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฀฀CSI฀Analysis฀Reference฀Manual ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ CSI Analysis Reference Manual For SAP2000®, ETABS®, SAFE® and CSiBridge® ISO# GEN062708M1 Rev.14 Berkeley, California, USA July 2015 COPYRIGHT Copyright © Computers & Structures, Inc., 1978-2015 All rights reserved. The C...

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CSi Analysis Reference Manual NH Bahar CSI Anal y sis Reference Manual For SAP2000 ® , ETABS ® , and SAFE Hani Salloum Int egrat ed Finit e Element Analysis and Design of St ruct ures ANALYSIS REFERENCE Adnan hamza

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CSI Analysis Reference Manual For SAP2000®, ETABS®, SAFE® and CSiBridge®

ISO# GEN062708M1 Rev.14 Berkeley, California, USA

July 2015

COPYRIGHT Copyright © Computers & Structures, Inc., 1978-2015 All rights reserved. The CSI Logo®, SAP2000®, ETABS®, SAFE®, CSiBridge®, and SAPFire® are registered trademarks of Computers & Structures, Inc. Model-AliveTM and Watch & LearnTM are trademarks of Computers & Structures, Inc. Windows® is a registered trademark of the Microsoft Corporation. Adobe® and Acrobat® are registered trademarks of Adobe Systems Incorporated. The computer programs SAP2000®, ETABS®, SAFE®, and CSiBridge® and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers & Structures, Inc. Unlicensed use of these programs or reproduction of documentation in any form, without prior written authorization from Computers & Structures, Inc., is explicitly prohibited. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior explicit written permission of the publisher.

Further information and copies of this documentation may be obtained from: Computers & Structures, Inc. www.csiamerica.com [email protected] (for general information) [email protected] (for technical support)

DISCLAIMER CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND TESTING OF THIS SOFTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THE PROGRAMS THESE PRODUCTS. THESE PRODUCTS ARE PRACTICAL AND POWERFUL TOOLS FOR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED. THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED.

ACKNOWLEDGMENT Thanks are due to all of the numerous structural engineers, who over the years have given valuable feedback that has contributed toward the enhancement of this product to its current state. Special recognition is due Dr. Edward L. Wilson, Professor Emeritus, University of California at Berkeley, who was responsible for the conception and development of the original SAP series of programs and whose continued originality has produced many unique concepts that have been implemented in this version.

Table of Contents Chapter I

Introduction Analysis Features . . . . . . . . . . . . Structural Analysis and Design . . . . . About This Manual . . . . . . . . . . . Topics. . . . . . . . . . . . . . . . . . Typographical Conventions . . . . . . Bold for Definitions . . . . . . . . Bold for Variable Data. . . . . . . Italics for Mathematical Variables . Italics for Emphasis . . . . . . . . Capitalized Names . . . . . . . . . Bibliographic References . . . . . . . .

Chapter II

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Objects and Elements

2 3 3 3 4 4 4 4 5 5 5

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Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Objects and Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Chapter III

Coordinate Systems Overview . . . . . . . . . . . . . . . . . . . . . Global Coordinate System . . . . . . . . . . . . Upward and Horizontal Directions . . . . . . . . Defining Coordinate Systems . . . . . . . . . . . Vector Cross Product . . . . . . . . . . . . . Defining the Three Axes Using Two Vectors

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CSI Analysis Reference Manual Local Coordinate Systems. . . . . . . . . . . . . . . . . . . . . . . . 14 Alternate Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . 16 Cylindrical and Spherical Coordinates . . . . . . . . . . . . . . . . . 17

