Structural Analysis Using Classical and Matrix Methods

by McCormac, Jack C.

• ISBN13: 9780470036082
• ISBN10: 0470036087
• Edition: 4th
• Format: Hardcover
• Copyright: 2006-10-13
• Publisher: WILEY

Summary

Presenting an introduction to elementary structural analysis methods and principles, this book will help readers develop a thorough understanding of both the behavior of structural systems under load and the tools needed to analyze those systems. Throughout the chapters, they'll explore both statically determinate and statically indeterminate structures. And they'll find hands-on examples and problems that illustrate key concepts and give them opportunity to apply what they've learned.

Author Biography

Jack C. McCormac is Alumni Distinguished Professor o Civil Engineering, Emeritus at Clemson University. He holds a BS in civil engineering from the Citadel, an MS in civil engineering from Massachusetts Institute of Technology, and a Doctor of Letters from Clemson University. His contributions to engineering education and the engineering profession have been recognized by many, including the American Society for Engineering Education, the American Institute of Steel Construction, and the American Concrete Institute. Professor McCormac was included in the International Who's Who in Engineering, and was named by the Engineering News-Record as one of the top 125 engineers or architects in the world in the last 125 years for his contributions to the construction industry. He was one of only two educators living in the world today to receive this honor.

Professor McCormac belongs to the American Society of Civil Engineers and served as the principal civil engineering grader for the National Council of Examiners for Engineering and Surveying for many years.

