§11.14 Strain Energy 273 deflection under the load is equal to the end deflection of either cantilever and given by eqn.(11.19), 6 6 or 6Wab 8.=5AGL (11.23) (e)Simply supported beam carrying uniformly distributed load Using a similar treatment to that described above,the equivalent cantilever system is shown in Fig.11.15,i.e.each cantilever now carries an end load of wL/2 in one direction and a uniformly distributed load w over its complete length L/2 in the opposite direction. From eqns.(11.19)and (11.20) 6 3wL2 ，= (11.24) 20AG w/unit length WL Fig.11.15.Equivalent loading for uniformly loaded beam. (f)I-section beams If the shear force is assumed to be uniformly distributed over the web area A,a similar treatment to that described above yields the following approximate results: WL cantilever with concentrated end load w δs= AG wL2 WL cantilever with uniformly distributed δ，= load w 2AG 2AG WL simply supported beam with concentrated 6,= end load w 4AG wL2 WL simply supported beam with uniformly 6,= distributed load w 8AG 8AG411.14 Strain Energy 213 deflection under the load is equal to the end deflection of either cantilever and given by eqn. (1 1.19), 6,=-(%)b 5AG 6 L or 6,=- 5AG (wb)a - L 6 Wab SAGL .. 6, = ~ (11.23) (e) Simply supported beam carrying uniformly distributed load Using a similar treatment to that described above, the equivalent cantilever system is shown in Fig. 11.15, i.e. each cantilever now carries an end load of wL/2 in one direction and a uniformly distributed load w over its complete length L/2 in the opposite direction. From eqns. (11.19) and (11.20) 3wL2 6, = ~ 20AG w/unif length (11.24) Fig. 11.15. Equivalent loading for uniformly loaded beam. (f) 1-section beams If the shear force is assumed to be uniformly distributed over the web area A, a similar treatment to that described above yields the following approximate results: WL 6 =- AG cantilever with concentrated end load W cantilever with uniformly distributed load w wL2 WL 2AG == 6, = __ WL 6, = - 4AG simply supported beam with concentrated end load W wL2 WL 6, = __ ~AG =8AG simply supported beam with uniformly distributed load w