Examples in Structural Analysis, Second Edition Textbook by William M.C. McKenzie

Book Description

This second edition of Examples in Structural Analysis uses a step-by-step approach and provides an extensive collection of fully worked and graded examples for a wide variety of structural analysis problems. It presents detailed information on the methods of solutions to problems and the results obtained. Also given within the text is a summary of each of the principal analysis techniques inherent in the design process and where appropriate, an explanation of the mathematical models used.

The text emphasises that software should only be used if designers have the appropriate knowledge and understanding of the mathematical modelling, assumptions and limitations inherent in the programs they use. It establishes the use of hand-methods for obtaining approximate solutions during preliminary design and an independent check on the answers obtained from computer analyses.

What’s New in the Second Edition:

New chapters cover the development and use of influence lines for determinate and indeterminate beams, as well as the use of approximate analyses for indeterminate pin-jointed and rigid-jointed plane-frames. This edition includes a rewrite of the chapter on buckling instability, expands on beams and on the use of the unit load method applied to singly redundant frames. The x-y-z co-ordinate system and symbols have been modified to reflect the conventions adopted in the structural Eurocodes.

William M. C. McKenzie is also the author of six design textbooks relating to the British Standards and the Eurocodes for structural design and one structural analysis textbook. As a member of the Institute of Physics, he is both a chartered engineer and a chartered physicist and has been involved in consultancy, research and teaching for more than 35 years.

Table of Contents

1. Structural Analysis and Design

Introduction

Equilibrium

Mathematical Modelling

Structural Loading

Statical Indeterminacy

Structural Degrees-of-Freedom

2. Material and Section Properties

Introduction

Elastic Cross-Section Properties

Plastic Cross-Section Properties

Example 2.1: Plastic Cross-section Properties – Section 1

Problems: Plastic Cross-section Properties

Solutions: Plastic Cross-section Properties

3. Pin-Jointed Frames

Introduction

Method of Sections

Method of Joint Resolution

Method of Tension Coefficients

Unit Load for Deflection

Unit Load Method for Singly-Redundant Pin-Jointed Frames

4. Beams

Statically Determinate Beams

McCaulay’s Method for the Deflection of Beams

Equivalent Uniformly Distributed Load Method for the Deflection of Beams

The Principle of Superposition

Unit Load for Deflection of Beams

Statically Indeterminate Beams

Moment Distribution Method for Multi-Redundant Beams

Redistribution of Moments

Shear Force and Bending Moment Envelopes

5. Rigid-Jointed Frames

Rigid-Jointed Frames

Unit Load Method for Singly-Redundant, Rigid-Jointed Frames

Moment Distribution for No-Sway, Rigid-Jointed Frames

Moment Distribution for Rigid-Jointed Frames with Sway

6. Buckling Instability

Introduction

Secondary Stresses

Critical Stress

Perry-Robertson Formula

European Column Curves

Example 6.1: Slenderness

Example 6.2: Rolled Universal Column Section

Example 6.3: Compound Column Section

Built-up Compression Members

Example 6.4: Laced Built-up Column

Problems: Buckling Instability

Solutions: Buckling Instability

7. Direct Stiffness Method

Direct Stiffness Method of Analysis

Element Stiffness Matrix

Structural Stiffness Matrix

Structural Load Vector

Structural Displacement Vector

Element Displacement Vector

Element Force Vector

Example 7.1: Two-span Beam

Example 7.2: Rigid-Jointed Frame

Problems: Direct Stiffness Method

Solutions: Direct Stiffness Method

8. Plastic Analysis

Introduction

Static Method for Continuous Beams

Kinematic Method for Continuous Beams

Problems: Plastic Analysis – Continuous Beams

Solutions: Plastic Analysis – Continuous Beams

Rigid-Jointed Frames

Problems: Plastic Analysis – Rigid-Jointed Frames

Solutions: Plastic Analysis – Rigid-Jointed Frames

Example 8.6: Joint Mechanism

Problems: Plastic Analysis – Rigid-Jointed Frames

Solutions: Plastic Analysis – Rigid-Jointed Frames

Gable Mechanism

Instantaneous Centre of Rotation

Example 8.7: Pitched Roof Frame

Problems: Plastic Analysis  Rigid-Jointed Frames

Solutions: Plastic Analysis  Rigid-Jointed Frames

9. Influence Lines for Beams

Introduction

Example 9.1: Influence Lines for a Simply Supported Beam

Müller-Breslau Principle for the Influence Lines for Beams

Influence Lines for a Statically Determinate Beam

Example 9.3: Influence Line for a Statically Indeterminate Beam

The use of Influence Lines

Example 9.6: Evaluation of Functions for a Statically Indeterminate Beam

Train of Loads

Problems: Influence Lines for Beams

Solutions: Influence Lines for Beams

10. Approximate Methods of Analysis

Introduction

Example 10.1 – Statically Indeterminate Pin-jointed Plane Frame

Example 10.2 – Statically Indeterminate Pin-jointed Plane Frame

Example 10.3 – Statically Indeterminate Single-span Beam

Example 10.4 – Multi-span Beam

Rigid-jointed Frames Subjected to Vertical Loads

Multi-storey, Rigid-jointed Frames Subjected to Horizontal Loads

Appendices

Index