Elements of Elasticity and Stress Distribution MCQs

Welcome to our comprehensive collection of Multiple Choice Questions (MCQs) on Elements of Elasticity and Stress Distribution, a fundamental topic in the field of Geotechnical Engineering. Whether you're preparing for competitive exams, honing your problem-solving skills, or simply looking to enhance your abilities in this field, our Elements of Elasticity and Stress Distribution MCQs are designed to help you grasp the core concepts and excel in solving problems.

In this section, you'll find a wide range of Elements of Elasticity and Stress Distribution mcq questions that explore various aspects of Elements of Elasticity and Stress Distribution problems. Each MCQ is crafted to challenge your understanding of Elements of Elasticity and Stress Distribution principles, enabling you to refine your problem-solving techniques. Whether you're a student aiming to ace Geotechnical Engineering tests, a job seeker preparing for interviews, or someone simply interested in sharpening their skills, our Elements of Elasticity and Stress Distribution MCQs are your pathway to success in mastering this essential Geotechnical Engineering topic.

Note: Each of the following question comes with multiple answer choices. Select the most appropriate option and test your understanding of Elements of Elasticity and Stress Distribution. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

So, are you ready to put your Elements of Elasticity and Stress Distribution knowledge to the test? Let's get started with our carefully curated MCQs!

Elements of Elasticity and Stress Distribution MCQs | Page 1 of 19

Discover more Topics under Geotechnical Engineering

Q1.
The normal stress component acting at the centre, in the given diagram, will be _________ to the face (B D D1 B1).

a.

increased to \((ฯƒ_y+\frac{โˆ‚ฯƒ_y}{โˆ‚y}\frac{dy}{2}) \)

b.

decreased to \((ฯƒ_y-\frac{โˆ‚ฯƒ_y}{โˆ‚y}\frac{dy}{2}) \)

c.

equal to ฯƒy

d.

equal to ฯƒz

Discuss
Answer: (a).increased to \((ฯƒ_y+\frac{โˆ‚ฯƒ_y}{โˆ‚y}\frac{dy}{2}) \)
Q2.
The normal stress component acting at the centre, in the given diagram, will be _________ to the face (A C C1 A1).

a.

increased to \((ฯƒ_y+\frac{โˆ‚ฯƒ_y}{โˆ‚y}\frac{dy}{2}) \)

b.

decreased to \((ฯƒ_y-\frac{โˆ‚ฯƒ_y}{โˆ‚y}\frac{dy}{2}) \)

c.

equal to ฯƒy

d.

equal to ฯƒz

Discuss
Answer: (b).decreased to \((ฯƒ_y-\frac{โˆ‚ฯƒ_y}{โˆ‚y}\frac{dy}{2}) \)
Q3.
The boundary condition equation for Xฬ…, where Xฬ… is the component of the surface force in x-direction per unit area is ___________

a.

a

b.

b

c.

c

d.

d

Discuss
Answer: (c).c
Q4.
The boundary condition equation for Yฬ…, where Yฬ… is the component of the surface force in y-direction per unit area is ___________

a.

a

b.

b

c.

c

d.

d

Discuss
Answer: (a).a
Q5.
The boundary condition equation for Zฬ…, where Zฬ… is the component of the surface force in z-direction per unit area is ___________

a.

a

b.

b

c.

c

d.

d

Discuss
Answer: (b).b
Q6.
The matrix form of the boundary condition equations is _____________

a.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ฯƒ_{xx} & ฯ„_{xy} & ฯ„_{xz} \\ ฯ„_{yx} & ฯƒ_{yy} & ฯ„_{yz} \\ ฯ„_{zx} & ฯ„_{zy} & ฯƒ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

b.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ฯƒ_{zz} & ฯ„_{xy} & ฯ„_{xz} \\ ฯ„_{yx} & ฯƒ_{yy} & ฯ„_{yz} \\ ฯ„_{zx} & ฯ„_{zy} & ฯƒ_{xx} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

c.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ฯƒ_{xx} & ฯ„_{zz} & ฯ„_{xz} \\ ฯ„_{yx} & ฯƒ_{yy} & ฯ„_{yz} \\ ฯ„_{zx} & ฯ„_{zy} & ฯƒ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

d.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ฯƒ_{xx} & ฯ„_{yy} & ฯ„_{xz} \\ ฯ„_{yx} & ฯƒ_{yy} & ฯ„_{yz} \\ ฯ„_{zx} & ฯ„_{yy} & ฯƒ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

Discuss
Answer: (a).\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} ฯƒ_{xx} & ฯ„_{xy} & ฯ„_{xz} \\ ฯ„_{yx} & ฯƒ_{yy} & ฯ„_{yz} \\ ฯ„_{zx} & ฯ„_{zy} & ฯƒ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)
Q7.
The partial differential of normal stress in y-direction in terms of effective stress is given by __________

a.

a

b.

b

c.

c

d.

d

Discuss
Answer: (c).c
Q8.
The equilibrium equation in X-direction in terms of effected stress for a saturated soil body is given by __________

a.

