can be different for each panel. If the beams
separating each panel are flat, the beam will adopt the
greatest depth of the two slabs on either of its sides. In the
case of dropped beams, the amount by which it drops is
measured as of the greatest depth. A fixity coefficient can
be applied to the edges of the panel whose value may vary
between 0 (pinned) and 1 (fixed).
The forms provided in th
e lightweight zone of the slab can
optionally be drawn.
Predefined reinforcement
Reinforcement can be defined in any position and direction
which is deducted from the necessary additional reinforcement in its zone of action.
The solid zones or drop panels can be generated automatically over columns or at any zone or the panel. These
adopt the same depth as the lightweight panel in which
they are situated. Their depth can be modified so their bottom surface drops below that of the lightweight section of
the slab.
Openings
Panels in which no floor slabs are introduced remain empty,
and are represented by a question mark; therefore users
must delete the panel which is the same as introducing an
opening, which is represented by two intersecting discontinuous lines.
When drop panels are generated automatically, the dimensions in each direction are adjusted to 1/6 of the distance
between the column in question and the one closest to it,
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Additionally, rectangula
r openings may be introduced in existing flat or waffle slabs.
strap and/or tie beams can be inserted which can also connect to strip footings below walls.
If the type of beam considered contains a reduced form at the
side at which the opening is located, it will not be taken into
account and the program will warn that the data is incorrect.
Strap beams are defined to absorb the moment transmitted
to the footing or pile cap they reach. Several beams may
act simultaneously to absorb the moment in a given direction, in which case it will be distributed proportionally to
their respective stiffnesses.
Rectangular footings are design as rigid solids and may
support several columns and/or shear walls. The same is
applicable to pile caps, in accordance with a defined type
of resolved cases.
Beams located between two openings or between an
opening and the external edge, if they have been defined
as flat and do not have a lateral slab, do not have their
depths defined and therefore must be
changed to dropped
beams, indicating their dimensions.
If, at any floor, there is an independent zone whose perimeter is
defined by beams contained within an internal opening, even
though there is no slab, the stiffness or non-deformable hypothesis of the floor is maintained.
1.9.10. Loads. Sloped beams. Diagonal bracing
Apart from the general surface loads, point, line and surface loads may also be introduced. All these are introduced
graphically on screen and may be visualised to be consulted or to be modified at any moment.
Therefore, if horizontal loads are present, incorrect results will
not be obtained. This situation is recommended when using sloped or exempt disconnected beams defined in the same group,
which are elements that possess 6 degrees of freedom and do
not consider the non-deformable hypothesis of the floor.
Each type of load has an easily identified graphic diagram,
as well as being displayed in different colours, if they belong to different loadcases.
If rein
forced concrete walls have been defined with acting lateral
pressures, and there are joist floor slabs running parallel to the
wall, these should have sufficient stiffness to behave as a rigid
diaphragm, and so the infills and corresponding details, which
the program does not carry out automatically will have to be provided.
In the case of sloped beams, their dimensions must be indicated, as well as the loads that may act on them (point,
line, strip, triangular,…), and where they span from and to
(initial and final groups). They always have 6 degrees of
freedom. They can consist of rectangular concrete sections
or steel sections. Their ends can be fixed or pinned. The diagonal bracing consists of sloped beams, crossing each
other between two supports and between two floors; these
are always steel sections.
For versions earlier than the 2012.a version, if there are empty
panels next to the wall and perpendicular beams exempt from
the wall, these must be placed as sloped beams so the
y may be
designed for compressive bending, as normal beams and slabs
are only designed for simple bending. Please refer to chapter 12.
Rigid diaphragm if the program version is greater than or equal
to the 2012.a version.
Integrated 3D structures can also be created between independent zones.
1.9.11. Stairs
1.9.9.3.6. Foundations
Please consult chapter 10. Stairs of this calculations
manual.
caps can be defined at starts of columns and shear walls
‘with external fixity’. Spanning between these elements,
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1.10. Analysis of the structure
until the end, emitting a report once it has concluded. It is
convenient that the error messages of all the elements be
checked.
Once all the data has been introduced, the structure can
be analysed. During the process, information messages
will appear regarding the analysis phase the program is
running through. Error messages are also emitted if data
exists which is incompatible with the analysis.
If one or
several Integrated 3D structures have been created, bear in mind that these can be processed individually
and in an independent manner to the floor groups. It is convenient this be done and the introduced sections designed.
