Engineering reference for Indian students

Structural engineering

Strength of Materials

4 self-contained study topics — notes, diagrams, formulas, and worked examples for exams and GATE.

Topics

Fig 10.1 — Normal stress σ acts perpendicular to the cut area; shear stress τ acts parallel. Bending σ is linear in y; torsion τ is zero at the centre and maximum at the outer fibre.
Schematic diagram for study — aligned with standard B.Tech / GATE syllabus.
Loading types and corresponding stresses. Reference table — axial, shear, bending, and torsion with stress distributions (RK Bansal / standard SOM convention).
Stress and Strain Basics
Stress is internal force intensity $\sigma=P/A$ (normal) or $\tau=V/A$ (shear). Strain is relative deformation $\varepsilon=\delta/L$ or $\gamma=\delta_s/L$ . The engineering stress–strain curve (RK Bansal / GATE SOM) defines elastic limit, yield, UTS, and fracture; true stress–strain accounts for instantaneous area.
$\sigma=\dfrac{P}{A}$
Elastic Constants
Remember the two linking identities E = 2G(1 + μ) and E = 3K(1 − 2μ); given any two elastic constants you can solve for the other two by simple substitution.
Bending and Shear Stress
Use σ = M/Z for the extreme-fibre bending stress and τ = VQ/(Ib) for the transverse shear; the section modulus Z = bh²/6 turns most rectangular-beam numericals into a single division.
$I = \frac{bh^{3}}{12} for rectangle; Z = \frac{bh^{2}}{6}$
Columns and Buckling
Fix the effective length L_eff = KL from the end conditions first, then apply Euler P_cr = π²EI/L_eff² — nearly every mistake here comes from using the wrong K.