A plate with an elliptical hole in the centre, with semi-major axis (a) perpendicular to the direction of loading and semi-minor axis (b) along the direction of loading, is subjected to a pull P. The maximum stress induced at the edge of the hole is equal to (where $$\sigma $$ = Stress for a plate with no hole i.e. nominal stress)

A $$\sigma \left( {1 + \frac{{\text{b}}}{{2{\text{a}}}}} \right)$$
B $$\sigma \left( {1 + \frac{{2{\text{a}}}}{{\text{b}}}} \right)$$
C $$\sigma \left( {1 + \frac{{\text{b}}}{{3{\text{a}}}}} \right)$$
D $$\sigma \left( {1 + \frac{{3{\text{a}}}}{{\text{b}}}} \right)$$

Correct Answer: $$\sigma \left( {1 + \frac{{2{\text{a}}}}{{\text{b}}}} \right)$$

Bissoy MCQ
#Mechanical Engineering #Machine Design

Related Questions

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 $$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$
In order to avoid tearing of the plate at an edge, the distance from the centre line of the rivet hole to the nearest edge of the plate should be equal to (where d = Diameter of rivet hole)
A 1 d
B 1.5 d
C 2.5 d
D 2 d
When a body is subjected to direct tensile stresses ($${\sigma _{\text{x}}}$$ and $${\sigma _{\text{y}}}$$) in two mutually perpendicular directions, accompanied by a simple shear stress $${\tau _{{\text{xy}}}}{\text{,}}$$  then in Mohr's circle method, the circle radius is taken as
A $$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} + \tau $$
B $$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} + \tau $$
C $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
D $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
The pull required to tear off the plate per pitch length is (where p = Pitch of rivets, t = Thickness of plates and $${\sigma _{\text{t}}},\,\tau $$  and $${\sigma _{\text{c}}}$$ = Permissible tensile, shearing and crushing stresses respectively)
A $$\left( {{\text{p}} - 2{\text{d}}} \right){\text{t}} \times {\sigma _{\text{c}}}$$
B $$\left( {{\text{p}} - {\text{d}}} \right){\text{t}} \times \tau $$
C $$\left( {{\text{p}} - {\text{d}}} \right){\text{t}} \times {\sigma _{\text{t}}}$$
D $$\left( {2{\text{p}} - {\text{d}}} \right){\text{t}} \times {\sigma _{\text{t}}}$$
To avoid the tearing off the plate of an edge, the margin (i.e., the minimum distance from the centre of the rivet hole to the nearest edge of the plate) should be equal to
A 0.5 d
B D
C 1.5 d
D 2.5 d
In order to avoid tearing off the plate at an edge, the distance from the center of the rivet hole to the nearest edge of the plate (i.e. margin) should be (where d = Diameter of rivet hole in mm)
A d
B 1.5 d
C 2 d
D 2.5 d
In order to avoid tearing of the plate at edge, the distance from the center line of the rivet hole to the nearest edge of the plate in terms of dia. of rivet d should be equal to
A 1 d
B 1.25 d
C 1.5 d
D 1.75 d
When a body is subjected to a direct tensile stress ($${\sigma _{\text{x}}}$$) in one plane accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), the maximum shear stress is
A $$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$
B $$\frac{{{\sigma _{\text{x}}}}}{2} - \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$
C $$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 - 4\tau _{{\text{xy}}}^2} $$
D $$\frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$
Tearing resistance required to tear off the plate per pitch length is (where p = Pitch of rivets, d = Dia. of rivet hole and $${\sigma _{\text{t}}}$$ = Permissible tensile stress for plate material)
A $${\text{pd}}{\sigma _{\text{t}}}$$
B $${\text{pt}}{\sigma _{\text{t}}}$$
C $$\left( {{\text{p}} - {\text{d}}} \right){\sigma _{\text{t}}}$$
D $$\left( {{\text{p}} - {\text{d}}} \right){\text{t}}{\sigma _{\text{t}}}$$
According to Fleming's right-hand rule for finding the direction of induced e.m.f., when middle finger points in the direction of induced e.m.f., forefinger will point in the direction of
A Motion of conductor
B Lines of force
C Either of the above
D None of the above

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