Explore topic-wise MCQs in Strength of Materials.

This section includes 104 Mcqs, each offering curated multiple-choice questions to sharpen your Strength of Materials knowledge and support exam preparation. Choose a topic below to get started.

51.

A cantilever beam having square cross-section of side a is subjected to an end load, If a is increased by 19%, the tip deflection decreases approximately by

A. 19%
B. 29%
C. 41%
D. 50%
Answer» E.
Discussion
52.

A cantiever beam of length, L with uniform crossection and flexural rigidity, EI is loaded uniformly by a vertical load, w per unit length. The maximum vertical deflection of the beam is given by

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>wL<sup>4</sup></center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">8EI</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>wL<sup>4</sup></center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">16EI</td></tr></table>
C.
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>wL<sup>4</sup></center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">4EI</td></tr></table>
E. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>wL<sup>4</sup></center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">24EI</td></tr></table>
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>wL<sup>4</sup></center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">16EI</td></tr></table>
Discussion
53.

A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of the beam cross section about the neutral axis is I and the Young's modulus is E The magnitude of the maximum deflection is

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>ML </center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">3EI</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>ML </center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">EI</td></tr></table>
C.
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2ML </center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">2EI</td></tr></table>
E. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4ML </center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">EI</td></tr></table>
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>ML </center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">EI</td></tr></table>
Discussion
54.

A hollow shaft of 1 m length is designed to transmit a power of 30 kW at 700 rpm. The maximum permissible angle of twist in the shaft is 1 . The inner diameter of the shaft is 0.7 times the outer diameter. The modulus of rigidity is 80 GPa. The outside diameter (in mm) of the shaft is ______.

A. 45 mm
B. 44.5213 mm
C. 43.613 mm
D. 46.7213 mm
Answer» C. 43.613 mm
Discussion
55.

A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is 1 unit. Radius of the Mohr's circle, characterizing the state at that point, is

A. 0.5 unit
B. 0 unit
C. 1 unit
D. 2 units
Answer» C. 1 unit
Discussion
56.

The minimum axial compressive load, P required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is

A. <table><tr><td rowspan="2">P =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <sup>2</sup>EI</center></td><td rowspan="2"></td></tr><td align="center">4L<sup>2</sup></td></table>
B. <table><tr><td rowspan="2">P =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <sup>2</sup>EI</center></td><td rowspan="2"></td></tr><td align="center">L<sup>2</sup></td></table>
C. <table><tr><td rowspan="2">P =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3 <sup>2</sup>EI</center></td><td rowspan="2"></td></tr><td align="center">4L<sup>2</sup></td></table>
D. <table><tr><td rowspan="2">P =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4 <sup>2</sup>EI</center></td><td rowspan="2"></td></tr><td align="center">L<sup>2</sup></td></table>
Answer» C. <table><tr><td rowspan="2">P =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3 <sup>2</sup>EI</center></td><td rowspan="2"></td></tr><td align="center">4L<sup>2</sup></td></table>
Discussion
57.

A cantilever beam of length L and flexural modulus El is subjected to a point load Pat the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>P L<sup>3</sup></center></td></tr><td align="center">6EI</td></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>P L<sup>3</sup></center></td></tr><td align="center">4EI</td></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>P L<sup>3</sup></center></td></tr><td align="center">2EI</td></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>P L<sup>3</sup></center></td></tr><td align="center">8EI</td></table>
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>P L<sup>3</sup></center></td></tr><td align="center">4EI</td></table>
Discussion
58.

The state of stress at a point in a component is represented by a Mohr s circle of radius 100 MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point is ____ MPa.

A. 80 MPa
B. 79 MPa
C. 81 MPa
D. 70 MPa
Answer» B. 79 MPa
Discussion
59.

The value of maximum deflection of the beam is

A. 93.75 mm
B. 83.75 mm
C. 73.75 mm
D. 63.75 mm
Answer» B. 83.75 mm
Discussion
60.

The beam is subjected to a maximum bending moment of

A. 3375 kNm
B. 4750 kNm
C. 6750 kNm
D. 8750 kNm
Answer» B. 4750 kNm
Discussion
61.

A concentrated load P acts on a simply supported beam of span L at a distance L/3 from the left support. The bending moment at the point of application of the load is given by

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>PL</center></td></tr><td align="center">3</td></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2PL</center></td></tr><td align="center">3</td></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>PL</center></td></tr><td align="center">9</td></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2PL</center></td></tr><td align="center">9</td></table>
Answer» E.
Discussion
62.

For a simply supported beam on two end supports, the bending moment is maximum

A. usually on the supports
B. always at mid span
C. where there is no shear force
D. where the deflection is maximum
Answer» D. where the deflection is maximum
Discussion
63.

