List of top Structures Questions on Deflection of beams

A stepped cantilever beam, made of a material having Young's modulus \(E = 200\) GPa, is shown in the figure below.

The length and the moment of inertia of the beam from point A to B are \(L_1 = 100\) mm and \(I_1 = 100\) mm\(^4\), respectively. The length and the moment of inertia of the beam from point B to C are \(L_2 = 100\) mm and \(I_2 = 700\) mm\(^4\), respectively. A shear force \(P = 30\) N is applied at point A of the beam. The magnitude of the deflection of the beam at point A is _______ mm (rounded off to 1 decimal place).

Two cantilever beams AB and DC touch at their free ends through a roller. Both beams have a 50 mm × 50 mm square cross section and modulus \(E = 70\ \text{GPa}\). Beam AB carries a UDL of 20 kN/m. Determine the compressive force at the roller (round off to one decimal place).