Home
Class 12
PHYSICS
A bar of cross-section A is subjected tw...

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 ?

Text Solution

Verified by Experts

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. Tensile stress= force/area =F cos `theta`/A sec `theta` =`(F//A)cos^2theta`
(`because` Area of cross-section = `A sec theta` )
(b)Shearing stress= force/Area = `F sin theta//A sec theta=(F//2A)sin 2 theta`
(c ) Obviously , tensile stress on the plane is maximum when `cos^2 theta` is maximum that is cos `theta`=1
or `theta=0^@`
(d) Obviously , shearing stress is maximum when sin `2 theta` is maximum ,
i.e. sin `2 theta =1`
or `2theta=90^@ rArr theta =45^@`
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY AND WAVES

    FIITJEE|Exercise Solved Problems|27 Videos

  • ELASTICITY AND WAVES

    FIITJEE|Exercise Comprehension|16 Videos

  • CURRENT ELECTRICITY

    FIITJEE|Exercise Comprehension -4|3 Videos

  • ELECTROMAGNETIC INDUCTION

    FIITJEE|Exercise EXERCISE|9 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 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?

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 ?

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

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 for what alpha the shearing strain is maximum.