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Solid Mechanics Lecture Notes

  



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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