AL-NAHRAIN UNIVERSITY

COLLEGE OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
STAAD PRO NOTES
2014-2015
PREPARED BY: ZAHIR NOORI M. TAKI

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 1- Main steps for modeling structures:-

Regardless of the structure being analyzed, the following are

fundamental steps and STAAD command keywords shown in the
brackets:
1. Define whether the problem is 2D or 3D (STAAD PLANE or SPACE)
2. Define the length and force units (UNITS)
3. Define the nodes and their locations (JOINT COORDINATES)
4. Define the member and their nodes (MEMBER INCIDENCES)
5. Define the section properties of the members, I x , etc (MEMBER
PROPERTY)
6. Define the mechanical properties of the members such as the
Young's modulus, density, etc (CONSTANTS)
7. Define the support conditions (SUPPORTS)
8. Define the load cases (LOAD)
9. Define the loads of each load case as member loads, joint loads,
(or code loads) (MEMBER LOAD or JOINT LOAD)
10. Define the load combinations (LOAD COMB)
11. Analyze the structure (PERFORM ANALYSIS)
12. Define the output format (PRINT)
13. Finish the run (FINISH)

2- Coordinate Systems:
Since STAAD uses the Matrix Displacement Method of structural analysis,
there are 2 Cartesian coordinate systems - the local and the global. The
geometry of the structure as a whole is defined by the nodes at the ends of
the various structural members, and each node has a unique number. Each

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member also has a unique number and the topology of the member is defined
relative to the node numbers at its ends. This establishes the "MEMBER
INCIDENCES" table. The location of each node is defined relative to a global
coordinate system. By default, the origin of the global coordinate system is
at node number 1.The location of points or sections within each structural
member is defined relative to the local coordinate system with the origin at
the left end node of the member viewed horizontally. Each member has its
own local coordinate system.
3- Types of Structures
A STRUCTURE can be defined as an assemblage of elements. STAAD is capable
of analyzing and designing structures consisting of both frame, plate/shell and
solid elements. Almost any type of structure can be analyzed by STAAD.
A SPACE structure, which is a three dimensional framed structure with loads
applied in any plane, is the most general.
A PLANE structure is bound by a global X-Y coordinate system with loads in
the same plane.
A TRUSS structure consists of truss members which can have only axial
member forces and no bending in the members.
A FLOOR structure is a two or three dimensional structure having no
horizontal (global X or Z) movement of the structure [FX, FZ & MY are
restrained at every joint]. The floor framing (in global X-Z plane) of a building
is an ideal example of a FLOOR structure. Columns can also be modeled with
the floor in a FLOOR structure as long as the structure has no horizontal
loading. If there is any horizontal load, it must be analyzed as a SPACE
structure.

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 4- Unit Systems
The user is allowed to input data and request output in almost all commonly
used engineering unit systems including MKS, SI and FPS. In the input file, the
user may change units as many times as required. Mix and match between
length and force units from different unit systems is also allowed. The input-
unit for angles (or rotations) is degrees. However, in JOINT DISPLACEMENT
output, the rotations are provided in radians. For all output, the units are
clearly specified by the program.

5- Structure Geometry and Coordinate Systems

A structure is an assembly of individual components such as beams, columns,
slabs, plates etc.. In STAAD, frame elements and plate elements may be used
to model the structural components. Typically, modeling of the structure
geometry consists of two steps:
A. Identification and description of joints or nodes.
B. Modeling of members or elements through specification of connectivity
(incidences) between joints.

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In general, the term MEMBER will be used to refer to frame elements and the
term ELEMENT will be used to refer to plate/shell and solid elements.
Connectivity for MEMBERs may be provided through the MEMBER INCIDENCE
command while connectivity for ELEMENTs may be provided through the
ELEMENT INCIDENCE command.
STAAD uses two types of coordinate systems to define the structure geometry
and loading patterns. The GLOBAL coordinate system is an arbitrary
coordinate system in space which is utilized to specify the overall geometry &
loading pattern of the structure. A LOCAL coordinate system is associated
with each member (or element) and is utilized in MEMBER END FORCE output
or local load specification. For input, refer the 'Related Topics' below.

6- Global Coordinate System

The following coordinate systems are available for specification of the
structure geometry.
1- Conventional Cartesian coordinate system: This coordinate system (Fig.
1.2) is a rectangular coordinate system (X, Y, Z) which follows the
orthogonal right hand rule. This coordinate system may be used to
define the joint locations and loading directions. The translational
degrees of freedom are denoted by u1, u2, u3 and the rotational
degrees of freedom are denoted by u4, u5 & u6.
2- Cylindrical Coordinate System: In this coordinate system, (Fig. 1.3) the
X and Y coordinates of the conventional Cartesian system are replaced
by R (radius) and Ø (angle in degrees). The Z coordinate is identical to
the Z coordinate of the Cartesian system and its positive direction is
determined by the right hand rule.
3- Reverse Cylindrical Coordinate System: This is a cylindrical type
coordinate system (Fig. 1.4) where the R- Ø plane corresponds to the X-
Z plane of the Cartesian system. The right hand rule is followed to
determine the positive direction of the Y axis.

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 7- Local Coordinate System
A local coordinate system is associated with each member. Each axis of the
local orthogonal coordinate system is also based on the right hand rule. Fig.
1.5 shows a beam member with start joint 'i' and end joint 'j'. The positive
direction of the local x-axis is determined by joining 'i' to 'j' and projecting it
in the same direction. The right hand rule may be applied to obtain the
positive directions of the local y and z axes. The local y and z-axes coincide
with the axes of the two principal moments of inertia. Note that the local
coordinate system is always rectangular.
A wide range of cross-sectional shapes may be specified for analysis.
These include rolled steel shapes, user specified prismatic shapes etc.. Fig. 1.6
shows local axis system(s) for these shapes.

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 8- Relationship Between Global & Local Coordinates
Since the input member loads can be provided in the local and global
coordinate system and the output for member-end-forces is printed in the
local coordinate system, it is important to know the relationship between the
local and global coordinate systems. This relationship is defined by an angle
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measured in the following specified way. This angle will be defined as the beta
(b) angle.
1- Beta Angle
When the local x-axis is parallel to the global Y-axis, as in the case of a column
in a structure, the beta angle is the angle through which the local z-axis has
been rotated about the local x-axis from a position of being parallel and in the
same positive direction of the global Z-axis.
When the local x-axis is not parallel to the global Y-axis, the beta angle is the
angle through which the local coordinate system has been rotated about the
local x-axis from a position of having the local z-axis parallel to the global X-Z
plane and the local y-axis in the same positive direction as the global Y-axis.
Figure 1.7 details the positions for beta equals 0 degrees or 90 degrees. When
providing member loads in the local member axis, it is helpful to refer to this
figure for a quick determination of the local axis system.
2- Reference Point
An alternative to providing the member orientation is to input the
coordinates (or a joint number) which will be a reference point located in the
member x-y plane but not on the axis of the member. From the location of
the reference point, the program automatically calculates the orientation of
the member x-y plane.

