Manual de calcule CYPE CYPE 3D
2
IMPORTANT: PLEASE READ THE FOLLOWING TEXT CAREFULLY.
The information contained in this document is property of CYPE Ingenieros, S.A. and cannot be reproduced nor transferred partially or
completely in any way or by any means, be it electrically or mechanically, under any circumstances, without previous written authorisation
of CYPE Ingenieros, S.A. Copyright infringement may be constituted as a crime (article 270 and onwards of the Penal code).
This document and the information it contains form an integral part of the documentation accompanying the User License of CYPE
Ingenieros S.A. programs and cannot be separated. Therefore it is protected by the same laws and rights.
Do not forget to read, understand and accept the User License Contract of the software of which this documentation forms part of before
using any component of the product. If the terms and conditions of the User License Contract are NOT accepted, immediately return the
software and all the elements accompanying
the product to where it was first acquired for a complete refund.
This manual corresponds to the software version indicated by CYPE Ingenieros, S.A. as Metal 3D. The information contained in this document substantially describes the properties and methods of use of the program or programs accompanying it. The information contained
in this document could have been modified after its mechanical edition without issuing a warning. The software accompanying this document can be submitted to modifications without issuing a previous warning.
CYPE Ingenieros, S.A. has other services available, one of these being the Updates, which allows the user to acquire the latest versions of
the software and accompanying documentation. If there are any doubts with respect to this text or with the software User License or for
any queries, please contact CYPE Ingenieros, S.A. by consulting the corresponding Authorised Local Distributor or the After-sales department at:
Avda. Eusebio Sempere, 5 – 03003 A
licante (Spain) • Tel : +34 965 92 25 50 • Fax: +34 965 12 49 50 • www.cype.com
CYPE Ingenieros, S.A.
1st Edition (November 2010)
Edited and printed in Alicante (Spain)
Windows is a registered trademark of Microsoft Corporation.
CYPE
Metal 3D - Calculations manual
Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
1.9.4.1. Moment rotation diagram . . . . . . . . . . . . . . . . . . . . . .24
1.9.4.2. Connection rotational stiffness analysis . . . . . . . . . . .25
1. Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
1.9.5. Reasons why a joint has not been designed . . . . . . . . . . .29
1.1. Description of problems to resolve . . . . . . . . . . . . . . . . . . . . .7
1.10. Hollow structural section design . . . . . . . . . . . . . . . . . . . . .29
1.2. Analysis carried out by the program . . . . . . . . . . . . . . . . . . . . .7
1.10.1. Types of hollow structural sections . . . . . . . . . .
. . . . . .29
1.3. Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
1.10.2. Checks
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
1.4. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
1.11. Composite beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
1.5.1. Additional loadcases . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
1.12.1. General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
1.5. Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
1.12. Fire resistance in Metal 3D . . . . . . . . . . . . . . . . . . . . . . . . .31
1.5.2. Limit states (combinations) . . . . . . . . . . . . . . . . . . . . . . . .9
1.12.2. Code selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
1.5.3. Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . .9
1.13. Foundations
1.5.4. Consideration of 2nd order effects (P) . . . . . . . . . . . . . .10
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
1.13.1. Pad footings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
1.6. Bar description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
1.13.1.1. Ground bearing pressures . . . . . . . . . . . . . . . . . . . .33
1.6.1. Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
1.13.1.2. Equilibrium states . . . . . . . . . . . . . . . . . . . . . . . . . .34
1.13.1.3. Concrete states . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
1.6.2. Lateral buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
1.13.1.4. Bending moments . . . . . . . . . . . . . . . . . . . . . . . . . .34
1.6.3. Elements and groups . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
1.13.1.5. Shear forces
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
1.6.4. Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
1.13.1.6. Reinforcement anchorage . . . . . . . . . . . . . . . . . . . . .34
1.6.4.1. Deflection groups . . . . . . . . . . . . . . . . . . . . . . . . . . .15
1.13.1.7. Minimum depths . . . . . . . . . . . . . . . . . . . . . . . . . . .34
1.7. Checks carried out by the program . . . . . . . . . . . . . . . . . . . .15
1.13.1.8. Reinforcement spacing . . . . . . . . . . . . . . . . . . . . . .34
1.8. Tie design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
1.13.1.9. Minimum and maximum steel areas . . . . . . . . . . . . .34
1.8.1. Method application . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
1.13.1.10. Minimum diameters . . . . . . . . . . . . . . . . . . . . . . . .34
1.9. I section joint design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
1.13.1.11.
