Bending and Shear Stress MCQs – Part 4

Question 46Medium

For a given shear force across a symmetrical I-section, the intensity of shear stress is maximum at the:

Answer: B. centroid of the section

τ jumps up at the junction (on the web side), then keeps rising parabolically to its peak at the centroid (neutral axis).

Question 47Easy

The most efficient and economical section used as a beam is:

Full explanation

Answer: A. I-section

The I-section puts most of its area in the flanges, far from the neutral axis, giving the largest Z per unit weight.

Question 48Medium

For a given stress, the ratio of the moment of resistance of a square beam placed with two sides horizontal to that with a diagonal horizontal is:

Full explanation

Answer: D. √2

Same I = b⁴/12 in both positions; y_max = b/2 versus b/√2. Z ratio = (b/√2)/(b/2) = √2.

Question 49Easy

The centre of gravity of an equilateral triangle with each side a is at a distance of ______ from any of the three sides.

Full explanation

Answer: B. a/(2√3)

Height h = √3a/2; centroid at h/3 = √3a/6 = a/(2√3) from each side.

Question 50Easy

A cantilever AB, fixed at A and free at B, carries no transverse load (only a couple acts at the free end). The absolute value of the shear force at A is:

Full explanation

Answer: C. 0 kN

No vertical force acts on the beam, so the vertical reaction and the shear force everywhere are zero.

Question 51Easy

For a beam with a rectangular cross-section, the shear stress at the neutral axis is always:

Full explanation

Answer: B. maximum

The parabolic distribution peaks at the N.A.: τmax = 1.5τavg.

Question 52Hard

A bar of square section (area a²) is placed with one diagonal vertical. The maximum shear stress develops at a depth h below the top corner, where h is:

Full explanation

Answer: B. 3√2a/8

τ ∝ (a/√2)x − 2x²/3. dτ/dx = 0 ⇒ x = 3a/(4√2) = 3√2a/8 from the top corner (d/8 from the N.A., d = diagonal).

Question 53Medium

The shear centre of a thin half-circular (semicircular) section of radius r and constant thickness lies at a distance x from the centre, where x is:

Full explanation

Answer: D. 4r/π

Moment of the shear flow about the centre: e = 4r/π (outside the arc, on the side away from the opening).

Question 54Medium

A cantilever of length l and uniform strength carries a UDL w. Keeping the depth d constant, the width varies from zero at the free end to ______ at the fixed end.

Full explanation

Answer: B. (3w/σd²) × l²

M = wx²/2 = σ·bd²/6 ⇒ b = 3wx²/(σd²); at x = l: b = 3wl²/(σd²).

Question 55Easy

The ratio of maximum shear stress to average shear stress in a circular beam is:

Full explanation

Answer: D. 4/3

Solid circle: τmax = (4/3)τavg.

Question 56Medium

An I-section has flanges 100 mm wide × 20 mm thick and a web 80 mm high × 20 mm thick. The shear stress at point P (in the flange, just above the flange–web junction) is 12 MPa. The shear stress at point Q (in the web, just below the junction) is:

Full explanation

Answer: B. 60 MPa

Same Aȳ and I just above and just below the junction, so τ ∝ 1/b: 12 × 100/20 = 60 MPa.

Question 57Easy

The ratio of the flexural rigidity of a beam of section b × d to that of another beam of section b × 2d of the same material is:

Full explanation

Answer: C. 1/8

EI ∝ d³ ⇒ (d/2d)³ = 1/8.

Question 58Easy

For a beam of uniform strength with constant depth:

Full explanation

Answer: A. width is directly proportional to the bending moment

σ = 6M/(bd²) constant, d constant ⇒ b ∝ M.

Question 59Easy

A rectangular beam of uniform strength, subjected to a bending moment M, has a constant width. The depth varies in proportion to:

Full explanation

Answer: C. √M

σ = 6M/(bd²) constant, b constant ⇒ d² ∝ M ⇒ d ∝ √M.

Question 60Medium

A double-U butt weld connects two plates of section 200 mm (depth d) × 20 mm (width b). If the weld is subjected to a moment of 10 000 kN·mm, the stress developed in the weld is:

Full explanation

Answer: D. 75 N/mm²

Z = bd²/6 = 20 × 200²/6 = 133 333 mm³. σ = 10⁷/133 333 = 75 N/mm².