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 9- Finite Element Information
STAAD is equipped with a plate/shell finite element, solid finite element and
an entity called the surface element. The features of each is explained in the
following sections:
9-1 Plate and Shell Element
The Plate/Shell finite element is based on the hybrid element formulation.
The element can be 3-noded (triangular) or 4-noded (quadrilateral). If all the
four nodes of a quadrilateral element do not lie on one plane, it is advisable
to model them as triangular elements. The thickness of the element may be
different from one node to another.

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"Surface structures" such as walls, slabs, plates and shells may be modeled
using finite elements. For convenience in generation of a finer mesh of
plate/shell elements within a large area, a MESH GENERATION facility is
available.
The following geometry related modeling rules should be remembered
while using the plate/shell element.
1- The program automatically generates a fictitious fifth node "O" (center
node - see Fig. 1.8) at the element center.
2- While assigning nodes to an element in the input data, it is essential
that the nodes be specified either clockwise or counter clockwise (Fig.
1.9). For better efficiency, similar elements should be numbered
sequentially.
3- Element aspect ratio should not be excessive. They should be on the
order of 1:1, and preferably less than 4:1.
4- Individual elements should not be distorted. Angles between two
adjacent element sides should not be much larger than 90 and never
larger than 180.

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 9-2 Theoretical Basis
The STAAD plate finite element is based on hybrid finite element
formulations. A complete quadratic stress distribution is assumed. For plane
stress action, the assumed stress distribution is as follows.

The following quadratic stress distribution is assumed for plate bending

action:

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 9-3 Plate Element Local Coordinate System
The orientation of local coordinates is determined as follows:
1- The vector pointing from I to J is defined to be parallel to the local x-
axis.
2- The cross-product of vectors IJ and IK defines a vector parallel to the
local z-axis, i.e., z = IJ x IK.
3- The cross-product of vectors z and x defines a vector parallel to the
local y- axis, i.e., y = z x x.
4- The origin of the axes is at the center (average) of the 4 joint
locations (3 joint locations for a triangle).

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 9-4 Output of Plate Element Stresses and Moments
For the sign convention of output stress and moments, please see Fig. 1.13.
ELEMENT stress and moment output is available at the following locations:
A. Center point of the element.
B. All corner nodes of the element.
C. At any user specified point within the element.
Following are the items included in the ELEMENT STRESS output.
• SQX, SQY Shear stresses (Force/ unit len./ thk.)
• SX, SY, SXY Membrane stresses (Force/unit len./ thk)
• MX, MY, MXY Moments per unit width (Force x Length/length) (For
Mx, the unit width is a unit distance parallel to the local Y axis. For My,
the unit width is a unit distance parallel to the local X axis. Mx and My
cause bending, while Mxy causes the element to twist out-of-plane.)
• SMAX, SMIN Principal stresses in the plane of the element
(Force/unit area)
• TMAX Maximum shear stress in the plane of the element
(Force/unit area)
• ANGLE Orientation of the principal plane (Degrees)

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 • VONT, VONB Von Mises stress, where
Notes:
• All element stress output is in the local coordinate system. The direction
and sense of the element stresses are explained in Fig. 1.13.
• To obtain element stresses at a specified point within the element, the
user must provide the coordinate system for the element. The origin of
the local coordinate system coincides with the center of the element.
• Principal stresses (SMAX & SMIN), the maximum shear stress (TMAX),
the orientation of the principal plane (ANGLE), the Von Mises stress
(VONT & VONB), and the Tresca stress (TRESCAT & TRESCAB) are also
printed for the top and bottom surfaces of the elements. The top and
the bottom surfaces are determined on the basis of the direction of the
local z-axis.

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Please note the following few restrictions in using the finite element
portion of STAAD:
• Both frame members and finite elements can be used together
in a STAAD analysis. The ELEMENT INCIDENCES command must
directly follow the MEMBER INCIDENCES input.
• The self-weight of the finite elements is converted to joint
loads at the connected nodes and is not used as an element
pressure load.
• Element stresses are printed at the centroid and joints, but not
along any edge.
• In addition to the stresses shown in Fig 1.13, the Von Mises
stresses at the top and bottom surface of the element are also
printed.

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 9-5 Plate Element Numbering
To save some computing time, similar elements should be numbered
sequentially. Fig. 1.14 shows examples of efficient and non-efficient
element numbering. However the user has to decide between
adopting a numbering system which reduces the computation time
versus a numbering system which increases the ease of defining the
structure geometry.

10- Solid Element

Solid elements enable the solution of structural problems involving
general three dimensional stresses. There is a class of problems such
as stress distribution in concrete dams, soil and rock strata where
finite element analysis using solid elements provides a powerful tool.

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10-1 Theoretical Basis
The solid element used in STAAD is of eight noded iso-parametric
type. These elements have three translational degrees-of-freedom
per node.

10-2 Local Coordinate System

The local coordinate system used in solid element is the same as the global
system as shown below:

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Unlike members and shell (plate) elements, no properties are required for
solid elements. However, the constants such as modulus of elasticity and
Poisson's ratio are to be specified.

10-3 Output of Element Stresses

Element stresses may be obtained at the center and at the joints of the solid
element. The items that are printed are:

Normal Stresses: SXX, SYY and SZZ

Shear Stresses: SXY, SYZ and SZX

Principal stresses: S1, S2 and S3.

Von Mises stresses:

11- Surface Element

For any surface type of structural component, modeling requires breaking it

down into a series of plate elements for analysis purposes. This is what is
known in stress analysis parlance as meshing. When a user chooses to model
the surface component using plate elements, he/she is taking on the
responsibility of meshing. Thus, what the program sees is a series of elements.
It is the user's responsibility to ensure that meshing is done properly.
Examples of these are available in example problems 9, 10, 23, 27, etc. (of the
Examples manual) where individual plate elements are specified.

With the new Surface type of entity, the burden of meshing is shifted from
the user to the program to some degree. The entire wall or slab is hence
represented by just a few "Surface" entities, instead of hundreds of elements.
When the program goes through the analysis phase, it will subdivide the
surface into elements by itself. The user does not have to instruct the program
in what manner to carry out the meshing.

