MCQOPTIONS
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MCQOPTIONS
This section includes 87 Mcqs, each offering curated multiple-choice questions to sharpen your Civil Engineering knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
If the concentrated load applied at the free end of a cantilever beam is doubled along with its length and moment of inertia also, then the deflection at the free end will increase by |
| A. | 2 times |
| B. | 4 times |
| C. | 8 times |
| D. | 10 times |
| Answer» D. 10 times | |
| 52. |
A concentrated load P is applied at the end of a cantilever as shown in figure. The cross section of the beam is a square of side ‘a’ with a hole of a dia ‘a/2’. The deflection at the tip of the cantilever is given by |
| A. | \(\frac{{3P}}{E}\frac{{{L^3}}}{{{a^4}}}\) |
| B. | \(\frac{{1024P}}{{\left( {256 - 3\pi } \right)E}}\frac{{{L^3}}}{{{a^4}}}\) |
| C. | \(\frac{{1024P}}{{\left( {256 - \frac{\pi }{{64}}} \right)E}}\frac{{{L^3}}}{{{a^4}}}\) |
| D. | \(\frac{{256P}}{{\left( {1025 - 3\pi } \right)}}\frac{{{L^3}}}{{{a^4}}}\) |
| Answer» C. \(\frac{{1024P}}{{\left( {256 - \frac{\pi }{{64}}} \right)E}}\frac{{{L^3}}}{{{a^4}}}\) | |
| 53. |
A beam of uniform cross-section, simply supported at ends carries a concentrated load W at mid span. If the ends of the beam are fixed and only load P is applied at the mid span such that the deflection at the centre remains the same, the value of the load P will be |
| A. | 6W |
| B. | 4W |
| C. | 2W |
| D. | W |
| Answer» C. 2W | |
| 54. |
A cantilever beam of span ‘I’ subjected to concentrated load ‘W’ at a distance ‘a’ from fixed end, the deflection under the point load is: |
| A. | Wa3/3EI |
| B. | (l - a) Wa2/3EI + Wa3/3EI |
| C. | Wl3/3EI |
| D. | W(l - a)3/3EI |
| Answer» B. (l - a) Wa2/3EI + Wa3/3EI | |
| 55. |
Maximum deflection at the mid-span of a simply-supported beam of span l, with uniformly distributed load (w) all over the beam span, and flexural rigidity EI, is (modulus of elasticity = E; moment of inertia of beam = I) |
| A. | \(\frac{{5w{l^4}}}{{48EI}}\) |
| B. | \(\frac{{5w{l^4}}}{{384EI}}\) |
| C. | \(\frac{{w{l^3}}}{{48EI}}\) |
| D. | \(\frac{{w{l^3}}}{{3EI}}\) |
| Answer» C. \(\frac{{w{l^3}}}{{48EI}}\) | |
| 56. |
A cantilever beam PQ of length L m and cross-section B x D mm2 is subjected to UDL of w kN/m throughout the span. Another cantilever beam RS (made-up of same material) of length 2L m and cross-section 2B x 2D mm2 is subjected to same amount of UDL throughout the span. What is the ratio of deflection at the ‘free end’ for beam PQ to that of beam RS? |
| A. | 1 |
| B. | 8 |
| C. | 1/2 |
| D. | 1/8 |
| Answer» B. 8 | |
| 57. |
A uniform cantilever beam ABC of length L is subjected to a point load P at point B and a concentrated moment M at point C (as shown in figure). Let E be the Young’s modulus of the beam material and / be the area moment of inertia of the beam’s cross-section. Assuming the validity of the Euler-Bernoulli theory of slender beams, the downward deflection at point C is |
| A. | \(\frac{PL^3}{3EI}+\frac{ML^2}{2EI}\) |
