Beam Deflection 1

[TTW2]

Hi,

I am trying to calculate the deflection of a horizontal cantilevered beam of a length l that has two loads on it at unequal distances. The loads are the same so P1 = P2. The distances a and b are from x = 0. I cannot find an equation to suit and when I try to derive it using Castiglianos Theorem I get unreasonable answers. Any help would be appreciated.

Thanks

 

[COEngineeer]

Use integration method, moment area method, conjugate beam method, virtual work method. Do a google search on all those methods, you will figure it out. This is a homework? you are not suppose to post HW problem.

Never, but never question engineer's judgement

 

[TTW2]

I am aware of the guide lines for this site. No this is not for home work it has just been a while since uni. One of the engineers has analysed a pipe support and the deflection does not seem intuitive to me.

 

[mark1234]

download enercalc and run the calc... pick a section that resembles the pipe... S and I (section modulus and moment of intertia)

MDJ

http://www.windspeedbyzip.com

http://www.groundsnowbyzip.com

 

[hokie66]

You should be able to find an equation for one load (AISC manual used to have it). Do it for both and add the deflections.

 

[TTW2]

hokie66 I don't think that is correct. As the deflection resulting from one load will influence the deflection produced by the other. So at the inner load the beam at that point will already have started to deflect from the outer load (if that make sense). So I don't think it is a matter of just summing them. Thanks for your input though.

 

[Ussuri]

The principle of superposition will apply if you are doing your analysis using a linear elastic approach.

 

[apsix]

Rest assured, TTW2, the principle of superposition has stood the test of time. The equation must be for the load case when the load is not at the tip of the cantilever.

 

[hokie66]

TTW2,

When you find the equations, which should be in most structural texts, there should be 4 different equations: deflection at tip, deflection at load, deflection at any point between load and tip, deflection at any point between load and support. So you can compute the deflection at any desired point on the beam. Do it for both loads, and as Ussuri and apsix have advised, use principle of superposition, or as I said, add them up.

 

[TTW2]

Thanks.