Mechanics of Structures and Strength of Materials
Scope of the domain
Mechanics of structures and strength of materials covers forces, equilibrium, supports, shear force, bending moment, stress, strain and elastic constants. The exam tests direct stress, Hooke's law and simple beam behaviour.
Core rules and concepts
- A force has magnitude, direction and point of application. For equilibrium, ΣF = 0 and ΣM = 0.
- Stress = load/area (N/mm² = MPa). Strain = change in length/original length (dimensionless).
- Hooke's law: stress is proportional to strain within the elastic limit; Young's modulus E = stress/strain.
- A simply supported beam with a central point load W over span L has reactions W/2 at each support and maximum bending moment WL/4 at mid-span.
- Shear force is the algebraic sum of vertical forces on one side of a section; bending moment is the sum of moments about that section.
Worked example
A steel rod of diameter 20 mm carries an axial tensile load of 50 kN. Area A = πd²/4 = π(20)²/4 = 314.16 mm². Stress σ = P/A = 50,000 N / 314.16 mm² = 159.2 N/mm². If the permissible stress is 165 N/mm², the rod is safe. Reasoning: convert kN to N and keep diameter in mm so the stress comes out in N/mm².
Traps
Do not use radius in place of diameter. Do not omit the kN-to-N conversion. Do not give Young's modulus in mm; its unit is N/mm². Do not treat bending moment and shear force as the same quantity. Watch the sign convention for sagging and hogging moments.