δ δ = ∂ ∂ U ∂ ∂ P δ δ = ∂ ∂ ∂ ∂ P ∫ ∫ 0 L M 2 ( x ) 2 E I d x = ∂ ∂ ∂ ∂ P ∫ ∫ 0 L ( P x ) 2 2 E I d x where E is Young's modulus, I is the second moment of area of the cross-section, and M ( x ) = P x is the expression for the internal moment at a point at distance x from the end. The integral evaluates to: δ δ = ∫ ∫ 0 L P x 2 E I d x = P L 3 3 E I .