Beam under a distributed load

koolsid

1. The problem statement, all variables and given/known data

A simple beam is under a distributed load q=c*sine(n*pi*x/L)? if there are two pivots at the end points supporting it, what will be the reactionary force on each one of them?

Here, L is the length of the beam and x=0 is the leftmost point. 0[tex]\leq[/tex]x[tex]\leq[/tex]L

The figure looks like this.

___________________
^............................^

2. Relevant equations



3. The attempt at a solution

I cannot figure out how to approach to this problem. can you please help me ?

PhanthomJay

How's your calculus (better than mine, I hope)? Start by integrating the load distribution from 0 to L to solve for the total load, which acts at the centroid of the sinusoidal load distribution. Then what?

koolsid

yes, but the problem is what to do with 'n'? it can change also....wat if n is odd and n is even?

PhanthomJay

Yes, good point, that n makes it more difficult. When n is an integer greater than 1, the distributed load curve crosses the x axis, so integrating the load curve from end to end will not help in determining the reactions. It looks like you have to perform separate integrations between n segments that are each (1/n)L in length, then place the load at the centroid of each section to get the end reactions. There's probably a formula to calculate this, but I don't know what it is.

koolsid

When n is an integer greater than 1, the distributed load curve crosses the x axis can u tell me in detail this point

PhanthomJay

it crosses at q=0, that is, when sin(n)(pi)x/l = 0, which occurs at x=0, and l/2 when n=2, at x=0, l/3, and 2l/3 when x=3, and in general, at x=0, l/n, .......(n-1)l/n.

koolsid

can u tell me where will be the centroid means how to calculate centroid for this case?

koolsid

where is the centroid for this case?