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11-1 Local Coordinate system for surfaces

The origin and orientation of the local coordinate system of a surface element
depends on the order in which the boundary nodal points are listed and
position of the surface element in relation to the global coordinate system.

Let X, Y, and Z represent the local and GX, GY, and GZ the global axis vectors,
respectively. The following principles apply.

• Origin of X-Y-Z is located at the first node specified.

• Direction of Z may be established by the right hand corkscrew rule,
where the thumb indicates the positive Z direction, and the fingers
point along the circumference of the element from the first to the last
node listed.
• X is a vector product of GY and Z (X = GY X Z). If GY and Z are parallel, X
is taken as a vector parallel to GX.
• Finally, Y is a vector product of Z and X (Y = Z X X).

The diagram below shows directions and sign convention of local axes and
forces.

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 12- Member Properties

The following types of member property specifications are available in

STAAD:

12-1 Prismatic Properties

The following prismatic properties are required for analysis:

AX = Cross sectional area

IX = Torsional constant

IY = Moment of inertia about y-axis.

IZ = Moment of inertia about z-axis.

In addition, the user may choose to specify the following properties:

AY = Effective shear area for shear force parallel to local y-axis.

AZ = Effective shear area for shear force parallel to local z-axis.

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YD = Depth of section parallel to local y-axis.

ZD = Depth of section parallel to local z-axis.

To specify T-beam or Trapezoidal beam, the following additional properties

must be provided.

YB = Depth of Web of T-section [See figure below]

ZB = Width of web of T-section or bottom width of Trapezoidal section.

Table 1.1 is offered to assist the user in specifying the necessary section
values. It lists, by structural type, the required section properties for any
analysis. For the PLANE or FLOOR type analyses, the choice of the required
moment of inertia depends upon the beta angle. If BETA equals zero, the
required property is IZ.

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 12-2 Built-In Steel Section Library

This feature of the program allows the user to specify section names of
standard steel shapes manufactured in different countries. Since the shear
areas of the sections are built into the tables, shear deformation is always
considered for these sections.

12-3 User Provided Steel Table

The user can provide a customized steel table with designated names and
proper corresponding properties. The program can then find member
properties from those tables. Member selection may also be performed with
the program selecting members from the provided tables only.

12-4 Tapered Sections

Properties of tapered I-sections may be provided through MEMBER

PROPERTY specifications. Given key section dimensions, the program is
capable of calculating cross-sectional properties which are subsequently used
in analysis.

12-5 Assign Command

Through this command, the user may instruct the program to automatically
select a steel section from the table for analysis and subsequent design. The
section types that may be ASSIGNed include BEAM, COLUMN, CHANNEL,
ANGLE and DOUBLE ANGLE. When a BEAM or COLUMN is specified, the
program will assign an I-beam section (WF for AISC) and subsequent member
selection or optimization will be performed with a similar type section.

Example

UNIT . . .

MEMBER PROPERTIES

1 TO 5 TABLE ST W8X31

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9 10 TABLE LD L40304 SP 0.25

12 TO 15 PRISMATIC AX 10.0 IZ 1520.0

17 18 TA ST PIPE OD 2.5 ID 1.75

20 TO 25 TA ST TUBE DT 12. WT 8. TH 0.5

27 29 32 TO 40 42 PR AX 5. IZ 400. IY 33. -

IX 0.2 YD 9. ZD 3.

43 TO 47 UPT 1 W10X49

50 51 UPT 2 L40404

52 TO 55 ASSIGN COLUMN

56 TA TC W12X26 WP 4.0 TH 0.3

57 TA CM W14X34 CT 5.0 FC 3.0

This example shows each type of member property input. Members 1 to 5 are
wide flanges selected from the AISC tables; 9 and 10 are double angles
selected from the AISC tables; 12 to 15 are prismatic members with no shear
deformation; 17 and 18 are pipe sections; 20 to 25 are tube sections; 27, 29,
32 to 40, and 42 are prismatic members with shear deformation; 43 to 47 are
wide flanges selected from the user input table number 1; 50 and 51 are single
angles from the user input table number 2; 52 through 55 are designated as
COLUMN members using the ASSIGN specification. The program will assign a
suitable I-section from the steel table for each member.

Member 56 is a wide flange W12X26 with a 4.0 unit wide cover plate of 0.3
units of thickness at the top. Member 57 is a composite section with a
concrete slab of 5.0 units of thickness at the top of a wide flange W14X34.
The compressive strength of the concrete in the slab is 3.0 force/length2.

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 12-6 Curved Members

Members can now be defined as being curved. Tapered sections are not
permitted. The cross-section should be uniform throughout the length.

13- Member and Element Release

13-1 Member Release

STAAD allows releases for both members and elements. One or both ends of
a member or element can be released. Members/Elements are assumed to
be rigidly framed into joints in accordance with the structural type specified.
When this full rigidity is not applicable, individual force components at either
end of the member can be set to zero with member release statements. By
specifying release components, individual degrees of freedom are removed
from the analysis. Release components are given in the local coordinate
system for each member. Note that PARTIAL moment release is also allowed.

In other words, a MEMBER RELEASE should not be applied on a member

which is declared TRUSS, TENSION ONLY or COMPRESSION ONLY.

Example

MEMBER RELEASE

1 3 TO 9 11 12 START KFX 1000.0 MY MZ

1 10 11 13 TO 18 END MZ KMX 200.0

In the above example, for members 1, 3 to 9, 11 and 12, the moments about
the local Y and Z axes are released at their start joints (as specified in MEMBER
INCIDENCES). Further, these members are attached to their START joint along
their local x axis through a spring whose stiffness is 1000.0 units of
force/length. For members 1, 10, 11 and 13 to 18, the moment about the local
Z axis is released at their end joint. Also, the members are attached to their
END joint about their local x axis through a moment-spring whose stiffness is

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200.0 units of force-length/Degree. Members 1 and 11 are released at both
start and end joints, though not necessarily in the same degrees of freedom.

Partial Moment Release

Moments at the end of a member may be released partially. This facility may
be used to model partial fixity of connections. The following format may be
used to provide a partial moment release. This facility is provided under the
MEMBER RELEASE option and is in addition to the existing RELEASE
capabilities

Example

MEMBER RELEASE

15 TO 25 START MP 0.25

The above RELEASE command will apply a factor of 0.75 on the moment
related stiffness coefficients at START of members 15 to 25.

