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Elements of Elasticity and Stress Distribution Online Exam Quiz

Important questions about Elements of Elasticity and Stress Distribution. Elements of Elasticity and Stress Distribution MCQ questions with answers. Elements of Elasticity and Stress Distribution exam questions and answers for students and interviews.

The normal stress component acting at the centre, in the given diagram, will be _________ to the face (B D D1 B1).

Options

A : a. increased to \((?_y+\frac{??_y}{?y}\frac{dy}{2}) \)

B : b. decreased to \((?_y-\frac{??_y}{?y}\frac{dy}{2}) \)

C : c. equal to ?y

D : d. equal to ?z

The boundary condition equation for X?, where X? is the component of the surface force in x-direction per unit area is ___________

Options

A : a. a

B : b. b

C : c. c

D : d. d

The boundary condition equation for Y?, where Y? is the component of the surface force in y-direction per unit area is ___________

Options

A : a. a

B : b. b

C : c. c

D : d. d

The boundary condition equation for Z?, where Z? is the component of the surface force in z-direction per unit area is ___________

Options

A : a. a

B : b. b

C : c. c

D : d. d

The matrix form of the boundary condition equations is _____________

Options

A : a. \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ?_{xx} & ?_{xy} & ?_{xz} \\ ?_{yx} & ?_{yy} & ?_{yz} \\ ?_{zx} & ?_{zy} & ?_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

B : b. \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ?_{zz} & ?_{xy} & ?_{xz} \\ ?_{yx} & ?_{yy} & ?_{yz} \\ ?_{zx} & ?_{zy} & ?_{xx} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

C : c. \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ?_{xx} & ?_{zz} & ?_{xz} \\ ?_{yx} & ?_{yy} & ?_{yz} \\ ?_{zx} & ?_{zy} & ?_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

D : d. \(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ?_{xx} & ?_{yy} & ?_{xz} \\ ?_{yx} & ?_{yy} & ?_{yz} \\ ?_{zx} & ?_{yy} & ?_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

The partial differential of normal stress in y-direction in terms of effective stress is given by __________

Options

A : a. a

B : b. b

C : c. c

D : d. d

The equilibrium equation in X-direction in terms of effected stress for a saturated soil body is given by __________

Options

A : a. \(\frac{??_x{‘}}{?x}+\frac{??_{yx}}{?y}=0\)

B : b. \(\frac{??_{xy}}{?x}+\frac{??_y{‘}}{?y}+\frac{??_{zy}}{?z}+?_w \frac{?h}{?x}=0\)

C : c. \(\frac{??_{xz}}{?x}+\frac{??_{yz}}{?y}+\frac{??_z{‘}}{?z}+?_w \frac{?h}{?x}=0\)

D : d. \(\frac{??_x{‘}}{?x}+\frac{??_{yx}}{?y}+\frac{??_{zx}}{?z}+?_w \frac{?h}{?x}=0\)

The equilibrium equation in Y-direction in terms of effected stress for a saturated soil body is given by __________

Options

A : a. \(\frac{??_x{‘}}{?x}+\frac{??_{yx}}{?y}+\frac{??_{zx}}{?z}+X=0\)

B : b. \(\frac{??_{xy}}{?x}+\frac{??_y{‘}}{?y}+\frac{??_{zy}}{?z}+?_w \frac{?h}{?y}=0\)

C : c. \(\frac{??_{xz}}{?x}+\frac{??_{yz}}{?y}+\frac{??_z{‘}}{?z}+Z=0\)

D : d. \(\frac{??_x{‘}}{?x}+\frac{??_{yx}}{?y}+\frac{??_{zx}}{?z}=0\)

The equilibrium equation in Z-direction in terms of effected stress for a saturated soil body is given by __________

Options

A : a. \(\frac{??_x{‘}}{?x}+\frac{??_{yx}}{?y}+\frac{??_{zx}}{?z}++?_w \frac{?h}{?z}=0\)

B : b. \(\frac{??_{xy}}{?x}+\frac{??_y{‘}}{?y}+\frac{??_{zy}}{?z}+?_w \frac{?h}{?z}=0\)

C : c. \(\frac{??_{xz}}{?x}+\frac{??_{yz}}{?y}+\frac{??_z{‘}}{?z}+?’+?_w \frac{?h}{?z}=0\)

D : d. \(\frac{??_x{‘}}{?x}+\frac{??_{yx}}{?y}+\frac{??_{zx}}{?z}=0\)

The following diagram represents the contact pressure of __________

Options

A : a. real elastic material

B : b. intermediate soil

C : c. cohesionless soil

D : d. gravel

In simple radial distribution, the three stress components ?r, ?? and ?r? are given by ___________

Options

A : a. \(?_r=K \frac{Q cos??}{r}, ?_?=0 \,and\, ?_{r?}=0 \)

B : b. ?r=KQ, ??=0 and ?r?=0

C : c. \(?_r=\frac{Q cos??}{r}, ?_?=0 \,and\, ?_{r?}=0\)

D : d. ?r=0, ??=0 and ?r?= 0

In simple radial distribution, if \(?_r=K \frac{Q cos??}{r},\) then the value of K is ________

Options

A : a. K=\(\frac{2}{2?+sin2?}\)

B : b. K=2?+sin?

