Have you done the bending and shear diagrams?
Ok Everyone, I'm in DIRE NEED OF HELP....
.... as I've been out of practice now for a while - though I'm sure this is an easy problem to solve. Please see attached free body diagram.
Need to find reactions, R1, R2, R3 to support a 185 lb load as per the attached. I have done summation of forces R1 + R2 + R3 - 185 = 0 and summation of Moments about R1=0. What's my 3rd equation?!?!?!?
Have you done the bending and shear diagrams?
Last edited by Cake of Doom; 10-04-2013 at 05:06 AM.
Your inquiry appears to have the possiblility of being a camouflaged homework assignment. Either way, the following is a small bit of guidance.
I have also been away from my basic mechanics of materials course so I took a look at my ancient text book (MECHANICS OF MATERIALS, P. Popov, Prentice-Hall Inc) for this subject and what you have is known as a "staticly indeterminate structure" that cannot be solved by simple statics equations. The basic problem is that the distribution of loading between R2 and R3 depends upon the flexibility of the horizontal member. There is a chapter in the textbook on these types of structure that solves a simlar problem but it is a complicated process.
Just as a side note, if your diagram is in the vertical plane then your diagram has a missing load and that is the distrbuted load of the horizontal member.
Kelly, in this case I am going to have to disagree. The three R1,R2,R3 unknowns require three equations for a solution. In your post you first rearrange the force equation into its various forms but in the end it is still only different forms of one equation. The second equation is your moment equation and once you have made a substitution of one of the forms of the first equation you will still be left with R2 and R3 as two unknowns and are missing a third required equation for substitution to resolve those. Resorting to using another form of the first equation is only looping and still result in an remaining unknown.
With regard to the attached video, this is a very elementary statics problem with two unknowns in the vertical plane loading and therefore solves with only two equations.
@ Kelly, I will have to agree with JAlberts on this one - I only arrive at 2 equations with 3 unknowns which is the prime issue.
@JAlberts & Cake, unfortunately not just a homework problem. We are attempting to lift a 185lb load at work and wanted to do this with a U-Beam aluminum channel. Your responses led me down the path to evaluate using beam equations for shear/moment diagrams. Unfortunately, my load case isn't represented by the typical ones DA6-BeamFormulas.pdf (see , fig 32). I have been unable to find a perfect fit for the beam equations.
What are your thoughts on setting P2 =0 and evaluating the equations for the different reactions? Dunno....smells fishy....
Last edited by Kelly_Bramble; 10-06-2013 at 02:34 PM.
studsup77, the only suggestion I can make is the possibility of using the indeterminate beam solution given in Example 1 of the below link I found with some searching. For your application you would simply set the distributed load in the example to zero. Just as a note, be aware that the example solution is started above the Example 1 beam illustration and that confused me when I began studying it.
Just be aware of the warning given that this solution has not had peer review and verification and I am not capable of giving any help there myself.
I spent some time on the web searching for another similar example using this solution but was unsuccessful in that effort. There is a lot of information about the theorem basis given but all of it is strictly academic.
As a general comment, the two main concerns in your application are the loads on the R1 and R2 supports and the bending stress in the aluminum channel between those two connections. The bending stress question could be conservatively resolved by treating the loaded section of the beam as a simply supported beam problem with a point load and R1 and R2 end supports. This will result in a very conservative bending stress value in for beam but at least it is a safe one. Also, the loading reaction on the R1 support would be safely determined using this same approach. The problem spot is the R2 support because the downward deflection of the loaded section of the beam is going to result in an upward deflection in the horizontal beam section between R2 and R3 and this deflection will place a vertical upward loading on R3 that will be transferred as an additional downward loading to R2. I am going to go out on limb here and suggest that as a result a conservative determination of the R2 loading would be achieved by analytically removing the R1 connection end of the horizontal beam and treating the section of that beam between your load point and R3 a lever with R2 as its center pivot and its other end restrained at R3. Obviously both of these methods are going give significantly conservative solution vaues, but if they do not exceed the limits of your supports and the C channel then you should be safe in your lifting application. On the other hand if the stress and loading values found in this method are too high for your structure then you are left with trying to utilize a more sophicated analysis.
Based upon your ability to do engineering beam analyses calculations I am assuming you are an engineer and as a result will carefully take into consideration all of the important details of your structure, ie the type of connections between the horizontal beam and the vertical supports, the risk of twisting due lateral forces on loading point of the beam, etc. The above calculations I have suggested to you are based upon idealized simply supported connections that are restrained from moving vertically up or down (ie, the vertical members are not hanging cables or rods; nor, is the horizontal beam rigidly welded to cross beams at the three reaction points) and with the applied 185lb loading in a purely vertical plane with the structure.
Last edited by Kelly_Bramble; 10-07-2013 at 07:52 PM. Reason: Added cautions