Notes

Member releases are a means for describing a type of end condition for
members when the default condition, namely, fully moment and force
resistant, is not applicable. Examples are bolted or riveted connections.
Partial moment releases are a way of specifying bending and torsional
moment capacity of connections as being a fraction of the full bending and
torsional strength.

13-2 Element Release

For example, if the incidences of the element were defined as 35 42 76 63, J1

represents 35, J2 represents 42, J3 represents 76, and J4 represents 63.
Element releases at multiple joints cannot be specified in a single line. Those
must be specified separately as shown below. FX through MZ represents
forces/moments to be released per local axis system.

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Example

ELEMENT RELEASE

10 TO 50 J1 MX MY

10 TO 50 J2 MX MY

10 TO 50 J3 MY

10 TO 50 J4 MY

14- Truss/Tension/Compression - Only Members

For analyses which involve members that carry axial loads only, i.e. truss
members, there are two methods for specifying this condition. When all the
members in the structure are truss members, the type of structure is declared
as TRUSS whereas, when only some of the members are truss members (e.g.
bracings of a building), the MEMBER TRUSS command can be used where
those members will be identified separately.

15- Tension, Compression - Only Springs

In STAAD, the SPRING TENSION or SPRING COMPRESSION command can be

used to limit the load direction the support spring may carry. The analysis will
be performed accordingly.

16- Cable Members

STAAD supports 2 types of analysis for cable members - linear and non-linear.

16-1 Linearized Cable Members

Cable members may be specified by using the MEMBER CABLE command.

While specifying cable members, the initial tension in the cable must be
provided. The following paragraph explains how cable stiffness is calculated.

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The increase in length of a loaded cable is a combination of two effects. The
first component is the elastic stretch, and is governed by the familiar spring
relationship:

The second component of the lengthening is due to a change in geometry (as

a cable is pulled taut, sag is reduced). This relationship can be described by

Therefore, the "stiffness" of a cable depends on the initial installed tension

(or sag). These two effects may be combined as follows

It may be noticed that as the tension increases (sag decreases) the combined
stiffness approaches that of the pure elastic situation.

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 16-2 Non Linear Cable Members

Cable members for the Non Linear Cable Analysis may be specified by using
the MEMBER CABLE command. While specifying cable members, the initial
tension in the cable or the unstressed length of the cable must be provided.
The user should ensure that all cables will be in sufficient tension for all load
cases to converge. Use self-weight in every load case and temperature if
appropriate; i.e. don’t enter component cases (e.g. wind only).

There are two cable types in the nonlinear PERFORM CABLE ANALYSIS
procedure. One is the cable whose stiffness is described in section 1.11.1
above. In the nonlinear cable analysis, the cable may have large motions and
the sag is checked on every load step and every equilibrium iteration. The
second cable type is not available yet. It is a catenary shaped cable that is
integrated along its length to determine its end forces on every load step and
every equilibrium iteration.

In addition there is a nonlinear truss which is specified in the Member Truss

command. The nonlinear truss is simply any truss with pretension specified.
It is essentially the same as a cable without sag. This member takes
compression. If all cables are taut for all load cases, then the nonlinear truss
may be used to simulate cables. The reason for using this substitution is that
the truss solution is more reliable.

17- Member Offsets

Some members of a structure may not be concurrent with the incident joints
thereby creating offsets. This offset distance is specified in terms of global or
local coordinate system (i.e. X, Y and Z distances from the incident joint).
Secondary forces induced, due to this offset connection, are taken into
account in analyzing the structure and also to calculate the individual member
forces. The new offset centroid of the member can be at the start or end
incidences and the new working point will also be the new start or end of the

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member. Therefore, any reference from the start or end of that member will
always be from the new offset points.

Example

ELEMENT OFFSET

1 START 7.0

1 END -6.0 0.0

2 END -6.0 -9.0

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 18- Material Constants

The material constants are: modulus of elasticity (E); weight density (DEN);
Poisson's ratio (POISS); co-efficient of thermal expansion (ALPHA), Composite
Damping Ratio, and beta angle (BETA) or coordinates for any reference (REF)
point. E value for members must be provided or the analysis will not be
performed. Weight density (DEN) is used only when self-weight of the
structure is to be taken into account. Poisson's ratio (POISS) is used to
calculate the shear modulus (commonly known as G) by the formula,

19- Supports
STAAD allows specifications of supports that are parallel as well as inclined to
the global axes. Supports are specified as PINNED, FIXED, or FIXED with
different releases. A pinned support has restraints against all translational
movement and none against rotational movement. In other words, a pinned
support will have reactions for all forces but will resist no moments. A fixed
support has restraints against all directions of movement. The restraints of a
fixed support can also be released in any desired direction Translational and
rotational springs can also be specified. The springs are represented in terms
of their spring constants. A translational spring constant is defined as the
force to displace a support joint one length unit in the specified global
direction. Similarly, a rotational spring constant is defined as the force to
rotate the support joint one degree around the specified global direction.

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Example

SUPPORTS

1 TO 4 7 PINNED

5 6 FIXED BUT FX MZ

8 9 FIXED BUT MZ KFX 50.0 KFY 75.

18 21 FIXED

27 FIXED BUT KFY 125.0

In this example, joints 1 to 4 and joint 7 are pinned. No moments are carried
by those supports. Joints 5 and 6 are fixed for all DOF except in force-X and
moment-Z. Joints 8 and 9 are fixed for all DOF except moment-Z and have
springs in the global X and Y directions with corresponding spring constants
of 50 and 75 units respectively. Joints 18 and 21 are fixed for all translational
and rotational degrees of freedom. At joint 27, all the DOF are fixed except
the FY DOF where it has a spring with 125 units spring constant.

20- Master-Slave Joints

The master/slave option is provided to enable the user to model rigid links in
the structural system. This facility can be used to model special structural
elements like a rigid floor diaphragm. Several slave joints may be provided
which will be assigned same displacements as the master joint. The user is
also allowed the flexibility to choose the specific degrees of freedom for
which the displacement constraints will be imposed on the slaved joints. If all
degrees of freedom (Fx, Fy, Fz, Mx, My and Mz) are provided as constraints,
the joints will be assumed to be rigidly connected.

21- Loads

Loads in a structure can be specified as joint load, member load, temperature

load and fixed-end member load. STAAD can also generate the self-weight of

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the structure and use it as uniformly distributed member loads in analysis.
Any fraction of this self-weight can also be applied in any desired direction.

21-1 Joint Load

Joint loads, both forces and moments, may be applied to any free joint of a
structure. These loads act in the global coordinate system of the structure.
Positive forces act in the positive coordinate directions. Any number of loads
may be applied on a single joint, in which case the loads will be additive on
that joint.

