Strength of Materials and Machine Design
Strength of Materials and Machine Design tests stress analysis, failure criteria, fatigue, buckling, and design of shafts, joints, and pressure components.
Core rules and concepts
- Normal stress sigma=F/A and strain epsilon=delta/L; Hooke's law sigma=E epsilon in the elastic range. Shear stress is tau=VQ/(It) in beams and tau=T r/J in torsion.
- Bending stress sigma=M y/I; deflection depends on boundary conditions and stiffness EI.
- Combined loading requires principal stresses: sigma_1,2=(sigma_x+sigma_y)/2 plus or minus sqrt[((sigma_x-sigma_y)/2)^2+tau_xy^2].
- Fatigue uses S-N curves and the endurance limit; stress concentration K_t multiplies nominal stress, with notch sensitivity for fatigue.
- Euler buckling P_cr=pi^2 EI/(KL)^2; slenderness determines whether buckling or yielding governs.
Worked example
A solid circular shaft carries torque T=500 N m with diameter d=40 mm. Polar moment J=pi d^4/32=pi(0.04)^4/32=2.513 x 10^-7 m^4. Maximum shear stress tau=T c/J=T(d/2)/J=500 x 0.02/(2.513 x 10^-7)=39.8 x 10^6 Pa, or 39.8 MPa. If allowable shear is 40 MPa, the design is marginal; a safety factor must be applied to the allowable or the load.
Traps
Using radius where diameter is required, mixing MPa and Pa, forgetting stress concentration at fillets, and applying Euler buckling outside the elastic slenderness range are common. Fatigue failures occur below yield, so yield checks alone are insufficient.