Structures · MCQ practice Bending and Shear Stress MCQs – Part 3
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Part 3 of 5 Question 31 Easy
The ratio of the maximum to the average shear stress on a rectangular section is:
A 1 B 1.25 C 1.5 D 2
Answer: C. 1.5
q_max = Fd²/(8I) = (3/2)F/(bd) ⇒ ratio 1.5.
Question 32 Easy
The moment of inertia of a circular section of diameter d about its diameter is:
A πd³/16 B πd⁴/32 C πd³/32 D πd⁴/64
Answer: D. πd⁴/64
Polar I = πd⁴/32; by the perpendicular axis theorem, I about a diameter = half of it = πd⁴/64.
Question 33 Medium
A simply supported beam of circular cross-section, diameter D and length l, carries a concentrated load W at the centre. The strength (load capacity) of the beam is proportional to:
A 1/D³ B 1/D² C D³/l D D²/l
Answer: C. D³/l
Wl/4 = σ·πD³/32 ⇒ W = πσD³/(8l) ∝ D³/l.
Question 34 Easy
The assumption(s) in the theory of bending of beams is/are:
A the material is homogeneous B the material is isotropic C Young's modulus is the same in tension and in compression D all options are correct
Answer: D. all options are correct
All three are standard assumptions of simple bending.
Question 35 Medium
Two beams, one of circular and the other of square cross-section, have equal areas of cross-section. When subjected to bending:
A the circular section is more economical B the square section is more economical C both sections are equally economical D both sections are equally stiff
Answer: B. the square section is more economical
Equal areas: a = 0.886d. Z_s/Z_c = (a³/6)/(πd³/32) = 1.18. The square resists more moment for the same material.
Question 36 Easy
The bending stress in a prismatic beam is given by:
A My/Z B My/I C MZ/y D MI/y
Answer: B. My/I
From M/I = σ/y: σ = My/I.
Question 37 Easy
The ratio of the moment of inertia about the neutral axis to the distance of the most distant point of the section from the neutral axis is called:
A polar modulus B section modulus C modulus of rupture D flexural rigidity
Answer: B. section modulus
Z = I / y_max is the section modulus.
Question 38 Easy
The section modulus of a rectangular section is:
A bd²/36 B bd³/6 C bd²/6 D bd³/12
Answer: C. bd²/6
Z = (bd³/12)/(d/2) = bd²/6.
Question 39 Easy
The shear stress distribution over a beam of solid circular section is such that:
A q_max = 2 q_mean B q_max = 1.5 q_mean C q_max = 1.33 q_mean D q_max = 1.25 q_mean
Answer: C. q_max = 1.33 q_mean
At the N.A. of a circle Aȳ = d³/12, b = d: q_max = Fd²/(12I) = (4/3)F/(πd²/4).
Question 40 Easy
(Mass) moment of inertia is a concept applicable in the case of:
A a rotating body B a body moving in a straight line C a body at rest D both (a) and (b)
Answer: A. a rotating body
Mass moment of inertia measures resistance to change in rotational motion — it applies to rotating bodies.
Question 41 Easy
The bending equation is written as:
A M/I = σb/y = E/R B I/M = σb/y = E/R C M/I = σb/y = R/E D M/I = y/σb = E/R
Answer: A. M/I = σb/y = E/R
M/I = σ/y = E/R.
Question 42 Easy
The moment of inertia of a rectangle of width d and depth b about its horizontal axis at mid-depth is:
A db³/12 B bd³/12 C bd³/3 D db³/3
Answer: A. db³/12
I = (width)(depth)³/12 = d·b³/12.
Question 43 Easy
Two beams of equal cross-sectional area are subjected to equal bending moments. If one beam has a square cross-section and the other a circular section:
A both beams will be equally strong B the circular section beam will be stronger C the square section beam will be stronger D the strength will depend on the nature of loading
Answer: C. the square section beam will be stronger
Equal areas: Z_square = 1.18 Z_circle, so the square has lower stress and is stronger.
Question 44 Easy
The maximum bending stress in an I-beam occurs at the:
A neutral axis B outermost fibre C junction of web and flange D section where shear stress is maximum
Answer: B. outermost fibre
σ = My/I is largest where y is largest — the outermost fibre.
Question 45 Easy
The shear stress at a distance y above the neutral axis (NA) of a prismatic beam due to a shear force V is:
A VAȳb/I B Vb/(AȳI) C VAȳ/(Ib) D VI/(bAȳ)
Answer: C. VAȳ/(Ib)
τ = VAȳ/(Ib): A = area above the level, ȳ = its centroid distance from the NA, b = width at the level.
Part 3 of 5