## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## WriteWise AI Model by Holooly Genius

Your Ultimate AI Essay Writer & Assistant.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

## Holooly Help Desk

Need Help? We got you covered.

Products

## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## WriteWise AI Model by Holooly Genius

Your Ultimate AI Essay Writer & Assistant.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

## Holooly Help Desk

Need Help? We got you covered.

## Q. 10.1

Calculate the strain energy of the stepped rod as shown in Figure 10.16. ## Verified Solution

From Eq. (10.17), we can say

$U_i=\int_0^{L_i} \frac{P^2}{2( AE )_i} d x ; \quad 1 \leq i \leq 3$           (10.17)

U = Total strain – Energy of the stepped rod

$=U_1+U_2=\frac{P^2(L / 2)}{2 A E}+\frac{P^2(L / 2)}{2(A / 2) E}$

as the same force is acting on both rods. So,

$U=\frac{P^2 L}{4 A E}+\frac{P^2 L}{2 A E}=\frac{3}{4} \frac{P^2 L}{A E}=\frac{3}{2} \frac{P^2 L}{2 A E}$

$\text { Thus, } U=1.5 U_0 \text { where } U_0=P^2 L / 2 A E$ is the strain energy of a prismatic rod of length L and cross-sectional area, A. It is observed that strain energy stored within the rod is 1.5 times that of an equivalent prismatic rod.

$U=\frac{3}{4} \frac{P^2 L}{A E}$