This way, when the complete structure is processed, including the defined Integrated 3D structures, the results will be
closer to the final section sizes that will be required.
The first phase of the program consists in generating the
geometric structure of all the elements forming a stiffness
matrix of the structure. If the program detects incorrect data, error messages will be emitted and the process will
stop. This phase can be executed independently for one
group or for all the job.
It is possible that in many cases, especially when concerning steel columns and beams and Integrated 3D structures
containing steel elements, that the section sizes have to be
modified before the analysis, and that, due to their inertias
varying significantly, make it obligatory t
o launch a new
analysis.
The second phase consists in inverting the stiffness matrix
using frontal methods. If it is singular, a message will be
emitted indicating it is a mechanism, if this situation is detected for an element or part of the structure. In this case
the process stops.
This occurs frequently in steel structures and should not
worry the user. Sometimes the analysis process must be
repeated several times until all the steel sections are those
to be used as the final section sizes. In the case of reinforced concrete, due to the program working with the gross
section of the element, if the sections do not vary, or if they
vary by a small amount, they are usually accepted as they
remain.
In the third phase, the displacements are obtained for all
the defined loadcases. A message will be emitted indicating there are excessive displacements at those points
where the structure exceeds a value, whether it be due to
an incorrect design of the structure or to the torsion stiffne
ssess defined for an element.
If global stability problems exist, the structure should be revised, when second order effects have been considered.
Regarding an analysis carried out with Stairs, the user
should bear in mind that the stairs are designed independently, obtaining the reactions at the start, end and intermediate supports, transforming these reactions into line loads
which are applied on the structure as live and dead loads.
With these loads applied to the structure, the program analyses the complete CYPECAD job. An integrated analysis
has not been undertaken because their contribution and influence on the structure when exposed to horizontal loads
is large and could provide results which do not usually arise
in common practice, especially when what traditionally is
done is apply their reactions and not integrate them.
The fourth phase consists in obtaining the combinations
and envelopes of all the defined combinations for each element: beams, slabs, columns, etc., and for
each limit state.
In the fifth phase the program designs and reinforces all
the defined elements in accordance with the combinations
and envelopes, geometry, materials and existing reinforcement tables. A message is emitted if any of the limits indicated in the code are exceeded. The program continues
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Upon concluding the analysis, the errors and problems that
have arisen during the analysis of the different elements can
be consulted. They may be consulted on screen or by printing out a file, depending on the type of error. Other errors
must be consulted per element, column, beam, slab, etc.
1.11.1.2. Results of regular beams and foundation
beams
1.11. Results
• Beam envelopes with or without seismic loading, with
bending moments, shear forces and torsion moments.
All this can be measured numerically or graphically.
All beam data may be consulted:
• Active deflection and other deflection, deflection/span
ratio, consideration of minimum moments.
Once t
he analysis has finished, the results can be consulted on screen, obtain reports from text files or via printer
and copy the job in any drive.
• Beam reinforcement, considering the number of bars,
their diameter, their lengths and the stirrups with their
lengths. These results may be modified. The design
and necessary top and bottom reinforcement areas can
be consulted, for longitudinal and transverse reinforcement.
Elements defined without ‘exterior fixity’: footings, pile caps,
strap and tie beams can be designed simultaneously or later on. All these foundation elements can be edited, modified, redesigned or checked in an isolated manner to the
rest of the structure.
• Beam errors: excessive deflection, bar spacing, anchorage lengths, compressed reinforcement, and oblique
compression due to shear and/or torsion and all the
other inadequate design or reinforcement data. Colour
codes can be assigned to valuate their importance.
1.11.1. Consulting on screen
The following da
ta can be consulted at any moment.
• Fixity coefficient at beam edges
1.11.1.1. Job general data
• Sections designed using steel beam option and sections which verifies all the checks of the section series.
In the case of composite steel beams, the shear studs
are designed.
It is convenient that the data introduced be revised:
columns, groups (live loads, dead loads), floor heights,
wind and seismic loading, materials used, options, reinforcement tables, etc. The options contained in this section
are saved with the job, as well as those reinforcement tables that have been converted into Special tables. It is convenient these be saved separately because if options or tables have been modified and the job is reanalysed after
some time, different results may be obtained.
Beam sections may be modified. If the dimensions of the
beams have varied, the Redesign option is available to obtain new reinforcement with same forces of the initial analysis. In this case the errors should be
rechecked.