| B. | \(\frac{PL^3}{24EI}+\frac{ML^2}{EI}\) |
| C. | \(\frac{PL^3}{48EI}+\frac{ML^2}{2EI}\) |
| D. | \(\frac{5PL^3}{48EI}+\frac{ML^2}{2EI}\) |
| Answer» E. | |
| 58. |
A cantilever beam AB as shown in figure is subjected to a point load of 12 kN over a span of 6 m with E = 2 × 105 N/mm2 and IXX = 6 × 107 mm4. The deflection at the free end will be |
| A. | 80 mm |
| B. | 72 mm |
| C. | 64 mm |
| D. | 56 mm |
| Answer» C. 64 mm | |
| 59. |
If 'L' is the span of a light suspension bridge, whose, each cable carries total weight (W) and the central displacement is 'y', the horizontal pull at each support is ________. |
| A. | WL/4y |
| B. | WL/8y |
| C. | WL/2y |
| D. | WL/y |
| Answer» C. WL/2y | |
| 60. |
If the deflection at the free end of a uniformly loaded cantilever beam is 15 mm and the slope of the deflection curve at the free end is 0.02 radian, then the length of the beam is |
| A. | 0.8 m |
| B. | 1.0 m |
| C. | 1.2 m |
| D. | 1.5 m |
| Answer» C. 1.2 m | |
| 61. |
\(\frac{{P{L^3}}}{{3EI}}\) is the deflection under the load P of a cantilever beam (length L, modulus of elasticity E, moment of inertia I). The strain energy due to bending is |
| A. | \(\frac{{{P^2}{L^3}}}{{3EI}}\) |
| B. | \(\frac{{{P^2}{L^3}}}{{6EI}}\) |
| C. | \(\frac{{{P^2}{L^3}}}{{4EI}}\) |
| D. | \(\frac{{{P^2}{L^3}}}{{48EI}}\) |
| Answer» C. \(\frac{{{P^2}{L^3}}}{{4EI}}\) | |
| 62. |
A cantilever beam, 3 m long, carries a uniformly distributed load over the entire length. If the slope at the free end is 1°, the deflection at the free end is |
| A. | 49.27 mm |
| B. | 39.27 mm |
| C. | 30.27 mm |
| D. | 20.27 mm |
| Answer» C. 30.27 mm | |
| 63. |
An overhanging beam of uniform EI is loaded as shown below. The deflection at the free end is |
| A. | \(\frac{{W\;{l^3}}}{{81\;EI}}\) |
| B. | \(\frac{{W\;{l^3}}}{{8\;EI}}\) |
| C. | \(\frac{{W\;{l^3}}}{{27\;EI}}\) |
| D. | \(\frac{{2\;W\;{l^3}}}{{27\;EI}}\) |
| Answer» C. \(\frac{{W\;{l^3}}}{{27\;EI}}\) | |
| 64. |
A simply supported beam of span 8 m carries a uniformly distributed load of 24 kN/m run over the whole span. The beam is propped at the middle of the span. The values of E = 200 × 106 kN/m2 and I = 20 × 10-5 m4. The amount by which the prop should yield in order to make all three reactions equal will be nearly |
| A. | 20 mm |
| B. | 15 mm |
| C. | 10 mm |
| D. | 5 mm |
| Answer» C. 10 mm | |
| 65. |
A beam is loaded as cantilever. If the load at the end is increased, the failure will occur: |
| A. | In the middle |
| B. | At the tip below the load |
| C. | At the support |
| D. | Anywhere |
| Answer» D. Anywhere | |
| 66. |
A cantilever beam is one which- |
| A. | Fixed at both ends |
| B. | Fixed at one end and free at other end |
| C. | Supported at its ends |
| D. | Supported on more than two supports |
| Answer» C. Supported at its ends | |
| 67. |
If a simply supported beam of span 4 m is subjected to terminal couple of 4 kN-m at both the ends, then the magnitude of the central deflection would be |
| A. | 4/EI |
| B. | 8/EI |
| C. | 2/EI |
| D. | 16/EI |