C : c. K=2?-sin?

D : d. K=sin?

When the ground is horizontal, \(?=\frac{?}{2}\) in constant K. What will be the radial stress ?? due to vertical line load?

Options

A : a. \(?_r=\frac{Q cos??}{r}\)

B : b. \(?_r=\frac{2Q cos??}{?r}\)

C : c. \(?_r=\frac{Q sin??}{r}\)

D : d. \(?_r=\frac{2Q sin??}{r}\)

The radial stress component ?? due to inclined line load of intensity Q per unit length is given by ___________

Options

A : a. \(?_r=\frac{2Q}{r}(\frac{cos?cos?}{2?+sin2?})\)

B : b. \(?_r=\frac{2Q}{r} (\frac{cos?cos?}{2?+sin2?}+\frac{sin?sin?}{2?-sin2?})\)

C : c. \(?_r=\frac{Q}{r} (\frac{cos?cos?}{2?+sin2?}+\frac{sin?sin?}{2?-sin2?})\)

D : d. \(?_r=\frac{2Q}{r}(\frac{sin?sin?}{2?-sin2?})\)

For any position of point P subtending angle ? with AB, the vertical stress is given by___________

Options

A : a. \(?_z=\frac{q}{a?} [x?(x-?)] \)

B : b. \(?_z=\frac{q}{a?} \)

C : c. \(?_z=\frac{q}{a?}\left[x?-\frac{az}{(x-?)^2+z^2}(x-?)\right] \)

D : d. \(?_z= \left[x?-\frac{az}{(x-?)^2+z^2}(x-?)\right] \)

For point P under the support A, the vertical stress is given by __________

Options

A : a. \(?_z=\frac{q}{a?} [x?(x-?)] \)

B : b. \(?_z=\frac{q}{a?} \)

C : c. \(?_z=\frac{q}{?} \left[\frac{az}{a^2+z^2}\right] \)

D : d. \(?_z=\left[x?-\frac{az}{(x-?)^2+z^2}(x-?)\right] \)

For point P under the support B, the vertical stress is given by __________

Options

A : a. \(?_z=\frac{q}{a?} [x?(x-?)] \)

B : b. \(?_z=\frac{q}{?}?_B \)

C : c. \(?_z=\frac{q}{?} \left[\frac{az}{a^2+z^2}\right] \)

D : d. \(?_z=\left[x?_B-\frac{az}{(x-?_B )^2+z^2}(x-?_B)\right] \)

For a linearly variable infinite load, for a point P, the vertical stress ?z is _________

Options

A : a. \(?_z=\frac{q}{a?} \left[x?+z\right] \)

B : b. \(?_z=\frac{q}{a?} \)

C : c. \(?_z=\frac{q}{?}\left[\frac{az}{a^2+z^2}\right] \)

D : d. \(?_z=\left[x?-\frac{az}{(x-?)^2+z^2}(x-?)\right] \)

For a symmetrically distributed triangular load, under the centre of the triangular load, the vertical stress at any point at a depth z is given by ___________

Options

A : a. \(?_z=\frac{q}{a?} \left[?_1+?_2 \right] \)

B : b. \(?_z=\frac{q}{?} \left[?_1+?_2 \right]\)

C : c. \(?_z=\frac{q}{?} \left[\frac{az}{a^2+z^2}\right]\)

D : d. \(?_z=\frac{q}{?} \left[?_1-?_2 \right]\)

For a symmetrically distributed triangular load, the shear stress ?xz at any point at a depth z is given by ___________

Options

A : a. \(?_{xz}=-\frac{qz}{a?} \left[?_1-?_2 \right] \)

B : b. \(?_{xz}=-\frac{q}{?} \left[?_1+?_2 \right]\)

C : c. \(?_{xz}=-\frac{q}{?} \left[\frac{az}{a^2+z^2}\right]\)

D : d. \(?_{xz}=-\frac{q}{?} \left[?_1-?_2 \right] \)

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