Finding Reactionary Forces on a Beam with Distributed Load

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Homework Help Overview

The discussion revolves around determining the reactionary forces on a beam subjected to a distributed load defined by the equation q=c*sine(n*pi*x/L). The beam is supported at two endpoints, and the participants are exploring how the variable 'n' affects the load distribution and the resulting reactions at the supports.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss integrating the load distribution to find the total load and its centroid, while questioning how the variable 'n' complicates the integration process. There are inquiries about the implications of 'n' being odd or even, and how this affects the load curve and the calculation of reactions.

Discussion Status

The conversation is ongoing, with participants raising questions about the behavior of the load distribution based on the value of 'n' and its impact on the centroid calculation. Some guidance has been offered regarding integration, but there is no consensus on the method to be used or the formula needed for the calculations.

Contextual Notes

Participants are considering the implications of the load curve crossing the x-axis for different values of 'n', which introduces complexity in determining the reactions. There is a focus on how to calculate the centroid for the distributed load across the segments defined by 'n'.

koolsid
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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[tex]\leq[/tex]x[tex]\leq[/tex]L

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 ?
 
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koolsid said:

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[tex]\leq[/tex]x[tex]\leq[/tex]L

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?
 
yes, but the problem is what to do with 'n'? it can change also...wat if n is odd and n is even?
 
koolsid said:
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
 
koolsid said:
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.
 
can u tell me where will be the centroid means how to calculate centroid for this case?
 
where is the centroid for this case?
 

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