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 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.
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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 ?
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 said:yes, but the problem is what to do with 'n'? it can change also...wat if n is odd and n is even?
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 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
A beam under a distributed load is a structural element that is subjected to a load spread out over its length, rather than at a single point. This type of load can be caused by the weight of the beam itself, as well as any other external forces acting on the beam.
The load is typically distributed evenly across the beam's length, creating a uniform load. However, there may be cases where the load is not evenly distributed, such as in the case of a concentrated load at a specific point on the beam.
A distributed load can cause various effects on a beam, including bending, shear, and deflection. These effects can lead to stress and deformation in the beam, which can ultimately affect its structural integrity.
To analyze a beam under a distributed load, engineers use principles from mechanics and physics to determine the internal forces and stresses within the beam. This information is then used to design a beam that can withstand the applied load without failing.
The effects of a distributed load on a beam can be minimized by using a design that takes into account the anticipated load and its distribution. This may involve using a different material or altering the shape and dimensions of the beam to better distribute the load and reduce stress concentrations.