Chapter 9, Problem 9.1P

Write the direct stress formula in its three forms and explain the meaning of each one.

To determine

To write: Direct stress formula in three forms and explain the meaning of each one.

Explanation of Solution

The three forms direct stress formula are as follows:

1.

  $\sigma =\frac{P}{A}$

Here,

  $\sigma =$ The average normal stress

  $P=$ Eternal applied force or load on the resection (lb, kips or N)

  $A=$ Area of cross- section over which the stress develops

It means the average normal stress in a member is equal to axial normal force acting on it divided by the area of cross-section on which the normal force acts. It is used to calculate the average stress developed in a member having a cross- sectional area A, when an external force of magnitude P act.

2.

  $P={\sigma }_{\max .}\times A$

Where,

P is the axial load capacity.

A is the cross-sectional area of the member.

${\sigma }_{\max }$ is maximum permissible stress

This form of the formula is used to calculate the maximum load capacity (maximum permissible axial load) of a member having maximum permissible stress, ${\sigma }_{\max }$ , and area of cross -section A.

3.

  $P=S_{all}.A$

Where,

P is the axial load capacity.

A is the cross-sectional area of the member.

  $S_{all}$ is Permissible axial stress.

This formula is applicable for Analysis of load capacity.