Question

A prismatic linearly elasitc bar of length L, cross-sectional area A, and made up of a material with Young's modulus E, is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile forces $P_1$ and $P_2$, the strain energies stored in the bar are $U_1$ and $U_2$ respectively.

If U is the strain energy stored in the same bar when subjected to an axial tensile forece$(P_1+P_2)$ , the correct relationship is

• A. $U=U_1-U_2$
• B. $U<U_1-U_2$
• C. $U>U_1+U_2$
• D. $U=U_1+U_2$

Answer 1

The correct option is C $U>U_1+U_2$


When bar is subjected to load $P_1$ the strain energy stored,
$U_1=\frac{P_1^{2}l}{2AE}...\left(1\right)$
wher $l$ =length of bar
when bar is subjected to load $P_1$, the strain energy stored,
$U_2=\frac{P_2^{2}l}{2AE}...\left(2\right)$
Now when bar is subjected to load $(P_1+P_2)$, the strain energy stored,
$U=\frac{(P_1+P_2{)}^{2}l}{2AE}$
$=\frac{P_1^{2}l}{2AE}+\frac{P_2^{2}l}{2AE}+\frac{2P_1{P}_{2}l}{2AE}..\left(3\right)$
Fro (1) ,(2) &(3), we can say
$U>U_1+U_2$
Hence option (c)