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Byju's Answer

Standard XII

Physics

Shear Strain

A bar of cros...

Question

A bar of cross-section A is subjected two equal and opposite tensile forces at its ends consider a plane section of the bar whose normal makes an angle $θ$ with the axis of the bar.
What is the shearing stress on this plane?

(F / 3 A) sin 2 θ

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(F / 2 A) sin 2 θ

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(F / 4 A) sin 2 θ

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(F / 5 A) sin 2 θ

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Solution

The correct option is B $(F / 2 A) sin 2 θ$ .

$Shear Stress = \frac{F_{along the plane}}{A plane}$

$\begin{matrix} = \frac{F sin θ}{A sec θ} = \frac{F sin θ \cdot cos θ}{A} = (\frac{F}{2 A}) (sin 2 θ) \end{matrix}$

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Similar questions

A bar of cross-section A is subjected to two equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle θ with the axis of the bar.

·What is the tensile stress on this plane?

·What is the shearing stress on this plane?

Q. A bar of cross-section A is subjected two equal and opposite tensile forces at its ends consider a plane section of the bar whose normal makes an angle

θ

with the axis of the bar.
For what value of

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is the shearing stress maximum?

Q. A bar of cross section

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is subjected to equal and opposite tensile forces

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at its ends. Consider the plane through the bar making an angle

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with a plane at right angles to the bar shown in the figure.
Shearing stress at this plane, in terms of

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and

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Q. A bar of cross-section A is subjected to two equal and opposite tensile forces at its ends consider a plane section of the bar whose normal makes an angle

θ

with the axis of the bar. For what value of

θ

is the tensile stress is maximum?

Q. A bar of cross-section A is subjected to equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle

θ

with the axis of the bar.
For what value of

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is the tensile stress maximum?

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A bar of cross-section A is subjected two equal and opposite tensile forces at its ends consider a plane section of the bar whose normal makes an angle θ with the axis of the bar.What is the shearing stress on this plane?

The correct option is B (F/2A)sin2θ. Shear Stress =Falong the plane A plane =FsinθAsecθ=Fsinθ⋅cosθA=(F2A)(sin2θ)

A bar of cross-section A is subjected two equal and opposite tensile forces at its ends consider a plane section of the bar whose normal makes an angle $θ$ with the axis of the bar.
What is the shearing stress on this plane?

The correct option is B $(F / 2 A) sin 2 θ$ .

$Shear Stress = \frac{F_{along the plane}}{A plane}$

$\begin{matrix} = \frac{F sin θ}{A sec θ} = \frac{F sin θ \cdot cos θ}{A} = (\frac{F}{2 A}) (sin 2 θ) \end{matrix}$