📘 Chapter

Notes

📘 Chapter 1: Introduction – Stress and Strain 1. Basic Concepts Mechanics of Materials studies how solid bodies deform and resist loads. Two key ideas: Stress → internal resistance forces within a material Strain → measure of deformation 2. Stress Normal Stress (axial loads): 𝜎 = 𝑃 𝐴 σ= A P ​ where 𝑃 P = axial load, 𝐴 A = cross-sectional area. Positive = tension Negative = compression Shear Stress (parallel to area): 𝜏 = 𝑉 𝐴 τ= A V ​ where 𝑉 V = shear force. Average stress vs. true distribution: Formula above assumes uniform stress (a simplification). In reality, stress can vary across the area. 3. Strain Normal Strain: 𝜀 = Δ 𝐿 𝐿 ε= L ΔL ​ (change in length / original length). Shear Strain: 𝛾 = tan ⁡ 𝜃 ≈ 𝜃 ( for small angles ) γ=tanθ≈θ(for small angles) where 𝜃 θ is the angular deformation. 4. Stress–Strain Relationships Hooke’s Law (Elastic Range): 𝜎 = 𝐸   𝜀 σ=Eε where 𝐸 E = Young’s modulus (stiffness of material). Shear Stress–Strain: 𝜏 = 𝐺   𝛾 τ=Gγ where 𝐺 G = shear modulus. Poisson’s Ratio ( 𝜈 ν): 𝜈 = − 𝜀 lateral 𝜀 axial ν=− ε axial ​ ε lateral ​ ​ Describes lateral contraction when stretched axiall...