MCQOPTIONS
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MCQOPTIONS
This section includes 180 Mcqs, each offering curated multiple-choice questions to sharpen your Geotechnical Engineering knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
The generalised Hooke’s law equation connecting the strain to stress contains ___________ elastic constants. |
| A. | 40 |
| B. | 36 |
| C. | 39 |
| D. | 38 |
| Answer» C. 39 | |
| 52. |
The stresses due to self weight of the soil are known as ______________ |
| A. | geostatic stresses |
| B. | boundary stresses |
| C. | external stresses |
| D. | boundary strain |
| Answer» B. boundary stresses | |
| 53. |
If θ is the apex angle which the line joining the apex makes with the outer edge of the loading of a circular area, then the Boussinesq’s vertical pressure σz under a uniformly loaded circular area is given by ______________ |
| A. | σz=q[1-sin³θ] |
| B. | σz=q[1-cos³θ] |
| C. | σz=q[1-tan³θ] |
| D. | σz=q[1-cos²θ] |
| Answer» C. σz=q[1-tan³θ] | |
| 54. |
In Terzaghi’s Theory of one dimensional consolidation, the boundary is considered to be __________ |
| A. | free surface offering resistance to flow of water |
| B. | free surface offering no resistance to flow of water |
| C. | fixed surface offering resistance to flow of water |
| D. | curved surface offering resistance to water flow |
| Answer» C. fixed surface offering resistance to flow of water | |
| 55. |
In Terzaghi’s Theory of one dimensional consolidation, soil is restrained against lateral deformation. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 56. |
If r/z ratio is 2 and load of 20 kN is acting at a point, then the vertical pressure at a depth 6m is ____________ |
| A. | 0.4356 kN/m² |
| B. | 0.244 kN/m² |
| C. | 0.1518 kN/m² |
| D. | 4.72*10¯³ kN/m² |
| Answer» E. | |
| 57. |
If a footing has a dimension of 1m*1m and load transfer of 20 kN, then the contact pressure is _______________ |
| A. | 20 kN/m² |
| B. | 30 kN/m² |
| C. | 50 kN/m² |
| D. | 70 kN/m² |
| Answer» B. 30 kN/m² | |
| 58. |
If the contact pressure is 14 kN/m², then find the load for 50 m². |
| A. | 500kN |
| B. | 600kN |
| C. | 700kN |
| D. | 800kN |
| Answer» D. 800kN | |
| 59. |
For a uniformly loaded rectangular area, the Newmark’s influence factor given by ___________ |
| A. | \(K= \left[\frac{20.20.4\sqrt{(0.2^2+0.4^2+1)}}{0.2^2+0.4^2+0.2^2 0.4^2+1}*\frac{0.2^2+0.4^2+2}{0.2^2+0.4^2+1}+tan^{-1}\frac{20.20.4\sqrt{(0.2^2+0.4^2+1)}}{0.2^2+0.4^2+0.2^2 0.4^2+1}\right] \) |
| B. | \(K= \frac{1}{4π} \left[\frac{20.20.4\sqrt{(0.2^2+0.4^2+1)}}{0.2^2+0.4^2+0.2^2 0.4^2+1}*\frac{0.2^2+0.4^2+2}{0.2^2+0.4^2+1}+tan^{-1}\frac{20.20.4\sqrt{(0.2^2+0.4^2+1)}}{0.2^2+0.4^2+0.2^2 0.4^2+1}\right] \) |
| C. | \(K= \frac{1}{4π}\) |
| D. | \(K= \frac{q}{4π} \left[\frac{20.20.4\sqrt{(0.2^2+0.4^2+1)}}{0.2^2+0.4^2+0.2^2 0.4^2+1}*\frac{0.2^2+0.4^2+2}{0.2^2+0.4^2+1}+tan^{-1}\frac{20.20.4\sqrt{(0.2^2+0.4^2+1)}}{0.2^2+0.4^2+0.2^2 0.4^2+1}\right] \) |
| Answer» C. \(K= \frac{1}{4π}\) | |
| 60. |
When the maximum vertical stress is 0.235 kN/m² at a radial distance of 4m from the point load is __________ kN. |
| A. | 42.34 |
| B. | 10.56 |
| C. | 20.76 |
| D. | 30.65 |
| Answer» B. 10.56 | |
| 61. |
The maximum vertical stress is _______ when a concentrated load of 20 kN acts at a radial distance of 2m. |
| A. | 0.444 kN/m² |
| B. | 0.555 kN/m² |
| C. | 0.666 kN/m² |
| D. | 0.777 kN/m² |
| Answer» B. 0.555 kN/m² | |
| 62. |
The stress function was introduced by __________ |
| A. | G.B Airy |
| B. | Terzaghi |
| C. | Darcy |
| D. | Meyerhof |
| Answer» B. Terzaghi | |
| 63. |
The equilibrium equation in polar coordinates is given by _____________ |
| A. | \(\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\) |
| B. | \(\frac{∂σ_r}{∂r}+\frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\) |
