Bending and Shear Stress MCQs – Part 5

6 questions. Tap an option to check it instantly, then read the solution.

Question 61Hard

Keeping the breadth b constant, the depth of a cantilever of length l and uniform strength, carrying a UDL w, varies from zero at the free end to ______ at the fixed end.

Full explanation

Answer: B. √(3w/(σb)) × l

wx²/2 = σ·b d²/6 ⇒ d = x√(3w/(bσ)); at x = l: d = l√(3w/(bσ)).

Question 62Easy

In a section undergoing pure bending, the neutral surface is subjected to:

Full explanation

Answer: C. zero strain

ε = y/R; at the neutral surface y = 0 ⇒ ε = 0.

Question 63Medium

Pick the incorrect statement. The intensity of horizontal shear stress at a layer of a beam section is directly proportional to:

Full explanation

Answer: D. the moment of inertia of the beam section about its neutral axis

τ = VAȳ/(Ib): τ ∝ V, A, ȳ but inversely ∝ I.

Question 64Medium

A pile of length L is lifted at two points. For the hogging moment at the two points of suspension to equal the sagging moment at the centre, the distance of each suspension point from its nearer end is:

Full explanation

Answer: B. 0.207 L

wa²/2 = wL²/8 − wLa/2 ⇒ a² + La − L²/4 = 0 ⇒ a = (√2 − 1)L/2 = 0.207L.

Question 65Medium

The maximum allowable shear stress in a material is 100 kg/cm². A square bar of this material carries a tensile force of 5000 kg. The side of the square should be:

Full explanation

Answer: B. 5 cm

Axial tension: τmax = σ/2 on 45° planes. 100 = 5000/(2a²) ⇒ a² = 25 ⇒ a = 5 cm.

Question 66Medium

The bending moment M is constant over a length l of a beam. The shear force over this length is:

Full explanation

Answer: D. none of the above

V = dM/dx. If M is constant, dM/dx = 0, so V = 0 — none of the listed values. (The book's key gives (a) M/l.)