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
1.13.1.12. Check for oblique compression . . . . . . . . . . . . . . .35
1.9.1. Types of I section joints . . . . . . . . . . . . . . . . . . . . . . . . . .18
1.9.2. I section joint design . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
1.13.2. Pile caps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
1.9.4. Rotational stiffnesses . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
1.13.2.2. Sign criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
1.13.2.1. Design criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
1.9.3. Check of I section joints . . . . . . . . . . . . . . . . . . . . . . . . .23
CYPE
3
4
Metal 3D
1.13.2.3. Design and geometry considerations . . . . . . . . . . . .36
1.13.3. Baseplates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
1.13.4. Mass concrete footings . . . . . . .
. . . . . . . . . . . . . . . . . .39
1.13.4.1. Design of footings as rigid solids . . . . . . . . . . . . . . .39
1.13.4.2. Design of footings as mass concrete structures . . . .39
1.13.4.3. Design report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
1.13.4.4. Minimum depth check . . . . . . . . . . . . . . . . . . . . . . .41
1.13.4.5. Minimum depth check (for reinforcement
anchorage lengths) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
1.13.4.6. Maximum slope angle check . . . . . . . . . . . . . . . . . .41
1.13.4.7. Check for overturning . . . . . . . . . . . . . . . . . . . . . . .41
1.13.4.8. Soil bearing pressures check . . . . . . . . . . . . . . . . . .41
1.13.4.9. Check for bending . . . . . . . . . . . . . . . . . . . . . . . . . .41
1.13.4.10. Check for shear . . . . . . . . . . . . . . . . . . . . . . . . . . .41
1.13.4.11. Check for oblique compression . . . . . . . . . . . . . . .42
1.13.4.12. Minimum reinforcement spacing ch
eck . . . . . . . . .42
1.13.5. Strap and tie beams . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
1.13.5.1. Strap beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
1.13.5.2. Tie beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
2. Code Implementation . . . . . . . . . . . . . . . . . . . . . .45
2.1. Load codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
2.2. Material codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
2.3. Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
CYPE
Metal 3D - Calculations manual
Presentation
Metal 3D is a powerful and efficient program brought about to carry out structural calculations
in 3 dimensions of steel, aluminium and timber bars.
The program obtains the forces and displacements based on an automatic design. It possesses a laminated, welded and cold formed steel section database. It analyses
any type of structure carrying out all the verifications and checks the selected code requires.
Thanks to the generation of structural views, the user can work with windows in 2D and 3D in a
completely interactive manner. The structure can equally be redesigned and hence obtain its maximum
optimisation. The element dimensions are created without the need of having to introduce coordinate
systems or rigid meshes.
This Calculations manual explains the methodology followed by the program using the implemented codes.
CYPE
5
6
Metal 3D
CYPE
Metal 3D - Calculations manual
1. Calculations
1.1. Description of problems to resolve
Any type of support can be used, fixed or pinned, or as a
function of its degrees of freedom. The support (or external
fixity) can be elastic, by defining the constant corresponding to each restricted degree of freedom.
Metal 3D designs three dimensional (3D) structures defined using bar type elements in space with nodes at their
intersections.
The number
of loadcases is established depending on their
origin and these can be assigned as dead, live, wind, seismic (static), snow and accidental loads. Dynamic seismic
loads can be considered.
Steel, aluminium, concrete, timber and generic section
bars can be used and these are defined using their mechanical and geometrical properties.
The program automatically designs steel, timber and aluminium bars.
Using the basic loadcases, any type of combination can be
defined with different combination coefficients in accordance with the selected code or defined by the user.
Reinforced concrete footings and pile caps and strap and
tie beams are resolved for supports defined using vertical
and inclined bars that bear on the on the foundation.
The limit states and combinations for each material and
state are as follows:
Data introduction and result consultation is done graphically.
• U.L.S. Concrete
• U.L.S. Foundation concrete
1.2. Analysis carried out by the program
• Ground bearing p
ressures (characteristic loads)
• Displacements (characteristic loads)
The program considers an elastic and linear behaviour of
the materials. Bars defined are linear elements.
• U.L.S. failure. Steel (rolled and welded)
• U.L.S. failure. Steel (cold formed)
Loads applied on bars can be established in any direction.
The program allows for the following types of loads to be
introduced: uniform, triangular, trapezoidal, point, moments
and different temperature increments on opposite sides.
• U.L.S. Timber
• U.L.S. Aluminium
All the combinations are generated for each case, indicating its name and coefficients, depending on the application code, material and use category.
Point loads can be applied at nodes in any direction. The
type of node used is completely generic, whereby nodes
with internal fixity can consist of fixed (moment) or pinned
(simple) connections; and bar ends can be defined using
fixity coefficients (between 0 and 1), rotational stiffness
(moment/rotation
) or defined as pinned connections.
Based on the geometry and loads that are introduced, the
stiffness matrix of the structure is obtained, as well as the
load matrices for each simple loadcase. The displacement
CYPE
7
8
Metal 3D
• Thermal expansion coefficient: α
matrix of the nodes of the structure is also obtained, inverting the stiffness matrix by frontal methods.
• Specific weight: γ = 78.5 kN/m3
• Limiting slenderness
Having found the displacements for each simple loadcase,
all the combinations are calculated for all the states and
the forces at any sections based on the forces at the ends
of the bars and any loads that have been applied.
Finally, the material parameters for bolts are included in
case baseplates are designed.
Steel sections used can be those belonging to the CYPE library or those that have been edited by the user.
1.3. Units
Metal 3D allows for MKS system of units as well as the international SI system of units to define applied loads and
obta
in the corresponding forces.
