Bentley 2006 User Manual

STAAD.Pro 2006

TECHNICAL REFERENCE MANUAL

Part Number: DAA036990-1/0001

A Bentley Solutions Center

www.reiworld.com
www.bentley.com/staad

STAAD.Pro 2006 is a suite of proprietary computer programs

of Research Engineers, a Bentley Solutions Center. Although
every effort has been made to ensure the correctness of these
programs, REI will not accept responsibility for any mistake,
error or misrepresentation in or as a result of the usage of
these programs.

RELEASE 2006

© 2006 Bentley Systems, Incorporated. All Rights Reserved.

Published March, 2006

About STAAD.Pro

STAAD.Pro is a general purpose structural analysis and design program with
applications primarily in the building industry - commercial buildings, bridges and
highway structures, industrial structures, chemical plant structures, dams, retaining
walls, turbine foundations, culverts and other embedded structures, etc. The program
hence consists of the following facilities to enable this task.

1. Graphical model generation utilities as well as text editor based commands for

creating the mathematical model. Beam and column members are represented using
lines. Walls, slabs and panel type entities are represented using triangular and
quadrilateral finite elements. Solid blocks are represented using brick elements.
These utilities allow the user to create the geometry, assign properties, orient cross
sections as desired, assign materials like steel, concrete, timber, aluminum, specify
supports, apply loads explicitly as well as have the program generate loads, design
parameters etc.

2. Analysis engines for performing linear elastic and pdelta analysis, finite element

analysis, frequency extraction, and dynamic response (spectrum, time history,
steady state, etc.).

3. Design engines for code checking and optimization of steel, aluminum and timber

members. Reinforcement calculations for concrete beams, columns, slabs and shear
walls. Design of shear and moment connections for steel members.

4. Result viewing, result verification and report generation tools for examining

displacement diagrams, bending moment and shear force diagrams, beam, plate and
solid stress contours, etc.

5. Peripheral tools for activities like import and export of data from and to other

widely accepted formats, links with other popular softwares for niche areas like
reinforced and prestressed concrete slab design, footing design, steel connection
design, etc.

6. A library of exposed functions called OpenSTAAD which allows users to access

STAAD.Pro’s internal functions and routines as well as its graphical commands to
tap into STAAD’s database and link input and output data to third-party software
written using languages like C, C++, VB, VBA, FORTRAN, Java, Delphi, etc.
Thus, OpenSTAAD allows users to link in-house or third-party applications with
STAAD.Pro.

About the STAAD.Pro Documentation

The documentation for STAAD.Pro consists of a set of manuals as described below.
These manuals are normally provided only in the electronic format, with perhaps some
exceptions such as the Getting Started Manual which may be supplied as a printed book
to first time and new-version buyers.

All the manuals can be accessed from the Help facilities of STAAD.Pro. Users who
wish to obtain a printed copy of the books may contact Research Engineers. REI also
supplies the manuals in the PDF format at no cost for those who wish to print them on
their own. See the back cover of this book for addresses and phone numbers.

Getting Started and Tutorials : This manual contains information on the contents of
the STAAD.Pro package, computer system requirements, installation process, copy
protection issues and a description on how to run the programs in the package.
Tutorials that provide detailed and step-by-step explanation on using the programs are
also provided.

Examples Manual

This book offers examples of various problems that can be solved using the STAAD
engine. The examples represent various structural analyses and design problems
commonly encountered by structural engineers.

Graphical Environment

This document contains a detailed description of the Graphical User Interface (GUI) of
STAAD.Pro. The topics covered include model generation, structural analysis and
design, result verification, and report generation.

Technical Reference Manual

This manual deals with the theory behind the engineering calculations made by the
STAAD engine. It also includes an explanation of the commands available in the
STAAD command file.

International Design Codes

This document contains information on the various Concrete, Steel, and Aluminum
design codes, of several countries, that are implemented in STAAD.

The documentation for the STAAD.Pro Extension component(s) is available separately.

