A bar of cross section A is subjected to equal and opposite tensile forces F at its ends- Consider the plane through the bar making an angle - with a plane at right angles to the bar shown in the figure-Shearing stress at this plane- in terms of F- A and -

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Shear Stress

A bar of cros...

Question

A bar of cross section $A$ is subjected to equal and opposite tensile forces $F$ at its ends. Consider the plane through the bar making an angle $θ$ with a plane at right angles to the bar shown in the figure.
Shearing stress at this plane, in terms of $F, A$ and $θ$

F s i n θ

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\frac{F s i n^{2} θ}{A}

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\frac{F s i n θ c o s θ}{A}

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\frac{F c o s^{2} θ}{A}

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Solution

The correct option is D $\frac{F c o s^{2} θ}{A}$
The resolved part of F along the normal is the tensile force on this plane and the resolved part parallel to the plane is the shearing force on the plane

Area of plane section = $A s e c θ$

Tensile stress = $\frac{F o r c e}{A r e a}$ = $\frac{F c o s θ}{A s e c θ}$

$\frac{F}{A} c o s^{2} θ$

Shearing stress applied on the top face

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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?

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A bar of cross section A is subjected to equal and opposite tensile forces F at its ends. Consider the plane through the bar making an angle θ with a plane at right angles to the bar shown in the figure.Shearing stress at this plane, in terms of F, A and θ

A bar of cross section $A$ is subjected to equal and opposite tensile forces $F$ at its ends. Consider the plane through the bar making an angle $θ$ with a plane at right angles to the bar shown in the figure.
Shearing stress at this plane, in terms of $F, A$ and $θ$