Example

JOINT LOAD

3 TO 7 9 11 FY -17.2 MZ 180.0

5 8 FX 15.1

12 MX 180.0 FZ 6.3

21-2 Member Load

Three types of member loads may be applied directly to a member of a

structure. These loads are uniformly distributed loads, concentrated loads,
and linearly varying loads (including trapezoidal). Uniform loads act on the full
or partial length of a member. Concentrated loads act at any intermediate,
specified point. Linearly varying loads act over the full length of a member.
Trapezoidal linearly varying loads act over the full or partial length of a
member. Trapezoidal loads are converted into a uniform load and several
concentrated loads.

Any number of loads may be specified to act upon a member in any

independent loading condition. Member loads can be specified in the
member coordinate system or the global coordinate system. Uniformly
distributed member loads provided in the global coordinate system may be

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specified to act along the full or projected member length. Positive forces act
in the positive coordinate directions, local or global, as the case may be.

21-3 Area/Floor Load

Many times a floor (bound by X-Z plane) is subjected to a uniformly

distributed load. It could require a lot of work to calculate the member load
for individual members in that floor. However, with the AREA LOAD
command, the user can specify the area loads (unit load per unit square area)
for members. The program will calculate the tributary area for these
members and provide the proper member loads. The Area Load is used for
one way distributions and the Floor Load is used for two way distributions.

The following assumptions are made while transferring the area/floor load to
member load:

a) The member load is assumed to be a linearly varying load for which the
start and the end values may be of different magnitude.

39
b) Tributary area of a member with an area load is calculated based on half
the spacing to the nearest approximately parallel members on both sides. If
the spacing is more than or equal to the length of the member, the area load
will be ignored.

c) Area/Floor load should not be specified on members declared as MEMBER

CABLE, MEMBER TRUSS, MEMBER TENSION or MEMBER COMPRESSION.

Figure 1.17 shows a floor structure with area load specification of 0.1.

Member 1 will have a linear load of 0.3 at one end and 0.2 at the other end.
Members 2 and 4 will have a uniform load of 0.5 over the full length. Member
3 will have a linear load of 0.45 and 0.55 at respective ends. Member 5 will
have a uniform load of 0.25. The rest of the members, 6 through 13, will have
no contributory area load since the nearest parallel members are more than
each of the member lengths apart. However, the reactions from the members

40
to the girder will be considered. Plates and solids are ignored in these
commands.

21-4 Fixed End Member Load

Load effects on a member may also be specified in terms of its fixed end loads.
These loads are given in terms of the member coordinate system and the
directions are opposite to the actual load on the member. Each end of a
member can have six forces: axial; shear y; shear z; torsion; moment y, and
moment z.

21-5 Prestress and Post-stress Member Load

Members in a structure may be subjected to prestress load for which the load
distribution in the structure may be investigated. The prestressing load in a
member may be applied axially or eccentrically. The eccentricities can be
provided at the start joint, at the middle, and at the end joint. These
eccentricities are only in the local y-axis. A positive eccentricity will be in the
positive local y-direction. Since eccentricities are only provided in the local y-
axis, care should be taken when providing prismatic properties or in specifying
the correct BETA angle when rotating the member coordinates, if necessary.
Two types of prestress load specification are available; PRESTRESS, where the
effects of the load are transmitted to the rest of the structure, and
POSTSTRESS, where the effects of the load are experienced exclusively by the
members on which it is applied

21-6 Temperature and Strain Load

Temperature difference through the length of a member as well as

differences of both faces of members and elements may also be specified.
The program calculates the axial strain (elongation and shrinkage) due to the
temperature difference. From this it calculates the induced forces in the
member and the analysis is done accordingly. The strain intervals of
elongation and shrinkage can be input directly.

41
Example

UNIT MMS

TEMP LOAD

1 TO 9 15 17 TEMP 70.0

17 TO 23 TEMP 90.0 66.0

8 TO 13 STRAIN 3.0

15 27 STRAINRATE 0.4E-4

NOTES:-

GENERAL FORMAT:

TEMPERATURE LOAD

MEM/ELEM LIST TEMP f1 f2 f3

STRAIN f3

STRAINRATE f5

f1 = the change in temperature which will cause axial elongation in the

members or uniform volume expansion in plates and solids. The temperature
unit is the same as the unit chosen for the coefficient of thermal expansion
ALPHA under the CONSTANT command. (Members/Plates/Solids.

f2 = The temperature differential from the top to the bottom of the member
or plate (Ttop surface-Tbottom surface). If f2 is omitted, no bending will be
considered. (Local Y axis) (Members/Plates). Section depth must be entered
for prismatic

42
f4 = The temperature differential from side to side of the member. (Local Z
axis) (Members). Section or flange width must be entered for prismatic.

f3 = Initial axial elongation (+)/ shrinkage (-) in member due to misfit, etc. in
length unit (Members only).

f5 = Initial axial elongation (+)/ shrinkage (-) per unit length, of members only.

21-7 Support Displacement Load

Static Loads can be applied to the structure in terms of the displacement of

the supports. Displacement can be translational or rotational. Translational
displacements are provided in the specified length while the rotational
displacements are always in degrees. Note that displacements can be
specified only in directions in which the support has an "enforced"
specification in the Support command.

Example

UNIT …

SUPPORT DISPL

5 TO 11 13 FY -0.25

18 21 TO 25 MX 15.0

In this example, the joints of the first support list will be displaced by 0.25
units in the negative global Y direction. The joints of the second support list
will be rotated by 15 degrees about the global X-axis.

43
 21-8 Loading on Elements

On Plate/Shell elements, the types of loading that are permissible are:

1) Pressure loading which consists of loads which act perpendicular to the

surface of the element. The pressure loads can be of uniform intensity or
trapezoidally varying intensity over a small portion or over the entire surface
of the element.

2) Joint loads which are forces or moments that are applied at the joints in
the direction of the global axes.

3) Temperature loads which may be constant across the depth of the element
(causing only in-plane elongation / shortening) or may vary across the depth
of the element causing bending on the element. The coefficient of thermal
expansion for the material of the element must be provided in order to
facilitate computation of these effects.

4) The self-weight of the elements can be applied using the SELFWEIGHT

loading condition. The density of the elements has to be provided in order to
facilitate computation of the self-weight.

On Solid elements, the only two loading types available are

1) The self-weight of the solid elements can be applied using the SELFWEIGHT
loading condition. The density of the elements has to be provided in order to
facilitate computation of the self-weight.