Table of Contents

STAAD.PRO Technical Reference Manual

Section 1 General Description 1 -

1.1 Introduction 1 - 1

1.2 Input Generation 2

1.3 Types of Structures 2

1.4 Unit Systems 3

1.5 Structure Geometry and Coordinate Systems 4

1.5.1 Global Coordinate System 4

1.5.2 Local Coordinate System 7

1.5.3 Relationship Between Global & Local Coordinates 11

1.6 Finite Element Information 18

1.6.1 Plate/Shell Element 18

1.6.2 Solid Element 31

1.6.3 Surface Element 35

1.7 Member Properties 37

1.7.1 Prismatic Properties 39

1.7.2 Built-In Steel Section Library 41

1.7.3 User Provided Steel Table 42

1.7.4 Tapered Sections 42

1.7.5 Assign Command 42

1.7.6 Steel Joist and Joist Girders 43

1.7.7 Composite Beams and Composite Decks 47

1.7.8 Curved Members 48

1.8 Member/Element Release 48

1.9 Truss/Tension/Compression - Only Members 49

1.10 Tension/Compression - Only Springs 49

1.11 Cable Members 50

1.11.1 Linearized Cable Members 50

1.11.2 Non Linear Cable & Truss Members 53

1.12 Member Offsets 54

1.13 Material Constants 55

1.14 Supports 56

1.15 Master/Slave Joints 57

1.16 Loads 57

1.16.1 Joint Load 57

1.16.2 Member Load 58

1.16.3 Area Load / Oneway Load / Floor Load 60

1.16.4 Fixed End Member Load 62

1.16.5 Prestress and Poststress Member Load 62

1.16.6 Temperature/Strain Load 1 - 65

1.16.7 Support Displacement Load 1 - 65

1.16.8 Loading on Elements 65

1.17 Load Generator 67

1.17.1 Moving Load Generator 67

1.17.2 Seismic Load Generator based on UBC, IBC and other
codes 68

1.17.3 Wind Load Generator 69

1.18 Analysis Facilities 70

1.18.1 Stiffness Analysis 70

1.18.2 Second Order Analysis 75

1.18.2.1 P-Delta Analysis 75

1.18.2.2 Imperfection Analysis 77

1.18.2.3 Non Linear Analysis 77

1.18.2.4 Multi-Linear Analysis 77

1.18.2.5 Tension / Compression Only Analysis 78

1.18.2.6 Nonlinear Cable/Truss Analysis 78

1.18.3 Dynamic Analysis 81

1.18.3.1 Solution of the Eigenproblem 81

1.18.3.2 Mass Modeling 81

1.18.3.3 Damping Modeling 83

1.18.3.4 Response Spectrum Analysis 83

1.18.3.5 Response Time History Analysis 84

1.18.3.6 Steady State and Harmonic Response 86

1.19 Member End Forces 88

1.19.1 Secondary Analysis 93

1.19.2 Member Forces at Intermediate Sections 93

1.19.3 Member Displacements at Intermediate Sections 93

1.19.4 Member Stresses at Specified Sections 94

1.19.5 Force Envelopes 94

1.20 Multiple Analyses 95

1.21 Steel/Concrete/Timber Design 96

1.22 Footing Design 96

1.23 Printing Facilities 96

1.24 Plotting Facilities 97

1.25 Miscellaneous Facilities 97

1.26 Post Processing Facilities 1 - 98

Section 2 American Steel Design 2 -

2.1 Design Operations 2 - 1

2.2 Member Properties 2

2.2.1 Built - in Steel Section Library 2

2.3 Allowables per AISC Code 7

2.3.1 Tension Stress 7

2.3.2 Shear Stress 7

2.3.3 Stress Due To Compression 7

2.3.4 Bending Stress 7

2.3.5 Combined Compression and Bending 9

2.3.6 Singly Symmetric Sections 2 - 9

2.3.7 Torsion per Publication T114 2 - 9

2.3.8 Design of Web Tapered Sections 11

2.3.9 Slender compression elements 11

2.4 Design Parameters 11

2.5 Code Checking 18

2.6 Member Selection 19

2.6.1 Member Selection by Optimization 20

2.6.2 Deflection Check With Steel Design 20

2.7 Truss Members 20

2.8 Unsymmetric Sections 21

2.9 Composite Beam Design as per AISC-ASD 21

2.10 Plate Girders 23

2.11 Tabulated Results of Steel Design 23

2.12 Weld Design 26

2.13 Steel Design per AASHTO Specifications 29

2.14 Steel Design per AISC/LRFD Specification 56

2.14.1 General Comments 56

2.14.2 LRFD Fundamentals 57

2.14.3 Analysis Requirements 58

2.14.4 Section Classification 59

2.14.5 Axial Tension 59

2.14.6 Axial Compression 60

2.14.7 Flexural Design Strength 61

2.14.8 Combined Axial Force And Bending 61

2.14.9 Design for Shear 61

2.14.10 Design Parameters 62

2.14.11 Code Checking and Member Selection 64

2.14.12 Tabulated Results of Steel Design 65

2.14.13 Composite Beam Design per the American LRFD

3rd edition code 66

2.15 Design per American Cold Formed Steel Code 73

2.16 Castellated Beams 2 - 82

Section 3 American Concrete Design 3 -

3.1 Design Operations 3 - 1

3.2 Section Types for Concrete Design 2

3.3 Member Dimensions 2

3.4 Design Parameters 3

3.5 Slenderness Effects and Analysis Consideration 6

3.6 Beam Design 7

3.6.1 Design for Flexure 7

3.6.2 Design for Shear 8

3.6.3 Design for Anchorage 8

3.6.4 Description of Output for Beam Design 9

3.6.5 Cracked Moment of Inertia – ACI Beam Design 12

3.7 Column Design 13

3.8 Designing elements, shear walls, slabs 18

3.8.1 Element Design 3 - 18

3.8.2 Shear Wall Design 3 - 20

3.8.3 Slabs and RC Designer 28

3.8.4 Design of I-shaped beams per ACI-318 3 - 35

Section 4 Timber Design 4 -

4.1 Timber Design 4 - 1

4.2 Design Operations 13

4.3 Input Specification 16

4.4 Code Checking 17

4.5 Orientation of Lamination 18

4.6 Member Selection 4 - 18

Section 5 Commands and Input Instructions 5 -

5.1 Command Language Conventions 5 - 2

5.1.1 Elements of The Commands 3

5.1.2 Command Formats 5

5.1.3 Listing of Members by Specification of Global Ranges 8

5.2 Problem Initiation And Title 10

5.3 Unit Specification 12

5.4 Input/Output Width Specification 14

5.5 Set Command Specification 15

5.6 Separator Command 19

5.7 Page New Command 20

5.8 Page Length/Eject Command 21

5.9 Ignore Specifications 22

5.10 No Design Specification 23

5.11 Joint Coordinates Specification 24

5.12 Member Incidences Specification 29

5.13 Elements and Surfaces 33

5.13.1 Plate and Shell Element Incidence Specification 34

5.13.2 Solid Element Incidences Specification 36

5.13.3 Surface Entities Specification 38

5.14 Element Mesh Generation 42

5.15 Redefinition of Joint and Member Numbers 48

5.16 Listing of entities by Specification of GROUPS 50

5.17 Rotation of Structure Geometry 53

5.18 Inactive/Delete Specification 54

5.19 User Steel Table Specification 56

5.20 Member Property Specification 65

5.20.1 Specifying Properties from Steel Tables 69

5.20.2 Prismatic Property Specification 73

5.20.2.1 Prismatic Tapered Tube Property Specification 75

5.20.3 Tapered Member Specification 77

5.20.4 Property Specification from User Provided Table 78

5.20.5 Assign Profile Specification 79

5.20.6 Examples of Member Property Specification 80

5.20.7 Composite Decks 5 - 82

5.20.8 Curved Member Specification 5 - 86

5.20.9 Applying Fireproofing on members

5.21 Element/Surface Property Specification 103

5.21.1 Element Property Specification 104

5.21.2 Surface Property Specification 105

5.22 Member/Element Releases 106

5.22.1 Member Release Specification 107

5.22.2 Element Release Specification 110

5.22.3 Element Ignore Stiffness 112

5.23 Member Truss/Cable/Tension/Compression Specification 113

5.23.1 Member Truss Specification 114

5.23.2 Member Cable Specification 116

5.23.3 Member Tension/Compression Specification 118

5.24 Element Plane Stress and Inplane Rotation Specification 123

5.25 Member Offset Specification 125

5.26 Specifying and Assigning Material Constants 127

5.26.1 The Define Material Command 129

5.26.2 Specifying CONSTANTS for members, plate elements
and solid elements 131

5.26.3 Surface Constants Specification 138

5.26.4 Modal Damping Information 140

5.26.5 Composite Damping for Springs 143

5.26.6 Member Imperfection Information 144

5.27 Support Specifications 145

5.27.1 Global Support Specification 146

5.27.2 Inclined Support Specification 150

5.27.3 Automatic Spring Support Generator for Foundations 153

5.27.4 Multi-linear Spring Support Specification 158

5.27.5 Spring Tension/Compression Specification 161

5.28 Master/Slave Specification 166

5.29 Draw Specifications 169

5.30 Miscellaneous Settings for Dynamic Analysis 170

5.30.1 Cut-Off Frequency, Mode Shapes or Time 171

5.30.2 Mode Selection 173

5.31 Definition of Load Systems 175

5.31.1 Definition of Moving Load System 176

5.31.2 Definitions for Static Force Procedures for Seismic
Analysis 181

5.31.2.1 UBC 1997 Load Definition 182

5.31.2.2 UBC 1994 or 1985 Load Definition 187

5.31.2.3 Colombian Seismic Load 192

5.31.2.4 Japanese Seismic Load 195

5.31.2.5 Definition of Lateral Seismic Load per IS:1893 198

5.31.2.6 IBC 2000/2003 Load Definition 201

5.31.2.7 CFE (Comision Federal De Electricidad)

Seismic Load 208

5.31.2.8 NTC (Normas Técnicas Complementarias)

Seismic Load 212

5.31.2.9 RPA (Algerian) Seismic Load 5 - 217

98

5.31.2.10 Canadian (NRC 1995) Seismic Load 5 - 221

5.31.3 Definition of Wind Load 234

5.31.4 Definition of Time History Load 238

5.31.5 Definition of Snow Load 244

5.32 Loading Specifications 245

5.32.1 Joint Load Specification 247

5.32.2 Member Load Specification 248

5.32.3 Element Load Specifications 251

5.32.3.1 Element Load Specification - Plates 252

5.32.3.2 Element Load Specification - Solids 256

5.32.3.3 Element Load Specification - Joints 258

5.32.3.4 Surface Loads Specification 261

5.32.4 Area Load/One Way Load/Floor Load Specification 264

5.32.5 Prestress Load Specification 278

5.32.6 Temperature Load Specification 285

5.32.7 Fixed-End Load Specification 287

5.32.8 Support Joint Displacement Specification 288

5.32.9 Selfweight Load Specification 291

5.32.10 Dynamic Loading Specification 292

5.32.10.1 Response Spectrum Specification 293

5.32.10.1.1 Response Spectrum Specification in
Conjunction with the Indian IS: 1893
(Part 1)-2002 Code for Dynamic Analysis 299

5.32.10.1.2 Response Spectrum Specification per
Eurocode 8 304

5.32.10.2 Application of Time Varying Load for Response

History Analysis 310

5.32.11 Repeat Load Specification 313

5.32.12 Generation of Loads 316

5.32.13 Generation of Snow Loads 330

5.33 Rayleigh Frequency Calculation 331

5.34 Modal Calculation Command 333

5.35 Load Combination Specification 334

5.36 Calculation of Problem Statistics 339

5.37 Analysis Specification 340

5.37.1 Steady State & Harmonic Analysis 346

5.37.1.1 Purpose 347

5.37.1.2 Define Harmonic Output Frequencies 350

5.37.1.3 Define Load Case Number 351

5.37.1.4 Steady Ground Motion Loading 352

5.37.1.5 Steady Force Loading 354

5.37.1.6 Harmonic Ground Motion Loading 357

5.37.1.7 Harmonic Force Loading 360

5.37.1.8 Print Steady State/Harmonic Results 364

5.37.1.9 Last Line of Steady State/Harmonic Analysis 367

5.38 Change Specification 368

5.39 Load List Specification 371

5.40 Section Specification 373

5.41 Print Specifications (includes CG and Story Drift) 5 - 375

5.42 Stress/Force output printing for Surface Entities 5 - 382

5.43 Print Section Displacement 384

5.44 Print Force Envelope Specification 386

5.45 Post Analysis Printer Plot Specifications 388

5.46 Size Specification 389

5.47 Steel and Aluminum

5.47.1 Parameter Specifications 392

5.47.2 Code Checking Specification 395

5.47.3 Member Selection Specification 396

5.47.4 Member Selection by Optimization 398

5.47.5 Weld Selection Specification 399

5.48 Group Specification 400

5.49 Steel Take Off Specification 403

5.50 Timber Design Specifications 404

5.50.1 Timber Design Parameter Specifications 405

5.50.2 Code Checking Specification 406

5.50.3 Member Selection Specification 407

5.51 Concrete Design Specifications 408

5.51.1 Design Initiation 409

5.51.2 Concrete Design-Parameter Specification 410

5.51.3 Concrete Design Command 412

5.51.4 Concrete Take Off Command 413

5.51.5 Concrete Design Terminator 414

5.52 Footing Design Specifications 415

5.52.1 Design Initiation 418

5.52.2 Footing Design Parameter Specification 419

5.52.3 Footing Design Command 420

5.52.4 Footing Design Terminator 422

5.53 Shear Wall Design 423

5.53.1 Definition of Wall Panels for Shear Wall Design 425

5.53.2 Shear Wall Design Initiation 426

5.54 End Run Specification 5 - 428

Design Specifications 391

Index

General Description

Section

1.1 Introduction

The STAAD.Pro 2006 Graphical User Interface (GUI) is normally used

to create all input specifications and all output reports and displays (See
the Graphical Environment manual). These structural modeling and
analysis input specifications are stored in a text file with extension
“.STD”. When the GUI does a File Open to start a session with an existing
model, it gets all of its information from the STD file. A user may
edit/create this STD file and have the GUI and the analysis engine both
reflect the changes.

