Home
Class 11
PHYSICS
A bar of cross section A is subjected to...

A bar of cross section `A` is subjected to equal and opposite tensile force at its ends. Consider a plane section of the bar whose normal makes an angle `theta` with the axis of the bar.

a. What is the tensile stress on the plane?
b. What is the shearing stress on the this plane?
c. For what value of `theta` is the tensile stress maximum?
d. For what value of `theta` is the shearing stress maximum?

Text Solution

Verified by Experts

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 this plane.

Therefore, tensile stress `=("Force")/("Area")=(Fcostheta)/(Asectheta)=F/Acos^(2)theta`
`(:'` Area of section `= Asectheta)`
b. Shearing stress `=("Force")/("Area")=(Fsintheta)/(Asectheta)=F/(2A)sin2theta`
c. Obviously, tensile stress on the plane is maximum when `cos^(2)theta` is maximum that is `costheta=1` or `theta=0^@`.
d.Obviously shearing stress is maximum when is `sin2theta` is maximum that is
`sin2theta=1` or `2theta=90^@` or `theta=45^@`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS|Exercise Solved Examples|11 Videos

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS|Exercise Exercise 5.1|12 Videos

  • NEWTON'S LAWS OF MOTION 2

    CENGAGE PHYSICS|Exercise Integer type|1 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS|Exercise Integer|11 Videos

Similar Questions

Explore conceptually related problems

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 theta with the axis of the bar . (i) What is the tensile stress on this plane? (ii) What is the shearing stress on this plane? (iii) For what value of theta is the tensile stress maximum (iv) For what value of theta is the shearing stress maximum?

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 makes an angle theta with the axis of the bar. (a) what is the tensile stress on this plane ? (b)what is the shearing stress on this plane ? (c )for what value of theta is the tensile stress is maximum ? (d) for what value of theta is the shearing stress maximum ?

A bar of cross- sectional area A is is subjected two equal and opposite tensile forces at its ends as shown in figure. Consider a plane BB' making an angle theta with length

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

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

A bar of cross section A is subjected to equal and opposite tensile forces F at its ends. Consider a plane through the bar making an angle theta with a plane at right angles to the bar as shown in figure. In the above problem, for what value of theta is the tensile stress maximum ?

A steel bar of cross section A is subjected to two equal and opposite pulling forces at the two ends. If there is a plane through the bar making an angle alpha as shown, find the shearing stress at this plane

In the above problem, for what angle is the shearing stress a maximum?

Shearing stress causes change in