It is possible to redesign only those frames that have undergone dimension changes, conserving those where only
the reinforcement has been modified, or redesign all, in
which case the reinforcement of all the beams which have
been modified is redesigned.
If this data is modified, the job must be reanalysed. If they
have been validated, the result consultation may continue.
Options and tables may be modified and then redesign the
structure to obtain a new result.
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1.11.1.5. Composite slab results
The reinforcement may also be blocked, then checked after another analysis has been run.
Please consult chapter 9. Composite slabs.
If the dimensions of the beams have varied greatly, it is highly
recommended the job be reanalysed.
1.11.1.6. Hollow core slab results
The beam reinforcement may be modified, if the user wishes to
do so and he/she is responsible for this. The program displays
a colour code to verify the beam contains no errors
. If beam dimensions have been modified in Errors, study whether it is
more convenient to redesign to obtain new reinforcement.
The following may be consulted:
• Bending moment and shear envelopes for the selected
panel strip and with a mean value per metre width
• Type of selected hollow core plate
• Top reinforcement at supports, indicating, depending
on the activated views, the number, diameter, spacing
and length of bars.
1.11.1.3. Loads
The values of all the loads introduced: point, line and surface, can be visualised graphically. Each group of loads
associated to different loadcases has a different colour
code. This way, it is possible to check whether the data is
correct. If any load modifications are undertaken, the job
should be reanalysed.
• Deflection information
• Analysis errors, be they due to moments, shear, deflection or environment.
The type of hollow core plate can be modified, as well as
the top reinforcement.
1.11.1.4. Joist floor slab results
1.1
1.1.7. Results of flat slabs, waffle slabs and mat
foundations
The following data can be consulted in regards to joist floor
slabs:
Data of introduced slabs.
• Bending moment and shear envelopes in joist alignments (with applied safety factor and per beam)
• Defined base reinforcement, and when required, that
modified in the design.
• Top reinforcement for joists. Their number, diameter
and length are taken into account.
• Discretised element mesh (see 3D model)
• Bending moments and shears at ends with applied
safety factor and per metre width for joists.
• Required reinforcement area envelopes displayed per
metre width, in the direction of the defined reinforcement, top and bottom.
The joist bending moments and shear can be made uniform in reference to mean values, percentage differences
or maximum values. All the previous values can be modified for drawings, to those values considered by the user.
Please consult chapter 6. Joist floor slabs for more information
on data and results.
• Displacements in mm. For any loadcase of any node.
• Forces per loadcase of any node and required design
steel area in each reinforcement direction. The method
used to obtain the design forces is the Wood method,
known internationally, required for the correct considerCYPE
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1.11.1.8. Column results
ation of moments possessing both signs and torsion
forces.
It is possible to consult column reinforcement and modify
the columns’ dimensions so to obtain a new reinforcement
arrangement. Their reinforcement can also be modified.
The forces (axial, moments, shear and torsion) in columns
by loadcase may also be consulted at any point along the
column, at any floor, as well as being able to visualise the
force diagrams.
• Maximum displacements of panels for each loadcase.
Not to be confused with deflection. In the case of mat
foundations this indicates the settlement. If the values
are positive, uplift is present and the analysis would not
b
e correct using the applied theory.
• Consultation of the reinforcement obtained in any longitudinal or transverse direction, top or bottom of the defined base reinforcement, if present.
Likewise, the worst case forces (with applied safety factor)
which determine the reinforcement to be placed, for any
span can be consulted (please recall that various worst
case combinations can exist for a specific reinforcement
i.e. reinforcement may be valid for those forces but the reinforcement checked immediately before is not). Deformation
and stress diagrams of the concrete and steel for a section
perpendicular to the neutral axis are also provided. The resultant moments due to the amplification because of accidental and second order (buckling) eccentricity, which appear, in red, below the worst case forces table.
• Check and design of punching shear reinforcement, if
required, of solid areas and ribs of the lightweight zone.
• Matching of reinforcement in any direction to obtain
maxim
um reinforcement areas and lengths.
• Excessive bearing pressures in mat foundations.
• Force, displacement and steel area, contour lines and
contour maps.
If flexure lines have been introduced before the analysis,
minimum reinforcement lengths and bottom reinforcement
overlaps must be provided, if required, in accordance to
that indicated in the option for minimum lengths for flat and
waffle slabs. It is recommended this introduction be done
before the analysis, as if it is carried out later, the overlaps
will be constructive (30cm) and will not be redesigned.
