**Solid Mechanics Lecture Notes**

CONTENTS

1. Introduction

Static and Solid Mechanics

Three Basic Criteria in Design and Analysis of Structures

Fundamental Assumption

Basic Condition in Analysis

Quantities to be Calculated

2. Plain Truss

Basic Truss Structure

Method of Joints

Method of Sections

3. Beam

Introduction

Shear Force and Bending Moment

Sign Convention

Distributed Loads

Shear Force and Bending Moment Diagram

Relationship between load, BM and SF

Applications in sketching BM and SF diagrams

Characteristics of SF and BM diagrams

Superposition method for constructing BM and SF diagram

Centroid of Plane Areas

Moment of Inertia of Plane Areas

Parallel – Axis Theorem

Polar Moment of Inertia

4. Stress and Strain

Deformable Body: Normal Stress and Normal Strain

St. Venant’s Principle

Stress-Strain Diagram

Elasticity and Plasticity

Linear Elasticity

Hooke’s Law

Shear Stress and Bearing Stress

Shear Strain

Shear Stress and Strain

Bearing Stress

Properties of Shear Deformation

Sign Convention for Stress and Strain

Poisson’s Ratio and Shear Modulus

Volume Change and Dilatation

Allowable Stress and Allowable Load

Stress on Inclined Sections

Strain Energy

Stress Concentration

Fatigue

Creep and Relaxation

Deformation of Axially Loaded Members

Stiffness and Flexibility

Temperature Effect

Statically Indeterminate Structures

Force Method

Displacement Method

More examples on statically indeterminate structures

Torsion of Circular Bars

Non-uniform Torsion

Statically Indeterminate Torsional Member

Pure Shear

Relationship Between Moduli E and G

Torsion of thin-walled tube

Pure Bending and Non-uniform Bending

Curvature of a Beam

Longitudinal Strains in Beam

Normal Stress in Beam

Design of Beam for Bending Stress

Shear Stress in Beams of Rectangular Cross Section

Shear Stress in I-beams

Built-up Beams and Shear Flow

Beams with Axial Loads

Composite Beams

Transformed-Section Methods

Doubly Symmetric Beams with Inclined Loads

The Shear Center Concept

Introduction (combined loading)

Plane Stress

Principal Stresses and Maximum Shear Stresses

Mohr’s Circle for Plane Stress

Hooke’s Law for Plane Stress

Triaxial Stress

Plane Strain

Introduction

Buckling and Stability

Columns with Pinned Ends

Columns with Other Support Conditions

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