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## Learning Objective:

Upon completion of the course, students will be able to:

CLO1: Comprehend and utilize mathematical tools to describe problems in structural mechanics

CLO2: Develop mathematical descriptions of deformation of structures

CLO3: Evaluate the state of stress in structural components under different loading conditions

CLO4: Compute approximate solutions to problems in structural mechanics

## Description:

Studies of stress and strain, failure theories, and yield criteria; flexure and torsion theories for solid and thin-walled members; and energy methods.

## Topics Covered:

1. Introduction and Mathematical Preliminaries: Mechanics of solids/structures; Vector algebra; Tensors and matrices; Vector and tensor calculus
2. Kinematics of deformation: Deformation map and deformation gradient, rotation and stretch; Strain and physical significance; compatibility
3. Stress and equilibrium of deformable bodies: Free body diagrams; Traction and stress; Equilibrium and balance principles; First and second Piola-Kirchhoff stresses
4. Material models: Material frame indifference; objectivity; Hyperelasticity; Isotropy; Hooke's model
5. Boundary value problems in solid mechanics: Strong and Weak forms, 1D problems; 2D Plane stress/strain, examples; 3D strong forms and solution methods, examples; Principle of virtual work
6. Energy Methods and Variational principles: Directional derivative; Vainberg's theorem
7. Numerical solutions to boundary value problems: Ritz method; Introduction to the Finite element method
8. Structural mechanics of beams: Kinematic hypothesis; Stress resultants; Planar beam: Timoshenko & Bernoulli-Euler formulations
9. Structural mechanics of plates: Kinematic hypothesis; Stress resultants

https://purdue.brightspace.com

## Web Content:

Syllabus, grades, lecture notes, homework assignments, solutions and quizzes

## Homework:

3 homework problems assigned on Monday of each week - due in 2 parts:

• Part 1: Due by Friday of the week; Solution posted immediately after due date
• Part 2: Correct errors and make comments - due by Friday of the following week
• Late submissions will NOT be evaluated

## Projects:

Individual student-led computing projects assigned each week - due in 2 phases:

• Phase 1: Student completes the project, prepares slides and records a short video presenting their project - due by Saturday of the week
• Phase 2: Students conduct a peer evaluation of 3 of their peers on Circuit tool in addition to instructor evaluation - due by Saturday of the following week
• Late submissions will NOT be evaluated

## Exams:

Short quizzes based on the reading and videos - maximum 3 attempts

• Quiz attempt 1 due by Tuesday of the week
• Quiz attempts 2 and 3 due by the end of the week

## Textbooks (tentative):

### Required:

KD Hjelmstad, Fundamentals of Structural Mechanics, Springer, 2005
(PDF available through Purdue Libraries

## Computer Requirements:

MATLAB

Obtain and run MATLAB at Purdue:

https://engineering.purdue.edu/ECN/Support/KB/Docs/MatlabToolboxes

Complete a 2-hour self-paced crash course (called MATLAB Onramp) at:

https://www.mathworks.com/help/matlab/getting-started-with-matlab.html

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