The state of stress at a point is

A. 50
B. 52
C. 55
D. 60
Answer» B. 52
Discussion
64.

In a plane stress condition, the components of stress at a point are

A. 20
B. 25
C. 50
D. 100
Answer» D. 100
Discussion
65.

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm

A. 1.788
B. 0.718
C. 1.718
D. 2.718
Answer» D. 2.718
Discussion
66.

A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is 200 MPa, the change in the strain is 0.001. If the Poisson's ratio of the rod is 0.3, the modulus of rigidity (in GPa) is

A. 76.92
B. 76.22
C. 76.72
D. 76
Answer» B. 76.22
Discussion
67.

The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic solid is _____.

A. G & are independent.
B. E & are independent.
C. G & E & are independent.
D. None of these
Answer» C. G & E & are independent.
Discussion
68.

The axial and circumferential stress ( a, c) experienced by the cylinder wall at mid-depth (m as shown) are

A. (10,10) MPa
B. (5,10) MPa
C. (10,5)MPa
D. (5, 5) MPa
Answer» C. (10,5)MPa
Discussion
69.

A 200 100 50 mm steel block is subjected to a hydro static pressure of 15 MPa. The Young's modulus and Poisson's ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in mm

A. 85
B. 90
C. 100
D. 110
Answer» C. 100
Discussion
70.

If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in%) is _______ (correct to two decimal places.)

A. 8.243%
B. 24%
C. 3%
D. 43%
Answer» B. 24%
Discussion
71.

A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is ___.

A. 6
B. 9
C. 1
D. 8
Answer» B. 9
Discussion
72.

A weighing machine consists of a 2 kg pan resting on a spring. In this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the undeformed length L and the spring constant k (stiffness) are

A. L = 220 mm, k= 1862 N/m
B. L = 210 mm, k= 1960 N/m
C. L = 200 mm, k = 1960 N/m
D. L = 200 mm, k= 2156 N/m
Answer» C. L = 200 mm, k = 1960 N/m
Discussion
73.

The figure shows arrangements of springs. They have stiffness k

A. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/Capture-1-a.png">
B. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/Capture-1-b.png">
C. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/Capture-1-c.png">
D. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/Capture-1-d.png">
Answer» E.
Discussion
74.

A motor driving a soiid circular steel shaft transmits 40 kW of power at 500 rpm. If the diameter of the shaft is 40 mm, the maximum shear stress in the shaft is ______ MPa.

A. 60
B. 60.79
C. 50.79
D. None of these
Answer» C. 50.79
Discussion
75.

The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>bxt </center></td></tr><tr><td style="text-align: center;">61</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>bxt </center></td></tr><tr><td style="text-align: center;">121</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>bxt </center></td></tr><tr><td style="text-align: center;">241</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>xt </center></td></tr><tr><td style="text-align: center;">121</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>bxt </center></td></tr><tr><td style="text-align: center;">241</td></tr></table>
Discussion
76.

For a loaded cantilever beam of uniform crosssection, the bending moment (in Nmm) along the length is M(x) = 5x + 10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross- section at x = 10 mm is _____.

A. 110N
B. 10N
C. 120N
D. None of these
Answer» B. 10N
Discussion
77.

A simply supported beam of length L is subjected to a varying distributed load sin (3 x/L) Nm

A. zero
B. L/3
C. L/
D. 2 L/
Answer» C. L/
Discussion
78.

The state of stress at a point is given by

A. 8
B. 8.43
C. 43
D. 3.4
Answer» C. 43
Discussion
79.

The state of plane-stress at a point is given by

A. 111.8
B. 150.1
C. 180.3
D. 223.6
Answer» B. 150.1
Discussion
80.

If the principal stresses in a plane stress problem are

A. 60
B. 50
C. 30
D. 20
Answer» D. 20
Discussion
81.

A shaft subjected to torsion experiences a pure shear stress x on the surface. The maximum principal stress on the surface which is at 45 to the axis will have a value

A. cos 45
B. 2 cos 45
C. cos 45
D. 2 sin 45 cos 45
Answer» E.
Discussion
82.

Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of east iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?

A. Both rods elongate by the same amount
B. Mild steel rod elongates more than the cast iron
C. Cast iron rod elongates more than the mild steel rod
D. As the stresses are equal strains are also equal in both the rods
Answer» D. As the stresses are equal strains are also equal in both the rods
Discussion
83.

An elastic body is subjected to a tensile stress X in a particular direction and a compressive stress Y in its perpendicular direction. X and Y are unequal in magnitude. On the plane of maximum shear stress in the body there will be

A. no normal stress
B. also the maximum normal stress
C. the minimum normal stress
D. both normal stress and shear stress
Answer» D. both normal stress and shear stress
Discussion
84.

A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be ______ .

A. 100 mm
B. 1000 mm
C. 1 mm
D. 10 mm
Answer» E.
Discussion
85.

The Poisson's ratio for a perfectly incompressible linear elastic material is

A. 1
B. 0.5
C. 0
D. infinity
Answer» C. 0
Discussion
86.

A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is

A. 0.5
B. 1.0
C. 2.0
D. 4.0
Answer» D. 4.0
Discussion
87.

A thin cylinder of inner radius 500 mm and thickness 10 mm subjected to an internal pressure of 5 MPa. The average circumferential (hoop) stress in MPa is

A. 100
B. 250
C. 500
D. 1000
Answer» C. 500
Discussion
88.

A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses.

