Principal Stresses and Plane

Q. The major and minor principal stresses at a point are 3 MPa and -3 MPa respectively. The maximum shear stress at the point is

1. Zero
2. 3 MPa
3. 6 MPa
4. 9 MPa

Q. In a plane stress problem, there are normal tensile stresses ${\sigma }_{x}and{\sigma }_{y}with{\sigma }_x>{\sigma }_y,$ accompanied by shear stress${\tau }_{xy}$ at a point in the x-plane. If it is observed that the minimum principal stress on a certain section is zero, then

1. ${\tau }_{xy}=\sqrt{{\sigma }_x\cdot {\sigma }_y}$

2. ${\tau }_{xy}=\sqrt{\frac{{\sigma }_x}{{\sigma }_y}}$

3. ${\tau }_{xy}=\sqrt{{\sigma }_x-{\sigma }_y}$

4. ${\tau }_{xy}=\sqrt{{\sigma }_x+{\sigma }_y}$

Q. The state of stresses on an element is shown in the given figure. The value of stresses are ${\sigma }_x(=32MPa);{\sigma }_y(=-10MPa)$ and major principal stress ${\sigma }_1(=40MPa)$. The minor principal stress ${\sigma }_2$ is

1. -22 MPa
2. -18 MPa
3. 22 MPa
4. indeterminable due to insufficient data

Q. Consider the following statements :

I. On a principal plane, only normal stress acts.
II. On a principal plane, both normal and shear stresses act.
III. On a principal plane, only shear stress acts.
IV. Isotropic state of stress is independent of frame of reference.

The TRUE statements are

1. I and IV
2. II
3. II and IV
4. II and III

Q. In a stressed body, an elementary cube of material is taken at a point with its faces perpendicular to X and Y reference axes. Tensile stresses equal to $15kN/c{m}^{2}and9kN/c{m}^2$ are observed on these respective faces. They are also accompanied by shear equal to 4 $kN/c{m}^2$. The magnitude of the principal stresses at the point are

1. 12 $kN/c{m}^2$ tensile and 3 $kN/c{m}^2$ tensile
2. 17 $kN/c{m}^2$ tensile and 7 $kN/c{m}^2$ tensile
3. 9.5 $kN/c{m}^2$ compressive and 6.5$kN/c{m}^2$ tensile compressive
4. 12 $kN/c{m}^2$ tensile and 3 $kN/c{m}^2$ tensile

Q. The rectangular block shown in the given figure is subjected to pure shear of intensity 'q'. If BE represents the principal plane and the principal stresses are ${\sigma }_1,{\sigma }_2$; then the value of $\theta ,{\sigma }_{1}and{\sigma }_2$ will be respectively.

1. 0°, 90°;+q and -q
2. 30°, 120°;+q and -q
3. 45°, 135°; $+\frac{q}{2}and-\frac{q}{2}$
4. 45°, 135°; + q and - q

Q. At a certain point in a strained material, there are two mutually perpendicular stresses ${\sigma }_x=100N/m{m}^2$ (tensile) and ${\sigma }_y=500N/m{m}^2$ (compressive).
[Notation : tension (+); compression (-)]
What are the values of the principal stresses in $N/m{m}^2$ at the point?

1. 100, -50
2. -100, 50
3. 75, -25
4. -75, 25

Q. If the maximum principal stress for an element under bi-axial stress situation is 100 MPa (tensile) and the maximum shear stress is also 100 MPa, then what is the other principal stress?

1. 200 MPa (tensile)
2. 200 MPa (compressive)
3. 100 MPa (compressive)
4. zero

Q. For a case of plane stress, ${\sigma }_x=40MN/m^2,{\sigma }_y=0,{\tau }_{xy}=80MN/m^2.$ What are the principal stresses$\left(inMN/m^2\right)$ and their orientation with x and y axes?

1. ${\sigma }_1=80,{\sigma }_2=40,{\theta }_1=30{}^{\circ }$
2. ${\sigma }_1=100,{\sigma }_2=-60,{\theta }_1=32{}^{\circ }$
3. ${\sigma }_1=102.5,{\sigma }_2=-62.5,{\theta }_1=36{}^{\circ }$
4. ${\sigma }_1=105,{\sigma }_2=62,{\theta }_1=36{}^{\circ }$

Q. Figure below shows a state of plane stress.


If the minimum principal stress is $-7MN/m^2$ then what is the value of ${\sigma }_x$?

1. 30 $MN/m^2$
2. 68 $MN/m^2$
3. 98 $MN/m^2$
4. 105 $MN/m^2$

Q. For the state of stress shown in the figure, the maximum and minimum principal stresses (taking tensile stress + and compressive stress as -) will be

1. 95 MPa and (-35) MPa
2. 60 MPa and 30 MPa
3. 95 MPa and (-30) MPa
4. 60 MPa and 35 MPa

Q. At a point in the web of a girder, the bending and the shearing stresses are 90 $N/m{m}^2$ (tensile) and 45 $N/m{m}^2$ respectively. The principal stresses are

1. 108.64 $N/m{m}^2$ (tensile) and 18.64 $N/m{m}^2$ (compressive)
2. 107.60 $N/m{m}^2$ (compressive) and 18.64 $N/m{m}^2$ (tensile)
3. 108.64 $N/m{m}^2$ (compressive) and 18.64 $N/m{m}^2$ (tensile)
4. 0.64 $N/m{m}^2$ (tensile) and 0.78 $N/m{m}^2$ (compressive)

Q. In a plane stress problem there are normal tensile stresses ${\sigma }_{x}and{\sigma }_y$ accompained by shear stress ${\tau }_{xy}$ at a point along orthogonal Cartesian co-ordinates x and y respectively. If it is observed that the minimum principal stress on certain plane is zero then

1. ${\tau }_{xy}=\sqrt{{\sigma }_x+{\sigma }_y}$

2. ${\tau }_{xy}=\sqrt{{\sigma }_x-{\sigma }_y}$

3. ${\tau }_{xy}=\sqrt{{\sigma }_x{\sigma }_y}$

4. ${\tau }_{xy}=\sqrt{\frac{{\sigma }_x}{{\sigma }_y}}$

Q. The principal stresses at a point in a stressed material are
${\sigma }_1=200N/m{m}^2$, ${\sigma }_2=150N/m{m}^2$, and ${\sigma }_3=200N/m{m}^2$. E = 210 $kN/m{m}^{2}and\mu =0.3$. The volumetric strain will be

1. $8.945\times {10}^{-4}$
2. $8.945\times {10}^{-2}$
3. $6.54\times {10}^{-3}$
4. $6.54\times {10}^{-4}$

Q. The state of two-dimensional stresses acting on a concrete lamina consists of a direct tensile stress ${\sigma }_x=1.5N/m{m}^2$ and shear stress $\tau =1.20N/m{m}^2$, when cracking of concrete is just impending. The permissible tensile strength of the concrete is

1. 1.50 $N/m{m}^2$
2. 2.17 $N/m{m}^2$
3. 2.08 $N/m{m}^2$
4. 2.29 $N/m{m}^2$

Q. In a strained material, the principal stresses in the X and Y directions respectively are 100 $N/m{m}^2$ (Tensile) and 60 $N/m{m}^2$ (Compressive). On an inclined plane, the normal to which makes an angle of 30° to the X-axis, the major prinipal stress, in $N/m{m}^2$, would be

1. 60
2. 80
3. 20
4. 40