Strength of Materials and Structural Analysis
Strength of materials and structural analysis tests your ability to compute stress, strain, bending, shear, deflection and stability, and to read shear-force and bending-moment diagrams. BTSC JE questions are numerical and formula-based, with a few conceptual items on determinacy and trusses.
Core rules
- Axial stress σ = P/A; strain ε = δL/L; Hooke’s law σ = Eε. Steel E ≈ 200 GPa; concrete modulus is 5000√fck N/mm² per IS 456.
- Bending: σ/y = M/I = E/R. Shear: τ = VQ/(Ib); average shear is V/A.
- A simply supported beam under UDL w over span L has maximum BM wL²/8 at midspan and maximum shear wL/2 at supports. A cantilever with UDL has maximum BM wL²/2 at the fixed end.
- Euler buckling load Pcr = π²EI/Le²; slenderness ratio = Le/r.
- A determinate structure has reactions equal to available equilibrium equations; indeterminacy is the excess.
Worked example
A 6 m simply supported beam carries a UDL of 10 kN/m. Maximum BM = wL²/8 = 10 × 6²/8 = 45 kNm; maximum shear = wL/2 = 30 kN. For a 300 mm × 500 mm rectangular section, I = bd³/12 = 300 × 500³/12 = 3.125 × 10⁹ mm⁴, and y = 250 mm. Bending stress = My/I = (45 × 10⁶ Nmm × 250 mm)/(3.125 × 10⁹ mm⁴) = 3.6 N/mm². Average shear stress = 30,000/(300 × 500) = 0.20 N/mm².
Traps
Forgetting to convert kNm to Nmm; using wL²/12 for a simply supported beam; placing maximum shear at midspan; using clear span instead of effective span.