Chapter IV

Joints and Degrees of Freedom Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling Considerations . . . . . . . . . . . . . . . . . . . Local Coordinate System . . . . . . . . . . . . . . . . . . . Advanced Local Coordinate System . . . . . . . . . . . . . Reference Vectors . . . . . . . . . . . . . . . . . . . . Defining the Axis Reference Vector . . . . . . . . . . . Defining the Plane Reference Vector. . . . . . . . . . . Determining the Local Axes from the Reference Vectors Joint Coordinate Angles . . . . . . . . . . . . . . . . . Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . Available and Unavailable Degrees of Freedom . . . . . Restrained Degrees of Freedom . . . . . . . . . . . . . Constrained Degrees of Freedom. . . . . . . . . . . . . Mixing Restraints and Constraints Not Recommended . Active Degrees of Freedom . . . . . . . . . . . . . . . Null Degrees of Freedom. . . . . . . . . . . . . . . . . Restraint Supports . . . . . . . . . . . . . . . . . . . . . . . Spring Supports . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Supports . . . . . . . . . . . . . . . . . . . . . . Distributed Supports . . . . . . . . . . . . . . . . . . . . . Joint Reactions . . . . . . . . . . . . . . . . . . . . . . . . Base Reactions . . . . . . . . . . . . . . . . . . . . . . . . Masses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Force Load . . . . . . . . . . . . . . . . . . . . . . . . . . Ground Displacement Load . . . . . . . . . . . . . . . . . . Restraint Displacements . . . . . . . . . . . . . . . . . Spring Displacements . . . . . . . . . . . . . . . . . . Link/Support Displacements . . . . . . . . . . . . . . . Generalized Displacements . . . . . . . . . . . . . . . . . . Degree of Freedom Output . . . . . . . . . . . . . . . . . . Assembled Joint Mass Output. . . . . . . . . . . . . . . . . Displacement Output . . . . . . . . . . . . . . . . . . . . . Force Output . . . . . . . . . . . . . . . . . . . . . . . . . Element Joint Force Output . . . . . . . . . . . . . . . . . .

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22 23 24 24 25 26 26 27 28 30 31 32 32 32 33 34 34 36 37 38 39 39 40 42 42 43 44 45 45 46 47 47 48 48

Table of Contents Chapter V

Constraints and Welds Overview . . . . . . . . . . . . . Body Constraint . . . . . . . . . . Joint Connectivity . . . . . . Local Coordinate System . . . Constraint Equations . . . . . Plane Definition . . . . . . . . . . Diaphragm Constraint . . . . . . . Joint Connectivity . . . . . . Local Coordinate System . . . Constraint Equations . . . . . Plate Constraint . . . . . . . . . . Joint Connectivity . . . . . . Local Coordinate System . . . Constraint Equations . . . . . Axis Definition . . . . . . . . . . Rod Constraint . . . . . . . . . . Joint Connectivity . . . . . . Local Coordinate System . . . Constraint Equations . . . . . Beam Constraint. . . . . . . . . . Joint Connectivity . . . . . . Local Coordinate System . . . Constraint Equations . . . . . Equal Constraint. . . . . . . . . . Joint Connectivity . . . . . . Local Coordinate System . . . Selected Degrees of Freedom Constraint Equations . . . . . Local Constraint . . . . . . . . . . Joint Connectivity . . . . . . No Local Coordinate System . Selected Degrees of Freedom Constraint Equations . . . . . Welds . . . . . . . . . . . . . . . Automatic Master Joints. . . . . . Stiffness, Mass, and Loads . . Local Coordinate Systems . . Constraint Output . . . . . . . . .

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50 51 51 51 51 52 53 53 53 54 55 55 55 55 56 56 57 57 57 58 58 59 59 59 60 60 60 60 61 61 62 62 62 65 66 66 67 67

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CSI Analysis Reference Manual Chapter VI

Material Properties

69

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Local Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . 70 Stresses and Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Isotropic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Uniaxial Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Orthotropic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Anisotropic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Temperature-Dependent Properties . . . . . . . . . . . . . . . . . . . 76 Element Material Temperature . . . . . . . . . . . . . . . . . . . . . 77 Mass Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Weight Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Material Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Modal Damping . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Viscous Proportional Damping. . . . . . . . . . . . . . . . . . . 80 Hysteretic Proportional Damping . . . . . . . . . . . . . . . . . 80 Nonlinear Material Behavior . . . . . . . . . . . . . . . . . . . . . . 80 Tension and Compression . . . . . . . . . . . . . . . . . . . . . 81 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Hysteresis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Friction and Dilitational Angles . . . . . . . . . . . . . . . . . . 84 Hysteresis Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Backbone Curve (Action vs. Deformation) . . . . . . . . . . . . 86 Cyclic Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Elastic Hysteresis Model . . . . . . . . . . . . . . . . . . . . . . 88 Kinematic Hysteresis Model . . . . . . . . . . . . . . . . . . . . 88 Degrading Hysteresis Model . . . . . . . . . . . . . . . . . . . . 89 Takeda Hysteresis Model. . . . . . . . . . . . . . . . . . . . . . 93 Pivot Hysteresis Model . . . . . . . . . . . . . . . . . . . . . . . 94 Concrete Hysteresis Model . . . . . . . . . . . . . . . . . . . . . 95 BRB Hardening Hysteresis Model . . . . . . . . . . . . . . . . . 97 Isotropic Hysteresis Model . . . . . . . . . . . . . . . . . . . . . 99 Modified Darwin-Pecknold Concrete Model . . . . . . . . . . . . . 100 Time-dependent Properties . . . . . . . . . . . . . . . . . . . . . . 101 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Time-Integration Control . . . . . . . . . . . . . . . . . . . . . 102 Design-Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

