272 Mechanics of Materials §11.14 Therefore shear deflection over the length of the small element dx 6w刘dx 5 AG from(11.19) Therefore total shear deflection L 6 wxdx 3wL2 0s= 5 AG 5AG (11.21) 0 (c)Simply supported beam carrying central concentrated load In this case it is convenient to treat the beam as two cantilevers each of length equal to half the beam span and each carrying an end load half that of the central beam load(Fig.11.13). The required central deflection due to shear will equal that of the end of each cantilever,i.e. from egn.(11.19),with W=W/2 and LL/2, 8,= 6 W L 3WL (11.22) 10AG 2 Fig.11.13.Shear deflection of simply supported beam carrying central concentrated load-equivalent loading diagram. (d)Simply supported beam carrying a concentrated load in any position If the load divides the beam span into lengths aand b the reactions at each end will be Wa/L and Wb/L.The equivalent cantilever system is then shown in Fig.11.14 and the shear Fig.11.14.Equivalent loading for offset concentrated load.272 Mechanics of Materials 511.14 Therefore shear deflection over the length of the small element dx - (wx) dx from (11.19) 5 AG Therefore total shear deflection L 6 wxdx 3wL2 5AG 6s= 5AG- -- s 0 (11.21) (c) Simply supported beam carrying central concentrated load In this case it is convenient to treat the beam as two cantilevers each of length equal to half the beam span and each carrying an end load half that of the central beam load (Fig. 11.13). The required central deflection due to shear will equal that of the end of each cantilever, i.e. from eqn. (11.19), with W = W/2 and L = L/2, (11.22) W W L W 2 2 - - Fig. 11.13. Shear deflection of simply supported beam carrying central concentrated load-equivalent loading diagram. (d) Simply supported beam carrying a concentrated load in any position If the load divides the beam span into lengths a and b the reactions at each end will be Wa/L and Wb/L. The equivalent cantilever system is then shown in Fig. 11.14 and the shear Fig. 11.14. Equivalent loading for offset concentrated load