Analyse the statically indeterminate beam illustrated below by integrating the governing differential equation, applying the boundary conditions appropriately. Find the shear force, bending moment and displacement at point A. The cross section of the beam is constant with EI = 1200 kN.m2. a = 3.0 m, b = 2.0 m, c = 3.0 m and d = 2.0 m. w = 6 kN/m, and P = 20 kN. The bar is also subjected to a differential temperature increase at the time the load is applied. This temperature change is constant over the length of the beam, but varies linearly over the beam height (which is 0.125 m) and is Ti = 50 °C at the top of the beam and T2 = 70 °C at the bottom of the beam (the coefficient of thermal expansion at = 1.5e-05°C-1).

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