When an initially straight beam sags under transverse loading, the ends contract because the neutral surface of zero strain neither extends nor contracts. The length of the deflected neutral surface is the same as the original beam length l. Consider a segment of the initially straight beam Δs. After bending, the x-direction component is shorter than Δs, namely, Δx. The contraction is Δs −Δx , and these summed for the entire beam gives the end contraction λ. Show that λ =