Finding Reactionary Forces on a Beam with Distributed Load

[koolsid]

Homework Statement

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\leqx\leqL

The figure looks like this.

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Homework Equations

The Attempt at a Solution

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

 

[PhanthomJay]

Homework Statement

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\leqx\leqL

The figure looks like this.

___________________
^......^

Homework Equations

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?

 

[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, 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.

 

[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]

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

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?