| C. | \(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\) |
| D. | \(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}=0\) |
| Answer» D. \(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}=0\) | |
| 64. |
The influence factor for the vertical stress under the corner of a uniformly loaded rectangular area of size 1m*2m at depth 5m and load of 80 kN/m² is given by ___________ |
| A. | 0.6212 |
| B. | 0.7465 |
| C. | 0.0328 |
| D. | 0.0624 |
| Answer» D. 0.0624 | |
| 65. |
The Westergaard’s equation is given by ___________ |
| A. | \(σ_z=\frac{1}{\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \) |
| B. | \(σ_z=\frac{1}{2\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \) |
| C. | \(σ_z=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}}\frac{Q}{z^2} \) |
| D. | \(σ_z=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \) |
| Answer» D. \(σ_z=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \) | |
| 66. |
The equilibrium equation in Z-direction in terms of effected stress for a saturated soil body is given by __________ |
| A. | \(\frac{∂σ_x{‘}}{∂x}+\frac{∂τ_{yx}}{∂y}+\frac{∂τ_{zx}}{∂z}++γ_w \frac{∂h}{∂z}=0\) |
| B. | \(\frac{∂τ_{xy}}{∂x}+\frac{∂σ_y{‘}}{∂y}+\frac{∂τ_{zy}}{∂z}+γ_w \frac{∂h}{∂z}=0\) |
| C. | \(\frac{∂τ_{xz}}{∂x}+\frac{∂τ_{yz}}{∂y}+\frac{∂σ_z{‘}}{∂z}+γ’+γ_w \frac{∂h}{∂z}=0\) |
| D. | \(\frac{∂σ_x{‘}}{∂x}+\frac{∂τ_{yx}}{∂y}+\frac{∂τ_{zx}}{∂z}=0\) |
| Answer» D. \(\frac{∂σ_x{‘}}{∂x}+\frac{∂τ_{yx}}{∂y}+\frac{∂τ_{zx}}{∂z}=0\) | |
| 67. |
The matrix form of the boundary condition equations is _____________ |
| A. | \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{xx} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\) |
| B. | \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{zz} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{xx} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\) |
| C. | \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{xx} & τ_{zz} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\) |
| D. | \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{xx} & τ_{yy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{yy} & σ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\) |
| Answer» B. \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{zz} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{xx} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\) | |
| 68. |
For any position of point P subtending angle α with AB, the vertical stress is given by___________ |
| A. | \(σ_z=\frac{q}{aπ} [xα(x-α)] \) |
| B. | \(σ_z=\frac{q}{aπ} \) |
| C. | \(σ_z=\frac{q}{aπ}\left[xα-\frac{az}{(x-α)^2+z^2}(x-α)\right] \) |
| D. | \(σ_z= \left[xα-\frac{az}{(x-α)^2+z^2}(x-α)\right] \) |
| Answer» D. \(σ_z= \left[xα-\frac{az}{(x-α)^2+z^2}(x-α)\right] \) | |
| 69. |
The radial stress component σᵣ due to inclined line load of intensity Q per unit length is given by ___________ |
| A. | \(σ_r=\frac{2Q}{r}(\frac{cosβcosθ}{2α+sin2α})\) |
| B. | \(σ_r=\frac{2Q}{r} (\frac{cosβcosθ}{2α+sin2α}+\frac{sinβsinθ}{2α-sin2α})\) |
| C. | \(σ_r=\frac{Q}{r} (\frac{cosβcosθ}{2α+sin2α}+\frac{sinβsinθ}{2α-sin2α})\) |
| D. | \(σ_r=\frac{2Q}{r}(\frac{sinβsinθ}{2α-sin2α})\) |
| Answer» C. \(σ_r=\frac{Q}{r} (\frac{cosβcosθ}{2α+sin2α}+\frac{sinβsinθ}{2α-sin2α})\) | |
| 70. |
For point P under the support B, the vertical stress is given by __________ |
| A. | \(σ_z=\frac{q}{aπ} [xα(x-α)] \) |
| B. | \(σ_z=\frac{q}{π}α_B \) |
| C. | \(σ_z=\frac{q}{π} \left[\frac{az}{a^2+z^2}\right] \) |
| D. | \(σ_z=\left[xα_B-\frac{az}{(x-α_B )^2+z^2}(x-α_B)\right] \) |
| Answer» C. \(σ_z=\frac{q}{π} \left[\frac{az}{a^2+z^2}\right] \) | |
| 71. |
For a triangular and uniformly distributed semi-infinite loads, the shear stress τxz in the plane xz is ___________ |
| A. | \(τ_{xz}=-\frac{qz}{aπ} α \) |