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Table of Contents Chapter VII

The Frame Element Overview. . . . . . . . . . . . . . . . . . . . . . Joint Connectivity . . . . . . . . . . . . . . . . . Insertion Points . . . . . . . . . . . . . . . . Degrees of Freedom . . . . . . . . . . . . . . . . Local Coordinate System . . . . . . . . . . . . . Longitudinal Axis 1 . . . . . . . . . . . . . . Default Orientation . . . . . . . . . . . . . . Coordinate Angle . . . . . . . . . . . . . . . Advanced Local Coordinate System . . . . . . . . Reference Vector . . . . . . . . . . . . . . . Determining Transverse Axes 2 and 3 . . . . Section Properties . . . . . . . . . . . . . . . . . Local Coordinate System . . . . . . . . . . . Material Properties . . . . . . . . . . . . . . Geometric Properties and Section Stiffnesses. Shape Type . . . . . . . . . . . . . . . . . . Automatic Section Property Calculation . . . Section Property Database Files. . . . . . . . Section-Designer Sections . . . . . . . . . . Additional Mass and Weight . . . . . . . . . Non-prismatic Sections . . . . . . . . . . . . Property Modifiers . . . . . . . . . . . . . . . . . Named Property Sets . . . . . . . . . . . . . Insertion Points . . . . . . . . . . . . . . . . . . Local Axes . . . . . . . . . . . . . . . . . . End Offsets. . . . . . . . . . . . . . . . . . . . . Clear Length. . . . . . . . . . . . . . . . . . Rigid-end Factor . . . . . . . . . . . . . . . Effect upon Non-prismatic Elements . . . . . Effect upon Internal Force Output . . . . . . Effect upon End Releases . . . . . . . . . . . End Releases . . . . . . . . . . . . . . . . . . . . Unstable End Releases . . . . . . . . . . . . Effect of End Offsets . . . . . . . . . . . . . Named Property Sets . . . . . . . . . . . . . Nonlinear Properties . . . . . . . . . . . . . . . . Tension/Compression Limits . . . . . . . . . Plastic Hinge . . . . . . . . . . . . . . . . . Mass . . . . . . . . . . . . . . . . . . . . . . . . Self-Weight Load . . . . . . . . . . . . . . . . .

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106 107 107 108 108 109 109 110 110 112 113 114 115 115 116 116 118 118 118 120 120 123 124 125 126 127 129 129 130 130 130 131 132 132 132 133 133 134 134 134

v

CSI Analysis Reference Manual Gravity Load . . . . . . . Concentrated Span Load . Distributed Span Load . . Loaded Length . . . Load Intensity . . . . Projected Loads . . . Temperature Load . . . . Strain Load . . . . . . . . Deformation Load . . . . Target-Force Load . . . . Internal Force Output . . Effect of End Offsets Stress Output . . . . . . .

Chapter VIII

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The Cable Element Overview. . . . . . . . . . . . Joint Connectivity . . . . . . . Undeformed Length . . . . . . Shape Calculator . . . . . . . . Cable vs. Frame Elements. Number of Segments . . . Degrees of Freedom . . . . . . Local Coordinate System . . . Section Properties . . . . . . . Material Properties . . . .

vi

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Hinge Properties Overview. . . . . . . . . . . . . . . . . . . . . . . Hinge Properties . . . . . . . . . . . . . . . . . . . Hinge Length . . . . . . . . . . . . . . . . . . Plastic Deformation Curve . . . . . . . . . . . Scaling the Curve . . . . . . . . . . . . . . . . Strength Loss . . . . . . . . . . . . . . . . . . Coupled P-M2-M3 Hinge . . . . . . . . . . . . Fiber P-M2-M3 Hinge . . . . . . . . . . . . . Hysteresis Models . . . . . . . . . . . . . . . . Automatic, User-Defined, and Generated Properties Automatic Hinge Properties . . . . . . . . . . . . . Analysis Modeling . . . . . . . . . . . . . . . . . . Analysis Results . . . . . . . . . . . . . . . . . . .

Chapter IX

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147 149 149 150 151 151 153 155 156 156 158 160 161

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