Table of Contents

Dedication	vii
Preface	xiii
PART ONE: STATICALLY DETERMINATE STRUCTURES	1	(572)
Introduction	3	(13)
Structural Analysis and Design	3	(1)
History of Structural Analysis	4	(3)
Basic Principles of Structural Analysis	7	(1)
Structural Components and Systems	8	(1)
Structural Forces	9	(2)
Structural Idealization (Line Diagrams)	11	(2)
Calculation Accuracy	13	(1)
Checks on Problems	13	(1)
Impact of Computers on Structural Analysis	14	(2)
Structural Loads	16	(27)
Introduction	16	(1)
Structural Safety	17	(1)
Specifications and Building Codes	17	(3)
Types of Structural Loads	20	(1)
Dead Loads	20	(1)
Live Loads	21	(2)
Live Load Impact Factors	23	(1)
Live Loads on Roofs	23	(1)
Rain Loads	24	(2)
Wind Loads	26	(3)
Simplified ASCE Procedure for Estimating Wind Loads	29	(2)
Detailed ASCE Procedure for Estimating Wind Loads	31	(1)
Seismic Loads	32	(2)
Equivalent Lateral Force Procedure for Estimating Seismic Loads	34	(3)
Snow Loads	37	(3)
Other Loads	40	(1)
Problems for Solution	41	(2)
System Loading and Behavior	43	(14)
Introduction	43	(1)
Tributary Areas	44	(4)
Influence Areas	48	(1)
Live Load Reduction	48	(2)
Loading Conditions for Allowable Stress Design	50	(2)
Loading Conditions for Strength Design	52	(3)
Concept of the Force Envelope	55	(1)
Problems for Solution	56	(1)
Reactions	57	(38)
Equilibrium	57	(1)
Moving Bodies	57	(1)
Calculation of Unknowns	58	(1)
Types of Support	59	(2)
Stability, Determinacy, and Indeterminacy	61	(3)
Unstable Equilibrium and Geometric Instability	64	(1)
Sign Convention	65	(1)
Free-Body Diagrams	66	(1)
Horizontal and Vertical Components	67	(1)
Reactions by Proportions	67	(1)
Reactions Calculated by Equations of Statics	68	(3)
Principle of Superposition	71	(1)
The Simple Cantilever	72	(1)
Cantilevered Structures	73	(2)
Reaction Calculations for Cantilevered Structures	75	(2)
Arches	77	(1)
Three-Hinged Arches	78	(5)
Uses of Arches and Cantilevered Structures	83	(1)
Cables	83	(5)
Problems for Solution	88	(7)
Shearing Force and Bending Moment	95	(22)
Introduction	95	(2)
Shear Diagrams	97	(1)
Moment Diagrams	98	(1)
Relations Among Loads, Shearing Forces, and Bending Moments	98	(1)
Moment Diagrams Drawn from Shear Diagrams	99	(7)
Shear and Moment Diagrams for Statically Determinate Frames	106	(4)
Shearing Force and Bending Moment Equations	110	(2)
Problems for Solution	112	(5)
Introduction to Plane Trusses	117	(26)
Introduction	117	(1)
Assumptions for Truss Analysis	118	(1)
Truss Notation	119	(1)
Roof Trusses	120	(1)
Bridge Trusses	121	(1)
Arrangement of Truss Members	122	(1)
Statical Determinacy of Trusses	123	(4)
Methods of Analysis and Conventions	127	(2)
Method of Joints	129	(5)
Computer Analysis of Statically Determinate Trusses	134	(1)
Example Computer Problem	135	(3)
Problems for Solution	138	(5)
Plane Trusses, Continued	143	(25)
Analysis by the Method of Sections	143	(1)
Application of the Method of Sections	144	(7)
Method of Shears	151	(2)
Zero-Force Members	153	(2)
When Assumptions Are Not Correct	155	(1)
Simple, Compound, and Complex Trusses	156	(1)
The Zero-Load Test	157	(2)
Stability	159	(2)
Equations of Condition	161	(1)
Problems for Solution	162	(6)
Three-Dimensional or Space Trusses	168	(17)
Introduction	168	(1)
Basic Principles	168	(1)
Equations of Static Equilibrium	169	(2)
Stability of Space Trusses	171	(1)
Special Theorems Applying to Space Trusses	171	(1)
Types of Support	172	(1)
Illustrative Examples	173	(5)
Solution Using Simultaneous Equations	178	(2)
Example Problem with SABLE32	180	(2)
Problems for Solution	182	(3)
Influence Lines for Beams	185	(19)
Introduction	185	(1)
The Influence Line Defined	185	(1)
Influence Lines for Simple Beam Reactions	186	(1)
Influence Lines for Simple Beam Shearing Forces	187	(1)
Influence Lines for Simple Beam Moments	188	(1)
Qualitative Influence Lines	189	(5)
Uses of Influence Lines; Concentrated Loads	194	(1)
Uses of Influence Lines: Uniform Loads	195	(1)
Common Simple Beam Formulas from Influence Lines	196	(1)
Determining Maximum Loading Effects Using Influence Lines	197	(1)
Maximum Loading Effects Using Beam Curvature	198	(1)
Impact Loading	199	(2)
Problems for Solution	201	(3)
Truss Influence Lines and Moving Loads	204	(21)
Influence Lines for Trusses	204	(1)
Arrangement of Bridge Floor Systems	204	(2)
Influence Lines for Truss Reactions	206	(1)
Influence Lines for Member Forces of Parallel-Chord Trusses	206	(2)
Influence Lines for Members Forces of Nonparallel Chord Trusses	208	(2)
Influence Lines for K Truss	210	(1)
Determination of Maximum Forces	211	(2)
Counters in Bridge Trusses	213	(2)
Live Loads for Highway Bridges	215	(4)
Live Loads for Railway Bridges	219	(1)
Maximum Values for Moving Loads	220	(3)
Problems for Solution	223	(2)
Deflections and Angle Changes Using Geometric Methods	225	(23)
Introduction	225	(1)
Sketching Deformed Shapes of Structures	225	(5)
Reasons for Computing Deflections	230	(2)
The Moment-Area Theorems	232	(2)
Application of the Moment-Area Theorems	234	(7)
Analysis of Fixed-End Beams	241	(2)
Maxwell's Law of Reciprocal Deflections	243	(2)
Problems for Solution	245	(3)
Deflections and Angle Changes Using Geometric Methods Continued	248	(16)
The Method of Elastic Weights	248	(1)
Application of the Method of Elastic Weights	249	(5)
Limitations of the Elastic-Weight Method	254	(1)
Conjugate-Beam Method	255	(2)
Summary of Conjugate Beams	257	(1)
Equilibrium	257	(1)
Summary of Beam Relations	258	(1)
Application of the Conjugate Method to Beams	258	(2)
Long Term Deflections	260	(1)
Application of the Conjugate Method to Frames	261	(1)
Problems for Solution	261	(3)
Deflection and Angle Changes Using Energy Methods	264	(33)
