# Beam bending problem watch

1. Hi

Wondering if anyone could point me in the right direction for solving this. I am looking to work out the approximate reaction forces (and eventually bending moments) for a trailer design I'm putting together and have approximated it to a simply supported beam with multiple reactions (2 x wheels, 1 x tow hitch) and multiple loads. I've so far tried removing the R2 reaction and solving through superposition, but I'm struggling using beam theory to calculate the deflection at its position (x=1.724).

For section EF I have:
M(x) = -798.758392x + 1211.009551

Which integrating gives:

EI (dv/dx) = -399.379196x^2 + 1211.009551x + C1
EIv = -133.1263987x^3 + 605.504775 x^2 + C1x + C2

But I'm unsure what boundary conditions to apply to this section to get C1 and C2.

Does anyone know of a good way to solve this easily without having to go into FEA methods?

EI = 8890

Thanks
2. Is this an actual trailer to be built?

In that case you have to take into consideration several cases of load distribution. For instance if you drive and stop abruptly, maybe all your load will slide to the front of the trailer and put a disproportionate amount of load on your tow bar. Or you could have all the load on the back end of the trailer and the tow bar would end up with a reaction in opposite direction of what you have drawn.
3. Which ones of your reactions are the wheels? Very little deflection there.
4. You can assume the vertical defection at both the wheels will be zero (for a simply supported beam, the deflection at the supports will be zero), that's two bc's which is enough to solve the equation.
5. (Original post by faultymonkey)
Hi

Wondering if anyone could point me in the right direction for solving this. I am looking to work out the approximate reaction forces (and eventually bending moments) for a trailer design I'm putting together and have approximated it to a simply supported beam with multiple reactions (2 x wheels, 1 x tow hitch) and multiple loads. I've so far tried removing the R2 reaction and solving through superposition, but I'm struggling using beam theory to calculate the deflection at its position (x=1.724).

For section EF I have:
M(x) = -798.758392x + 1211.009551...
(Original post by samir12)
You can assume the vertical defection at both the wheels will be zero (for a simply supported beam, the deflection at the supports will be zero), that's two bc's which is enough to solve the equation.
The expression the OP has come up with covers only section EF, which doesn't include either of the wheels! OP, you will need to determine the cut forces at E and F and solve the other bits of the beam (AE and FI) to get deflections which you can then use as your boundary conditions for EF. Actually, thinking about it, the cut forces won't be obvious either - you'll have to invent new variables for the shear and moment at each end, and solve all three bits of the beam together.

Or you could just combine standard beam results to get your expressions in much the same way?

Alternatively, if you're hell-bent on doing it "first principles", there was something we covered at uni called Macaulay's Method which was great for continuous beams - basically you write down an expression for the shear force along the whole beam (using some special notation to take account of the discontinuities) and integrate up to reach deflection, at which point you put in boundary conditions of v (or dv/dx if there are moment-resisting supports) to solve for your various integration constants.

In real life (if I was doing this at work) I'd put it into Tedds. Not sure whether Tedds uses FE, another numerical technique, or combines standard results. Don't really care, to be honest!
6. (Original post by thefish_uk)
The expression the OP has come up with covers only section EF, which doesn't include either of the wheels! OP, you will need to determine the cut forces at E and F and solve the other bits of the beam (AE and FI) to get deflections which you can then use as your boundary conditions for EF. Actually, thinking about it, the cut forces won't be obvious either - you'll have to invent new variables for the shear and moment at each end, and solve all three bits of the beam together.

Or you could just combine standard beam results to get your expressions in much the same way?

Alternatively, if you're hell-bent on doing it "first principles", there was something we covered at uni called Macaulay's Method which was great for continuous beams - basically you write down an expression for the shear force along the whole beam (using some special notation to take account of the discontinuities) and integrate up to reach deflection, at which point you put in boundary conditions of v (or dv/dx if there are moment-resisting supports) to solve for your various integration constants.

In real life (if I was doing this at work) I'd put it into Tedds. Not sure whether Tedds uses FE, another numerical technique, or combines standard results. Don't really care, to be honest!
the fish has spoken

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