There is a uniform, horizontal beam 4.8m in length supported by a pin at x = 0 and a roller at x= 3.2m. There is a distributed weight of 12kN/m from x = 0 to x = 1.6m. There is a concentrated, vertical force of 2.4kN in the downward direction at x = 4.8.
Find the deflection and define the coefficients of integration for each segment
EIY'' = double integral of Mdx
Y is deflection
The Attempt at a Solution
I calculated the moment for each segment, but I can't seem to figure out what the coefficients are. I think I'm supposed to use symmetry conditions, and I know the deflection is 0 at x = 0 and x = 3.2 where there are supports. I can't figure out past that though.
M1 = 13.2x - 6x^2
M2 = -6x + 15.36
M3 = 2.4x - 11.52
EIV1 = 2.2x^3 - .5x^5 + C1x + C2
C2 = 0
EIV2 = -x^3 + 7.68x^2 + C1x + C2
EIV3 = .4x^3 - 5.76x^2 + C1x + C2
I believe the moments I calculated are correct, but I'm not sure. Any help would be appreciated.