55 The simply supported beam shown in Figure P1055 consists

.55 The simply supported beam shown in Figure P10.55 consists of a W410 x 60 structural steel wide-flange shape [E 00 GPa; I 216 x 106 mm4]. For the loading shown, deter- mine the beam deflection at point B. 60 kN 45 kN-m 3 m 6 m.

Solution

solution:

1)here for given simply supported beam deflection occured due to point load at B and moment at C hence resultant deflection would be algebric sum of deflection from point load and moment

2)deflection due to point load at B is given by

y1=-[F*lb^2*m^2/3*E*I*L]

F=60000 N,lb=3000mm,m=6000mm,L=9000 mm

L=lb+m=9000=3000+6000

so we get

y1=-16.666 mm

3)here deflection due to moment at right end is given by at point b as follows

y2=[M*L*x/6*E*I][1-x^2/L^2]

M=45 KNm here for x=lb=3000 mm we get that

y2=4.166 mm4)hence resultant deflection is

y=y1+y2=-16.66+4.166=-12.50 mm