The STD file is processed by the STAAD analysis “engine” to produce
results that are stored in several files with extensions such as ANL, BMD,
TMH, etc. The ANL text file contains the printable output as created by
the specifications in this manual. The other files contain the results
(displacements, member/element forces, mode shapes, section
forces/moments/displacements, etc.) that are used by the GUI in post
processing mode.

This section of the manual contains a general description of the analysis
and design facilities available in the STAAD engine. Specific information
on steel, concrete, and timber design is available in Sections 2, 3, and 4 of
this manual, respectively. Detailed STAAD engine STD file command
formats and other specific user information is presented in Section 5.

The objective of this section is to familiarize the user with the basic
principles involved in the implementation of the various analysis/design
facilities offered by the STAAD engine. As a general rule, the sequence in

1

1-1

General Description

F

Section 1

1-2

which the facilities are discussed follows the recommended sequence of
their usage in the STD input file.

1.2 Input Generation

The GUI (or user) communicates with the STAAD analysis engine through
the STD input file. That input file is a text file consisting of a series of
commands which are executed sequentially. The commands contain either
instructions or data pertaining to analysis and/or design. The elements and
conventions of the STAAD command language are described in Section 5
of this manual.

The STAAD input file can be created through a text editor or the GUI
Modeling facility. In general, any text editor may be utilized to edit/create
the STD input file. The GUI Modeling facility creates the input file
through an interactive menu-driven graphics oriented procedure.

1.3 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

or input,

see section

5.2

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.

Section 1

F

Specification of the correct structure type reduces the number
of equations to be solved during the analysis. This results in a
faster and more economic solution for the user. The degrees of
freedom associated with frame elements of different types of
structures is illustrated in Figure 1.1.

Structure Types

1-3

Figure 1.1

1.4 Unit Systems

or input,

see section

5.3

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.

General Description

F

Section 1

1-4

1.5 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.

In general, the term MEMBER will be used to refer to frame

or input,

see sections

5.11 to 5.17

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.

1.5.1 Global Coordinate System

The following coordinate systems are available for specification of
the structure geometry.

A. 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

Section 1

directions. The translational degrees of freedom are denoted by

, u2, u3 and the rotational degrees of freedom are denoted by u4,

u

1

& u6.

u

5

B. 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.

C. 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.

1-5

Figure 1.2 : Cartesian (Rectangular) Coordinate System

General Description
Section 1

1-6

Figure 1.3 : Cylindrical Coordinate System

Figure 1.4 : Reverse Cylindrical Coordinate System

Section 1

1.5.2 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. 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.

1-7

General Description
Section 1

1-8

Figure 1.5a

Figure 1.5b

Section 1

1-9

Figure 1.6a - Local axis system for various cross sections

when global Y axis is vertical.

NOTE: The local x-axis of the above sections is going into the paper

1-10

General Description
Section 1

Figure 1.6b - Local axis system for various cross sections

when global Z axis is vertical (SET Z UP is specified).

Section 1

F

1.5.3 Relationship Between Global & Local
Coordinates

Since the input for 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 measured in the following
specified way. This angle will be defined as the beta (β) angle.
For offset members the beta angle/reference point specifications
are based on the offset position of the local axis, not the joint
positions.

Beta Angle

When the local x-axis is parallel to the global Vertical axis, as in

or input,

see section

5.26

the case of a column in a structure, the beta angle is the angle
through which the local z-axis (or local Y for SET Z UP) 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 (global Y axis
for SET Z UP).

When the local x-axis is not parallel to the global Vertical 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 (or local Y for SET Z UP) parallel to the
global X-Z plane (or global X-Y plane for SET Z UP)and the local
y-axis (or local z for SET Z UP) in the same positive direction as
the global vertical 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.

1-11

1-12

General Description
Section 1

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 (x-z plane for SET Z UP) 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 (x-z plane for SET Z UP).

Y

x

x

y

z

y

z

x

x

y

x

Z

z

y

z

z

x

y

z

y

x

x

y

y

x

x

z

z

y

z

y

z

z

y

y

z

x

X

x

Relationship between Global and Local axes

Figure 1.7

Section 1

1-13

Figure 1.8

1-14

General Description
Section 1

Figure 1.9

Section 1

1-15

Figure 1.10

1-16

General Description
Section 1

Figure 1.11

Section 1

1-17

Figure 1.12

General Description

F

1-18

Section 1

1.6 Finite Element Information

or input, see

sections 5.11, 5.13,

5.14, 5.21, 5.24, and

5.32.3

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 below.

1.6.1 Plate/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.

“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 facility is described in
detail in Section 5.14.

The user may also use the element for PLANE STRESS action
only (i.e. membrane/in-plane stiffness only). The ELEMENT
PLANE STRESS command should be used for this purpose.

Section 1

Geometry Modeling Considerations

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.

Load Specification for Plate Elements

Following load specifications are available:

1) Joint loads at element nodes in global directions.

1-19

2) Concentrated loads at any user specified point within the
element in global or local directions.

3) Uniform pressure on element surface in global or local
directions

4) Partial uniform pressure on user specified portion of element
surface in global or local directions

5) Linearly varying pressure on element surface in local
directions.

6) Temperature load due to uniform increase or decrease of
temperature.

7) Temperature load due to difference in temperature between top
and bottom surfaces of the element.

1-20

General Description
Section 1

Correct numberin g

Generated Node

(Center Node)

Incorrect numbering

Figure 1.8

Figure 1.9

Good Element s

Figure 1.10

Bad El ements

Figure 1.11

Figure 1.13

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.

σ

y

τyx

σ

x

τxy

τ

yx

σ

y

Figure 1.14

τxy

σ

x

Section 1

Complete quadratic assumed stress distribution:

a

⎞

⎛

1

⎟
⎛
⎜

⎜
⎜

⎜
⎝

⎡

⎞

σ

x

⎟

⎢

⎟

σ

=

⎢

y

⎟

⎢

⎟

τ

xy

⎢

⎠

⎣

2

2

⎜

⎤

0xy2x0000yx1

a

⎟

⎜

2

⎥

⎟

⎜

xy20y0yx1000

⎥

22

⎥

xyxy21x000y0

−−−−−

⎥

⎦

a

3

⎟

⎜

⎟

⎜

M

⎟

⎜

a

10

⎠

⎝

through a10 = constants of stress polynomials.

a

1

The following quadratic stress distribution is assumed for plate
bending action:

Q

Q

x

M

xy

Z

M

x

Y

X

M

yx

Q

y

M

y

M

y

y

M

yx

Q

x

M

x

M

xy

Figure 1.15

Complete quadratic assumed stress distribution:

a

⎛

⎜
⎜
⎜
⎜
⎜
⎜

⎜
⎝

a

through a13 = constants of stress polynomials.

1

⎢

M

⎟

y

⎢

⎟

⎢

M

xy

=

⎟

⎢

⎟

Q

⎢

x

⎟

⎢

⎟

Q

y

⎠

⎣

⎡

M

⎞

⎛

x

⎟

2

−

00xyx000000yx1

2

yxy00000yx1000

xy00xyyx1000000

−−

x0yx100000010

−

yx0y010100000

1

⎤

⎜

a

⎥

⎜

2

⎥

⎜

a

3

⎥

⎜

⎥

⎜

M

⎥

⎜

M

⎥

⎜
⎜

⎦

a

13

⎝

1-21

⎞
⎟

⎟
⎟
⎟
⎟
⎟
⎟

⎟
⎠

1-22

General Description
Section 1

The distinguishing features of this finite element are:

1) Displacement compatibility between the plane stress component
of one element and the plate bending component of an adjacent
element which is at an angle to the first (see Fig. below) is
achieved by the elements. This compatibility requirement is
usually ignored in most flat shell/plate elements.

Figure 1.16

2) The out of plane rotational stiffness from the plane stress
portion of each element is usefully incorporated and not
treated as a dummy as is usually done in most commonly
available commercial software.

3) Despite the incorporation of the rotational stiffness mentioned
previously, the elements satisfy the patch test absolutely.

4) These elements are available as triangles and quadrilaterals,
with corner nodes only, with each node having six degrees of
freedom.

5) These elements are the simplest forms of flat shell/plate
elements possible with corner nodes only and six degrees of
freedom per node. Yet solutions to sample problems converge
rapidly to accurate answers even with a large mesh size.

6) These elements may be connected to plane/space frame
members with full displacement compatibility. No additional
restraints/releases are required.

7) Out of plane shear strain energy is incorporated in the
formulation of the plate bending component. As a result, the
elements respond to Poisson boundary conditions which are
considered to be more accurate than the customary Kirchoff
boundary conditions

Section 1

8) The plate bending portion can handle thick and thin plates,
thus extending the usefulness of the plate elements into a
multiplicity of problems. In addition, the thickness of the plate is
taken into consideration in calculating the out of plane shear.

9) The plane stress triangle behaves almost on par with the well
known linear stress triangle. The triangles of most similar flat
shell elements incorporate the constant stress triangle which
has slow rates of convergence. Thus the triangular shell
element is useful in problems with double curvature where the
quadrilateral element may not be suitable.

