![Hw#2 Solution :
Let W(x)= C1*X^3+C2*x^2+C3*X+C4
W’(X)=3*C1*X+2*C2*X+C3
W’’(X)=6*C1*X+2*C2
W’’’(x)=6*C1
Apply B.C’S
At X=0……. Fixed edge
W(X=0)= 0=0Ϩ
W’(X=0)= 0= 0Ө
At X=L…………Roller edge
W(X=L)=Ϩ
EIW’’=M0
C4=0
0=0+0+0+C3
C3=0
C1*L^3+C2*L^2= Ϩ
EI[6*C1*L+2*C2]=0
C2=-3*C1*L
C1*L^3-3*C1*L^3= Ϩ
C1=- /2*L^3Ϩ
C2=1.5* /L^2Ϩ
M(X)=EI*W’’(x)
=EI*[-3* /L^3 +6* /L^2]Ϩ Ϩ](https://image.slidesharecdn.com/hw2-140325065326-phpapp02/85/hw-2-1-320.jpg)
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Hw #2
- 1. Hw#2 Solution : Let W(x)= C1*X^3+C2*x^2+C3*X+C4 W’(X)=3*C1*X+2*C2*X+C3 W’’(X)=6*C1*X+2*C2 W’’’(x)=6*C1 Apply B.C’S At X=0……. Fixed edge W(X=0)= 0=0Ϩ W’(X=0)= 0= 0Ө At X=L…………Roller edge W(X=L)=Ϩ EIW’’=M0 C4=0 0=0+0+0+C3 C3=0 C1*L^3+C2*L^2= Ϩ EI[6*C1*L+2*C2]=0 C2=-3*C1*L C1*L^3-3*C1*L^3= Ϩ C1=- /2*L^3Ϩ C2=1.5* /L^2Ϩ M(X)=EI*W’’(x) =EI*[-3* /L^3 +6* /L^2]Ϩ Ϩ
- 2. S(x)=dM/dX=M’(X)=-3* /L^3Ϩ To get reaction and moments : At X=0……. M(0)=6* /L^2Ϩ S(0)=-3* /L^3Ϩ At X=L…….. M(L)=-3* /L^2Ϩ S’(L)=0