2) Joint loads which are forces or moments that are applied at the joints in
the direction of the global axes.

3) Temperature loads which may be constant throughout the solid elements

(causing only elongation / shortening). The coefficient of thermal expansion
for the material of the element must be provided in order to facilitate
computation of these effects.

44
Note that only translational stiffness is supported in solid elements. Thus, at
joints where there are only solid elements, moments may not be applied. For
efficiency, rotational supports should be used at these joints.

22- Load Generator

STAAD is equipped with built-in algorithms to generate moving loads and

lateral seismic loads (per the Uniform Building Code and the IS 1893 code) on
a structure. Use of the load generation facility consists of two parts :

1) Definition of the load system(s).

2) Generation of primary load cases using previously defined load system(s).

The following sections describe the salient features of the moving load
generator, the seismic load generator and the wind load generator available.

22-1 Moving Load Generator

This feature enables the user to generate moving loads on a structure. Moving
load system(s) consisting of concentrated loads at fixed specified distances in
both directions on a plane can be defined by the user. A user specified
number of primary load cases will be subsequently generated by the program
and taken into consideration in analysis. American Association of State
Highway and Transportation Officials (AASHTO, 1983) loadings are available
within the program and can be specified using standard AASHTO
designations. Moving Loads can be generated for frame members only. They
will not be generated for finite elements. Note: All loads and distances are in
current unit system.

22-2 UBC / IBC Seismic Load Generator

The STAAD seismic load generator follows the UBC procedure of equivalent
lateral load analysis. It is assumed that the lateral loads will be exerted in X
and Z directions and Y will be the direction of the gravity loads. Thus, for a

45
building model, Y axis will be perpendicular to the floors and point upward
(all Y joint coordinates positive). The user is required to set up his model
accordingly. Total lateral seismic force or base shear is automatically
calculated by STAAD using the appropriate UBC equation. Note that IBC 2000,
UBC 1997, 1994, or 1985, IS: 1893, Japanese, or Colombian specifications may
be used. For load generation per the 1994 code, the user is required to
provide seismic zone coefficients, importance factors, periods, etc. See
section 5.31.2 for the detailed input required for each code. Instead of using
approximate UBC formulas to estimate the building period in a certain
direction, the program calculates the period using Raleigh quotient
technique. This period is then utilized to calculate seismic coefficient C.

After the base shear is calculated from the appropriate equation, it is

distributed among the various levels and roof per UBC specifications. The
distributed base shears are subsequently applied as lateral loads on the
structure. These loads may then be utilized as normal load cases for analysis
and design.

22-3 Wind Load Generator

The STAAD Wind Load generator is capable of calculating wind loads on the
structure from user specified wind intensities and exposure factors. Different
wind intensities may be specified for different height zones of the structure.
Openings in the structure may be modeled using exposure factors. An
exposure factor is associated with each joint of the structure and is defined
as the fraction of the influence area on which the wind load acts. Built-in
algorithms automatically calculate the wind load on a SPACE structure and
distribute the loads as lateral joints loads.

46
 23- Analysis Facilities

The following PERFORM ANALYSIS facilities are available in STAAD.

1) Stiffness Analysis / Linear Static Analysis

2) Second Order Static Analysis

P-Delta Analysis

Non-Linear Analysis

Multi Linear Spring Support

Member/Spring Tension/Compression only

3) Dynamic Analysis

Time History

Response Spectrum

23-1 Stiffness Analysis / Linear Static Analysis

The stiffness analysis implemented in STAAD is based on the matrix

displacement method. In the matrix analysis of structures by the
displacement method, the structure is first idealized into an assembly of
discrete structural components (frame members or finite elements). Each
component has an assumed form of displacement in a manner which satisfies
the force equilibrium and displacement compatibility at the joints. Structural
systems such as slabs, plates, spread footings, etc., which transmit loads in 2
directions have to be discretized into a number of 3 or 4 noded finite elements
connected to each other at their nodes. Loads may be applied in the form of
distributed loads on the element surfaces or as concentrated loads at the
joints. The plane stress effects as well as the plate bending effects are taken
into consideration in the analysis.

47
 23-2 Second Order Static Analysis

23-2-1 P-Delta Analysis

Structures subjected to lateral loads often experience secondary forces due

to the movement of the point of application of vertical loads. This secondary
effect, commonly known as the P-Delta effect, plays an important role in the
analysis of the structure. In STAAD, a unique procedure has been adopted to
incorporate the P-Delta effect into the analysis. The procedure consists of the
following steps:

1- First, the primary deflections are calculated based on the provided

external loading.
2- Primary deflections are then combined with the originally applied
loading to create the secondary loadings. The load vector is then revised
to include the secondary effects. Note that the lateral loading must be
present concurrently with the vertical loading for proper consideration
of the P-Delta effect. The REPEAT LOAD facility (see Section 5.32.11) has
been created with this requirement in mind. This facility allows the user
to combine previously defined primary load cases to create a new
primary load case.

3. A new stiffness analysis is carried out based on the revised load vector
to generate new deflections.
4. Element/Member forces and support reactions are calculated based on
the new deflections.

It may be noted that this procedure yields very accurate results with all
small displacement problems. STAAD allows the user to go through multiple
iterations of the P-Delta procedure if necessary. The user is allowed to specify
the number of iterations based on the requirement. To set the displacement
convergence tolerance, enter a SET DISP f command before the Joint
Coordinates. If the change in displacement norm from one iteration to the
next is less than f then it is converged. The P-Delta analysis is recommended
by several design codes such as ACI 318, LRFD, IS456-1978, etc. in lieu of the

48
moment magnification method for the calculation of more realistic forces and
moments. P-Delta effects are calculated for frame members only. They are
not calculated for finite elements or solid elements. P-Delta and Nonlinear
analysis is restricted to structures where members carry the axial load from
one structure level to the next.

23-2-2 Non Linear Analysis

STAAD also offers the capability to perform non-linear analysis based on

geometric non-linearity. The non-linear analysis algorithm incorporates both
member geometric stiffness corrections and secondary loadings. Nonlinear
analysis methodology is generally adopted for structures subject to large
displacements. As large displacements generally result in significant
movement of the point of application of loads, consideration of secondary
loadings becomes an important criteria. In addition, geometric stiffness
corrections are applied to take into consideration the modified geometry.
Since the geometric stiffness corrections are based on generated
displacements, they are different for different load cases. This makes the non-
linear analysis option load dependent. The STAAD non-linear analysis
algorithm consists of the following steps:

1- First, primary displacements are calculated for the applied

loading.
2- Stiffness corrections are applied on the member/element
stiffness matrices based on observed displacements. New global
stiffness matrix is assembled based on revised member/element
stiffness matrices.
3- Load vectors are revised to include the secondary effects due to
primary displacements.
4- The new set of equations are solved to generate new
displacements.
5- Element/Member forces and support reactions are calculated
from these new displacements.