10) Stress retrieval at nodes and at any point within the element.

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).

1-23

Figure 1.17

1-24

General Description
Section 1

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). The 3

TMAX Maximum 2D shear stress in the plane of the

element (Force/unit area)

ANGLE Orientation of the 2D principal plane (Degrees)
VONT, VONB 3D Von Mises stress, where

()

2

TRESCAT, TRESCAB Tresca stress, where

TRESCA = MAX[ |(Smax-Smin)| , |(Smax)| , |(Smin)| ]

rd

principal stress is 0.0

22

SMINSMAXSMINSMAX707.0 VM ++−=

Section 1

Notes:

1. All element stress output is in the local coordinate system. The
direction and sense of the element stresses are explained in
Fig. 1.13.

2. To obtain element stresses at a specified point within the
element, the user must provide the location (local X, local Y)
in the coordinate system for the element. The origin of the
local coordinate system coincides with the center of the
element.

3. The 2 nonzero Principal stresses at the surface (SMAX &
SMIN), the maximum 2D shear stress (TMAX), the 2D
orientation of the principal plane (ANGLE), the 3D Von Mises
stress (VONT & VONB), and the 3D 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.

4. The third principal stress is assumed to be zero at the surfaces
for use in Von Mises and Tresca stress calculations. However,
the TMAX and ANGLE are based only on the 2D inplane
stresses (SMAX & SMIN) at the surface. The 3D maximum
shear stress at the surface is not calculated but would be equal
to the 3D Tresca stress divided by 2.0.

1-25

1-26

General Description
Section 1

Sign Convention of Plate Element Stresses and

Moments

Figure 1.18

Figure 1.19

Section 1

1-27

Figure 1.20

Figure 1.21

1-28

General Description
Section 1

Figure 1.22

Figure 1.23

Section 1

1-29

Figure 1.24

Figure 1.25

1-30

General Description
Section 1

Please note the following few restrictions in using the finite
element portion of STAAD:

1) Members, plate elements, solid elements and surface elements
can all be part of a single STAAD model. The MEMBER
INCIDENCES input must precede the INCIDENCE input for
plates, solids or surfaces. All INCIDENCES must precede
other input such as properties, constants, releases, loads, etc.

2) The selfweight of the finite elements is converted to joint
loads at the connected nodes and is not used as an element
pressure load.

3) Element stresses are printed at the centroid and joints, but not
along any edge.

4) In addition to the stresses shown in Fig 1.18, the Von Mises
stresses at the top and bottom surface of the element are also
printed.

Plate Element Numbering

During the generation of element stiffness matrix, the program
verifies whether the element is same as the previous one or not. If
it is same, repetitive calculations are not performed. The sequence
in which the element stiffness matrix is generated is the same as
the sequence in which elements are input in element incidences.

Therefore, to save some computing time, similar elements should
be numbered sequentially. Fig. 1.14 shows examples of efficient
and non-efficient element numbering.

Section 1

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.

1-31

1.6.2 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.

1

1

234

5678

Efficient Element numbering

3

2

4

Inefficient Element numbering

5

7

6

8

Figure 1.26

1-32

General Description
Section 1

Theoretical Basis

The solid element used in STAAD is of eight noded isoparametric
type. These elements have three translational degrees-of-freedom
per node.

Figure 1.27

By collapsing various nodes together, an eight noded solid element
can be degenerated to the following forms with four to seven
nodes. Joints 1, 2, and 3 must be retained as a triangle.

Figure 1.28

The stiffness matrix of the solid element is evaluated by numerical
integration with eight Gauss-Legendre points. To facilitate the
numerical integration, the geometry of the element is expressed by
interpolating functions using natural coordinate system, (r,s,t) of
the element with its origin at the center of gravity. The
interpolating functions are shown below:

Section 1

8

xhii

=

x y z, , zh yhii

i

=∑1

8

=

i

=∑1

8

ii

=

i

=∑1

where x, y and z are the coordinates of any point in the element

, yi, zi, i=1,..,8 are the coordinates of nodes defined in the

and x

i

global coordinate system. The interpolation functions, h

are

i

defined in the natural coordinate system, (r,s,t). Each of r, s and t
varies between -1 and +1. The fundamental property of the
unknown interpolation functions h

is that their values in natural

i

coordinate system is unity at node, i, and zero at all other nodes of
the element. The element displacements are also interpreted the
same way as the geometry. For completeness, the functions are
given below:

u =

8

, v = , w = huii

i=∑1

i=∑1

8

hvii

8

hwii

i=∑1

where u, v and w are displacements at any point in the element and
u

, wi, i=1,8 are corresponding nodal displacements in the

i,vi

coordinate system used to describe the geometry.

Three additional displacement “bubble” functions which have zero
displacements at the surfaces are added in each direction for
improved shear performance to form a 33x33 matrix. Static
condensation is used to reduce this matrix to a 24x24 matrix at the
corner joints.

1-33

1-34

General Description
Section 1

Local Coordinate System

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

Figure 1.29

Properties and Constants

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. Also,
Density needs to be provided if selfweight is included in any load
case.

Section 1

Output of Solid 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: __________________________
SIGE= .707 √ (S1-S2)

2

+ (S2-S3)2 + (S3-S1)

Direction cosines : 6 direction cosines are printed, following the
expression DC, corresponding to the first two principal stress
directions.

1.6.3 Surface Element

For any panel 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 panel 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.

1-35

2

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.

1-36

General Description
Section 1

The attributes associated with surfaces, and the sections of this
manual where the information may be obtained, are listed below:

Attributes Related

Sections

Surfaces incidences - 5.13.3

Openings in surfaces - 5.13.3

Local coordinate system for surfaces - 1.6.3

Specifying sections for stress/force output - 5.13.3

Property for surfaces - 5.21.2

Material constants - 5.26.3

Surface loading - 5.32.3.4

Stress/Force output printing - 5.42

Shear Wall Design - 3.8.2, 5.53

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:

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

c. 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.

d. Finally, Y is a vector product of Z and X (Y = Z x X).

.

Section 1

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

1-37

1.7 Member Properties

The following types of member property specifications are
available in STAAD:

A) PRISMATIC property specifications

See section

5.20

B) Standard Steel shapes from built-in section library
C) User created steel tables
D) TAPERED sections
E) Through ASSIGN command
F) CURVED specification

Shear Area for members refers to the shear stiffness effective area.
Shear stiffness effective area is used to calculate shear stiffness
for the member stiffness matrix. As an example: for a rectangular
cross section, the shear stiffness effective area is usually taken as

0.83 (Roark) to 0.85 (Cowper) times the cross sectional area. A

shear area of less than the cross sectional area will reduce the
stiffness. A typical shearing stiffness term is

Figure 1.30

1-38

General Description
Section 1

3

(12EI/L

)/(1+Φ) where

Φ = (12 EI) / (GA

L2) and As is the shear stiffness effective area.

s

PHI (Φ)is usually ignored in basic beam theory. STAAD will
include the PHI term unless the SET SHEAR command is entered.

Shear stress effective area is a different quantity that is used to
calculate shear stress and in code checking. For a rectangular cross
section, the shear stress effective area is usually taken as 2/3 rds of
the cross sectional area.

Shear stress in STAAD may be from one of 3 methods.

1. (Shear Force)/(Shear stress effective area)

This is the case where STAAD computes the area based on
the cross section parameters.

2. (Shear Force)/(Shear stiffness effective area)

This is the case where STAAD uses the shear area entered.

3. (V Q)/(I t)

In some codes and for some cross sections, STAAD uses
this method.

Section 1

1.7.1 Prismatic Properties

The following prismatic properties are required for analysis:

See section

5.20.2

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

For T-beams, YD, ZD, YB & ZB must be specified. These terms,
which are shown in the next figure are :

YD = Total depth of section (top fiber of flange to bottom fiber of

web)
ZD = Width of flange
YB = Depth of stem
ZB = Width of stem

For Trapezoidal beams, YD, ZD & ZB must be specified. These
terms, which too are shown in the next figure are :

YD = Total depth of section
ZD = Width of section at top fiber
ZB = Width of section at bottom fiber

Note : The above definitions for YD,ZD,YB & ZB are applicable
when Y is the vertical axis.

Top & bottom are defined as positive side of the local Z axis, and
negative side of the local Z axis respectively.

1-39

1-40

General Description
Section 1

STAAD automatically considers the additional deflection of
members due to pure shear (in addition to deflection due to
ordinary bending theory). To ignore the shear deflection, enter a
SET SHEAR command before the joint coordinates. This will
bring results close to textbook results.

The depths in the two major directions (YD and ZD) are used in
the program to calculate the section moduli. These are needed only
to calculate member stresses or to perform concrete design. The
user can omit the YD & ZD values if stresses or design of these
members are of no interest.

The default value is 253.75 mm (9.99
inches) for YD and ZD. All the prismatic properties are input in
the local member coordinates.

ZD

ZD

YD

ZB

YB

ZB

Figure 1.31

YD

To define a concrete member, the user must not provide AX, but
instead, provide YD and ZD for a rectangular section and just YD
for a circular section. If no moment of inertia or shear areas are
provided, the program will automatically calculate these from YD
and ZD.

