Home/MCQ Practice/Strength of Materials MCQs/Bending Moment and Shear Force

Structures·MCQ practice

Bending Moment and Shear Force MCQs – Part 1

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

Practice SSC JE and other civil engineering exam questions on shear force and bending moment: support reactions, SFD and BMD of cantilevers, simply supported and overhanging beams, point loads, UDL, triangular loads and applied couples, points of contraflexure, the load–shear–moment relations, and a few related questions on elastic constants that the book places in this chapter. Tap an option to check it, then open the full explanation for each question.

Question 1Easy
For a linearly elastic, homogeneous and isotropic material with modulus of rigidity G and modulus of elasticity E, the range of G is:
Full explanation

Answer: D. E/3 to E/2

E = 2G(1 + μ) with 0 ≤ μ ≤ 0.5. μ = 0 gives G = E/2; μ = 0.5 gives G = E/3. So G lies between E/3 and E/2.

Question 2Easy
The modulus of elasticity of a material is:
Full explanation

Answer: B. only defined in the linearly elastic region

E = stress/strain holds only where stress is proportional to strain — the linearly elastic region. It has the unit of stress.

Question 3Medium
A cantilever beam AB of length l carries a downward load P at its free end and an upward load P at a distance x from the free end. The shear force will be:
Full explanation

Answer: D. equal to P, between the two point loads

Between the loads only the end load P acts on one side of a section, so V = P. Beyond the upward load the two cancel and V = 0.

Question 4Medium
A material has a modulus of elasticity equal to 3 times its modulus of rigidity. Which of the following statements may be INCORRECT?
Full explanation

Answer: C. There is a change in the volume of the material.

E = 3G gives μ = 0.5, so K = E/3(1 − 2μ) = ∞ and volumetric strain is zero: the volume does not change. Statement (c) is wrong.

Question 5Easy
If a cantilever beam is subjected to an upward point load at the free end, the nature of the stresses developed will be:
Full explanation

Answer: D. compressive above the neutral axis and tensile below the neutral axis of the beam cross-section

An upward end load bends the cantilever concave upward: top fibres shorten (compression), bottom fibres lengthen (tension).

Question 6Medium
An overhanging beam CADEBF rests on supports A and B (AB = 4.5 m). The left overhang CA is 1.5 m and a UDL of 9 kN/m acts over 3 m from C to D; a 5 kN point load acts at E, 1.8 m left of B; the right overhang BF is 1.5 m and carries a UDL of 3 kN/m. Ignoring signs, the sum of the bending moments at A and B is:
Full explanation

Answer: B. 13.50 kN·m

M_A = 9 × 1.5²/2 = 10.125 kN·m (left overhang); M_B = 3 × 1.5²/2 = 3.375 kN·m (right overhang). Sum = 13.5 kN·m.

Question 7Easy
The ratio of Young's moduli of two materials, E₁/E₂, is 2.5. Bars of the two materials have the same length and area and carry the same force P. The ratio of their elongations δl₁/δl₂ is:
Full explanation

Answer: D. 0.4

δl = PL/AE; with P, L, A equal, δl ∝ 1/E. δl₁/δl₂ = E₂/E₁ = 1/2.5 = 0.4.

Question 8Easy
A simply supported beam of length 4 m carries a UDL of 10 kN/m over the entire span. The maximum shear force anywhere in the beam is:
Full explanation

Answer: B. 20 kN

Total load 40 kN, shared equally: R_A = R_B = 20 kN. Shear is greatest at the supports: 20 kN.

Question 9Medium
A simply supported beam of span L carries a clockwise couple M at mid-span. The shear force at one-fourth of the span from the left support is:
Full explanation

Answer: D. M/L (−ve)

The reactions must form a counter-couple: R_B = M/L upward, R_A = M/L downward. Shear anywhere = −M/L.

Question 10Medium
A simply supported beam AB of span L carries a UDL w over the entire span. The bending moment at a distance L/4 from end A is:
Full explanation

Answer: D. 3wL²/32

R_A = wL/2. M = (wL/2)(L/4) − w(L/4)(L/8) = wL²/8 − wL²/32 = 3wL²/32.

Question 11Easy
A simply supported beam of span 6 m carries a UDL of 20 kN/m on the left half of the span. The support reactions are:
Full explanation

Answer: C. 45 kN (left), 15 kN (right)

Total load 60 kN at 1.5 m from A. R_B = 60 × 1.5/6 = 15 kN; R_A = 60 − 15 = 45 kN.

Question 12Easy
A cantilever 2 m long, fixed at the left end, carries 20 kN at 1 m from the fixed end and 30 kN at the free end. The bending moment at mid-span is:
Full explanation

Answer: A. 30 kN·m

From the free-end side, only the 30 kN load at 1 m acts: M = 30 × 1 = 30 kN·m.

Question 13Easy
A cantilever 2 m long, fixed at the left end, carries 20 kN at 1 m from the fixed end and 30 kN at the free end. The shear force and bending moment at the support are:
Full explanation

Answer: B. SF = 50000 N, BM = 80 kN·m

SF = 20 + 30 = 50 kN = 50000 N. BM = 30 × 2 + 20 × 1 = 80 kN·m.

Question 14Medium
A cantilever ABCD is fixed at A and carries 300 N at B (0.5 m from A), 500 N at C (0.7 m from B) and 800 N at the free end D (0.8 m from C). Identify the INCORRECT statement.
Full explanation

Answer: C. Shear force at point C is greater than that at point B.

SF: 800 N on CD, 1300 N on BC, 1600 N on AB — shear grows towards A, so SF at C is less than at B. BM: D 0, C 640, B 1550, A 2350 N·m.

Question 15Easy
A prismatic bar of cross-section 30 mm × 30 mm and length 1 m carries an axial tensile force of 90 kN. If the strain is 0.0005, Young's modulus is:
Full explanation

Answer: B. 200 × 10³ N/mm²

σ = 90 000/900 = 100 N/mm². E = σ/ε = 100/0.0005 = 2 × 10⁵ N/mm².