Beams and bending 1

[trawets]

I have been trying to work out some reaction forces and bending momnets. Not too difficult normally but I seem to have hit a stumbling block. My problem is that the beam has 2 UDL's I spans the whole beam but the other just a small section, Im having troube working things out, could anyone point me in the right direction.
Beam sketch attached

 

[hokie66]

This appears to be a homework problem, and student posting is not allowed on the site.

 

[rb1957]

superposition ... apply one loading at a time and add the results

 

[trawets]

Whilst I can understand your reply, as the problem is quite elementary, I can assure you it isn't a homework problem nor am I a student, I just can't remember how to deal with the second UDL its many years since I have done anything like this

 

[hydromech]

I have to say that this does smell suspiciously like a college/uni task. I say that because I did one very similar last year.

I'll give you the benefit of the doubt.

Moments about Ra first, then moments about Rb. Reation is just total load acting on beam, you just need to work out the proportion...how much act at Ra and how much at Rb and remember that UDL load is always taken at the centre of the UDL.

You are more likely to remember it if you do it yourself.

Adrian

 

[rb1957]

instead of the complete solution (deriving M(x) and integrating) ... you can determine the reactions for the partial udl by replacing it with a point load at the CG of the load.

you can then determine the moment in the beam by method of cuts, bfore the udl, at its middle, at the far end.

else you can use roark.

 

[Ussuri]

You can use dummy udls also

 

[drawoh]

trawets,

You can also use the pointy, conditional brackets, to construct your bending equations. It really helps if you did not throw away your old textbooks after college.

JHG

 

[NomLaser]

But then how would you pay for beer and the following semester's books

 

[hokie66]

trawets,

The most elementary and informative way of doing it is to solve for the right reaction by summing the moments about the left support. Then the left reaction is just the difference between the total load and the right reaction. Draw a shear diagram. With the shear diagram, the points of zero shear locate the points of maximumn moment. The areas under the shear diagram are the changes in moment.