If the default section library provided by CYPE is used, the
existing section types can be used by selecting those to be
used in each job.
If, on the contrary, the user wishes to create new section series and types, the x and y section geometry values will
have to be indicated for each section, as well as the thicknesses of the plates and the remaining data for its correct
definition.
1.4. Materials
The materials used in this program are classified into the
following groups:
1.
2.
3.
4.
5.
6.
Rolled and welded steel
Cold-formed steel
Timber
Extruded aluminium
Concrete
Generic sections
1 and 2. If the selected material is steel, various
steel files are present with their properties:
• Type of steel: rolled or welded
• Longitudinal modulus of elasticity: E
• Elastic limit σe, depending on the type
• Steel reduction coefficient γs
• Poisson coefficient: υ. The transverse modulus
of elasticity is calculated internally
Fig. 1.1
CYPE
Meta
l 3D - Calculations manual
The remaining loadcases are additional loadcases, with the
option to be able to create different load dispositions for
each loadcase. When different load dispositions are created, the user must define whether they are simultaneous,
compatible or incompatible. When several additional loadcases of the same type are defined, it must be stated
whether they can be combined or not. All this can be defined by the user.
3. Timber. The type and resistance class of the timber is
selected in accordance with the selected code, where its
properties are defined.
4. Extruded aluminium. The aluminium alloy and temper
is to be selected. These sections are designed in accordance to Eurocode 9.
5. Concrete. The type of concrete (resistance, control level, etc) is selected in accordance with the available codes.
1.5.2. Limit states (combinations)
6. Generic section. The user defines its geometry, mechanical characteristics and material properties.
Once a material, use cate
gory and code have been selected, all the combinations for all the limit states are generated
automatically.
1.5. Loads
• Concrete
Loads can be static or dynamic (in the case of earthquake
loads) and are defined in accordance with their nature as
simple loadcases.
• Foundation concrete
• Cold formed steel
• Rolled steel
1.5.1. Additional loadcases
• Timber
• Aluminium
Metal 3D considers the characteristic loads for each of the
simple loadcases defined as additional loadcases:
• Ground bearing pressures
• Displacements
• Dead load
• Live load
• Wind load
Different project situations, general code or user defined,
can be defined for each limit state.
• Snow load
1.5.3. Loads
Automatic loadcases are those generated by program itself, such as:
• Loads on bars
• Seismic load
• Accidental load
The following load types can be defined for each simple
loadcase:
-
• The self weight of the bars
• Dynamic seismic loading, when activated.
CYPE
Point
Uniform
Strip
9
10
Metal 3D
-
Triangular
Trapezoidal
Applied moment
Increase in uniform temperature
Increase in variable temperature
• Surface loads
This type of load acts in the same way as loads applied
on panels, with the exception that the vertices of the
surface can consist of nodes or any intermediate point
of the bars of a panel.
• Loads on nodes
Point, in any direction in accordance with the general
axes, or by defining the direction vector with respect to
those axes (X,Y, Z).
• Loads on panels
A panel is an area defined by coplanar nodes. Uniform
or variable surface loads can be defined acting on the
surface of a panel to simulate a one-way spanning
slab. The span direction can be defined parallel to one
of the straight lines joining the perimeter nodes of the
panel. The resultant loads are applied on the bars after
carrying out a simply supported simulation of the load
distribution.
Fig. 1.3
The load is distributed in the distribution direction indi
cated on the panel.
A surface load can only be defined on a single panel.
• Prescribed displacements
Displacements in the direction of the general axes can
be defined on nodes that act as supports (displacement and rotation), for each loadcase. A common example would be the settling of a foundation, Dz, which
would cause the corresponding forces to arise in the
structure linked to that support.
∆
1.5.4. Consideration of 2nd order effects (P∆)
Fig. 1.2
Users can optionally choose to, when wind or seismic loadcases are defined, amplify forces produced by these horizontal loads. It is recommended this option be activated for
the analysis.
CYPE
Metal 3D - Calculations manual
This method is based on the P-delta effect due to the displacements produced by the horizontal loads, taking into
account the second order effects, based on a first order
analysis, a linear behaviour of the materials, with mechanical characteristics calculated using the gross section of the
materials and t
heir secant modulus of elasticity.
where:
γfgi: Safety coefficient for dead loads belonging to loadcase i
γfqj: Safety coefficient for variable loads belonging to loadcase j
Due to the horizontal forces, at each node i, a horizontal
force Hi is present, producing a displacement ∆i. A load, Pi,
due to gravitational loadcases, transmitted to the node by
the structure acts at each node.
γz: Global stability coefficient
To calculate the displacements due to each horizontal load
loadcase, the user must recall that a first order analysis has
been carried out using the gross sections of the elements.
If the forces have been calculated for ultimate limit state design, it seems logical that the displacements be calculated
for cracked and homogenised sections. This is very laborious as it assumes the materials, geometry and load states
are non linear. This cannot be taken on from a practical perspective using the normal means available for design.
Therefore, a simplified method must b
e established, assuming a stiffness reduction of the sections, which implies
an increase of the displacements, as these are inversely
proportional. The program asks the user to introduce the
‘displacement multiplication factor’ to be able to account
for this stiffness reduction.