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.

Section 1

Table 1.1 Required properties

Structural Required

Type Properties

TRUSS structure AX

PLANE structure AX, IZ or IY
FLOOR structure IX, IZ or IY
SPACE structure AX, IX, IY, IZ

1.7.2 Built-In Steel Section Library

This feature of the program allows the user to specify section

See section

2.2.1 and

5.20.1

names of standard steel shapes manufactured in different
countries. Information pertaining to the American steel shapes is
available in section 2.

For information on steel shapes for other countries, please refer to
the International Codes manual.

STAAD.Pro comes with the non-composite castellated beam tables
supplied by the steel products manufacturer SMI Steel Products.
Details of the manufacture and design of these sections may be
found at

http://www.smisteelproducts.com/English/About/design.html

1-41

Figure 1.32

Since the shear areas of the sections are built into the tables, shear
deformation is always considered for these sections.

General Description

E

p

1-42

Section 1

1.7.3 User Provided Steel Table

The user can provide a customized steel table with designated

See sections 5.19,

5.20.4 and
xamples Manual

roblem 17

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.

These tables can be provided as a part of a STAAD input or as
separately created files from which the program can read the
properties. The user who does not use standard rolled shapes or
who uses a limited number of specific shapes may create
permanent member property files. Analysis and design can be
limited to the sections in these files.

1.7.4 Tapered Sections

See section

5.20.3

Properties of tapered I-sections and several types of tapered tubes
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. Specification of TAPERED sections is described in
Section 5 of this manual.

1.7.5 Assign Command

If one wishes to avoid the trouble of defining a specific section
name, but instead wants to leave it to the program to assign a

See section

5.20.5

section name by itself, the ASSIGN command is available. The
section types that may be ASSIGNed include BEAM, COLUMN,
CHANNEL, ANGLE and DOUBLE ANGLE.

When the keyword BEAM is specified, the program will assign an
I-shaped beam section (Wide Flange for AISC, UB section for
British).

Section 1

For the keyword COLUMN also, the program will assign an I­shaped beam section (Wide Flange for AISC, UC section for
British).

If steel design-member selection is requested, a similar type
section will be selected. See section 5.20.5 for the command
syntax and description of the ASSIGN Command.

1.7.6 Steel Joist and Joist Girders

STAAD.Pro now comes with the facilities for specifying steel
joists and joist girders. The basis for this implementation is the
information contained in the 1994 publication of the American
Steel Joist Institute called “Fortieth edition standard
specifications, load tables and weight tables for steel joist and
joist girders”. The following are the salient features of the
implementation.

Member properties can be assigned by specifying a joist
designation contained in tables supplied with the program. The
following joists and joist girder types have been implemented:

Open web steel joists – K series and KCS joists
Longspan steel joists – LH series
Deep Longspan steel joists – DLH series
Joist Girders – G series

The pages in the Steel Joist Institute publication where these
sections are listed are shown in the following table.

Joist type Beginning page number

K series 24
KCS 30
LH series 54
DLH series 57
Joist girders 74

1-43

1-44

General Description
Section 1

The designation for the G series Joist Girders is as shown in page
73 of the Steel Joist Institute publication. STAAD.Pro incorporates
the span length also in the name, as shown in the next figure.

Figure 1.33

Modeling the joist - Theoretical basis

Steel joists are prefabricated, welded steel trusses used at closely
spaced intervals to support floor or roof decking. Thus, from an
analysis standpoint, a joist is not a single member in the same
sense as beams and columns of portal frames that one is familiar
with. Instead, it is a truss assembly of members. In general,
individual manufacturers of the joists decide on the cross section
details of the members used for the top and bottom chords, and
webs of the joists. So, joist tables rarely contain any information
on the cross-section properties of the individual components of a
joist girder. The manufacturer’s responsibility is to guarantee that,
no matter what the cross section details of the members are, the
joist simply has to ensure that it provides the capacity
corresponding to its rating.

The absence of the section details makes it difficult to incorporate
the true truss configuration of the joist in the analysis model of the
overall structure. Any load or selfweight applied on the joist is
transferred to its end nodes through simply supported action as if
it were a truss. The joist makes no contribution to the stiffness of
the overall structure.

Section 1

As a result of the above assumption, the following points must
be noted with respect to modeling joists:

1) The entire joist is represented in the STAAD input file by
a single member. Graphically it will be drawn using a
single line.

2) After creating the member, the properties should be
assigned from the joist database.

3) The 3D Rendering feature of the program will display
those members using a representative Warren type truss.

4) The intermediate span-point displacements of the joist
cannot be determined.

1-45

Figure 1.34

1-46

General Description
Section 1

Assigning the joists

The procedure for assigning the joists is explained in the Graphical
User Interface manual.

The STAAD joists database includes the weight per length of the
joists. So, for selfweight computations in the model, the weight of
the joist is automatically considered.

An example of a structure with joist (command file input data) is
shown below.

STAAD SPACE EXAMPLE FOR JOIST GIRDER
UNIT FEET KIP

JOINT COORDINATES
1 0 0 0; 2 0 10 0
3 30 10 0; 4 30 0 0

MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;

MEMBER PROPERTY AMERICAN
1 3 TABLE ST W21x50

MEMBER PROPERTY SJIJOIST
2 TABLE ST 22K6

CONSTANTS
E STEEL ALL
DENSITY STEEL ALL
POISSON STEEL ALL

SUPPORTS
1 4 FIXED

UNIT POUND FEET
LOAD 1
SELFWEIGHT Y -1

LOAD 2
MEMBER LOAD
2 UNI GY -250

Section 1

LOAD COMB 3
1 1 2 1

PERF ANALY PRINT STAT CHECK
PRINT SUPP REAC

FINISH

1.7.7 Composite Beams and Composite Decks

There are two methods in STAAD for specifying composite beams.
Composite beams are members whose property is comprised of an
I-shaped steel cross section (like an American W shape) with a
concrete slab on top. The steel section and concrete slab act
monolithically. The two methods are:

a) The EXPLICIT definition method – In this method, the

member geometry is first defined as a line. It is then assigned
a property from the steel database, with the help of the ‘CM’
attribute. This method is described in Section 5.20.1 of this
manual. Additional parameters like CT (thickness of the slab),
FC (concrete strength), CW (effective width of slab), CD
(concrete density), etc., some optional and some mandatory,
are also provided.

Hence, the responsibility of determining the attributes of the
composite member, like concrete slab width, lies upon the
user. If the user wishes to obtain a design, additional terms
like rib height, rib width, etc. also have to be separately
assigned with the aid of design parameters. Hence, some
amount of effort is involved in gathering all the data and
assigning them.

1-47

General Description

1-48

Section 1

b) The composite deck generation method – The laboriousness of

the previous procedure can be alleviated to some extent by
using the program’s composite deck definition facilities. The
program then internally converts the deck into individual
composite members (calculating attributes like effective width
in the process) during the analysis and design phase. The deck
is defined best using the graphical tools of the program since a
database of deck data from different manufacturers is
accessible from easy-to-use dialog boxes. Since all the
members which make up the deck are identified as part of a
single object, load assignment and alterations to the deck can
be done to just the deck object, and not the individual
members of the deck.

The graphical procedure for creating the deck can be found in
section AD.2004.22.2 of the Software Release Report for
STAAD.Pro 2004’s second edition. The command input is
described in section 5.20.7 of this manual.

1.7.8 Curved Members

See section

5.20.8

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

1.8 Member/Element Release

STAAD allows releases for members and plate elements.

One or both ends of a member or element can be released.

See
section 5.22

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. PARTIAL
moment release is also allowed.

Section 1

Only one of the attributes described in sections 1.8 and 1.9 can be
assigned to a given member. The last one entered will be used. In
other words, a MEMBER RELEASE should not be applied on a
member which is declared TRUSS, TENSION ONLY or
COMPRESSION ONLY.

1.9 Truss/Tension/Compression - Only Members

For analyses which involve members that carry axial loads only,

See section

5.23

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.

In STAAD, the MEMBER TENSION or MEMBER
COMPRESSION command can be used to limit the axial load type
the member may carry. Refer to Section 5.23.3 for details on this
facility.

1-49

1.10 Tension/Compression - Only Springs

In STAAD, the SPRING TENSION or SPRING COMPRESSION
command can be used to limit the load direction the support spring

See section

5.23

may carry. The analysis will be performed accordingly. Refer to
Section 5.23.4 for details on this facility.

General Description

s

1-50

Section 1

1.11 Cable Members

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

1.11.1 Linearized Cable Members

Cable members may be specified by using the MEMBER CABLE

See

ection 5.23,

5.37 &

1.18.2.5

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

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:

F

==Kx where K

elastic

EA

L

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

3

T

F

=Kx but here K

12

=

sag

23

wL

where w = weight per unit length of cable

T = tension in cable
α = angle that the axis of the cable makes with a
horizontal plane (= 0, cable is horizontal; = 90,
cable is vertical).

