Core Concepts
Statics
The study of forces on bodies at rest. ΣF = 0 and ΣM = 0.
Stress and Strain
Stress = Force/Area (σ = F/A). Strain = Deformation/Original Length (ε = ΔL/L). Young's Modulus: E = σ/ε.
Types of Loads
Dead loads (self-weight), Live loads (occupancy), Wind loads, Seismic loads, Snow loads, Impact loads.
Factor of Safety
Ratio of ultimate load to working load. FS = Ultimate Load / Allowable Load. Typically 1.5-3.0.
Worked Examples & Applications
Stress Calculation: Steel column: Load = 500 kN, Cross-section = 0.01 m². Stress σ = 500,000 N / 0.01 m² = 50,000,000 Pa = 50 MPa. Steel yield strength = 250 MPa. Factor of Safety = 250/50 = 5.0.
Beam Deflection: Maximum deflection for simply supported beam with point load at center: δ = (PL³)/(48EI). P = 10 kN, L = 4 m, E = 200 GPa, I = 0.0001 m⁴. δ = (10,000 × 64)/(48 × 200×10⁹ × 0.0001) = 0.000667 m = 0.67 mm.
Practice Questions
Q: What is the factor of safety? A: The ratio of the ultimate load a structure can withstand to the allowable working load. Higher FS = more conservative design.
Q: What is the difference between stress and strain? A: Stress is the internal force per unit area (σ = F/A). Strain is the resulting deformation per unit length (ε = ΔL/L).