An overturning moment MH is defined due to the horizontal
action Hi, at elevation zi with respect to elevation 0.00 or elevation without horizontal displacements, for each acting
direction:
Similarly, a moment can be defined due to P-delta effects,
MP∆, due to loads transmitted by the bars to the Pi nodes,
for each of the gravitational loadcases (k) defined, because
of the displacements due to the horizontal load ∆i.
where:
At this point, there is no single criteria, hence it is left to the
user’s judgement as to what value is to be introduced depending on the type of structure, estimated cracking grade,
other stiffening elements that may be present, nuclei, stairs,
etc, which in reality may reduc
e the calculated displacements.
k: For each gravitational loadcase (dead load, live load…)
By calculating
, which is the stability index for
each gravitational loadcase, an amplification coefficient
can be obtained of the safety coefficient of the horizontal
load loadcases for all the combinations for which these
horizontal loads act.
In Brazil, a longitudinal elastic modulus reduction coefficient
of 0.90 is usually considered as well as a cracked inertia reduction coefficient with respect to the gross section of 0.70.
Therefore the stiffness is reduced by the product of these
coefficients:
This value, γz is calculated using the following formula:
CYPE
11
12
Metal 3D
Regarding the displacement amplification coefficient, the
code indicates that as the horizontal loads are temporary
and short-term, a reduction of the inertia of 70% can be
considered, and as the module of elasticity is smaller
(15100/1900 = 0.8), i.e. a displacement amplification coefficient of 1 / (0.7 · 0.
8) = 1.78 and, in accordance with the
global stability coefficient, not exceeding a value of 1.35
would be reasonable.
Reduced stiffness = 0.9 · 0.70 · Gross stiffness =
= 0.63 · Gross stiffness
As the displacements are the inverse of the stiffness, the
multiplying factor of the displacements will be equal to
1 / 0.63 = 1.59, which is the value to be introduced in the
program. It is generally considered that if γz > 1.20, the
structure requires more stiffness, as it has high deformation
and little stability in that direction. If γz < 1.1, its effect is
small and practically negligible.
It can be appreciated that the criteria of the model code is
recommended and easy to recall, as well as advisable for
all its application cases:
The NBR 6118:2003 code, using a simplified method, recommends amplifying the displacements by 1/0.7 = 1.43
and limit the value of γz to 1.3.
Displacement multiplication coefficient = 2
Global stability coefficient limit = 1.5
The Model Code CEB-FIP 1
990 applies a moment amplification method which recommends, due to the lack of a
more precise calculation, to reduce the stiffnesses by 50%
or, apply a displacement amplification coefficient equal to
14/0.50 = 2.00. For this case, it may be considered that if
γz > 1.50, the structure has to be stiffened in that direction,
as the structure is very deformable and has little stability in
that direction. If γz < 1.35, its effect is small and practically
negligible.
It is true that, on the other hand, stiffening elements are always present in buildings: façades, stairs, bearing walls,
etc. which ensure a reduced displacement due to horizontal loads than those that have been calculated. Because of
this, the displacement amplification coefficient is left at
1.00. The user is left to choose whether or not to modify it,
as not all the elements can be discretised in the structure
analysis.
ACI-318-95 describes a stability index Q per floor, not for
the global stability of the building, even
though a relationship could be established with the global stability coefficient if the floors are similar, using the following formula:
Once the analysis has finished, a report can be obtained
(Reports > Global stability analysis) where the maximum global stability coefficient in each direction can be
seen.
γz: global stability coefficient = 1 / (1-Q)
It may occur that the structure is not stable, in which case,
a message can be emitted before finishing the analysis,
where the program warns that a global instability phenomenon is present. This will occur when the value of γz tends to
∞or, which is the same using the formula, where it takes a
null or negative value because:
Regarding the limit it establishes to consider the floor as
part of a non-sway frame, or what in this case would be the
limit as to whether it is to be considered or not, it is taken
as Q = 0.05, i.e. 1/0.95 = 1.05.
For this case it has to be calculated and always taken into
account when this value is excee
ded, which definitively implies that it practically always has to be considered in the
analysis and the forces are amplified using this method.
CYPE
Metal 3D - Calculations manual
This may be studied for wind and/or seismic loads and its
analysis is always recommended, as an alternative second
order analysis calculation method, especially for buildings
with sway or slightly sway frames, as is the case of most
buildings.
Additionally, the following hypotheses are assumed:
1.6. Bar description
• The stiffness of the beams is not modified due to normal forces.
• The supports buckle simultaneously.
• The elastic shortening of the supports is ignored.
• The beams behave elastically and are joined in a rigid
manner to the supports.
The user has to define the material, section shape (edited
by the user or from the section library) and its disposition,
which is how the bar section is adjusted with respect to the
drawing axes.