Therefore, the "stiffness" of a cable depends on the initial installed
tension (or sag). These two effects may be combined as follows

( 1.0 / cos2 α )

Section 1

K

=

comb

KK

11//

sag elastic

1

+

= (EA/L) / [1+w2L2EA(cos2 α)/12T3]

K

comb

Note: When T = infinity, K
When T = 0, K

comb

comb

= EA/L
= 0

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

The following points need to be considered when using the linear
cable member in STAAD :

1) The linear cable member is only a truss member whose
properties accommodate the sag factor and initial tension. The
behavior of this cable member is identical to that of the truss
member. It can carry axial loads only. As a result, the
fundamental rules involved in modeling truss members have to
be followed when modeling cable members. For example,
when two cable members meet at a common joint, if there isn't
a support or a 3rd member connected to that joint, it is a point
of potential instability.

2) Due to the reasons specified in 1) above, applying a transverse
load on a cable member is not advisable. The load will be
converted to two concentrated loads at the 2 ends of the cable
and the true deflection pattern of the cable will never be
realized.

3) A tension only cable member offers no resistance to a
compressive force applied at its ends. When the end joints of
the member are subjected to a compressive force, they "give
in" thereby causing the cable to sag. Under these
circumstances, the cable member has zero stiffness and this
situation has to be accounted for in the stiffness matrix and the
displacements have to be recalculated. But in STAAD, merely
declaring the member to be a cable member does not guarantee
that this behavior will be accounted for. It is also important

1-51

1-52

General Description
Section 1

that the user declare the member to be a tension only member
by using the MEMBER TENSION command, after the CABLE
command. This will ensure that the program will test the
nature of the force in the member after the analysis and if it is
compressive, the member is switched off and the stiffness
matrix re-calculated.

4) Due to potential instability problems explained in item 1
above, users should also avoid modeling a catenary by
breaking it down into a number of straight line segments. The
linear cable member in STAAD cannot be used to simulate the
behavior of a catenary. By catenary, we are referring to those
structural components which have a curved profile and develop
axial forces due to their self weight. This behavior is in reality
a non-linear behavior where the axial force is caused because
of either a change in the profile of the member or induced by
large displacements, neither of which are valid assumptions in
an elastic analysis. A typical example of a catenary is the main
U shaped cable used in suspension bridges.

5) The increase of stiffness of the cable as the tension in it
increases under applied loading is updated after each iteration
if the cable members are also declared to be MEMBER
TENSION. However, iteration stops when all tension members
are in tension or slack; not when the cable tension converges.

Section 1

s

1.11.2 Non Linear Cable & Truss 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 may be provided. The user should
ensure that all cables will be in sufficient tension for all load cases
to converge. Use selfweight in every load case and temperature if
appropriate; i.e. don’t enter component cases (e.g. wind only).

See

ection 5.23,

5.37 &

1.18.2.5

The nonlinear cable may have large motions and the sag is checked
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 but also 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.

Points 1, 2, and 4 in the prior section above will not apply to
nonlinear cable analysis if sufficient pretension is applied, so
joints may be entered along the shape of a cable (in some cases a
stabilizing stiffness may be required and entered for the first
loadstep). Point 3 above:

The Member Tension command is
unnecessary and ignored for the nonlinear cable & truss analysis.
Point 5 above: The cable tensions are iterated to convergence in
the nonlinear cable analysis.

1-53

General Description

1-54

Section 1

1.12 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

See section

5.25

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

WP refers to the location of the

Y

centroid of the starting or ending
point of the member

7" 6"

WP

n1 n2

WP

1

2

WP

MEMBER OFFSET
1 START 7
1 END -6
2 END -6 -9

Figure 1.35

9"

X

Section 1

1.13 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

See
section 5.26

(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 selfweight 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,

G = 0.5 x E/(1 + POISS)

If Poisson's ratio is not provided, STAAD will assume a value for
this quantity based on the value of E. Coefficient of thermal
expansion (ALPHA) is used to calculate the expansion of the
members if temperature loads are applied. The temperature unit for
temperature load and ALPHA has to be the same.

Composite damping ratio is used to compute the damping ratio for
each mode in a dynamic solution. This is only useful if there are
several materials with different damping ratios.

BETA angle and REFerence point are discussed in Sec 1.5.3 and
are input as part of the member constants.

Note: Poisson’s Ratio must always be defined after the Modulus of
Elasticity for a given member/element.

1-55

General Description

1-56

Section 1

1.14 Supports

See
section 5.27

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 (known as FIXED BUT). 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 BUT support can be released in any
desired direction as specified in section 5.27.

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.
For static analysis, Multi-linear spring supports can be used to
model the varying, non-linear resistance of a support (e.g. soil).
See section 5.27 for descriptions of the elastic footing and elastic
foundation mat facilities.

The Support command is also used to specify joints and directions
where support displacements will be enforced.

Section 1

1.15 Master/Slave Joints

The master/slave option is provided to enable the user to model

See
section 5.28

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.

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

1-57

1.16.1 Joint Load

Joint loads, both forces and moments, may be applied to any free

See section

5.32.1

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.

General Description

1-58

Section 1

1.16.2 Member Load

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

See section

5.32.2

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 specified to act along the full or
projected member length. Refer to Fig. 1.3 to find the relation of
the member to the global coordinate systems for specifying
member loads. Positive forces act in the positive coordinate
directions, local or global, as the case may be.

Section 1

Member Load Configurations - Figure 1.36

1-59

General Description

1-60

Section 1

1.16.3 Area Load / Oneway Load / Floor Load

Often a floor is subjected to a uniform pressure. It could require a
lot of work to calculate the equivalent member load for individual
members in that floor. However, with the AREA, ONEWAY or

See section

5.32.4

FLOOR LOAD facilities, the user can specify the pressure (load
per unit square area). The program will calculate the tributary area
for these members and calculate the appropriate member loads.
The Area Load and Oneway load are used for one way distribution
and the Floor Load is used for two way distribution.

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.

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, MEMBER COMPRESSION or CURVED.

Section 1

Figure 1.37 shows a floor structure with area load specification
of 0.1.

4m 5m6m

6789

12 3 4 5

10 11 12 13

5m

X

1-61

4m

Z

6m

Figure 1.37

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 to the girder will be considered.

Only member loads are generated from the Area, Oneway and
Floor load input. Thus, load types specific to plates, solids or
surface are not generated. That is because, the basic assumption is
that, a floor load or area load is used in situations where the basic
entity (plate, solid or surface) which acts as the medium for
application of that load, is not part of the structural model.

General Description

L

=

1-62

Section 1

1.16.4 Fixed End Member Load

Load effects on a member may also be specified in terms of its

See section

5.32.7

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.

1.16.5 Prestress and Poststress 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

See section

5.32.5

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.

1) The cable is assumed to have a generalized parabolic profile.

The equation of the parabola is assumed to be

ybx

=++2c

ax

where

where es = eccentricity of cable at start of member (in local

1

a

L

1

b

ces

es em ee=−+

24 2

()

2

em ee es=−−

43

()

y-axis)

Section 1

θ==

(

em = eccentricity of cable at middle of member (in

local y-axis)

ee = eccentricity of cable at end of member (in local

y-axis)

L = Length of member

2) The angle of inclination of the cable with respect to the local

x-axis (a straight line joining the start and end joints of the
member) at the start and end points is small which gives rise to
the assumption that

sin /θ

Hence, if the axial force in the cable is P, the vertical
component of the force at the ends is

horizontal component of the cable force is,

P

12−

Users are advised to ensure that their cable profile meets this
requirement. An angle under 5 degrees is recommended.

3) The member is analyzed for the prestressing/poststressing

effects using the equivalent load method. This method is well
documented in most reputed books on Analysis and Design of
Prestressed concrete. The magnitude of the uniformly
distributed load is calculated as

udl

where P = axial force in the cable

L = length of the member

4) The force in the cable is assumed to be same throughout the

member length. No reduction is made in the cable forces to
account for friction or other losses.

dy dx

dy

⎛
⎜

⎝

dx

Pe

8

=

2

L

es ee

+

e

2

Pdy dx(/)

⎞
⎟

⎠

)

em=

−

and the

1-63

1-64

General Description
Section 1

5) The term MEMBER PRESTRESS as used in STAAD signifies

the following condition. The structure is constructed first.
Then, the prestressing force is applied on the relevant
members. As a result, the members deform and depending on
their end conditions, forces are transmitted to other members
in the structure. In other words, "PRE" refers to the time of
placement of the member in the structure relative to the time
of stressing.

6) The term MEMBER POSTSTRESS as used in STAAD

signifies the following condition. The members on which such
load is applied are first cast in the factory. Following this, the
prestressing force is applied on them. Meanwhile, the rest of
the structure is constructed at the construction site. Then, the
prestressed members are brought and placed in position on the
partially built structure. Due to this sequence, the effects of
prestressing are "experienced" by only the prestressed
members and not transmitted to the rest of the structure. In
other words, "POST" refers to the time of placement of the
member in the structure relative to the time of stressing.

7) As may be evident from Item (6) above, it is not possible to

compute the displacements of the ends of the
POSTSTRESSED members for the effects of
POSTSTRESSing, and hence are assumed to be zero. As a
result, displacements of intermediate sections (See SECTION
DISPLACEMENT command) are measured relative to the
straight line joining the start and end joints of the members as
defined by their initial JOINT COORDINATES.

