Question

A bar is subjected to axial forces as shown . if E is the modulus of elasticity of the bar and A is its cross-section area . Its elongation will be

Answer 1

The elongation of the bar will be $\frac{PL}{AE}$.

When the bar is subject to a axial force (P) than the stress generate by the bar is given as

σ=P/A

Here, A is the area of the bar

According to the Hook's law stress is directly proportional to the strain, with in the elastic limit

σ=Eε

Here E is the young's modulus

Plugging the values

P/A=E*(Δl/l)

here Δl is the elongation, and l is the initial length of the bar

Rearranging the above formula for elongation of the bar

Δl=$\frac{PL}{AE}$

Hence the elongation of the bar is $\frac{PL}{AE}$.

Answer 2

Considering the halves separately