The formulas applied are:
• Non-sway frames
Steel. The user can choose amongst a range of simple
or composed sections provided by the program for
rolled, welded and cold-formed steel.
where:
• Timber. Circular, square or rectangular (with constant
or variable depth) bars can be defined
• Aluminium. I-sections, C-section, symmetrical angle,
plate, T-sections, angle, rectangular and circular hollow
sections, and, round and square bars are available.
1.6.1. Buckling
To study the buckling effects due to axial forces for each
axis, the effective buckling length lk, or the coefficient β,
where lk=β · l, where l is the distance between bar nodes.
When the bar has intermediate nodes, the length or the coefficient corresponding to the real bar between its supports
must be provided, bearing in mind it is being defined for a
bar which is a fraction of the whole bar.
Ib: Inertia of the beams reaching the node
Lb: Length of the beams reaching the node
Ic: Inertia of the columns reaching the node
Lc: Length of the columns reach
ing the node
The user may also use the “approximate calculation of
buckling lengths” by defining the structure as a sway frame
or non sway frame structure, according to the simplified
method and its validity for structures which are slightly orthogonal to each other, where the user can consult the accepted hypotheses in the help dialogue.
• Sway frames
CYPE
13
14
Metal 3D
1.6.3. Elements and groups
where
When a bar is initially introduced between two points. Its
properties are maintained, even if later on they may intersect other bars. It is also possible to create an element later
on consisting of aligned bars containing several spans by
marking the ends.
By grouping, the user can assign common properties to a
group of grouped bars, and they are designed so the most
unfavourable bar of the group does not fail. These may be
ungrouped later on.
Limitations of the approximate calculation
The following warnings should be taken into account by the
users:
• The presence
of intermediate nodes in continuous
bars, to which no other bars reach, invalidates the
method. Hence, in these cases, the appropriate manual
corrections must be undertaken.
1.6.4. Deflections
The ‘deflection’ is taken as the maximum distance between
the straight line joining the end nodes of a bar, and the deformed shape of the bar, without taking into account the
displacement of the end nodes if these have moved. This
distance is measured perpendicularly to the bar.
• To apply the approximate method, the structure must
be classified as having sway or non sway frames, therefore care should be taken when defining the structure.
• All that has been described is only applicable to metallic bars.
The ‘absolute deflection’ is the value in millimetres of the
deflection in the direction in question.
• If the structure that has been introduced is a plane
frame, the values obtained are valid in its plane, and
may not be valid in the plane perpendicular to it, as
there are n
o transverse elements defined, especially
when there is symmetry in the geometry, such as a dual
slope frame calculated in an isolated manner.
The ‘relative deflection’ is established as the span between
intersecting points of the deformed shape with the bar, divided by a value to be defined by the user. There may be an
intermediate point or points, as well as the end nodes of
the bars with no displacements, depending on the deformed shape of the bar.
1.6.2. Lateral buckling
The ‘active deflection’ is the maximum absolute difference
between the maximum deflection and the minimum deflection of all the combinations defined for the displacements
state.
The user can define the distance or separation between
bracing for both the top flange and bottom flange, or the
coefficient that multiplies the length of the bars between
nodes. The applicable moment coefficient, which varies in
different codes and depends on the moment distribution
between braced points, can also be defined.
CYPE
Metal 3D - Calculations manual
If the limit is exceeded, upon checking the bar after the
analysis, it will be displayed in red, as well as all the other
bars that fail.
1.7. Checks carried out by the program
In accordance with that explained previously, the program
checks and designs the bars of the structure according to the
criteria established in each code for each type of material:
• Steel
• Timber
• Aluminium
Fig. 1.4
The program only obtains forces for concrete and generic
sections.
It is possible to establish a limit, be it a value for the maximum deflection, active deflection or relative deflection with
respect to each of the local xy or xz planes of the bar.
If these limit states are exceeded, Metal 3D will allow for a
design to be carried out, whereby it will search through the
section tables to find a suitable section which complies with
all the conditions.
1.6.4.1. Deflection groups
Any bars failing any checks are displayed in red.
Bars can be group
ed when these are aligned and so obtain the deflection between the ends of that particular
group of bars whereby the deflection is calculated between
the end nodes ‘i’ and ‘f’, instead of the local deflection between each pair of consecutive nodes.
The user is to bear in mind that when a bar is modified, the
stiffness matrix will have changed and hence, should reanalyse the job and check the bars.
• Check bars
Upon selecting a bar, a table displaying the section series appears. Those sections which fail are marked with a
red cross and those which are suitable with a green tick.
Any errors that have been encountered are indicated.
• U.L.S. Checks
This is a detailed report indicating each and every code
check that has been carried out, providing the article,
Fig 1.5. A deflection group
CYPE
15
16
Metal 3D
formula and applied values for the worst case requirements of the consulted section.
As well as the resistance checks, the program carries out:
• Fire resistanc
e checks
• Deflection checks
These two options are optional and have to be activated by
the user if they are to be carried out.
1.8. Tie design
Fig. 1.6
2. The axial stiffness of the ties (AE/L) is less than 20% of
the axial stiffness of the elements framing the bracing
elements.
