Equations for Bending and Deflection of a Beam

[goolai]

bending for beam -- deflection

Homework Statement

bending for beam -- deflection

Homework Equations

The Attempt at a Solution

 

[radou]

In order to get help, you should show some attempts in solving the problem. Filling up the part "Relevant equations" would be a step forward.

You may consider yourself lucky that I wrote that, since it's self-understood on this forum and can be found in guidelines etc. ; the only reason I pointed it out (again and again) is that I don't want anybody new to PF to think that questions are ignored.

 

[goolai]

my solution

The Attempt at a Solution

i was tried, but the answer was wrong

my solution
vertical equilibirum: Ra=Rc=1/2(P+3*W)

Second moment of area: I = (PI/64)*(D^4-d^4)=4.2726*10^-6 m^4
bending moment equation from load intensity
M=Ra<x>^1-P<x-1.5>^1-(w<x-1.5>^2)/2+Rc<x-3>^1

Integrated:

EI(dv/dx)=(Ra<x>^2)/2-(P<x-1.5>^2)/2-(w<x-1.5>^3)/6+(Rc<x-3>^2)/2+C1

Integrated one more time

EIV=(Ra<x>^3)/6-(P<x-1.5>^3)/6-(w<x-1.5>^4)/24+(Rc<x-3>^3)/6+C1*X+C2


NOW take the boundary conditions:

at x=0, deflection V=0, so C2=0
at x=1.5m deflection v=3mm so, caculate the C1

 

[goolai]

after caculate the C1, LHS=RHS=0

so i can't continue

thanks

 

[goolai]

Thank for your remind!

 

[radou]

There is one more boundary condition you need to use on w'(x) in order to obtain a system of two equations with two unknowns, C1 and P.