Find required distance of support for beam

[diadiaria]

1. There is a beam with labels point A on the left hand side of the beam and point B on the right hand side of the beam. The beam is supported by bolts on side B (that can handle up to 4000 lb). There is no support on side A, so a support has to placed at some distance from B to support the beam. The beam weighs 2000 lb and is 100 feet long.

Homework Equations

Sum Fx=0
Sum Fy= Fsupport + ForceB - Fbeam=0

Sum of Moments (taken through point B)
Sum of CCW Moments=0=Sum of CW Moments
(Fbeam)(distance from acting weight of beam to B)= (Fsupport)(Distance from support to B)

The Attempt at a Solution

First, I solve the sum Fy equation so I can solve for Fsupport.

Sum Fy= Fsupport + ForceB - Fbeam=0
Sum Fy= Fsupport + 4000- 2000=0

But this gives me Fsupport = -2000 lb. Theoretically, there could be a negative force, but this support is supposed to be underneath the beam, giving an upward and positive force.

Anyway, I didn't think this was right, but the next step would obviously be to solve for distance from support to B. I assume the distance from the force of the beam to B is half the length of the beam

0= (Fbeam)(distance from acting weight of beam to B)= (Fsupport)(Distance from support to B)

0= (2000 lb)(50')= (-2000 lb)(distance from support to b)


I guess to sum up the questions:1) If the bolt force is greater than the weight of the roll, how am I supposed to prove this scenario will hold when the forces equation says I need an extra downward force from the support?

Thanks!

 

[gneill]

Are there no other constraints on the placement of the support? What's to prevent you from simply placing it at the midpoint of the beam, thus supporting its entire weight and rendering the net moments about the ends zero?

 

[diadiaria]

Oh right, well yea, I suppose I can. Ok, but I guess for sake of learning, if there was a constraint that prevented me from doing so (something in the path of the midpoint for example), what would be the next step? I guess anything in between the midpoint and point B would cause the moments to not equal 0. It just seems obvious to me that, OK, these bolts can hold more than the weight of the beam, but I want to prove that via these calculations as well (as opposed to just looking at the fact that force bolts> force beam).

 

[gneill]

I suppose if you were an engineer you would worry about the whether the strength of the bolts was shear strength or tension strength, and you'd have to look at the specifics of how the bolts were arranged at the end of the beam to see if shear forces or tension forces are acting on the bolts. The force on each bolt might not be the same, and forces might be multiplied by leverage effects (like the beam pivoting at its bottom edge and exerting large tensional forces on the bolts at the top edge). This assumes that the beam has real dimensions -- width and height as well as length.

 

[PhanthomJay]

What is the question? I think you are being asked to solve at what minimum distance the support must be placed from B such that the force at the B does not exceed 4000 pounds. Please indicate the question. And maybe that 4000 pounds at B acts downward on the beam in the negative direction.

 

[diadiaria]

Yes sorry,

The question at the end of the description says "what is the minimum distance the support can be placed from point B?" Right, so I guess it may not necessarily be the center.

Thanks so much for all of your help!

 

[PhanthomJay]

Yes sorry,

The question at the end of the description says "what is the minimum distance the support can be placed from point B?" Right, so I guess it may not necessarily be the center.

Thanks so much for all of your help!

OK, so where is it??

 

[diadiaria]

well, I think now it seems it has to be at the center. Anything closer to b will give a negative force for the support. Again, to me that doesn't physically make sense, since the support is underneath the beam giving a positive force upward.

 

[PhanthomJay]

If the support is at the center, then it takes all the loading (sum all the moments about B to show this...as noted by gneill), and the bolts at B take no load. This is not what the problem is asking. It wants you to put the 4000 pound load at B, with the 2000 pound weight of the beam load at midpoint, and solve for the support force and its distance from B. Assume that the support load acts positively up, and see what you get when you use the equilibrium equations.

 

[gneill]

I don't see any load being mentioned in the problem statement. As far as I can tell it's just the 2000 pound beam attached to a vertical surface at point b. The bolts holding the beam end can support 4000 pounds.

As I mentioned earlier, the problem statement is vague on things like how many bolts are used and in what configuration, what the cross sectional dimensions of the beam is (important for bolt placement and strain calculations).

With the available information, the best one can do is solve for the minimum distance that the support can be placed from b such that the resulting "weight" of the beam at b does not exceed 4000 lb force (either upwards or downwards -- it's a lever action).

 

[PhanthomJay]

I don't see any load being mentioned in the problem statement. As far as I can tell it's just the 2000 pound beam attached to a vertical surface at point b. The bolts holding the beam end can support 4000 pounds.

Yes, that's the load mentioned..2000 pound beam weight and 4000 pound max load at B

As I mentioned earlier, the problem statement is vague on things like how many bolts are used and in what configuration, what the cross sectional dimensions of the beam is (important for bolt placement and strain calculations).

The problem is not seeking this info

With the available information, the best one can do is solve for the minimum distance that the support can be placed from b such that the resulting "weight" of the beam at b does not exceed 4000 lb force (either upwards or downwards -- it's a lever action).

Yes, and that is all the problem is asking