49
 6- The STAAD non-linear analysis algorithm allows the user to go
through multiple iterations of the above procedure. The number
of iterations may be specified by the user based on the
requirement. It may be noted, however, that multiple iterations
may increase the computer resource requirements and execution
time substantially.

Note: The following points may be noted with respect to the non-linear
analysis facility -

1- Since the procedure is load dependent, the user is required to use

the SET NL and CHANGE commands properly. The SET NL
command must be provided to specify the total number of
primary load cases. The CHANGE command should be used to
reset the stiffness matrices after each load case.
2- As the geometric corrections are based on displacements, all
loads that are capable of producing significant displacements
must be part of the load case(s) identified for non-linear analysis.
3- To set the displacement divergence tolerance, enter a SET DISP f
command before the Joint Coordinates. If any displacement on
any iteration exceeds f, then the solution is diverging and is
terminated. The default value for f is the largest of the total width,
height, or depth of the structure divided by 120.

P-Delta and Nonlinear analysis is restricted to structures where members

carry the axial load from one structure level to the next.

23-2-3 Multi-Linear Analysis

When soil is to be modeled as spring supports, the varying resistance it offers

to external loads can be modeled using this facility, such as when its behavior
in tension differs from its behavior in compression. Load-Displacement
characteristics of soil can be represented by a multi-linear curve. Amplitude
of this curve will represent the spring characteristic of the soil at different
displacement values. The load cases in a multi-linear spring analysis must be

50
separated by the CHANGE command and PERFORM ANALYSIS command. The
SET NL command must be provided to specify the total number of primary
load cases. There may not be any PDELTA, NONLINEAR, dynamic, or TENSION/
COMPRESSION member cases. The multi-linear spring command will initiate
an iterative analysis which continues to convergence.

23-2-4 Tension / Compression Only Analysis

When some members or support springs are linear but carry only tension (or
only compression), then this analysis may be used. This analysis is
automatically selected if any member or spring has been given the tension or
compression only characteristic. This analysis is an iterative analysis which
continues to convergence. Any member/ spring that fails its criteria will be
inactive (omitted) on the next iteration. Iteration continues until all such
members have the proper load direction or are inactive (default iteration limit
is 10). This is a simple method that may not work in some cases because
members are removed on interim iterations that are needed for stability. If
instability messages appear on the 2nd and subsequent iterations that did not
appear on the first cycle, then do not use the solution. If this occurs on cases
where only springs are the tension/compression entities, then use multi-
linear spring analysis. The load cases in a tension/compression analysis must
be separated by the CHANGE command and PERFORM ANALYSIS command.
The SET NL command must be provided to specify the total number of primary
load cases. There may not be any Multi-linear springs, NONLINEAR, or
dynamic cases.

23-2-5 Non Linear Cable/Truss Analysis (available

in limited form)

When all of the members, elements and support springs are linear except for
cable and/or preloaded truss members, then this analysis type may be used.
This analysis is based on applying the load in steps with equilibrium iterations
to convergence at each step. The step sizes start small and gradually increase
(15-20 steps is the default). Iteration continues at each step until the change
in deformations is small before proceeding to the next step. If not converged,

51
then the solution is stopped. The user can then select more steps or modify
the structure and rerun.

Structures can be artificially stabilized during the first few load steps in case
the structure is initially unstable (in the linear, small displacement, static
theory sense).

The user has control of the number of steps, the maximum number of
iterations per step, the convergence tolerance, the artificial stabilizing
stiffness, and the minimum amount of stiffness remaining after a cable sags.

This method assumes small displacement theory for all

members/trusses/elements other than cables & preloaded trusses. The
cables and preloaded trusses can have large displacement and
moderate/large strain. Cables and preloaded trusses may carry tension and
compression but cables have a reduced E modulus if not fully taut. Pretension
is the force necessary to stretch the cable/truss from its unstressed length to
enable it to fit between the two end joints. Alternatively, you may enter the
unstressed length for cables.

The current nonlinear cable analysis procedure can result in compressive

forces in the final cable results. The procedure was developed for structures,
loadings, and pretensioning loads that will result in sufficient tension in every
cable for all loading conditions. The possibility of compression was considered
acceptable in the initial implementation because most design codes strongly
recommend cables to be in tension to avoid the undesirable dynamic effects
of a slack cable such as galloping, singing, or pounding. The engineer must
specify initial preloading tensions which will ensure that all cable results are
in tension. In addition this procedure is much more reliable and efficient than
general nonlinear algorithms. To minimize the compression the SAGMIN
input variable can be set to a small value such as 0.01, however that can lead
to a failure to converge unless many more steps are specified and a higher
equilibrium iteration limit is specified. SAGMIN values below 0.70 generally
requires some adjustments of the other input parameters to get convergence.

52
Currently the cable and truss are not automatically loaded by self-weight,
but the user should ensure that self-weight is applied in every load case. Do
not enter component load cases such as wind only; every case must be
realistic. Member loads will be lumped at the ends for cables and trusses.
Temperature load may also be applied to the cables and trusses. It is OK to
break up the cable/truss into several members and apply forces to the
intermediate joints. Y-up is assumed and required.

The member force printed for the cable is Fx and is along the chord line
between the displaced positions of the end joints.

The analysis sequence is as follows:

1- Compute the unstressed length of the nonlinear members based on

joint coordinates, pretension, and temperature.
2- Member/Element/Cable stiffness is formed. Cable stiffness is from
EA/L and the sag formula plus a geometric stiffness based on current
tension.
3- Assemble and solve the global matrix with the percentage of the total
applied load used for this load step.
4- Perform equilibrium iterations to adjust the change in directions of the
forces in the nonlinear cables, so that the structure is in static
equilibrium in the deformed position. If force changes are too large or
convergence criteria not met within 15 iterations then stop the
analysis.
5- Go to step 2 and repeat with a greater percentage of the applied load.
The nonlinear members will have an updated orientation with new
tension and sag effects.
6- After 100% of the applied load has converged then proceed to
compute member forces, reactions, and static check. Note that the
static check is not exactly in balance due to the displacements of the
applied static equivalent joint loads.

