9-1: for the loading shown,determine (a) the equation of the elastic curve for the cantileve AB, (b)the deflection at the free end (c) the slope at the free end.
solution:
Fy=0 Ry=0
Ma=0 M=Mo
EI(d^2V/dX^2)=Mo
EI(dV/dX)=Mo+C1 EIV=(Mo^2*X^2/2)+C1X+C2
AT X=0 V=0 C2=0 AT X=0 (dV/dX)=0 C1=0
EI(dV/dX)=MoX slop= (dV/dX)=(MoX/EI)
EIV=MoX^2/2 the equation of the elastic curve= (MoX^2/2EI)
AT X=Lthe deflection at the end=V=MOL^2/2EI the solp at the end=(MoL/EI)
for the loading shown,determine (a) the equation of the elastic curve for the cantileve AB, (b)the deflection at the free end
(c) the slope at the free end.
Fy=0
Ry=0
Ma=0 M=Mo
EI(d^2V/dX^2)=Mo
EI(dV/dX)=Mo+C1
EIV=(Mo^2*X^2/2)+C1X+C2
AT X=0 V=0 C2=0
AT X=0 (dV/dX)=0 C1=0
EI(dV/dX)=MoX slop= (dV/dX)=(MoX/EI)
EIV=MoX^2/2 the equation of the elastic curve= (MoX^2/2EI)
AT X=L the deflection at the end=V=MOL^2/2EI
the solp at the end=(MoL/EI)