### Multiple Choice Questions and Answers (MCQs) on Strength of Materials

01. A cube subjected to three mutually perpendicular stress of equal intensity p expenses a volumetric strain

(A) 3p/E × (2/m – 1)
(B) 3p/E × (2 – m)
(C) 3p/E × (1 – 2/m)
(D) E/3p × (2/m – 1)

02. The strain energy stored in a solid circular shaft subjected to shear stress (τ), is: (Where G = Modulus of rigidity for the shaft material)

(A) τ²/ 2G × Volume of shaft
(B) τ/ 2G × Volume of shaft
(C) τ²/ 4G × Volume of shaft
(D) τ/ 4G × Volume of shaft

03. The strain energy stored in a solid circular shaft in torsion, subjected to shear stress (τ), is: (Where, G = Modulus of rigidity for the shaft material)

(A) τ²/ 2G × Volume of shaft
(B) τ/ 2G × Volume of shaft
(C) τ²/ 4G × Volume of shaft
(D) τ/ 4G × Volume of shaft

04. The stress induced in a body, when suddenly loaded, is ________ the stress induced when the same load is applied gradually.

(A) Equal to
(B) One-half
(C) Twice
(D) Four times

05. A material obeys hook’s law up to

(A) Plastic limit
(B) Elastic limit
(C) Yield point
(D) Limit of proportionality

06. A body is subjected to a tensile stress of 1200 MPa on one plane and another tensile stress of 600 MPa on a plane at right angles to the former. It is also subjected to a shear stress of 400 MPa on the same planes. The maximum normal stress will be

(A) 400 MPa
(B) 500 MPa
(C) 900 MPa
(D) 1400 MPa

07. The torque transmitted by a hollow shaft of outer diameter (d1) and inner diameter (d2) is (where τ = Maximum allowable shear stress)

(A) π/4 × τ × (d14 – d24)/d1
(B) π/16 × τ × (d14 – d24)/d1
(C) π/32 × τ × (d14 – d24)/d1
(D) π/64 × τ × (d14 – d24)/d1

08. If Th is the torque resisting capacity of a hollow shaft and Ts is that of a solid shaft, of the same material, length and weight. Then,

(A) Th > Ts
(B) Th < Ts
(C) Th = Ts
(D) None of these

09. If Kh is the torque resisting capacity of a hollow shaft and Ks is that of a solid shaft, of the same material, length and weight. Then,

(A) Kh > Ks
(B) Kh < Ks
(C) Kh = Ks
(D) None of these

10. After reaching the yielding stage while testing a mild steel specimen, strain

(A) Becomes constant
(B) Starts decreasing
(C) Increases without any increase in load
(D) None of the above

11. Principal planes are planes having

(A) Maximum shear stress
(B) No shear stress
(C) Minimum shear stress
(D) None of the above

12. If the slenderness ratio for a column is 100, then it is said to be a _________ column.

(A) Long
(B) Medium
(C) Short
(D) None of these

13. The torque transmitted by a solid shaft of diameter (D) is (where τ = Maximum allowable shear stress)

(A) π /4 × τ × D³
(B) π /16 × τ × D³
(C) π /32 × τ × D³
(D) π /64 × τ × D³

14. Young’s modulus of a wire is defined as the stress which will increase the length of wire compared to its original length by

(A) Half
(B) Same amount
(C) Double
(D) One-fourth

15. True stress strain-curve for materials is plotted between

(A) Load/original cross-sectional area and change in length/original length
(B) Load/ instantaneous cross-sectional area and loge (original area/ instantaneous area)
(C) Load/ instantaneous cross-sectional area and change in length/ original length (D) Load/ instantaneous area and instantaneous area/original area

16. A hollow shaft of same cross-section area as compared to a solid shaft transmit

(A) Same torque
(B) Less torque
(C) More torque
(D) Unpredictable

17. A steel bar of 5 mm is heated from 25°C to 45°C and it is free to expand. The bar will induce

(A) No stress
(B) Shear stress
(C) Tensile stress
(D) Compressive stress

18. Two shafts ‘A’ and ‘B’ transmit the same power. The speed of shaft ‘A’ is 250 r.p.m. and that of shaft ‘B’ is 300 r.p.m.

(A) The shaft ‘B’ has the greater diameter
(B) The shaft ‘A’ has the greater diameter
(C) Both are of same diameter
(D) None of these

19. The intensity of stress which causes unit strain is called

(A) Unit mass
(B) Modulus of rigidity
(C) Bulk modulus
(D) Modulus of Elasticity

20. A thick cylindrical shell having ro and ri as outer and inner radii, is subjected to an internal pressure (p). The maximum tangential stress at the inner surface of the shell is

(A) (ro2– ri2)/ 2p ri2
(B) 2p ri2/ (ro2 – ri2)
(C) p (ro2 + ri2)/ (ro2 – ri2)
(D) p (ro2– ri2)/ (ro2 + ri2)

21. A vertical column has two moments of inertia (i.e. Ixx and Iyy ). The column will tend to buckle in the direction of the

(B) Perpendicular to the axis of load
(C) Maximum moment of inertia
(D) Minimum moment of inertia

22. Strain energy is the

(A) Energy stored in a body when strained within elastic limits
(B) Energy stored in a body when strained up to the breaking of a specimen
(C) Maximum strain energy which can be stored in a body
(D) Proof resilience per unit volume of a material

23. The neutral axis of the cross-section a beam is that axis at which the bending stress is

(A) Zero
(B) Minimum
(C) Maximum
(D) Infinity

24. A composite bar made up of steel and copper bars of equal lengths are heated through 100°C. The stresses developed shall be

(A) Tensile in both the material
(B) Tensile in steel and compressive in copper
(C) Compressive in steel and tensile in copper
(D) Compressive in both the materials