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The given figure shows the Mohr's circle of stress for two unequal and like principal stresses (σ<sub>x</sub> and σ<sub>y</sub>) acting at a body across two mutually perpendicular planes. The resultant stress is given by<br> <img src="/images/question-image/mechanical-engineering/strength-of-materials/1528354721-24.JPG" title="Strength of Materials mcq question image" alt="Strength of Materials mcq question image">
A
OC
B
OP
C
OQ
D
PQ
Correct Answer:
OP
The given figure shows the Mohr's circle of stress for two unequal and like principal stresses (σ
x
and σ
y
) acting at a body across two mutually perpendicular planes. The normal stress on an oblique section making an angle θ with the minor principle plane is given by
A
OC
B
OP
C
OQ
D
PQ
If p
1
and p
2
are mutually perpendicular principal stresses acting on a soil mass, the normal stress on any plane inclined at angle $${\theta ^ \circ }$$ to the principal plane carrying the principal stress p
1
, is:
A
$$\frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2}\sin \,2\theta $$
B
$$\frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2}\cos\,2\theta $$
C
$$\frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2}\cos\,2\theta $$
D
$$\frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2}\sin \,2\theta $$
The 3-dimensional state of stress consists of 3 unequal principal stresses acting on a point, this is called the triaxial state of stress. If two of the three principal stresses are equal, the state of stress is known as __________
A
cylindrical
B
uniaxial
C
spherical/hydrostatic
D
triaxial
The three-dimensional state of stress consists of 3 unequal principal stresses acting on a point, this is called the triaxial state of stress. If all the three principal stresses are equal, the state of stress is known as __________
A
cylindrical
B
uniaxial
C
spherical/hydrostatic
D
triaxial
The figure shows a shape ABC and its mirror image A
1
B
1
C
1
across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A
1
B
1
C
1
is
A
\\
B
</span> \\
Body with material properties that are different in three mutually perpendicular directions at a point in the body and further has three mutually perpendicular planes of material property symmetry are called as ________
A
Orthotropic materials
B
Anisotropic materials
C
Non-homogeneous materials
D
Isotropic materials
The pictorial view of the frustum of a square pyramid is shown in figure 'X'. Its top view, when viewed in the direction of the arrow, will look like which of the given alternatives 1, 2, 3 and 4?
A
1
B
2
C
3
D
4
When a body is subjected to biaxial stress i.e. direct stresses $$\left( {{\sigma _{\text{x}}}} \right)$$ and $$\left( {{\sigma _{\text{y}}}} \right)$$ in two mutually perpendicular planes accompanied by a simple shear stress $$\left( {{\tau _{{\text{xy}}}}} \right),$$ then maximum normal stress is
A
$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
B
$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
C
$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
D
$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
When a body is subjected to biaxial stress i.e. direct stresses $$\left( {{\sigma _{\text{x}}}} \right)$$ and $$\left( {{\sigma _{\text{y}}}} \right)$$ in two mutually perpendicular planes accompanied by a simple shear stress $$\left( {{\tau _{{\text{xy}}}}} \right),$$ then minimum normal stress is
A
$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
B
$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
C
$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
D
$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
When a body is subjected to biaxial stress i.e. direct stresses ($${\sigma _{\text{x}}}$$) and ($${\sigma _{\text{y}}}$$) in two mutually perpendicular planes accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), then maximum shear stress is
A
$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
B
$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
C
$$\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$
D
$$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$
