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Join Date: Dec 2010
Posts: 6

Deflection of Beam

01/03/2011 12:28 AM

Hi Guys,

I am research about deflection of beam, in case one fixed-one hinged, the midspan deflection of the beam is 1/185 wl4/EI, I have tried some ways but I haven't obtained this value yet.

Does any guys know how to get this value?

Thanks guys.

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Join Date: Mar 2007
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#1

Re: Deflection of Beam

01/03/2011 9:23 AM

1- You compute the beam WITHOUT support at left side

2- You introduce a force at left side considering the beam WITHOUT distributed load so that the resulting deflection will be zero.

You compute the deflection ad midd point as sum of the two effects.

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Join Date: Nov 2007
Location: Sherwood Park, Alberta, Canada
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#2

Re: Deflection of Beam

01/03/2011 4:47 PM

Note also that the maximum deflection does not occur at midspan. It occurs at 0.4215*l from the hinged end.

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#3
In reply to #2

Re: Deflection of Beam

01/04/2011 3:24 AM

Thank a lot for your reply.

in second effect, how magnitude of the introduce force?

and I am thinking that Can I use "conjugate beam theory" to solve this problem, Do anyone in forum know about this method, please help me , thanks.

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#5
In reply to #3

Re: Deflection of Beam

01/04/2011 12:46 PM

There are several methods you could use. Conjugate beam method is certainly one of them. In that method, you load the conjugate beam with the M/EI diagram, solve for reactions of the conjugate beam (which are end rotations of the real beam), then solve for moments of the conjugate beam (which are deflections of the real beam).

Alternatively, you could use the equation for deflection of the beam:

Δx = wx(l3 - 3lx2 +2x3)/48EI

To find the location of the maximum deflection, differentiate the above expression and set the result to zero, then solve for x to give you the location of the maximum deflection. Finally, solve for deflection at that value of x. It should agree with your expression in the original post.

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#4

Re: Deflection of Beam

01/04/2011 7:30 AM

This is a good explanation.

http://www.youtube.com/watch?v=vSrdVM_9nrA

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