Structural Analysis Fundamentals

Ramez Gayed, Amin Ghali

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000432541
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

Structural Analysis Fundamentals presents fundamental procedures of structural analysis, necessary for teaching undergraduate and graduate courses and structural design practice. It applies linear analysis of structures of all types, including beams, plane and space trusses, plane and space frames, plane and eccentric grids, plates and shells, and assemblage of finite-elements. It also treats plastic and time-dependent responses of structures to static loading, as well as dynamic analysis of structures and their response to earthquakes. Geometric nonlinearity in analysis of cable nets and membranes are examined.

This is an ideal text for basic and advanced material for use in undergraduate and higher courses. A companion set of computer programs assist in a thorough understanding and application of analysis procedures. The authors provide a special program for each structural system or each procedure. Unlike commercial software, the user can apply any program of the set without a manual or training period. Students, lecturers and engineers internationally employ the procedures presented in in this text and its companion website.

Ramez B. Gayed is a Civil Engineering Consultant and Adjunct Professor at the University of Calgary. He is expert on analysis and design of concrete and steel structures.

Amin Ghali is Emeritus Professor at the University of Calgary. He is consultant on major international structures. He is inventor of several reinforcing systems for concrete. He has authored over 300 papers and eight patents. His books include Concrete Structures (2012), Circular Storage Tanks and Silos (CRC Press, 2014), and Structural Analysis (CRC Press, 2017).

Chapter 1

Structural analysis modeling

DOI: 10.1201/9780429286858-1

1.1 Introduction

This book may be used by readers familiar with basic structural analysis and also by those with no previous knowledge beyond elementary mechanics. It is mainly for the benefit of people in the second category that Chapter 1 is included. It will present a general picture of the analysis but, inevitably, it will use some concepts that are fully explained only in later chapters. Readers may therefore find it useful, after studying Chapter 2 and possibly even Chapter 3, to reread Chapter 1.

The purpose of structures, other than aircraft, ships, and floating structures, is to transfer applied loads to the ground. The structures themselves may be constructed specifically to carry loads (for example, floors or bridges) or their main purpose may be to give protection from the weather (for instance, walls or roofs). Even in this case, there are loads (such as self-weight of the roofs and also wind forces acting on them) that need to be transferred to the ground.

Before a structure can be designed in a rational manner, it is essential to establish the loads on various parts of the structure. These loads will determine the stresses and their resultants (internal forces) at a given section of a structural element. These stresses or internal forces have to be within desired limits in order to ensure safety and to avoid excessive deformations. To determine the stresses (forces/unit area), the geometrical and material properties must be known. These properties influence the self-weight of the structure, which may be more or less than originally assumed. Hence, iteration in analysis may be required during the design process. However, consideration of this is a matter for a book on design.

The usual procedure is to idealize the structure by one-, two-, or three-dimensional elements. The lower the number of dimensions considered, the simpler the analysis. Thus, beams and columns, as well as members of trusses and frames, are considered as one-dimensional; in other words, they are represented by straight lines. The same applies to strips of plates and slabs. One-dimensional analysis can also be used for some curvilinear structures, such as arches or cables, and also certain shells. Idealization of structures by an assemblage of finite-elements, considered in Chapter 13, is sometimes necessary.

Idealization is applied not only to members and elements but also to their connections to supports. We assume the structural connection to the supports to be free to rotate(i.e. treat the supports as hinges), or to be fully restrained, that is, built-in or encastré. In reality, perfect hinges rarely exist, because of friction and also because nonstructural members such as partitions restrain free rotation. At the other extreme, a fully built-in condition does not recognize imperfections in construction or loosening owing to temperature cycling.

Once the analysis has been completed, members and their connections are designed: the designer must be fully conscious of the difference between the idealized structure and the actual outcome of construction.

The structural idealization transforms the structural analysis problem into a mathematical problem that can be solved by computer or by hand, using a calculator. The model is analyzed for the effects of loads and applied deformations, including the self-weight of the structure, superimposed stationary loads or machinery, live loads such as rain or snow, moving loads, dynamic forces caused by wind or earthquake, and the effects of temperature as well as volumetric change of the material (e.g. shrinkage of concrete). This chapter explains the type of results that can be obtained by different types of models.

Other topics discussed in this introductory chapter are: transmission (load path) of forces to the supports and the resulting stresses and deformations; axial forces in truss members; bending moments and shear forces in beams; axial and shear forces, and bending moments in frames; arches; the role of ties in arches; sketching of deflected shapes and bending moment diagrams; and hand checks on computer results.

1.2 Types of structures

Structures come in all shapes and sizes, but their primary function is to carry loads. The form of the structure, and the shape and size of its members are usually selected to suit this load-carrying function, but the structural forces can also be dictated by the function of the system of which the structure is part. In some cases, the form of the structure is dictated by architectural considerations.

The simplest structural form, the beam, is used to bridge a gap. The function of the bridge in Figure 1.1 is to allow traffic and people to cross the river: the load-carrying function is accomplished by transferring the weight applied to the bridge deck to its supports.

Figure 1.1 Highway bridge.

A similar function is provided by the arch, one of the oldest structural forms. Roman arches (Figure 1.2a) have existed for some 2000 years and are still in use today. In addition to bridges, the arch is also used in buildings to support roofs. Arches were developed because of confidence in the compressive strength of the material being used, and this material, stone, is plentiful. An arch made of stone remains standing, despite there be no cementing material between the arch blocks because the main internal forces are compressive. However, this has some serious implications, as we shall see later. The arch allows longer spans than beams with less material: today, some very elegant arch bridges are built of concrete (Figure 1.2b) or steel.

Figure 1.2 Arch bridges. (a) Stone blocks. (b) Concrete.

The third, simple form of structural type, is the cable. The cable relies on the tensile capacity of the material (as opposed to the arch, which uses the compressive capacity of the material) and hence its early use was in areas where natural rope-making materials are plentiful. Some of the earliest uses of cables are in South America where local people used cables to ...

Table of contents

• Cover
• Half-Title
• Title
• Copyright
• Contents
• Introduction to Structural Analysis Fundamentals
• Preface to Structural Analysis Fundamentals
• Notations
• The SI System of Units of Measurements
• Authors
• 1 Structural analysis modeling
• 2 Statically determinate structures
• 3 Introduction to the analysis of statically indeterminate structures
• 4 Force method of analysis
• 5 Displacement method of analysis
• 6 Time-dependant displacements in structural concrete
• 7 Strain energy and virtual work
• 8 Virtual work applications
• 9 Application of displacement method: Moment distribution
• 10 Effects of axial forces on flexural stiffness
• 11 Analysis of shear wall structures
• 12 Methods of finite differences and finite-elements
• 13 Finite-element analysis
• 14 Plastic analysis of plane frames
• 15 Yield-line analysis of reinforced concrete slabs
• 16 Structural dynamics
• 17 Response of structures to earthquakes
• 18 Nonlinear analysis
• 19 Computer analysis of framed structures
• 20 Computer programs
• Appendix A: Displacements of prismatic members
• Appendix B: Fixed-end forces of prismatic members
• Appendix C: End-forces caused by end displacements of prismatic members
• Appendix D: Reactions and bending moments at supports of continuous beams due to unit displacement of supports
• Appendix E: Properties of geometrical figures
• Appendix F: Torsional constant J
• Appendix G: Values of the integral ∫I Mu M dl
• Appendix H: Forces due to prestressing of concrete members
• Answers to problems
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• Index