Section 1

1.16.6 Temperature/Strain Load

1-65

See section

5.32.6

Uniform temperature difference throughout members and elements
may be specified. Temperature differences across both faces of
members and through the thickness of plates may also be specified
(uniform temperature only for solids).. The program calculates the
axial strain (elongation and shrinkage) due to the temperature
difference for members. 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.

1.16.7 Support Displacement Load

Static Loads can be applied to the structure in terms of the
displacement of the supports. Displacement can be translational or

See section

5.32.8

rotational. Translational displacements are provided in the
specified length while the rotational displacements are always in
degrees. Displacements can be specified only in directions in
which the support has an “enforced” specification in the Support
command.

1.16.8 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 throughout the plate

element (causing only elongation / shortening) or may vary
across the depth of a plate element causing bending on the plate
element. The coefficient of thermal expansion for the material

1-66

General Description
Section 1

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 self­weight.

Solid elements, the loading types available are

On

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.

4.

Pressure on the faces of solids.

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.

Section 1

1.17 Load Generator – Moving load, Wind &
Seismic

Load generation is the process of taking a load causing unit such
as wind pressure, ground movement or a truck on a bridge, and
converting it to a form such as member load or a joint load which
can be then be used in the analysis.

For seismic loads, a static analysis method or a dynamic analysis
method can be adopted. The static analysis method, which is the
one referred to here, is based on codes such as UBC, IBC, AIJ,
IS1893 etc. For dynamic analysis, see the sections in this chapter
on response spectrum and time history analysis.

Input for 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.

1-67

1.17.1 Moving Load Generator

This feature enables the user to generate static loads on members
due to vehicles moving on a structure. Moving load system(s)

See sections

5.31.1 and

5.32.12

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) vehicles are available within the program and
can be specified using standard AASHTO designations.

General Description

1-68

Section 1

1.17.2 Seismic Load Generator based on UBC,
IBC and other codes

See sections

5.31.2 and

5.32.12

The STAAD seismic load generator follows the procedure of
equivalent lateral load analysis explained in UBC, IBC and several
other codes. It is assumed that the lateral loads will be exerted in
X and Z (or X and Y if Z is up) directions (horizontal) and Y (or Z
if Z is up) will be the direction of the gravity loads. Thus, for a
building model, Y (or Z if Z is up) axis will be perpendicular to
the floors and point upward (all Y (or Z if Z is up) 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 equation
from the code. IBC 2003, IBC 2000, UBC 1997, 1994, or 1985,
IS:1893, Japanese, Colombian and other specifications may be
used.

For load generation per the codes, the user is required to provide
seismic zone coefficients, importance factors, soil characteristic
parameters, etc. See section 5.31.2 for the detailed input required
for each code.

Instead of using the approximate code based 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 the
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.

Section 1

1.17.3 Wind Load Generator

1-69

See sections

5.31.5 and

5.32.12

The Wind Load Generator is a utility which takes as input wind
pressure and height ranges over which these pressures act and
generates nodal point and member loads.
This facility is available for two types of structures.

a)

Panel type or Closed structures

b)

Open structures

Closed structures are ones like office buildings where non­structural entities like a glass façade, aluminum sheets, timber
panels or non-load bearing walls act as an obstruction to the wind.
If these entities are not included in the structural model, the load
generated as a result of wind blowing against them needs to be
computed. So, the steps involved in load generation for such
structures are i) identify the panels – regions circumscribed by
members so that a polygonal closed area is formed. The area may
also be formed between the ground level along one edge and
members along the other. ii) Calculate the panel area and multiply
it by the wind pressure. iii) Convert the resulting force into nodal
point loads.

Plates and solids are not considered in the calculation of the panel
area. Openings within the panels may be modelled with the help of
exposure factors. An exposure factor is associated with each joint
of the panel and is a fractional number by which the area affecting
a joint of the panel can be reduced or increased.

Open structures are those like transmission towers, in which the
region between members is “open” allowing the wind to blow
through. The procedure for load generation for open structures is i)
Calculate the exposed area of the individual members of the
model. ii) Multiply that exposed area by the wind pressure to
arrive at the force and apply the force on individual members as a
uniformly distributed load. It is assumed that all members of the
structure within the specified ranges are subjected to the pressure

General Description

1-70

Section 1

and hence, they will all receive the load. The concept of members
on the windward side shielding the members in the inside regions
of the structure does not exist for open structures.

As a large structure may consist of hundreds of panels and
members, a considerable amount of work in calculating the loads
can be avoided by the user with the help of this facility.

1.18 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

Imperfection Analysis

Multi Linear Spring Support
Member/Spring Tension/Compression only
Nonlinear Cable/Truss Analysis

3) Dynamic Analysis
Time History
Response Spectrum
Steady State / Harmonic

Salient features of each type of analysis are discussed in the
following sections. Detailed theoretical treatments of these
features are available in standard structural engineering textbooks.

1.18.1 Stiffness Analysis

The stiffness analysis implemented in STAAD is based on the
matrix displacement method. In the matrix analysis of structures

See section

5.37

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.

Section 1

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.

Assumptions of the Analysis

For a complete analysis of the structure, the necessary matrices are
generated on the basis of the following assumptions:

1) The structure is idealized into an assembly of beam, plate and
solid type elements joined together at their vertices (nodes).
The assemblage is loaded and reacted by concentrated loads
acting at the nodes. These loads may be both forces and
moments which may act in any specified direction.

2) A beam member is a longitudinal structural member having a
constant, doubly symmetric or near-doubly symmetric cross
section along its length. Beam members always carry axial
forces. They may also be subjected to shear and bending in
two arbitrary perpendicular planes, and they may also be
subjected to torsion. From this point these beam members are
referred to as "members" in the manual.

1-71

3) A plate element is a three or four noded planar element having
variable thickness. A solid element is a 4-8 noded three
dimensional element. These plate and solid elements are
referred to as "elements" in the manual.

4) Internal and external loads acting on each node are in
equilibrium. If torsional or bending properties are defined for
any member, six degrees of freedom are considered at each
node (i.e. three translational and three rotational) in the
generation of relevant matrices. If the member is defined as
truss member (i.e. carrying only axial forces) then only the
three degrees (translational) of freedom are considered at each
node.

1-72

General Description
Section 1

5) Two types of coordinate systems are used in the generation of
the required matrices and are referred to as local and global
systems.

Local coordinate axes are assigned to each individual element and
are oriented such that computing effort for element stiffness
matrices are generalized and minimized. Global coordinate axes
are a common datum established for all idealized elements so that
element forces and displacements may be related to a common
frame of reference.

Basic Equation

The complete stiffness matrix of the structure is obtained by
systematically summing the contributions of the various member
and element stiffness. The external loads on the structure are
represented as discrete concentrated loads acting only at the nodal
points of the structure.

The stiffness matrix relates these loads to the displacements of the
nodes by the equation:

A

= aj + Sj x Dj

j

This formulation includes all the joints of the structure, whether
they are free to displace or are restrained by supports. Those
components of joint displacements that are free to move are called
degrees of freedom. The total number of degrees of freedom
represent the number of unknowns in the analysis.

Method to Solve for Displacements

There are many methods to solve the unknowns from a series of
simultaneous equations. An approach which is particularly suited
for structural analysis is called the method of decomposition. This
method has been selected for use in STAAD. Since the stiffness
matrices of all linearly elastic structures are always symmetric, an
especially efficient form of the decomposition called Modified
Cholesky's method may be applied to these problems. This method
is reasonably accurate and well suited for the Gaussian elimination
process in solving the simultaneous equations.

Section 1

Consideration of Bandwidth

The method of decomposition is particularly efficient when
applied to a symmetrically banded matrix. For this type of matrix
fewer calculations are required due to the fact that elements
outside the band are all equal to zero.

STAAD takes full advantage of this bandwidth during solution, as
it is important to have the least bandwidth to obtain the most
efficient solution. For this purpose, STAAD offers features by
which the program can internally rearrange the joint numbers to
provide a better bandwidth.

Structural Integrity

The integrity of the structure is an important requirement that must
be satisfied by all models. Users must make sure that the model
developed represents one single structure only, not two or more
separate structures.

An "integral" structure or "one" structure may be defined as a system
in which proper "stiffness connections" exist between the
members/elements. The entire model functions as a single integrated
load resisting system. Two or more independent structures within one
model results in erroneous mathematical formulation and therefore,
generates numerical problems. STAAD checks structural integrity
using a sophisticated algorithm and reports detection of multiple
structures within the model.

1-73

1-74

General Description
Section 1

Modeling and Numerical Instability Problems

Instability problems can occur due to two primary reasons.

1) Modeling problem

There are a variety of modeling problems which can give rise
to instability conditions. They can be classified into two
groups.

a) Local instability - A local instability is a condition where

the fixity conditions at the end(s) of a member are such as
to cause an instability in the member about one or more
degrees of freedom. Examples of local instability are:

(i) Member Release: Members released at both ends for

any of the following degrees of freedom (FX, FY, FZ
and MX) will be subjected to this problem.

