Shear Stress And Bending Stress in Strength Of Materials : Practice MCQ Questions & Answers with Explanations

Explanation Shear stress at any point in a cross-section is given by the following formula: ${\rm{f}} = \frac{{{\rm{VQ}}}}{{{\rm{Ib}}}}$ Where, f = shear stress Q = First moment of area about the neutral axis of the area above the point where we want to calculate the shear stress Q = A × y V is Shear force y is the centroid of the area above the point where we want to calculate the shear stress measured from the neutral axis. A = Cross-sectional area above the point where we want to calculate the shear stress I = moment of inertia about the neutral axis b= width of the section where shear stress is to be calculated. Shear stress is zero at extreme fibres For a symmetric ‘I’ section, the intensity of shear stress is maximum at the centroid of the section which is neutral axis as shown in the figure.

Explanation: Bending equation states that: $\frac{\sigma }{y} = \frac{M}{I} = \frac{E}{R}$ Various terms in above bending equation are: σ = Bending stress y = Distance from neutral axis M = Bending moment I = Area moment of inertia E = Modulus of elasticity R = Radius of curvature Bending Stress distribution for I section: Bending stress is directly proportional to y (Distance from the neutral axis). Bending stress will be zero at neutral axis. The maximum stress always occurs at the outermost fibre.