Question

9.14 Uniformly distributed loads are applied to beam AE as shown. (a) Selecting the x axis through the centers A and E of the end sections of the beam, determine the equation of the elastic curve for portion AB of the beam. (b) Knowing that the beam is a W200 x 35.9 rolled shape and that L = 3 m, w 5 kN/m, and 200 GPa, determine the distance of the center of the beam from the x axis. E 3w B E I A L/3 Fig. P9.14

Answer 1

Rolution 3W B A TA I W W200X35.9 L3 L./3 hese 20 SKN/M a),&b) Cawsides a seetion & E=200 GPa 20 in pottion Coce) AB take left past af the sectia fos A X M 0 M W2 EI d'y dx2 fulegedeng EI. dy dx + C +Cr EL(y)

conidee the ection in past BD ie 니3 B A M applying equilibria eu K + M . C) wx 3w -M, a. +( 2- MH 2. EI d 2- dx 2 on botth sides feteyradinw FI. dy= dx wx wxi 24 4) now opply ing bounchy Condifias a-0,yo) at 0-044410)+ G y at AB from e k w O C3 C3 C=

at x ABD from C-C3 h 2 Comstauts 50 C1=C3 =O from symmetry boundey Condition here at x from an , from eqn c,=-W +w 48 432 CR s4 *>t &X 24 meaus since ro) (4 we have slope en sy C,=

a) elastfc cvve in potliw AB we t C1t C2 24 wi 24 ET S4 b). distance pf Centre of beam trom -oxis ie deflectian at centre. Cat L/2) in portricn Bp wE 1 centre 24 EI wL'Y lo8 E1 Cantre 384 10368 3S Ceutre EI S184 these given data 200X10 pa E 200 GPa -6 34.4x10 m4 I n= 34.4X10 mm wide -flange shape Cfoi of waox35.9 - 35 ycartre now, S84C200)3 3y.YXI0 2O397 mm 2-397 X1O m Cetre C4) O.397 mm yentre sign means downuad ve deflectton)