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 $$\frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

Correct Answer: $$\frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

Bissoy MCQ
#Mechanical Engineering #Strength Of Materials In ME

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 $$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$
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 $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
When a body is subjected to a direct tensile stress ($$\sigma $$) in one plane, then tangential or shear stress on an oblique section of the body inclined at an angle $$\theta $$ to the normal of the section is
A $$\sigma \sin 2\theta $$
B $$\sigma \cos 2\theta $$
C $$\frac{\sigma }{2}\sin 2\theta $$
D $$\frac{\sigma }{2}\cos 2\theta $$
When a body is subjected to a direct tensile stress ($$\sigma $$) in one plane, then normal stress on an oblique section of the body inclined at an angle $$\theta $$ to the normal of the section is
A $$\sigma \cos \theta $$
B $$\sigma {\cos ^2}\theta $$
C $$\sigma \sin\theta $$
D $$\sigma {\sin ^2}\theta $$
When a body is subjected to a direct tensile stress (σ) in one plane, the maximum shear stress is __________ the maximum normal stress.
A Equal to
B One-half
C Two-third
D Twice
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 $$\left( {2{\text{p}} - {\text{d}}} \right){\text{t}} \times {\sigma _{\text{t}}}$$
The strain energy stored in a body due to shear stress, is (where $$\tau $$ = Shear stress, C = Shear modulus and V = Volume of the body)
A $$\frac{{\tau {\text{V}}}}{{2{\text{C}}}}$$
B $$\frac{{2{\text{C}}}}{{\tau {\text{V}}}}$$
C $$\frac{{{\tau ^2}{\text{V}}}}{{2{\text{C}}}}$$
D $$\frac{{2{\text{C}}}}{{{\tau ^2}{\text{V}}}}$$
A body is subjected to a direct tensile stress (σ) in one plane. The shear stress is maximum at a section inclined at __________ to the normal of the section.
A 45° and 90°
B 45° and 135°
C 60° and 150°
D 30° and 135°
When a body is subjected to a direct tensile stress (σ) in one plane, then maximum normal stress occurs at a section inclined at _________ to the normal of the section.
A 0°
B 30°
C 45°
D 90°
A closely coiled helical spring is acted upon by an axial force. The maximum shear stress developed in the spring is $$\tau $$. The half of the length of the spring if cut off and the remaining spring is acted upon by the same axial force. The maximum shear stress in the spring in new condition will be
A $$\frac{\tau }{2}$$
B $$\tau $$
C $$2\tau $$
D $$4\tau $$

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