Beam Bending Problem 1

[310toumad]

Assume a set up in the attached PDF, where you have two twin loads acting on a beam that is welded to two hook ends which are simply supported and not constrained. How would you approach calculating the bending moment at the joint where the beam is connected to the hooks? In my opinion, you can't assume that the beam is totally fixed at both ends because the hooks themselves will deflect to some degree. It also wouldn't make sense to just assume the beam is simply supported along its entire span because of the welded connection. Would this be considered a statically indeterminate problem?

 

[JStephen]

If the hooks are rigid, treat beam+hooks as a simply-supported beam with length equal to the span between the support points. In this case, presumably the bending in the hooks will be the critical loading, not the bending in the beam at the end.
If the hooks are flexible (a strap hanging over the top of a wall), treat the beam as simply-supported with length equal to the actual beam length. Design of the hooks would be a separate problem.

 

[drawoh]

310toumad,

Both cases are described in handbooks like Roark's Equations for Stress and Strain. You can solve for both cases, and assume the true result is somewhere in between.

You can assume some spring rate for the hook ends under load, and apply this as a boundary condition.

You can solve for the fixed attachment at each end, and work out the moments at the end. Then, you can apply those moments to your hook ends and see what happens.

--
JHG

 

[BrianE22]

Does it matter? Are you looking for stress or deflection? The moment at the junction doesn't care about the supports.

 

[rb1957]

it sounds like the SS span is the full span (hook to hook) and so the moment at the weld is simply determined for the beam moment diagram (as 2500*x). If you say the weld doesn't carry moment then the hook reaction point has to; the beam is SS from weld-to-weld, the hook fitting becomes a cantilever from weld-to-end_point.

another day in paradise, or is paradise one day closer ?

 

[dhengr]

310toumad:
As usual we are far short on meaningful engineering info. for starting to have a good discussion on this problem. Are the dimensions in weeks or miles? What are the actual reaction points and why the funny end fixings? What is the approx. beam size, etc? The stiffness of those hook pls. is bd^3/12 (a plate flatwise) vs. the beam stiffness, and you can pick the moment of inertia out of the beam from a beam table. But, run this fixed end calc. too, it will come into play in the weld design. for the beam ends. The ratio of those stiffness values determines any potential for an end moment, and it will be very low. That is basically a simple beam, so design it accordingly, for the max. moment at mid beam, and with a 2.5k shear at each end. The 2.5k shear and some small moment are part of your weld design problem of the beam to the hook pl., and then, also check this bending stress in the hook pl., just above the top flg. weld. There will be a 2.5k shear in the web to the hook pl. weld, and there will be some small tension and compression in the top and bottom flanges which represents the end moment, as a function of the hook pl. stiffness, they are all fillet welds.

 

[verymadmac]

definitely short on information.

You could possible treat the hooks as portal frames with a moment at the foot. Then use excel to solve for the moment that gives the same angular deflection as the end of the beam.

 

[tmschrader]

Hello
The free body shows only one reaction point/Load arrow at center of hook made of plates. If so it is pinned and simply supported. But it looks like there is a hole for a bolt on the ends which would be another reaction support increasing the load on the plates in the hook. As this would fix it to the wall to some degree. Also the inside end could work against the wall. The beam to plate at ends would be A high stress as noted in pdf. I am assuming it is connected to wall at the ends

The beam itself could be analyzed as SS and be conservative. Otherwise you could analyze the degree of restraint by the hook plated ends to lighten the beam.

I do not think a FEA is required, but could be done.

 

[mreg]

Due to symmmetry, I would consider your beam fixed at the two load points....then apply 2,500 lbs upwards to each of your welded hooks. Easy?

 

[rb1957]

sure easy, but why ? if the hooks are pinned then beam is a simple SS beam. and, yes, I get that the moment in the beam between the loads is constant.

if you want to simplify, then use the mid-point of the beam as an axis of symmetry (and to remove the redundancy, notice that there is no shear on the CL).

or solve the SS beam.

another day in paradise, or is paradise one day closer ?