| Answer» C. 2/EI | |
| 68. |
A simply supported rectangular beam of span 'L' and depth 'd' carries a central load 'w'. The ratio of maximum deflection to maximum bending stress is- |
| A. | \(\frac{{{L^2}}}{{8Ed}}\) |
| B. | \(\frac{{{L^2}}}{{48Ed}}\) |
| C. | \(\frac{{{L^2}}}{{12Ed}}\) |
| D. | \(\frac{{{L^2}}}{{6Ed}}\) |
| Answer» E. | |
| 69. |
Deflection of the free end of cantilever having point load at the mid span is |
| A. | \(\frac{{w{l^3}}}{{3EI}}\) |
| B. | \(\frac{{5w{l^3}}}{{24EI}}\) |
| C. | \(\frac{{5w{l^3}}}{{48EI}}\) |
| D. | \(\frac{{w{l^3}}}{{48EI}}\) |
| Answer» D. \(\frac{{w{l^3}}}{{48EI}}\) | |
| 70. |
A cantilever of length l is subjected to a couple M at its free end. The deflection is |
| A. | \(\frac{{M{l^2}}}{{2\;EI}}\) |
| B. | \(\frac{{M{l^2}}}{{4\;EI}}\) |
| C. | \(\frac{{M{l^2}}}{{8\;EI}}\) |
| D. | \(\frac{{M{l^2}}}{{16\;EI}}\) |
| Answer» B. \(\frac{{M{l^2}}}{{4\;EI}}\) | |
| 71. |
A simply supported beam of span ‘l’ carries a point load ‘W’ at the centre, the slope at the support will be |
| A. | \(\dfrac{Wl^3}{6EI}\) |
| B. | \(\dfrac{Wl^3}{24EI}\) |
| C. | \(\dfrac{Wl^2}{16EI}\) |
| D. | \(\dfrac{Wl^3}{2EI}\) |
| Answer» D. \(\dfrac{Wl^3}{2EI}\) | |
| 72. |
A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment, M, as shown in the figure. The deflection of the beam at x - L/2 |
| A. | \(\frac{ML^2}{16EI}\) |
| B. | \(\frac{ML^2}{4EI}\) |
| C. | \(\frac{ML^2}{8EI}\) |
| D. | \(\frac{ML^2}{2EI}\) |
| Answer» D. \(\frac{ML^2}{2EI}\) | |
| 73. |
A simply supported beam of length ‘a carries point load ‘W’ at point ‘C’ as shown in the figure. The maximum deflection lies at |
| A. | Point A |
| B. | Point B |
| C. | Point C |
| D. | Between points B and C |
| Answer» E. | |
| 74. |
A support is said to be no yielding if ______. |
| A. | It can take any amount of reaction |
| B. | It is frictionless |
| C. | It holds the beam firmly |
| D. | The beam has zero slope at the support |
| Answer» E. | |
| 75. |
A beam of length L is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is EI. The reaction at the simple support at the right end is |
| A. | WL/2 |
| B. | 3WL/8 |
| C. | WL/4 |
| D. | WL/8 |
| Answer» C. WL/4 | |
| 76. |
A strut is made of a circular bar, 5 m long and pin-jointed at both ends. When freely supported the bar gives a mid-span deflection of 10 mm under a load of 80 N at the centre. The critical load will be |
| A. | 8485 N |
| B. | 8340 N |
| C. | 8225 N |
| D. | 8110 N |
| Answer» D. 8110 N | |
| 77. |
Maximum deflection of a simply-supported beam with the total uniformly distributed load 'W' is: |
| A. | \(\frac{{W{l^2}}}{{384EI}}\) |
| B. | \(\frac{{5W{l^3}}}{{384EI}}\) |
| C. | \(\frac{{W{l^3}}}{{48EI}}\) |
| D. | \(\frac{{5W{l^3}}}{{48EI}}\) |
| Answer» C. \(\frac{{W{l^3}}}{{48EI}}\) | |
| 78. |
Maximum deflection for a simply supported beam subjected to UDL ‘W’ throughout span ‘l’ is |
| A. | \(\frac{{w{l^3}}}{{48EI}}\) |
| B. | \(\frac{{w{l^4}}}{{48EI}}\) |
| C. | \(\frac{{5w{l^3}}}{{384EI}}\) |
| D. | \(\frac{{5w{l^4}}}{{384EI}}\) |
| Answer» E. | |
| 79. |
