## Beam under a distributed load

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$$\leq$$x$$\leq$$L

The figure looks like this.

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

2. Relevant equations

3. The attempt at a solution

 PhysOrg.com science news on PhysOrg.com >> Hong Kong launches first electric taxis>> Morocco to harness the wind in energy hunt>> Galaxy's Ring of Fire

Recognitions:
Gold Member
Homework Help
 Quote by 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$$\leq$$x$$\leq$$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 ?
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?

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

Recognitions:
Gold Member
Homework Help

## Beam under a distributed load

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

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

Recognitions:
Gold Member
Homework Help