A simple beam is subjected to two concentrated  loads as shown. The beam section is a rectangular  one, A = b×h and k = 1.2. Parameters G, E, I, M, V, and A. Please find  a. The strain energy (ub and us) of the deformed  beam under the applied loads. The strain energy  ub due to bending and another one us due to shear.  b.The deflection at mid-span due to bending and  shear.

Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has circular cross sections and length L. It is subjected to a distributed torque of intensity t per unit distance. The intensity varies linearly from t = 0 at the free end to a maximum value t = to at the support. Express your answer in terms of maximum value zo , length L, shear modulus G and polar moment of inertia Ip . U =

The three equally spaced vertical rods in Fig. (a) are securely attached to a rigid horizontal bar. The two outer rods are made of an aluminum alloy, and the middle rod is steel. The cross- sectional areas of the rods are shown in the figure. Determine the residual stresses in the rods after the load P has been increased from zero to the limit load and then removed. The material properties are E = 70 GPa, Oyp = 330 M Pafor aluminum, and E = 200 GPa, Typ 290 MPa for steel. Neglect the weight of the bar. Aluminum 600 mm² Steel (a) շատ (06 Aluminum 600 mm² 250 mm 100 mm

Do not copy.