Assume the temperature function to vary linearly over the length of a bar as T = t1 + t2...

Assume the temperature function to vary linearly over the length of a bar as T = t₁ + t₂x; that is, express the temperature function as {T} = [N {t}, where [N = is the shape function matrix for the two-node bar element. In other words, [N = [1 – x /L x/L]. Determine the force matrix in terms of E, A, α, L, t₁, and t₂. [Hint: Use Eq. (15.1.18).]

Eq. (15.1.18).]