A prismatic beam of uniform flexural rigidity EI is simply supported over a span, L. If a moment, M is applied at one support, the resulting bending strain energy is: |
| A. | \(\frac{{M{L^2}}}{{EI}}\) |
| B. | \(\frac{{{M^2}L}}{{2EI}}\) |
| C. | \(\frac{{{M^2}L}}{{4EI}}\) |
| D. | \(\frac{{{M^2}L}}{{6EI\;}}\) |
| Answer» E. | |
| 80. |
Maximum deflection in a beam of span l supported freely at both ends due to central load P at middle with young’s modulus E and moment of inertia I is |
| A. | Pl3/64 EI |
| B. | Pl3/32 EI |
| C. | Pl3/48 EI |
| D. | Pl3/96 EI |
| Answer» D. Pl3/96 EI | |
| 81. |
A simply supported beam of span length L and flexure stiffness EI has another spring support at the centre span of stiffness K as shown in figure. The central deflection of the beam due to a central concentrated load of P would be |
| A. | \( \frac{{P{L^3}}}{{48EI {}}} +\frac{P}{K}\) |
| B. | \( \frac{{P{L^3}}}{{48EI + K{L^3}}} \) |
| C. | \( \frac{{P{L^3}}}{{48EI {}}} \times \frac{P}{K}\) |
| D. | \( \frac{{P{L^3}}}{{48EI {}}} +{K}\) |
| Answer» C. \( \frac{{P{L^3}}}{{48EI {}}} \times \frac{P}{K}\) | |
| 82. |
A cantilever beam of length 100 mm is subjected an end load of 150 N. If Young’s modulus is 200 GPa and Moment of Inertia is 5000 mm4, the maximum deflection of this beam is: |
| A. | 5 mm |
| B. | 0.5 mm |
| C. | 0.05 mm |
| D. | 0.01 mm |
| Answer» D. 0.01 mm | |
| 83. |
A beam El-constant of span L is subjected to clockwise moments M at both the ends A and B. The rotation of end A works out to be |
| A. | \(\frac{ML}{2EI}\) |
| B. | \(\frac{ML}{3EI}\) |
| C. | \(\frac{ML}{4EI}\) |
| D. | \(\frac{ML}{6EI}\) |
| Answer» E. | |
| 84. |
A cantilever beam PQ of uniform flexural rigidity (EI) is subjected to a concentrated moment M at R as shown in the figure.The deflection at the free end Q is |
| A. | \(\frac{{M{L^2}}}{{6EI}}\) |
| B. | \(\frac{{M{L^2}}}{{4EI}}\) |
| C. | \(\frac{{3M{L^2}}}{{8EI}}\) |
| D. | \(\frac{{3M{L^2}}}{{4EI\;}}\) |
| Answer» D. \(\frac{{3M{L^2}}}{{4EI\;}}\) | |
| 85. |
A simply supported beam deflects by 5 mm when it is subjected to a concentrated load of 10 kN at its centre. What will be the deflection in a 1/10 model of the beam, if the model is subjected to a 1 kN load at its centre? |
| A. | 5 mm |
| B. | 0.5 mm |
| C. | 0.05 mm |
| D. | 0.005 mm |
| Answer» B. 0.5 mm | |
| 86. |
In a simply supported shaft carrying a uniformly distributed mass, the maximum deflection at the midspan is: |
| A. | \(\frac{{5mg{l^2}}}{{384EI}}\) |
| B. | \(\frac{{5mg{l^4}}}{{384EI}}\) |
| C. | \(\frac{{mg{l^4}}}{{384EI}}\) |
| D. | \(\frac{{3mg{l^2}}}{{384EI}}\) |
| Answer» C. \(\frac{{mg{l^4}}}{{384EI}}\) | |
| 87. |
Maximum deflection of a cantilever beam of length l, Young’s modulus E, moment of inertia I and concentrated load at tip P. |
| A. | pl3 |
| B. | \(\frac{{{\rm{p}}{{\rm{l}}^{\rm{2}}}}}{{{\rm{2EI}}}}\) |
| C. | \(\frac{{{\rm{p}}{{\rm{l}}^{\rm{3}}}}}{{{\rm{3EI}}}}\) |
| D. | \(\frac{{{\rm{p}}{{\rm{l}}^{\rm{4}}}}}{{{\rm{8EI}}}}\) |
| Answer» D. \(\frac{{{\rm{p}}{{\rm{l}}^{\rm{4}}}}}{{{\rm{8EI}}}}\) | |