\(\frac{โˆ‚ฯƒ_x{โ€˜}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yx}}{โˆ‚y}=0\)

b.

\(\frac{โˆ‚ฯ„_{xy}}{โˆ‚x}+\frac{โˆ‚ฯƒ_y{โ€˜}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zy}}{โˆ‚z}+ฮณ_w \frac{โˆ‚h}{โˆ‚x}=0\)

c.

\(\frac{โˆ‚ฯ„_{xz}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yz}}{โˆ‚y}+\frac{โˆ‚ฯƒ_z{โ€˜}}{โˆ‚z}+ฮณ_w \frac{โˆ‚h}{โˆ‚x}=0\)

d.

\(\frac{โˆ‚ฯƒ_x{โ€˜}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yx}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zx}}{โˆ‚z}+ฮณ_w \frac{โˆ‚h}{โˆ‚x}=0\)

Discuss
Answer: (d).\(\frac{โˆ‚ฯƒ_x{โ€˜}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yx}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zx}}{โˆ‚z}+ฮณ_w \frac{โˆ‚h}{โˆ‚x}=0\)
Q9.
The equilibrium equation in Y-direction in terms of effected stress for a saturated soil body is given by __________

a.

\(\frac{โˆ‚ฯƒ_x{โ€˜}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yx}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zx}}{โˆ‚z}+X=0\)

b.

\(\frac{โˆ‚ฯ„_{xy}}{โˆ‚x}+\frac{โˆ‚ฯƒ_y{โ€˜}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zy}}{โˆ‚z}+ฮณ_w \frac{โˆ‚h}{โˆ‚y}=0\)

c.

\(\frac{โˆ‚ฯ„_{xz}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yz}}{โˆ‚y}+\frac{โˆ‚ฯƒ_z{โ€˜}}{โˆ‚z}+Z=0\)

d.

\(\frac{โˆ‚ฯƒ_x{โ€˜}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yx}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zx}}{โˆ‚z}=0\)

Discuss
Answer: (b).\(\frac{โˆ‚ฯ„_{xy}}{โˆ‚x}+\frac{โˆ‚ฯƒ_y{โ€˜}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zy}}{โˆ‚z}+ฮณ_w \frac{โˆ‚h}{โˆ‚y}=0\)
Q10.
The equilibrium equation in Z-direction in terms of effected stress for a saturated soil body is given by __________

a.

\(\frac{โˆ‚ฯƒ_x{โ€˜}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yx}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zx}}{โˆ‚z}++ฮณ_w \frac{โˆ‚h}{โˆ‚z}=0\)

b.

\(\frac{โˆ‚ฯ„_{xy}}{โˆ‚x}+\frac{โˆ‚ฯƒ_y{โ€˜}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zy}}{โˆ‚z}+ฮณ_w \frac{โˆ‚h}{โˆ‚z}=0\)

c.

\(\frac{โˆ‚ฯ„_{xz}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yz}}{โˆ‚y}+\frac{โˆ‚ฯƒ_z{โ€˜}}{โˆ‚z}+ฮณโ€™+ฮณ_w \frac{โˆ‚h}{โˆ‚z}=0\)

d.

\(\frac{โˆ‚ฯƒ_x{โ€˜}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yx}}{โˆ‚y}+\frac{โˆ‚ฯ„_{zx}}{โˆ‚z}=0\)

Discuss
Answer: (c).\(\frac{โˆ‚ฯ„_{xz}}{โˆ‚x}+\frac{โˆ‚ฯ„_{yz}}{โˆ‚y}+\frac{โˆ‚ฯƒ_z{โ€˜}}{โˆ‚z}+ฮณโ€™+ฮณ_w \frac{โˆ‚h}{โˆ‚z}=0\)
Page 1 of 19