# Stress and strain

Let us consider a rod having a young's modulus $Y$. Let it be of length $l$, and suppose it is suspended from a point P. Let us pull the rod with a force $F$ at a point Q which is at a distance $2/3l$ from the point P. Next let us apply the same force at the other end point of the rod. Is the length of the rod in both the cases same?

• It is not clear over what length you apply $F$ the second time. Same stress, cross-section and stiffness will however always lead to the same strain, so in the frist case the rod will be $l+\frac{2}{3}l\varepsilon$, in the second (whole length loaded??) $l+l\varepsilon$, where strain $\varepsilon=\frac{F/A}{Y}$, where $A$ is cross-section. Sep 27, 2011 at 15:41

So in the first case the strain is $\Delta l/(2/3 L) = 3 \Delta l/ 2 L$.
Deflection is $$\delta = \frac{F\,L}{Y\,A}$$ where $F$ is force, $L$ is the loaded length, $Y$ is modulus of elasticity and $A$ is the cross sectional area.
So the deflection $\delta$ is proportional to the loaded length. In your case a) that is $L=\frac{2}{3}l$, but in case b) I cannot figure out from the wording where points P and Q are. Figure out what $L$ is since the rest is the same, you will have your answer.