The program allows for bars to be defined as Ties. The fact
the tie bars are composed of a straight axis and only admit
tensile forces in the direction of the axis, implies that this
model would only be strictly exact if a non-linear analysis
were to be carried out, in which, all the bars resulting in
compression would be deleted after each analysis.
3. The diagonal ties of a frame must both be of the same
section.
Additionally, to undertake a dynamic analysis without taking
into account the bars in compression, an analysis in the
time domain with accelerograms would be required.
1.8.1. Method application
The analysis method is linear and elastic using matrix formulae. Each tie is introduced in the
stiffness matrix with only its axial stiffness term (AE/L), whereby this is equal to half
the real axial stiffness of the tie. This way, displacements
are achieved in the stiffness plane, similar to those obtained if the tie in compression were deleted from the matrix
analysis and considering the real cross sectional area of
the tie in tension.
As an approximation to the exact method, we propose an
alternative method whose results, with the requirement that
all the conditions detailed below are met, are sufficiently
acceptable for every day design of structures with bracing
elements.
The method has the following limitations, which the program ensures are met:
The final forces in each tie are obtained for each loadcase
and the following steps are taken for those ties in which the
axial force is in compression:
1. The tie element forms part of a rigid bracing system
framed at its four sides, or three of its sides if the bracing reaches external fixities. Additionally, each rigid
frame
must form a rectangle (four internal angles must
be right angles).
CYPE
Metal 3D - Calculations manual
A. The axial force of the tie in compression is cancelled
B. This axial force is added to the axial force of the
other diagonal tie of the same stiffening frame.
C. With this new axial force configuration, the equilibrium of the nodes is restored.
Given that the method deals with force compatibility and not displacements, it is important to bear in mind the axial stiffness restrictions of the sections making up the stiffening frame indicating
in part 2 of the previous section; the method is more exact the
smaller the relative length differences are of the bars framing the
ties. In all the cases analysed by CYPE, the discrepancies between the results obtained using this method and those obtained
using linear analysis have been negligible.
Fig. 1.8
B. Distribution (by force resolution) of the increment
of axial force in the tie in tension (C*)
The increment in axial force (C*) in
the tie is resolved into the direction of the bars (or fixity reactions) reaching
the nodes.
The following figures display a scheme of the previously described process.
Forces resulting from each of the combinations:
N1, N2, N3, R1h, R2h, R3h, R2v: forces and reactions of
the elements forming the rigid frame without considering the increase in tension of the tie in tension.
Fig. 1.7
T: axial force corresponding to the tie in tension
C: axial force corresponding to the tie in compression
Fig. 1.9
A. Cancelling out of the force of the tie in compression.
Assigning the compression value to the tie in tension.
The axial force of the tie in compression (C=0) is eliminated and is added to the tie in tension (T* = T + |C| ).
CYPE
C. Equilibrium restoration in the end nodes of the
ties. Force equilibrium.
The vector sum of the components of the increment in
tension (with the same absolute value as the compression of the tie in compression) is carried out.
17
18
Metal 3D
1.9.1.
Types of I section joints
The final force and reaction distribution is displayed in
the following diagram:
For I sections (Joints I, II, III and IV modules), the program
provides two types of design:
Welded, e.g.:
Fig. 1.10
Fig. 1.12
These values can be consulted in each bar or node for
each loadcase or combination loadcase. Each loadcase is treated as a unit combination.
1.9. I section joint design
As of the 2008 version, Metal 3D incorporates the analysis
and design of I section joints, by means of welded and
bolted connections.
Fig. 1.13
Additionally, as of the 2009.1.g version, the program considers upon designing the connections that bar ends are
rigid spans along the length taken up by the node.
Fig. 1.14
Fig. 1.11
CYPE
Metal 3D - Calculations manual
Bolted (using ordinary or prestressed bolts), e.g.:
Fig. 1.15
Fig. 1.18
Fig. 1.16
Fig. 1.19
Fig. 1.20
Fig. 1.17
For a more complete list of available welded connections,
please consult the corresponding website a
t
www.cypecad.en.cype.com/joints_welded.htm
www.cypecad.en.cype.com/joints_welded_building.htm
Fig. 1.21
CYPE
19
20
Metal 3D
Analysis of the joints of the job . EN 1993-1-8:2005,
CTE DB-SE-A and ABNT NBR 8800:2006.
Joints are designed with welded connections or bolted
connections using prestressed or ordinary bolts.
The program checks that the sections and components
(stiffeners, bolts, plates etc.) of the joint do not interfere with
one another: that the joints can be executed on site, that
there is sufficient space to be able either weld or provide
the required bolts and be able to tighten them correctly.
Fig. 1.22
The complete node is designed considering the 6 forces at
each bar end reaching the node, then optimising the components upon knowing the arrangement, behaviour and
geometry of the node.
Detail drawings are provided as well as a report justifying all
the checks that have been carried out, together with a take
off summary of the joint and its components.
Fig. 1.