| B. | \(τ_{xz}=-\frac{q}{π} α\) |
| C. | \(τ_{xz}=-\frac{q}{π} \left[\frac{az}{a^2+z^2}\right]\) |
| D. | \(τ_{xz}=-\frac{q}{π} z\) |
| Answer» B. \(τ_{xz}=-\frac{q}{π} α\) | |
| 72. |
The maximum shear stress is the difference between major and minor principal stresses. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 73. |
Trapezoidal load is encountered in earth fills. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 74. |
The triangular load is also known as ___________ |
| A. | uniformly distributed load |
| B. | uniformly varying load |
| C. | point load |
| D. | equivalent uniformly distributed load |
| Answer» C. point load | |
| 75. |
The equilibrium equations in terms of total stresses formed by summing all forces on y-direction is ________ |
| A. | \(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\) |
| B. | \(\frac{∂τ_{xy}}{∂x}+\frac{∂σ_y}{∂y}+\frac{∂τ_{zy}}{∂z}=0\) |
| C. | \(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\) |
| D. | \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\) |
| Answer» C. \(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\) | |
| 76. |
The greatest value of maximum shear stress τmax occurs when angle θ is _________ |
| A. | π |
| B. | π/2 |
| C. | π/3 |
| D. | π/4 |
| Answer» C. π/3 | |
| 77. |
The three equations of static equilibrium of the problem of elasticity are not sufficient to solve the six unknown stress components. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 78. |
The following diagram represents the contact pressure of __________ |
| A. | real elastic material |
| B. | intermediate soil |
| C. | cohesionless soil |
| D. | gravel |
| Answer» D. gravel | |
| 79. |
The following diagram represents the contact pressure of __________ |
| A. | real elastic material |
| B. | intermediate soil |
| C. | cohesionless soil |
| D. | gravel |
| Answer» C. cohesionless soil | |
| 80. |
In simple radial distribution, if \(σ_r=K \frac{Q cosθ}{r},\) then the value of K is ________ |
| A. | K=\(\frac{2}{2α+sin2α}\) |
| B. | K=2α+sinα |
| C. | K=2α-sinα |
| D. | K=sinα |
| Answer» B. K=2α+sinα | |
| 81. |
The component τyz denotes ________ |
| A. | normal stress in x-direction |
| B. | normal stress perpendicular to y-axis |
| C. | normal acting perpendicular to x-axis |
| D. | shear stress acting perpendicular to y-axis |
| Answer» E. | |
| 82. |
The component σz denotes __________ |
| A. | normal stress in x-direction |
| B. | normal stress acting perpendicular to z-axis |
| C. | shear stress acting perpendicular to z-axis |
| D. | shear stress acting perpendicular to y-axis |
| Answer» C. shear stress acting perpendicular to z-axis | |
| 83. |
In a stress tensor, each stress component in it is represented by__________ |
| A. | magnitude only |
| B. | direction only |
| C. | both magnitude and direction |
| D. | opposite direction |
| Answer» D. opposite direction | |
| 84. |
The equilibrium equation obtained by summing all forces on y-direction is ________ |
| A. | \(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\) |
| B. | \(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\) |
| C. | \(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\) |
| D. | \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\) |
| Answer» C. \(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\) | |
| 85. |
The equilibrium equation obtained by summing all forces on x-direction is ________ |
| A. | \(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\) |
| B. | \(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\) |
| C. | \(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\) |
| D. | \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\) |
| Answer» B. \(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\) | |
| 86. |