If the column does not verify a check, an abbreviation appears to indicate why the column fails e.g. SAe: Excessive ratio: due to it exceeding the limits stated in the code,
even though in this case, the program does provide column reinforcement.
More messages can appear which should be consulted.
All these modifications are carried out on screen and according to the user’s criteria.
If the reinforcement or the column
dimensions are modified
and the column still fails, a sign appears to the left indicating the maximum steel ratios have been exceeded.
Flat and waffle slabs may be redesigned after the first
analysis. By executing the Redesign option (introducing a
matching line) to obtain new reinforcement using the forces
of the initial analysis.
If important modifications have been carried out it is highly
recommended the job be reanalysed, as the stiffnesses will
have varied.
Once the data has been consulted, the next phase consists in obtaining graphical results.
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If a column is present with insufficient section, it will not be
drawn or measured.
analysis can be consulted and the amplification values of
the applied forces and resultant factor due to the horizontal
load of each intervening combination viewed on screen. All
is explained when entering the data and a report of the results may also be printed out.
A column’s reinforcement can be blocked and
maintained;
hence after running through another analysis, it may be
checked to see if it does not fail.
1.11.1.11. Wind results
Using the Column schedule option, columns can be
grouped amongst each other. Those that fail are displayed
in red.
The values of the wind load in X and the wind load in Y at
each floor level can be consulted and the results printed
out.
1.11.1.9. Results of shear walls, reinforced concrete
walls and masonry walls
1.11.1.12. Earthquake results
The normal and tangential stress diagrams may be consulted for the whole height of the shear wall for each calculated combination, as well as displacement diagrams for
the defined loadcases. The force distribution diagrams are
displayed in colour scales, indicating the maximum and
minimum values.
The values of the vibration period for each mode considered can be consulted, the participation coefficient of the
mobilised masses in each direction and the seismic coefficient corresponding to the resultant displacement
spectrum.
1.11.1.13. Contour maps and contour lines in flat and
waffle slabs, and mat foundations
The reinforcement can be consulted and modified to the
user’s judgement, as well as the thickness. The wall is displayed in red if it fails. It may be redesigned.
In this section of the program, the displacements, forces
and steel areas in cm2/m may be consulted for all the panels of any group.
A coded information text exists with messages explaining
the state of the design.
The Compliance factor of the reinforcement provided may
also be consulted, given as a %, and the areas where additional reinforcement is required.
1.11.1.14. Deformed shape
1.11.1.10. Results of the analysis with 2nd order effects
1.11.2. Printed reports
A 3D model can be observed displaying the deformed
shape for each loadcase and combination, as well as its
animated deformation.
A report of the worst case forces of the span is also available as well as the forces per loadcase of the resultant.
The data i
ntroduced and the analysis results are displayed
in a report which can be printed out or saved as a text file.
If 2nd order effects have been considered in the analysis,
be it because of wind or seismic loading, the results of the
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• Report on earthquake participation coefficients, which
include mode periods, mobilised mass participation coefficient, and resultant seismic coefficient in each direction (dynamic analysis).
The following data can be printed out:
• General reports. These include the name of the job,
groups, floors, heights, coordinates, column dimensions and their fixity, shear walls, gravitational load data, wind data, seismic data, materials used, control levels, slabs used in the job, geometry and self weight.
• Report on maximum displacements of columns, at
each floor for all the columns, for the most unfavourable
combination for each direction.
• Report of combinations used in the analysis.
• Maximum column distortion report.
Beam reinforcement report. Contains the necessary
mechanical capacity envelopes, moments, shear
forces, torsion, provided reinforcement and active deflection.
• Foundation report. Provides a report on the material data, loads and pad footing, pile cap and strap and tie
beam geometry as well as their takeoff.
A report on the design checks of the foundation elements is also obtained.
• Envelopes report, with bending moment, shear and torsion envelope drawings.
• Beam takeoff report
• Corbel report
• Beam interchange file. This is a text file which includes
information on beam reinforcement.
• Column and beam ultimate limit state checks
• Integrated 3D structures report
• Beam fabrication tag list
The reports are a complement to the graphical information
obtained on screen, just as the drawings define the geometry and reinforcement of the project.
