Energy stored in a strained wire is equal to work done by the load to increase the length of wire.
\(\therefore\) Energy, \(U=\) Work done
\(=\) Average force (load)\(\times\) Extension in the wire
\(=\left(\frac{0+F}{2}\right) \times\) Extension
\(=\frac{F}{2} \times\) Extension
\(=\frac{1}{2} \times\) Load \(\times\) Extension