Strain Energy 279 the deflection is given by 60, 800×5×10-3 1×10的 =4×10-3 =4mm Example 11.4 A horizontal steel beam of I-section rests on a rigid support at one end,the other end being supported by a vertical steel rod of 20mm diameter whose upper end is rigidly held in a support 2.3m above the end of the beam(Fig.11.17).The beam is a 200 x 100mm B.S.B.for which the relevant I-value is 23 x 10-6mand the distance between its two points of support is 3 m.A load of 2.25kN falls on the beam at mid-span from a height of 20 mm above the beam. Determine the maximum stresses set up in the beam and rod,and find the deflection of the beam at mid-span measured from the unloaded position.Assume E =200 GN/m2 for both beam and rod. 20mm dig. L23m W=2.25kN 20 mm -15m 3m Fig.11.17. Solution Let the shock load cause a deflection aof the beam at the load position and an extension g of the rod.Then if We is the equivalent static load which produces the deflection a and P is the maximum tension in the rod, P2 LR 1 total strain energy work done by falling massStrain Energy 279 the deflection is given by = 4 x 10-3 800 x 5 x - 1 x 103 = 4mm Example 11.4 A horizontal steel beam of I-section rests on a rigid support at one end, the other end being supported by a vertical steel rod of 20mm diameter whose upper end is rigidly held in a support 2.3 m above the end of the beam (Fig. 11.17). The beam is a 200 x 100 mm B.S.B. for which the relevant I-value is 23 x m4 and the distance between its two points of support is 3 m. A load of 2.25 kN falls on the beam at mid-span from a height of 20 mm above the beam. Determine the maximum stresses set up in the beam and rod, and find the deflection of the beam at mid-span measured from the unloaded position. Assume E = 200 GN/m2 for both beam and rod. dio W =225kN Fig. 11.17. Solution Let the shock load cause a deflection SBof the beam at the load position and an extension SR of the rod. Then if WE is the equivalent static load which produces the deflection SB and P is the maximum tension in the rod, P2LR 1 2AE 2 total strain energy = - +- WES, = work done by falling mass