23
For a more complete list of available bolted connections
please consult the corresponding website at
Options are available for each type of bolt, stiffeners and
baseplates at foundation level.
w w w. c y p e c a d . e n . c y p e . c o m / j o i n t s _ b o l t e d . h t m
www.cypecad.en.cype.com/joints_bolted_building.htm
Nodes possessing the same geometry, same sections and
materials, same fixity coefficient or rotational stiffness with
less than a 10% difference, and a similar structural behaviour, are automatically grouped. This simplifies the execution of the job by grouping similar joints.
1.9.2. I section joint design
When analysing the job, the program enquires whether the
user wishes to activate the welded or bolted connection
design. Nonetheless, if the option is not activated, the joints
may be designed after the analysis using the option Joints
> Analyse, bearing in mind what has already been indicated regarding node size consideration and the rigid consideration o
f the end span of a bar with the finite dimension of
the node.
In the case of bolted joints, the rotational stiffness of the
designed connections is established and the program
emits a warning if the difference between the stiffness obtained and that assigned is greater than 20%. It is important
the user redesigns the joint if the rotational stiffness has
been modified, as differences may be present that invalidate the analysis results.
If nodes whose type of joint is resolved in the program are
detected during the design process of the structure, the
program will design the connections and will provide a detail drawing of the results.
CYPE
Metal 3D - Calculations manual
Welded I section joint checks
The following checks are carried out on the components:
• Shear and slenderness of the panel made up by the
web of the column. It is reinforced using a plate welded
to the web.
• Combined stresses at the simply connected column
web.
K = 0.90 (EC3)
K = 1.00 (CTE)
• Combine
d stresses at stiffeners and plates which are
coplanar with beams fixed to the column web.
• Shear-bending interaction at separation plates with sections with different depths (splices, column transitions,
beams fixed to the web).
• Sufficient net area for round threaded ties.
• Bending and punching shear due to perpendicular
forces of the web or flange of the supporting elements
of simply connected sections.
• Stiffener buckling resistance.
Below are the checks carried out on the welds:
• Minimum thickness of elements to be welded
• Real and absolute minimum effective lengths and relative to the throat weld.
• Minimum and maximum (0.7tmin) throat weld thickness.
• The contributing material must have at least, the same
resistance as the materials to be joined.
• Minimum and maximum angle between the surfaces to
be welded.
• Weld resistance: The 3 stress components in the plane
of the throat and the equations are checked for all the
load combinations of the co
de. In the case of double
angle welds, the check is carried out for the acute angle and obtuse angle.
CYPE
21
22
Metal 3D
Bolted I section joint checks
Check
1
3
M.C.E. S.C.E.
×
×
×
×
×
Distances (maximum and minimum) to edge, between bolts and to elements
Shear in ordinary bolts and U.L.S. slipping for prestressed bolts
2
4
5
6
7
8
9
Bolt tension (including prying forces)
Shear-tension interaction of ordinary bolts
Crushing of the bolts and plate
Crushing of the bolts and simply connected section web
×
×
Crushing of the bolts and supporting section flange
Punching shear of the plate
Punching shear of the simply connected section web
×
×
×
10 Punching shear of the supporting section flange
11 Bending of the end-plate
12 Bending of the supporting section flange
13 Bending of the supporting section web
14 Bending of the simply connected section web
15 Buckling of the simply connected section web
16 Buckling of the plate
×
17 Shear and slenderness of the
panel made up by the column web
18 Tearing of the plate
19 Tearing of the simply connected section web
20 Tension of the section flange welded to the plate
21 Tension of the section web welded to the plate
22 Tension of the column web or continuous beam
23 Tension or compression of the stiffeners
24 Compression with shear interaction and torsion of the section flange welded to the plate
25 Compression with shear interaction and torsion of the section web welded to the plate
26 Combined stresses at the simply connected section web
×
×
×
×
×
×
27 Combined stresses of the plate
28 Punching shear of the supporting section web due to the plate
29 Punching shear of the supporting section flange due to the plate
30 Effective weld throat stresses. The bolt stress influence is taken into account
31 Rotation capacity. Resistant moment Mj.Rd. Critical mechanism 1 or 2 (double or single hinge)
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
S.C.L.
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
Detail export: link between the project and its fabrication
M.C.E.: With end-plate
S.C.E.: Simple connection with end-plate
Having designed the structure and its joints, the project can
be exported to Tekla Structures, TecnoMetal 4D and in
CIS/2 format, achieving direct communication between the
project phase of the project and its fabrication.
S.C.L.: Simple connection with lateral plate
CYPE
Metal 3D - Calculations manual
Baseplates
Even if the user does not dispose of the joints module in
his/her license, the program allows the user to activate the
joint design. Once concluded, the 3D views of the joints
that could be deigned with the non-acquired modules can
be visualised. The details or check and take off reports are
not displayed. When the cursor is placed over one of these
nodes, a warning is displayed indicating the non-acquired
modules that could design the joint.
Baseplates are designed using the welded joints module:
dimension
s, stiffeners, welds and bolts according to the
selected code.
1.9.3. Check of I section joints
The joints that have been resolved can be seen after the
analysis using the Consult option within the Joints menu.
Upon activating this option and clicking on a node whose
joint has been designed (displayed in green), the details of
the joint will be displayed.