(ii) A framed structure with columns and beams where the

columns are defined as "TRUSS" members. Such a
column has no capacity to transfer shears or moments
from the superstructure to the supports.

b)

Global Instability - These are caused when the supports of the

structure are such that they cannot offer any resistance to
sliding or overturning of the structure in one or more
directions. For example, a 2D structure (frame in the XY
plane) which is defined as a SPACE FRAME with pinned
supports and subjected to a force in the Z direction will topple
over about the X-axis. Another example is that of a space
frame with all the supports released for FX, FY or FZ.

2) Math precision

A math precision error is caused when numerical instabilities
occur in the matrix decomposition (inversion) process. One of the
terms of the equilibrium equation takes the form 1/(1-A), where
A=k1/(k1+k2); k1 and k2 being the stiffness coefficients of two
adjacent members. When a very "stiff" member is adjacent to a

Section 1

very "flexible" member, viz., when k1>>k2, or k1+k2
A=1 and hence, 1/(1-A) =1/0. Thus, huge variations in stiffnesses
of adjacent members are not permitted. Artificially high E or I
values should be reduced when this occurs.

Math precision errors are also caused when the units of length
and force are not defined correctly for member lengths,
member properties, constants etc.

Users should ensure that the model defined represents one single
structure only, not two or more separate structures. For example,
in an effort to model an expansion joint, the user may end up
defining separate structures within the same input file. Unintended
multiple structures defined in one input file can lead to grossly
erroneous results.

≅ k1,

1.18.2 Second Order Analysis

STAAD offers the capability to perform second order stability

See
section 5.37

analyses.

1-75

1.18.2.1 P-Delta Analysis

See
section 5.37

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.

1-76

General Description
Section 1

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.

This procedure yields reasonably accurate results with 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 moment
magnification method for the calculation of more realistic forces
and moments.

P-Delta effects are calculated for frame members and plate
elements only. They are not calculated for solid elements. P-Delta
and Nonlinear analysis is restricted to structures where members
and plate elements carry the vertical load from one structure level
to the next.

Section 1

1.18.2.2 Imperfection Analysis

Structures subjected to vertical and lateral loads often experience

See
section 5.37
and
section

5.26.6

secondary forces due to curvature imperfections in the columns
and beams. This secondary effect is similar to the P-Delta effect.
In STAAD the procedure consists of the following steps:

1.

First, the deflections and the axial forces in the selected

imperfect members are calculated based on the provided
external loading.

2.

The axial forces and the input imperfections are then used to

compute an additional loading on the selected imperfect
members that are in compression. These additional loads are
combined with the originally applied loading.

3.

The static analysis is now performed with the combined

loading to obtain the final result.

1.18.2.3 Non Linear Analysis (available in limited

1-77

form)

See
section 5.37

REMOVED. Contact Technical Support for further information.

1.18.2.4 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. Stiffness-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 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

General Description

1-78

Section 1

any PDELTA, NONLINEAR, dynamic, or TENSION/
COMPRESSION member cases. The multi-linear spring command
will initiate an iterative analysis which continues to convergence.

1.18.2.5 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 2
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.

There may not be any Multi-linear springs, NONLINEAR, or
dynamic cases.

nd

and subsequent

1.18.2.6 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

See sections

5.30, 5.37,

1.11

step sizes start small and gradually increase (145 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, then the solution is stopped. The user can then change
analysis parameters or modify the structure and rerun.

Section 1

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. Preloaded trusses may carry tension and
compression while 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 procedure was developed for structures, loadings, and
pretensioning loads that will result in sufficient tension in every
cable for all loading conditions. 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 should specify realistic initial preloading tensions which
will ensure that all cable results are in tension. 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.

Currently the cable is not automatically loaded by selfweight, but the
user should ensure that selfweight 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.

1-79

1-80

General Description
Section 1

The analysis sequence is as follows:

Compute the unstressed length of the nonlinear members based

1.
on joint coordinates, pretension, and temperature.

Member/Element/Cable stiffness is formed. Cable stiffness is

2.
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 default number
of 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. The static
check is not exactly in balance due to the displacements of the
applied static equivalent joint loads.

The load cases in a non linear 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 cases. There may not be any Multi­linear 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.

Section 1

8.

Do not apply Prestress load, Fixed end load.
Do not use Load Combination command to combine cable

9.
analysis results. Use a primary case with Repeat Load instead.

1.18.3 Dynamic Analysis

Currently available dynamic analysis facilities include solution of
the free vibration problem (eigenproblem), response spectrum
analysis and forced vibration analysis.

1.18.3.1 Solution of the Eigenproblem

The eigenproblem is solved for structure frequencies and mode

See sections

5.30,

5.32.10, 5.34

shapes considering a diagonal, lumped mass matrix, with masses
possible at all active d.o.f. included. Two solution methods may be
used: the subspace iteration method for all problem sizes (default
for all problem sizes), and the optional determinant search method
for small problems.

1-81

1.18.3.2 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 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

1-82

General Description
Section 1

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-length

2

units).

Please enter selfweight, 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 also be used to generate joint
translational masses. 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 selfweight 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.

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.

Section 1

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.

1.18.3.3 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.

1-83

1.18.3.4 Response Spectrum Analysis

See section

5.32.10

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
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

General Description

=

+

ω

1-84

Section 1

be created to include either the positive or negative contribution of
seismic results.

1.18.3.5 Response Time History Analysis

STAAD is equipped with a facility to perform a response history

See Sections

5.31.6 and

5.32.10.2

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
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

+

Using the transformation

p

{} {}

∑

=

1i

Equation 1 reduces to "p" separate uncoupled equations of the
form

ξ 2i q =++

where
frequency for the i

These are solved by the Wilson- θ method which is an
unconditionally stable step by step scheme. The time step for the
response is entered by the user or set to a default value, if not
entered. The q
displacements {x} at each time step.

is the modal damping ratio and ξ

"mass modeling" for additional information

&&&

q x φ=

i

… … … … (2)

i

2

&&&

i

i qi ωi

th

s are substituted in equation 2 to obtain the

i

q ω

i

mode.

(t) i R

… … (1)

{P(t)} [k]{x} }x[c]{ }x[m]{

… … (3)

the natural

Section 1

=

ω

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

)t ( sinF)t( F

φ+ω

0

In the above equation,

F(t) = Value of the forcing function at any instant of time "t"
F

= Peak value of the forcing function

0

= Frequency of the forcing function

φ = Phase Angle

A plot of the above equation is shown in the figure below.

1-85

Figure 1.38

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 time­force 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

General Description

φ

ω

1-86

Section 1

are chosen 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.

F

= AMPLITUDE

0

ω = FREQUENCY
φ = PHASE

1.18.3.6 Steady State and Harmonic Response

A structure [subjected only to harmonic loading, all at a given
forcing frequency and with non-zero damping] will reach a steady
state of vibration that will repeat every forcing cycle. This steady
state response can be computed without calculating the transient
time history response prior to the steady state condition.

) ( sin)(

+=tRtR

0

The result, R, has a maximum value of R
These two values for displacement, velocity, and acceleration at each joint
may be printed or displayed

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
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.

and a phase angle φ.

0

"mass modeling" for

Section 1

=

ω

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

)t ( sinF)t( F

φ+ω

0

In the above equation,

F(t) = Value of the forcing function at any instant of time "t"
F

= Peak value of the forcing function

0

= Frequency of the forcing function

φ = Phase Angle

A plot of the above equation is shown in the figure below.

1-87

Figure 1.38

The results are the steady-state response which is the absolute
maximum of displacement (and other output quantities) and the
corresponding phase angle after the steady state condition has been
reached.

In addition, a Harmonic response can be calculated. This response
consists of a series of Steady State responses for a list of
frequencies. The joint displacement, velocity, or acceleration can
be displayed as the response value versus frequency. Load case
results are the maximums over all of the frequencies.

All results are positive as in the Response Spectrum and Time
history analyses. This means section results should be ignored
(BEAM 0.0 in Parameters for code checking). Because of this,
you may want to add the steady state response to Dead & Live
loads for one combination case and subtract the steady state
response from those loads for another combination case.

1-88

General Description
Section 1

Ground motion or a joint force distribution may be specified.
Each global direction may be at a different phase angle.

Output frequency points are selected automatically for modal
frequencies and for a set number of frequencies between modal
frequencies. There is an option to change the number of points
between frequencies and an option to add frequencies to the list of
output frequencies.

The load case that defines the mass distribution must be the case
just before the PERFORM STEADY STATE ANALYSIS
command. Immediately after that command is a set of data
starting with BEGIN STEADY and ending with END STEADY.
The list of additional frequencies and the steady state load cases
with joint loads or ground accelerations and phasing data are
entered here. The optional print command for the maximum
displacement and associated phase angle for selected joints must
be at the end of this block of input.

[Stardyne-Dynre2 data beginning with START2 and ending with ALL DONE may
substitute for the BEGIN to END STEADY data if the STRESS data is omitted.]

1.19 Member End Forces

Member end forces and moments in the member result from loads

See
section 5.41

applied to the structure. These forces are in the local member
coordinate system. Figure 1.18a through 1.18d shows the member
end actions with their directions.