Sketch the free-body diagram of element 2 for the frame analysed in Problem 12.27 highlighting all actions applied to it. Problem 12.27 Using the stiffness method, determine the nodal displacements...

Sketch the free-body diagram of element 2 for the frame analysed in Problem 12.27 highlighting all actions applied to it.

Problem 12.27

Using the stiffness method, determine the nodal displacements and reactions induced by a temperature change for the frame shown. A linear temperature change is assumed to be applied over the doubly-symmetric cross-sections of both elements 1 and 2 (with depth equal to 0.4 m), with top and bottom variations equal to ΔTa = 20°C and ΔTb = 10°C. The temperature changes are constant over the length of each element. Assume I = 300 × 106 mm4, A = 10 × 103 mm2, E = 200 GPa and α = 11 × 10−6/°C.