A. 109.75 & 40.25 MPa
B. 19.75 & 40.25 MPa
C. 101.75 & 41.25 MPa
D. 19.75 & 44.25 MPa
E. None of these
Answer» B. 19.75 & 40.25 MPa
Discussion
89.

A cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m, and it has wall thickness of 10 mm. The magnitude of maximum in-plane shear stress (in MPa) is ________.

A. 25 MPa
B. 5 MPa
C. 20 MPa
D. 15 MPa
Answer» B. 5 MPa
Discussion
90.

The beams, one having square cross-section and another circular cross-section, are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then

A. maximum bending stress developed in both the beams is the same
B. the circular beam experience more bending stress than the square one
C. the square beam experiences more bending stress than the circular one
D. as the material is same both beams will experience same deformation
Answer» C. the square beam experiences more bending stress than the circular one
Discussion
91.

The second moment of a circular area about the diameter is given by (D is the diameter)

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> D<sup>4</sup></center></td></tr><tr><td style="text-align: center;">4</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> D<sup>4</sup></center></td></tr><tr><td style="text-align: center;">16</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> D<sup>4</sup></center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">32</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> D<sup>4</sup></center></td><td rowspan="2"></td></tr><tr><td style="text-align: center;">64</td></tr></table>
Answer» E.
Discussion
92.

Which one of the following diagrams shows correctly the distribution of transverse shear stress across the depth h of a rectangular beam subjected to varying bending moment along its length?

A. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/as-174.jpg">
B. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/as-175.jpg">
C. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/as-176.jpg">
D. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/as-177.jpg">
Answer» C. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/as-176.jpg">
Discussion
93.

A cyiindrical elastic body subjected to pure torsion about its axis develops

A. tensile stress in a direction 45 to the axis
B. no tensile or compressive stress
C. maximum shear stress along the axis of the shaft
D. maximum shear stress at 45 to the axis
Answer» B. no tensile or compressive stress
Discussion
94.

If the Poisson's ratio of an elastic material is 0.4, the ratio of modulus of rigidity to Young's modulus is ______

A. 57
B. 0.357
C. 0.57
D. None of the above
Answer» C. 0.57
Discussion
95.

A metallic rod of 500 mm length and 50 mm diameter, when subjected to a tensile force of 100 kN at the ends, experiences an increase in its length by 0.5 mm and a reduction in its diameter by 0.015 mm. The Poisson's ratio of the rod material is _______

A. 0.3
B. 0.8
C. 10
D. 1
Answer» B. 0.8
Discussion
96.

A rectangular region in a solid is in a state of plane strain. The (x, y) coordinates of the corners of the undeformed rectangle are given by P(0, 0), Q(4, 3), S(0, 3). The'rectangle is subjected to uniform strain

A. 5.015 units
B. 15 units
C. 5 units
D. None of the above
Answer» B. 15 units
Discussion
97.

Consider a steel (Young's modulus E = 200 GPa) column hinged on both sides. Its heights is 1.0 m and cross-section is 10 mm x 20 mm. The lowest Euler critical buckling load (in N) is ___.

A. 3289 N
B. 3289.8681 N
C. 32.898 N
D. 3298.8186 N
Answer» C. 32.898 N
Discussion
98.

For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

A. 1
B. 2
C. 4
D. 8
Answer» D. 8
Discussion
99.

For the case of a slender column of length l, and flexural rigidity El built in at its base and free at the top, the Euler's critical buckling load is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4 <sup>2</sup>El</center></td></tr><tr><td style="text-align: center;">l<sup>2</sup></td></tr></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2 <sup>2</sup>El</center></td></tr><tr><td style="text-align: center;">l<sup>2</sup></td></tr></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <sup>2</sup>El</center></td></tr><tr><td style="text-align: center;">l<sup>2</sup></td></tr></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <sup>2</sup>El</center></td></tr><tr><td style="text-align: center;">4l<sup>2</sup></td></tr></table>
Answer» E.
Discussion
100.

A pin-ended column of length L, modulus of elasticity E and second moment of the crosssectional area I is loaded concentrically by a compressive load P. The critical buckling load (P

A. <table><tr><td rowspan="2">P<sub>cr</sub> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>EI</center></td></tr><tr><td style="text-align: center;"> L<sup>2</sup></td></tr></table>
B. <table><tr><td rowspan="2">P<sub>cr</sub> =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <sup>2</sup>EI</center></td></tr><tr><td style="text-align: center;">3L<sup>2</sup></td></tr></table>
C. <table><tr><td rowspan="2">P<sub>cr</sub> =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> EI</center></td></tr><tr><td style="text-align: center;">L<sup>2</sup></td></tr></table>
D. <table><tr><td rowspan="2">P<sub>cr</sub> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <sup>2</sup>EI</center></td></tr><tr><td style="text-align: center;">L<sup>2</sup></td></tr></table>
Answer» E.
Discussion