Introduction to Energy Methods	264	(1)
Conservation of Energy Principle	264	(1)
Virtual Work or Complementary Virtual Work Method	265	(2)
Truss Deflections by Virtual Work	267	(2)
Application of Virtual Work to Trusses	269	(4)
Deflections of Beams and Frames by Virtual Work	273	(1)
Example Problems for Beams and Frames	274	(7)
Rotations or Angle Changes by Virtual Work	281	(2)
Introduction to Castigliano's Theorems	283	(1)
Castigliano's Second Theorem	284	(5)
Problems for Solution	289	(8)
PART TWO: STATICALLY INDETERMINATE STRUCTURES
Classical Methods
Introduction to Statically Indeterminate Structures	297	(8)
Introduction	297	(1)
Continuous Structures	298	(2)
Advantages of Statically Indeterminate Structures	300	(2)
Disadvantages of Statically Indeterminate Structures	302	(1)
Methods of Analyzing Statically Indeterminate Structures	302	(2)
Looking Ahead	304	(1)
Force Methods of Analyzing Statically Indeterminate Structures	305	(17)
Beams and Frames with One Redundant	305	(9)
Beams and Frames with Two or More Redundants	314	(2)
Support Settlement	316	(4)
Problems for Solution	320	(2)
Force Methods for Analyzing Statically Indeterminate Structures Continued	322	(25)
Analysis of Externally Redundant Trusses	322	(4)
Analysis of Internally Redundant Trusses	326	(3)
Analysis of Trusses Redundant Internally and Externally	329	(1)
Temperature Changes, Shrinkage, Fabrication Errors, and So On	330	(2)
Castigliano's First Theorem	332	(9)
Analysis Using Computers	341	(1)
Problems for Solution	342	(5)
Influence Lines for Statically Indeterminate Structures	347	(16)
Influence Lines for Statically Indeterminate Beams	347	(6)
Qualitative Influence Lines	353	(3)
Influence Lines for Statically Indeterminate Trusses	356	(4)
Problems for Solution	360	(3)
Slope Deflection: A Displacement Method of Analysis	363	(26)
Introduction	363	(1)
Derivation of Slope-Deflection Equations	363	(3)
Application of Slope Deflection to Continuous Beams	366	(3)
Continuous Beams with Simple Ends	369	(2)
Miscellaneous Items Concerning Continuous Beams	371	(1)
Analysis of Beams with Support Settlement	372	(2)
Analysis of Frames---No Sides way	374	(2)
Analysis of Frames with Sidesway	376	(6)
Analysis of Frames with Sloping Legs	382	(1)
Problems for Solution	382	(7)
PART THREE: STATICALLY INDETERMINATE STRUCTURES
Common Methods in Current Practice
Approximate Analysis of Statically Indeterminate Structures	389	(24)
Introduction	389	(1)
Trusses with Two Diagonals in Each Panel	390	(1)
Continuous Beams	391	(4)
Analysis of Building Frames for Vertical Loads	395	(3)
Analysis of Portal Frames	398	(2)
Analysis of Building Frames for Lateral Loads	400	(7)
Approximate Analyses of Frame Compared to ``Exact'' Analysis by SABLE32	407	(1)
Moment Distribution	408	(1)
Analysis of Vierendeel ``Trusses''	408	(2)
Problems for Solution	410	(3)
Moment Distribution for Beams	413	(20)
Introduction	413	(2)
Basic Relations	415	(2)
Definitions	417	(2)
Sign Convention	419	(1)
Application of Moment Distribution	419	(5)
Modification of Stiffness for Simple Ends	424	(1)
Shearing Force and Bending Moment Diagrams	425	(3)
Computer Solution with SABLE32	428	(2)
Problems for Solution	430	(3)
Moment Distribution for Frames	433	(28)
Frames with Sidesway Prevented	433	(2)
Frames with Sidesway	435	(2)
Sidesway Moments	437	(10)
Frames with Sloping Legs	447	(4)
Multistory Frames	451	(4)
Computer Analysis of Frame	455	(2)
Problems for Solution	457	(4)
Introduction to Matrix Methods	461	(9)
Structural Analysis Using the Computer	461	(1)
Matrix Methods	461	(1)
Review of Matrix Algebra	462	(1)
Force and Displacement Methods of Analysis	462	(1)
Introduction to the Force or Flexibility Method	463	(5)
Problems for Solution	468	(2)
Fundamentals of the Displacement or Stiffness Method	470	(24)
Introduction	470	(1)
General Relationships	470	(2)
Stiffness Equations for Axial Force Members	472	(6)
Stiffness Equations for Flexural Members	478	(9)
Stiffness Matrix for Combined Axial and Flexural Members	487	(2)
Characteristics of Stiffness Matrices	489	(1)
Relation Between Stiffness and Flexibility Matrices	490	(2)
Problems for Solution	492	(2)
Stiffness Matrices for Inclined Members	494	(24)
General	494	(1)
Axial Force Members	494	(6)
Flexural Members	500	(10)
Loading Between Nodes	510	(5)
Problems for Solution	515	(3)
Additional Matrix Procedures	518	(55)
General	518	(1)
Addition of Stiffness Equations	518	(2)
Stiffness Matrices for Inclined Members	520	(3)
Stiffness Equations for Structures with Enforced Displacements	523	(1)
Stiffness Equations for Structures with Members Experiencing Temperature Changes	524	(2)
Stiffness Equations for Structures Whose Members Have Incorrect Lengths	526	(1)
Applications of Matrix Partitioning	526	(1)
Condensation	527	(1)
Band Width of Stiffness Matrices for General Structures	528	(3)
Problems for Solution	531	(2)
APPENDICES
Appendix A The Catenary Equation	533	(5)
Appendix B Matrix Algebra	538	(15)
B.1 Introduction	538	(1)
B.2 Matrix Definitions and Properties	538	(1)
B.3 Special Matrix Types	539	(1)
B.4 Determinant of a Square Matrix	540	(1)
B.5 Adjoint Matrix	541	(1)
B.6 Matrix Arithmetic	542	(5)
B.7 Gauss's Method for Solving Simultaneous Equations	547	(1)
B.8 Special Topics	548	(5)
Appendix C Wind, Seismic, and Snow Load Tables and Figures	553	(12)
Appendix D Computer Analysis of Various Structures Using SAP2000	565	(8)
D.1 Introduction	565	(1)
D.2 Analysis of Plane Trusses	565	(2)
D.3 Analysis of Space Trusses	567	(1)
D.4 Analysis of Statically Indeterminate Plane Trusses	568	(2)
D.5 Analysis of Composite Structures	570	(1)
D.6 Analysis of Continuous Beams and Frames	571	(2)
Glossary	573	(6)
Index	579