If the user clicks on a node whose joint has not been designed (displayed in red), the program will display a 3D
view with the bars reaching the joint, so the user may see
whether or not the bars interfere with one another so as to
prevent the joint from being designed.
Fig. 1.24
By clicking on a node that has been partially resolved (displayed in orange), only the resolved joints will be displayed.
The following tabs may be consulted:
• Detail. These are the detail drawings of the designed
joints.
• Report. This is a report summarising the analysis that
has been carried out and its take off.
Fig. 1.25
• 3DView. This is
a three dimensional view of the node
and its connections.
CYPE
23
24
Metal 3D
As the program carries out an elastic analysis of the structure, the following relationships arise from the previous
three models:
Type of model
Simple support
Connection classification
Continuous
Semi-continuous
Elastic analysis Pinned connection Rigid connection Semi-rigid connection
The assumptions corresponding to semi-rigid connections
are analysed below.
1.9.4.1. Moment rotation diagram
The behaviour of the connections is studied by analysing
the moment- rotation properties diagram, which allows to
define the three main structural properties of the connection:
Fig. 1.26
• Bending moment resistance Mj,Rd: Maximum ordinate
of the diagram.
• Rotational stiffness Sj: the secant stiffness for an acting
bending moment value Mj,Ed, defined up to rotation φXd
which corresponds to the point at which Mj,Ed is equal
to Mj,Rd.
1.9.4. Rotational stiffnesses
When performing the global analysis o
f the structure, it is
important to take into account the behaviour of the joints to
obtain the correct distribution of the internal forces, stresses and deformations.
• Rotation capacity φCd: represents the maximum rotation of the moment-rotation diagram.
To establish how the effect of the behaviour of the connections should be taken into account in the analysis of the
structure, three different simplified models are used:
The following figure displays a typical connection momentrotation:
• Simple supports: those in which no moments are transmitted.
• Continuous: those in which the behaviour of the connections does not intervene significantly in the analysis
of the structure.
• Semi-continuous: those in which the behaviour of the
connection must be taken into account in the global
analysis of the structure.
Fig. 1.27
CYPE
Metal 3D - Calculations manual
According to its rotational stiffness Sj connections are classified as: pinned connections, rigid connections or se
mirigid connections. The boundaries between one type and
another are shown in the figure below:
Where:
E: Steel elastic modulus
z: Connection lever arm
ki: Stiffness coefficient for the basic ith component
µ: stiffness ratio:
µ can be found as follows:
Fig. 1.28
When
Where:
When
Zone 1. Rigid connections
(elastic behaviour)
:
Zone 2. Semi-rigid connections
Zone 3. Pinned connections
1.9.4.2. Connection rotational stiffness analysis
To calculate the initial stiffness of the connection Sj,ini the
component method is used, according to which:
1.9.4.2.1. Initial stiffness calculation Sj,ini
For splices and ridge intersections:
The program constructs the characteristic Myy moment rotation in the xz plane diagram for each joint at the end of
an element where its rotational stiffness has been calculated due to the presence of deformable components in the
node.
For column-beam joints:
For axial forces not exceeding 5% of the transverse section’s capacity, the stiffness Sj
of the connection for an acting moment Mj,Ed can be obtained using the following expression:
Where:
zeq: Equivalent connection lever arm:
CYPE
25
26
Metal 3D
For splices and ridge intersections:
k3: Fitted joints of the beam and the column flange: Stiffness coefficient of the tension-resisting column web.
hr: Distance between row r and the compression centre
(which is considered to coincide with the compressed flange)
Fitted joints of the beam and the column web: Stiffness coefficient of the tension-resisting vertical plate.
n: Number of rows in tension
k1: Fitted joints of the beam and the column flange: Stiffness coefficient of the shear-resisting column web.
k4: Fitted joints of the beam and the column flange: Stiffness coefficient of the flexure-resisting column flange.
Fitted joints of the beam and the column web: Stiffness coefficient of the shear-resisting column flanges.
Fitted joints of the beam and the column web: Stiffness coefficient of the flexure-resistin
of the connection for an acting moment Mj,Ed can be obtained using the following expression:
Where:
zeq: Equivalent connection lever arm:
CYPE
25
26
Metal 3D
For splices and ridge intersections:
k3: Fitted joints of the beam and the column flange: Stiffness coefficient of the tension-resisting column web.
hr: Distance between row r and the compression centre
(which is considered to coincide with the compressed flange)
Fitted joints of the beam and the column web: Stiffness coefficient of the tension-resisting vertical plate.
n: Number of rows in tension
k1: Fitted joints of the beam and the column flange: Stiffness coefficient of the shear-resisting column web.
k4: Fitted joints of the beam and the column flange: Stiffness coefficient of the flexure-resisting column flange.
Fitted joints of the beam and the column web: Stiffness coefficient of the shear-resisting column flanges.
Fitted joints of the beam and the column web: Stiffness coefficient of the flexure-resistin
... ascunde
Alte documentatii ale aceleasi game Vezi toate
Fisa tehnica
44 p | EN
CYPE 3D
Instructiuni montaj, utilizare
46 p | EN
CYPE 3D