# Finding deflection on a uniform beam with fixed supports ~ Incorrect answer :(

This question has asked us to find the deflection of a beam (in millimeters) if the beam is under a load of:

f(x) = 9.46(x+0.82)(9.2288-x) N/M

• The beam is supported with fixed supports at both ends
• The beam is a uniform beam that is 4.57 meters long with a flexural rigidity of 28532Nm^2

I am asked to find deflection at various x coordinates, the following: x = 0.55 x = 1.01 x = 1.97 x = 3.34 x = 4.02

However my answers were incorrect. We are asked to calculate it to 10 decimal places and in mm and i got the following. x = 0.55, y(x) = 0.0000114139 x = 1.01, y(x) = -0.0000245458 x = 1.97, y(x) = 0.0002053990 x = 3.34, y(x) = -0.0000072908 x = 4.02, y(x) = 0.0000327515 The answers are given after my working out so scroll down to see that c:

I will briefly explain my working out (for sake of not being verbose) but let me know if I should be more detailed. However I am unsure how to properly type out maths here, it looks quite unsightly I am sorry until I figure out formatting please bare with me :<.

1. First I used the following formula y(x)=1/EI(IntegralM(x)dxdx + C1x +C2) where y(x) is the deflection at position, EI is the flexural rigidity of the beam M(x) is the moment at x position due to the distributed load, and C1 and C2 are integration constants that can be solved for using the boundary conditions.

which gave me f(x) = 9.46(x+0.82)(9.2288-x) N/m

1. I then tried to integrate this to get M(x) and plug into the deflection formula This is so hard to transcribe without maths keyboard so I may just leave a photo Im sorry This was then integrated to get the deflection at y(x)

2. I then used the boundary conditions to solve for C1 and C2 as the beam is fixed supported. (This is too long too type out on this site so heres another pic Im sorry if you cannot view them :< )

after this i solved for deflection by plugging in the values.

I then found boundary conditions - since for fixed supports the deflection and slope are zero at both ends; x=0 and 4.57m; therefore:

Then I used this ugly equations to evaluate at each coordinate given. here is the working out that lead me to the incorrect answers :(

the actual correct answers are: x = 0.55, y(x) = 1.305548mm x = 1.01, y(x) = 3.532257mm x = 1.97, y(x) = 7.471858mm x = 3.34, y(x) = 5.036247mm x = 4.02, y(x) = 1.485468mm

I just want to know if my method is incorrect and how these answers were arrived to :( any help will be rl appreciated thank you guys!