At a point there are ______ shear stresses. |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 87. |
There are _______ independent shearing stresses. |
| A. | 2 |
| B. | 3 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 88. |
For a load intensity of q=20kN/m, find the shear stress τxz at a depth 5m from the given diagram. |
| A. | -5.2 kN/m² |
| B. | -6.2 kN/m² |
| C. | -7.2 kN/m² |
| D. | -8.2 kN/m² |
| Answer» C. -7.2 kN/m² | |
| 89. |
For a load intensity of q=20kN/m, find the vertical stress σz from the given diagram. |
| A. | 5.62 kN/m² |
| B. | 6.23 kN/m² |
| C. | 13.33 kN/m² |
| D. | 8.32 kN/m² |
| Answer» D. 8.32 kN/m² | |
| 90. |
For a triangular and uniformly distributed semi-infinite loads, the vertical stress σz is given by ___________ |
| A. | \(σ_z=\frac{q}{aπ}[xα+z] \) |
| B. | \(σ_z=\frac{q}{aπ}(aβ+xα) \) |
| C. | \(σ_z=\frac{q}{π} \left[\frac{az}{a^2+z^2}\right]\) |
| D. | \(σ_z=[xα-\frac{az}{(x-α)^2+z^2}(x-α)]\) |
| Answer» C. \(σ_z=\frac{q}{π} \left[\frac{az}{a^2+z^2}\right]\) | |
| 91. |
Dimensionally a body force is defined as _____________ |
| A. | force at a point |
| B. | pressure per unit area |
| C. | force per unit area |
| D. | force per unit volume |
| Answer» E. | |
| 92. |
Surfaces forces are applied _________ |
| A. | externally at boundaries of body |
| B. | internally at boundaries of body |
| C. | only on one side in internal of the body |
| D. | throughout the volume of the body |
| Answer» B. internally at boundaries of body | |
| 93. |
Dimensionally a surface force is defined as _____________ |
| A. | force at a point |
| B. | pressure per unit area |
| C. | force per unit area |
| D. | force per unit volume |
| Answer» D. force per unit volume | |
| 94. |
The stress tensor is given by ___________ |
| A. | \begin{bmatrix} σ_{xx} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{zz} \end{bmatrix} |
| B. | \begin{bmatrix} σ_{zz} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{xx} \end{bmatrix} |
| C. | \begin{bmatrix} σ_{xx} & τ_{zz} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{zz} \end{bmatrix} |
| D. | \begin{bmatrix} σ_{xx} & τ_{yy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{yy} & σ_{zz} \end{bmatrix} |
| Answer» B. \begin{bmatrix} σ_{zz} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{xx} \end{bmatrix} | |
| 95. |
The Boussinesq influence factor for r/z ratio equal to 0.3 is given by ____________ |
| A. | 0.3840 |
| B. | 0.5465 |
| C. | 0.9873 |
| D. | 0.2312 |
| Answer» B. 0.5465 | |
| 96. |
The partial differential of normal stress in y-direction in terms of effective stress is given by __________ |
| A. | \(\frac{∂σ_y{‘}}{∂y}\) |
| B. | \(\frac{∂σ_y{‘}}{∂y}-γ_w \frac{∂h}{∂y}\) |
| C. | \(\frac{∂σ_y{‘}}{∂y}+γ_w \frac{∂h}{∂y}\) |
| D. | \(\frac{∂σ_y{‘}}{∂y}*γ_w \frac{∂h}{∂y}\) |
| Answer» D. \(\frac{∂σ_y{‘}}{∂y}*γ_w \frac{∂h}{∂y}\) | |
| 97. |
The Boussinesq equation representing the polar radial stress is ___________ |
| A. | \(σ_R=\frac{3Q}{2} \frac{cosβ}{R^2} \) |
| B. | \(σ_R=\frac{3Q}{2π} \frac{cosβ}{R^2}\) |
| C. | \(σ_R=\frac{3Q}{2π} \frac{cosβ}{R}\) |
| D. | \(σ_R=\frac{3Q}{2π} \frac{cosβ}{R^3} \) |
| Answer» C. \(σ_R=\frac{3Q}{2π} \frac{cosβ}{R}\) | |
| 98. |
_________ is more accurate method of determining the vertical stress at any point. |
| A. | Isobar chart |
| B. | equivalent point load method |
| C. | Influence chart |
| D. | Fenske’s chart |
| Answer» D. Fenske’s chart | |
| 99. |
What will be the intensity of shear stress at a depth of 4m and at a radial distance of 1m from concentrated load of 20 kN? |
| A. | 0.4356 kN/m² |
| B. | 0.244 kN/m² |
| C. | 0.652 kN/m² |
| D. | 0.128 kN/m² |
| Answer» E. | |
| 100. |
In the generalised Hook’s law equation, εₓ=C₁₁σₓ+ C₁₂ (σᵧ+σz), the constant C₁₁ is __________ |
| A. | E |
| B. | 1/E |
| C. | 0 |
| D. | μ |
| Answer» C. 0 | |