## COURSE OBJECTIVES

This course is the foundation to many advanced techniques that allow engineers to design machine components, mechanisms, predict failure and understand the physical properties of materials. Mechanics of Materials gives the student basic tools for stress, strain and deformation analysis. Methods for determining the stresses, strains and deformations produced by applied loads are presented. Engineering design concepts are integrated throughout the course. At the completion of the course, students must be able to:

• Analyze and design components and structural members subjected to tension, compression, torsion, bending and combined loads using fundamental concepts of stress, strain, elastic and inelastic behavior.
• Conduct themselves in a professional manner and with regard to their responsibilities to society; especially with regard to design of mechanisms and prevention of failure.
• Communicate their results and conclusions effectively.
• Recognize the nature of a comp

## COURSE LEARNING OUTCOMES (CLO)

CLO-1: Comprehend key concepts, such as stresses and strains and constitutive relationships. (C2)
CLO-2: Analyze statically determinate and indeterminate structures for safety based on strength or deflection considerations. (C4)
CLO-3: Write a report for an assigned research project related to solid mechanics. (A2)

## COURSE CONTENTS

1. Introduction to Stress Analysis – Six Lectures
• Review of Fundamentals and Introduction to the Stress
• Direct stresses (normal and shear) in axial members and connections (force method/equilibrium considerations for 1D problems) under a variety of loading scenarios (i.e. direct axial and direct shear cases)
• Stresses for 1 D axial problems under distributed loads and body forces.
• Stress as a design criterion and design /analysis examples
• Direct determination of Biaxial stresses in case of stresses on inclined plane and stresses in thin walled pressure vessels.
• Introduction to Stress concentrations and use of stress concentration factors in design for direct stresses
• Introduction to the 3D Stress tensor, complementary property of shear and differential form of equilibrium equations.

2. Introduction to Strain Analysis – Four Lectures

• Introduction to displacement field, the 3D Strain tensor and strain displacement relations
• Direct determination of strain components for axial and shear loading.
• Direct determination of strain for distributed loading using integration method.
• Indirect determination of stress from strain using constitutive relations.

3. Mechanical Properties of Solids (The Constitutive relations) – Four Lectures

• Experimental determination of constitutive relations and introduction to strain gauges
• Elastic plastic constitutive laws and usage of idealized material models
• Strain energy and modulus of resilience.
• Thermal Stresses and relevant constitutive relations.
• Three dimensional Hook’s Law for isotropic Materials
• Relationship between E, G and v
• Dilation and Bulk Modulus

4. Stress and strain analysis for axially loaded members – Six Lectures

• Bringing together the equilibrium, compatibility and constitutive equations
• Examples relate to point loads, distributed loads, rotating assemblies, thermally induced loads and residual stresses for compound members (i.e. structurally composite members)

5. Stress & Strain analysis for member under torsional loading – Six Lectures

• Torsion of Circular Members and power transmission shafts
• Derivation of torsional formula for thin walled and thick walled cylinders
• Torsion loading of co-axial compound shafts
• Gear basics and Motor driven shafts (power transmission)
• Stress Concentrations in shafts
• Torsion of non-circular members
• Torsion in thin walled arbitrary shaped sections
• Torsional analysis for combined elastic-plastic deformation

6. Bending loads (beams) – Six Lectures

• Principle of moments, centroids and moment of inertia.
• Shear force diagrams and bending moment diagrams.
• Flexure Formula
• Unsymmetrical Bending
• Composite Beams
• Inelastic Bending