Strength of Materials (Mech)

Stress and Strain:

• Stress = Force/Area (units: N/m² = Pa).
• Strain = Δ length / original length (dimensionless).
• Young's Modulus Y = stress/strain (elastic range).
• Hooke's Law: stress = Y × strain.

Types of stress:

• Tensile: stretching.
• Compressive: squeezing.
• Shear: parallel to face.
• Bulk: volume change.

Poisson's ratio: ν = lateral strain / longitudinal strain. Typical 0.2-0.5.

Beams:

• Cantilever: fixed at one end, free at other.
• Simply supported: supported at both ends.
• Continuous: supported at 3+ points.

Bending moment & shear force diagrams:

• M = ∫V dx; V = ∫w dx.
• Maximum BM occurs where SF = 0.

Flexure formula: σ/y = M/I = E/R.
Where σ = stress at distance y from neutral axis; M = BM; I = moment of inertia; R = radius of curvature.

Torsion:
τ/r = T/J = Gθ/L.
Where τ = shear stress at distance r; T = torque; J = polar MI; G = rigidity modulus; θ = angle of twist; L = length.

Columns:

• Euler formula: P_cr = π²EI/L² (for long columns).
• Slenderness ratio = L/k.

RRB JE focus: numerical on simple beams, basic stress/strain, Euler buckling.