• Floor slab and beam, surface and volume report
• Joist takeoff report for each type of joist and length
• F
orm takeoff report
• Joist floor slab reinforcement takeoff
1.11.3. Drawings
• Report on the reinforcement per square metre of the
job
The project drawings can be configured in different formats, be it a standard format or one defined by the user.
Similarly for the paper sizes to be used. They can also be
drawn using different peripherals: printer, plotter or DXF/
DWG and PDF files. They will have to be configured in Windows for them to work correctly and have the corresponding drivers installed.
• Flat and waffle slab reinforcement report
• Report on forces in sloped beams, with moment, axial
force and shear moments and provided reinforcement.
• Report on columns and shear walls, which includes the
reinforcement report, forces at column starts, forces by
loadcase and worst case forces in columns and shear
walls.
Any type of construction detail or drawing in DXF or DWG
format can be included, as well as using the edition resources the program allows: texts, lines, arcs
, DXF. Any
scale, line thickness, text size, title block, etc. can be applied, in such a way that the drawing can be completely
personalised, including the active DXF or DWG template.
• Report on the displacements per loadcase for each column and at each floor.
• Second order effects report
• Wind load report
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6. Foundation loads. Drawing of all the foundation starts
with the loads at the starts (by loadcase), expressed in
general axes. Columns and shear walls are included.
All the elements are defined by layers and the elements to
be drawn in each drawing can be selected. Basically, the
following drawings can be drawn:
7. Reinforced concrete and load bearing wall elevations. Elevation of each wall span, with a reinforcement
table for each span and floor, including an approximate
takeoff.
1. Layout plan. Draws and dimensions all the elements
per floor and in reference to the layout axes. Includes,
as an option, the surfaces and volumes of
slabs, as
well as the reinforcement areas in the information block.
8. Load distribution. Special applied loads are drawn by
loadcase for each group.
2. Floor plans. Geometry of all the elements on the floor:
beams, columns, shear walls, walls, joist floor slabs (indicating positive moments and shear forces at joist
ends, lengths and bars of additional top reinforcement),
flat and waffle slab reinforcement, with a block detailing
the base reinforcement in flat slabs, and drop panels
and ribs of waffle slabs, punching shear reinforcement
in solid and lightweight zones. A summary block can be
detailed with their corresponding takeoff and total takeoffs. Drawings of the foundation elements can also be
obtained.
9. Corbels drawing. The geometry and reinforcement is
drawn.
10. Contour lines. The contour lines and contours are
drawn for flat and waffle slabs.
11. 3D Structure. This is drawn if the user possesses Metal 3D and Integrated 3D structures have been created.
1.12. Design and
check of elements
3. Beam drawings. Drawing of the beam alignments, including their name, scales, dimension, reinforcement
number, diameters, lengths and spacing, as well as
their position, stirrup type, diameter and spacing. The
detailing can be displayed in a summary block together
with the total takeoff.
The parabola-rectangle and rectangular diagram methods
are used for the design of reinforced concrete sections at
ultimate limit state, together with stress-deformation diagrams of the concrete and for each type of steel, in accordance with the current code (see Code implementation
chapter).
4. Column and baseplate schedule. Diagram of the
column sections, indicating their references, position,
stirrups, type, diameter, lengths, steel sections and is
grouped by equal types. A block is provided containing
the baseplates at steel column starts, with their dimensions, anchorage bolts and geometry. They can be
drawn or selected by floor, as well as including a summary of their takeof
f.
The limits required for both geometric and mechanical,
minimum and maximum steel areas indicated in the codes
are used. The required bar layout, regarding the number of
steel bars to provide, minimum diameter and minimum and
maximum spacing between bars, is also taken into account. These limits can be consulted and modified on
screen in Options. Other parameters are saved in internal
files.
5. Detailing of columns. Drawing providing details on
the columns and shear walls, including an elevation of
the lengths and a block with the lengths of all the bars.
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1.12.1. Horizontal and inclined panel beams
The second and third types may be of a smaller length, but
are always symmetrical, complying with minimum percentage lengths (d and e in the figure) of the span specified in
Options.
1.12.1.1. Longitudinal reinforcement due to bending
The reinforcement is determined by carrying out a simple
bending calculation at, at least, 14 points of each beam
span, limited
by the elements with which it contacts, be it
joists, flat or waffle slabs. At each point, and based on the
bending moment envelopes, the required top and bottom
reinforcement (tension and compression reinforcement depending on the sign of the moments) is determined. This
reinforcement is checked with the minimum geometric and
mechanical values provided in the code, adopting the
largest value. It is determined for seismic and non-seismic
envelopes and the largest steel area obtain for both is
placed.