The load cases in a nonlinear cable analysis must be separated by the

CHANGE command and PERFORM CABLE ANALYSIS command. The SET NL
command must be provided to specify the total number of primary load
53
cases. There may not be any Multi-linear springs, compression only, PDelta,
NONLINEAR, or dynamic cases.

Also for cables and preloaded trusses:

1- Do not use Member Offsets.

2- Do not include the end joints in Master/Slave command.
3- Do not connect to inclined support joints.
4- Y direction must be up.
5- Do not impose displacements.
6- Do not use Support springs in the model.
7- Applied loads do not change global directions due to displacements.
8- Do not apply Prestress load, Fixed end load.
9- Do not use Load Combination command to combine cable analysis
results. Use a primary case with Repeat Load instead.

23-3 Dynamic Analysis

Currently available dynamic analysis facilities include solution of the free

vibration problem (Eigen problem), response spectrum analysis and forced
vibration analysis.

Solution of the Eigen problem

The Eigen problem is solved for structure frequencies and mode shapes
considering a lumped mass matrix, with masses at all active d.o.f. included.
Two solution methods are used: the subspace iteration method for almost all
problems, and the determinant search method for very small problems.

Mass Modeling

The natural frequencies and mode shapes of a structure are the primary
parameters that affect the response of a structure under dynamic loading.
The free vibration problem is solved to extract these values. Since no external
forcing function is involved, the natural frequencies and mode shapes are

54
direct functions of the stiffness and mass distribution in the structure. Results
of the frequency and mode shape calculations may vary significantly
depending upon the mass modeling. This variation, in turn, affects the
response spectrum and forced vibration analysis results. Thus, extreme
caution should be exercised in mass modeling in a dynamic analysis problem.

In STAAD, all masses that are capable of moving should be modeled as loads
applied in all possible directions of movement. Even if the loading is known to
be only in one direction there is usually mass motion in other directions at
some or all joints and these mass directions (“loads” in weight units) must be
entered to be correct. Joint moments that are entered will be considered to
be weight moment of inertias (force-length2 units).

Please enter self weight, joint and element loadings in global directions with
the same sign as much as possible so that the “masses” do not cancel each
other.

Member/Element loadings may be used to generate joint translational

masses. Note that member end joint moments that are generated by the
member loading (including concentrated moments) are discarded as
irrelevant to dynamics. Enter mass moments of inertia, if needed, at the joints
as joint moments.

STAAD uses a diagonal mass matrix of 6 lumped mass equations per joint. The
self-weight or uniformly loaded member is lumped 50% to each end joint
without rotational mass moments of inertia. The other element types are
integrated but roughly speaking the weight is distributed equally amongst the
joints of the element.

The members/elements of finite element theory are simple mathematical

representations of deformation meant to apply over a small region. The FEA
procedures will converge if you subdivide the elements and rerun; then
subdivide the elements that have significantly changed results and rerun; etc.
until the key results are converged to the accuracy needed.

55
An example of a simple beam problem that needs to subdivide real members
to better represent the mass distribution (and the dynamic response and the
force distribution response along members) is a simple floor beam between
2 columns will put all of the mass on the column joints. In this example, a
vertical ground motion will not bend the beam even if there is a concentrated
force (mass) at mid span.

In addition, the dynamic results will not reflect the location of a mass within
a member (i.e. the masses are lumped at the joints). This means that the
motion, of a large mass in the middle of a member relative to the ends of
the member, is not considered. This may affect the frequencies and mode
shapes. If this is important to the solution, split the member into two.
Another effect of moving the masses to the joints is that the resulting
shear/moment distribution is based as if the masses were not within the
member. Note also that if one end of a member is a support, then half of
the that member mass is lumped at the support and will not move during
the dynamic response.

Damping Modeling

Damping may be specified by entering values for each mode, or using a

formula based on the first two frequencies, or by using composite modal
damping. Composite modal damping permits computing the damping of a
mode from the different damping ratios for different materials (steel,
concrete, soil). Modes that deform mostly the steel would have steel damping
ratio, whereas modes that mostly deform the soil, would have the soil
damping ratio.

Response Spectrum Analysis

This capability allows the user to analyze the structure for seismic loading. For
any supplied response spectrum (either acceleration vs. period or
displacement vs. period), joint displacements, member forces, and support
reactions may be calculated. Modal responses may be combined using one of
the square root of the sum of squares (SRSS), the complete quadratic
combination (CQC), the ASCE4-98 (ASCE), the Ten Percent (TEN) or the

56
absolute (ABS) methods to obtain the resultant responses. Results of the
response spectrum analysis may be combined with the results of the static
analysis to perform subsequent design. To account for reversibility of seismic
activity, load combinations can be created to include either the positive or
negative contribution of seismic results.

Response Time History Analysis

STAAD is equipped with a facility to perform a response history analysis on a

structure subjected to time varying forcing function loads at the joints and/or
a ground motion at its base. This analysis is performed using the modal
superposition method. Hence, all the active masses should be modeled as
loads in order to facilitate determination of the mode shapes and frequencies.
Please refer to the section above on "mass modeling" for additional
information on this topic. In the mode superposition analysis, it is assumed
that the structural response can be obtained from the "p" lowest modes. The
equilibrium equations are written as

These are solved by the Wilson- method which is an unconditionally stable

step by step scheme. The time step for the response is chosen as 0.1 T where
T is the period of the highest mode that is to be included in the response. The

57
q is are substituted in equation 2 to obtain the displacements {x} at each time
step.

Time History Analysis for a Structure Subjected to a Harmonic Loading

A Harmonic loading is one in which can be described using the following

equation:

The results are the maximums over the entire time period, including start-up
transients. So, they do not match steady-state response.

Definition of Input in STAAD for the Above Forcing Function

As can be seen from its definition, a forcing function is a continuous function.

However, in STAAD, a set of discrete time-force pairs is generated from the
forcing function and an analysis is performed using these discrete time-
forcing pairs. What that means is that based on the number of cycles that the
user specifies for the loading, STAAD will generate a table consisting of the
magnitude of the force at various points of time. The time values are chosen
58
from this time ¢0¢ to n*tc in steps of "STEP" where n is the number of cycles
and tc is the duration of one cycle. STEP is a value that the user may provide
or may choose the default value that is built into the program. STAAD will
adjust STEP so that a ¼ cycle will be evenly divided into one or more steps.
Users may refer to section 5.31.4 of this manual for a list of input parameters
that need to be specified for a Time History Analysis on a structure subjected
to a Harmonic loading. The relationship between variables that appear in the
STAAD input and the corresponding terms in the equation shown above is
explained below.

59