Fig. 1.25
NOTE: The first type always passes beyond the support by 10
diameters measured from the face of the support.
Bottom reinforcement
Once the required design area is known for all the calculated points, the reinforcement sequence immediately after
the required area is located in the bottom reinforcement
table. The reinforcement tables are defined for the specified width and depth.
When a reinforcement combination cannot be found within
the reinforcements table that covers the
required steel area
for the dimensions of the beam, φ25 will be provided. The
program will indicate: Bottom reinforcement outside table.
The total reinforcement in the reinforcement tables is divided into 3 types. Each one may have a different diameter.
The first type consists of the reinforcement spanning between supports but goes beyond them and anchored in a
constructive manner. In other words, the support axis passes up to the opposite face by at least 3 centimetres, except
if (because the bottom reinforcement is close to or reaches
the support or because compression reinforcement is required at the supports) it is necessary to anchor the reduced anchorage length as of the axis. The default reinforcement tables provide this first type of reinforcement
whose steel are is always greater than a third or a quarter
of the total reinforcement in the default reinforcement tables of the program. If the tables are modified, the user
must ensure this proportion is maintained.
Top reinforc
ement
There are two types of top reinforcement:
Top reinforcement (in normal beams, bottom in foundation beams). Once the required design area is known
for the calculated points, the reinforcement sequence immediately proceeding the necessary reinforcement in the
top reinforcement table is placed. Reinforcement with up to
three different cut off lengths can be placed; in Beam reinforcement options, a minimum span % can be defined for
each group. The reinforcement tables are defined for the
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CYPECAD - Calculations manual
forcement is divided into three types. Each type can be of a
different diameter.
Other longitudinal reinforcement considerations
• For T sections, additional reinforcement is place to hold
the ends of the stirrups at the top of the T.
Fig. 1.26
Within the support zone of the column, a linear variation of
the depth of the beam will be considered (1/3), which leads
to a reduction of the required reinfo
rcement. This will be the
greatest obtained between the faces of the edges of the
support, where the most usual case will consist of it being
close to or at the edge of the support.
Assembly reinforcement: Continuous or stirrup-holder. Continuous assembly reinforcement is used when the
steel of beams spanning from one support to the next is
constructed in the workshop, including the top reinforcement and stirrups, and having to place the additional top
reinforcement (or bottom in the case of foundation beams)
at the supports on site. The user can choose whether or
not to consider the assembly reinforcement as collaborating in regards to top reinforcement. When top compression
reinforcement is required, it always collaborates. The anchorage of this assembly reinforcement is optional, with a
hook or straight, as of its end or the axis, and is displayed
clearly in the options dialogue box.
Regarding shear walls and walls, depending on the width of
the side to which the beam reaches, a l
ength or design
span equal to the smaller of the following two values is calculated:
• The assembly stirrup holder reinforcement is used for
in-situ assembly, by placing it between the ends of the
top reinforcement, using small diameter bars and a
construction splice with the reinforcement. This is required so there is reinforcement holding the stirrups. It
may also be used in seismic zones where the splices of
the nodes are to be placed further away. It is convenient it be selected and choose what is usually used.
• The distance between shear wall axes (or mid-point of
the axis of the cut beam)
• The free span (between faces) plus two times the depth
With this criteria, the envelopes within the shear wall are obtained and the cut-off length of the reinforcement, which do
not exceed the design span by a value of two depths, is also obtained.
When one which does not fail cannot be found in the reinforcement tables, the required number of 25mm diameter
bars will be placed. The
ength or design
span equal to the smaller of the following two values is calculated:
• The assembly stirrup holder reinforcement is used for
in-situ assembly, by placing it between the ends of the
top reinforcement, using small diameter bars and a
construction splice with the reinforcement. This is required so there is reinforcement holding the stirrups. It
may also be used in seismic zones where the splices of
the nodes are to be placed further away. It is convenient it be selected and choose what is usually used.
• The distance between shear wall axes (or mid-point of
the axis of the cut beam)
• The free span (between faces) plus two times the depth
With this criteria, the envelopes within the shear wall are obtained and the cut-off length of the reinforcement, which do
not exceed the design span by a value of two depths, is also obtained.
When one which does not fail cannot be found in the reinforcement tables, the required number of 25mm diameter
bars will be placed. The
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