How to calculate bending moment for a “+” shaped frame made from square tubing with a point load in the center?

[frogcobbler5]

Hello - I’m wanting to determine bending moment for a “+” shaped frame made from square tubing with a point load in the center in order to determine material sizing.

For example, for a 4’ simply supported beam with a 5-ton point load in the center, the bending moment would be (10,000lb*4ft)/4=10kip-ft, and you would choose a size of square tubing accordingly based on available flexural strength.

How does this calculation change when you weld a couple of 2’ pieces perpendicular to that piece to make a “+” shape?

 

[SWComposites]

the applied moment does not change.
the stresses in the cross section change.
its just stress = Mc/I at the extreme fibers of the cross section.

 

[ANE91]

the applied moment does not change.

There is no “applied moment.” There is an applied normal force, and it generates internal bending moments.

Per your example, assuming you’re still dealing with a simply supported beam and not a frame, you simply have now a geometric non-linearity. Basically, the beam is no longer prismatic; it is relatively much stiffer where the perpendicular pieces are welded. You would account for the effect of this additional stiffness in the analysis of deflections. If the beam remains simply supported, then the welded pieces have no effect on the distribution or magnitude of internal moments. Indeterminate structures are when you really start to see the load effects of such non-linearities.

Don’t get force/moment confused with stress; stress is what you use for member sizing.

Model this in any student-licensed software (e.g., VisualAnalysis) to see how it all works out. Should take you 5 minutes.

 

[BAretired]

Hello - I’m wanting to determine bending moment for a “+” shaped frame made from square tubing with a point load in the center in order to determine material sizing.

For example, for a 4’ simply supported beam with a 5-ton point load in the center, the bending moment would be (10,000lb*4ft)/4=10kip-ft, and you would choose a size of square tubing accordingly based on available flexural strength.

How does this calculation change when you weld a couple of 2’ pieces perpendicular to that piece to make a “+” shape?

A "+" shaped frame makes no sense. The meaning is not clear. Adding two pieces to make the "+" shape does not change the strength of the continuous piece, so the flexural strength remains the same, to all intents and purposes.

A question like this warrants inclusion of a sketch of the structure to show how the parts of the so-called frame are loaded and supported. Otherwise, we are all just guessing about the meaning of the question.

 

[GregLocock]

It'd be half. If I am correctly visualising what you mean. This is why we draw things.

 

[rb1957]

Are there supports at the ends of these extra pieces {you haven't said so, though it may be obvious to you) ?

So the load is supported on 4 points instead of 2 (like Greg has assumed) ?
Then 1/2 the load in each beam, with a confused section in the middle (bi-axial stress).

 

[BAretired]

"When you weld a couple of 2’ pieces perpendicular to that piece to make a “+” shape", you do not double the strength of the continuous HSS because the vertical walls of the added pieces are not continuous through the load point. Furthermore the welds of the horizontal walls occur at the curved corner of the continuous piece, which is a specialty weld and not recommended.

 

[rb1957]

yeah, sure for a practical problem. You'd need to check the welds to ensure that they can pass the load you'd expect, but I don't think you can say they won't work. and I reckon there are other things to check before you can say how strong the structure is. And of course there are several practical issues (like strength reduction in the HAZ of the weld ... things to check, but on the face of it I think the four legs would work together, but maybe not to 200% of the original load.

 

[BAretired]

yeah, sure for a practical problem. You'd need to check the welds to ensure that they can pass the load you'd expect, but I don't think you can say they won't work. and I reckon there are other things to check before you can say how strong the structure is. And of course there are several practical issues (like strength reduction in the HAZ of the weld ... things to check, but on the face of it I think the four legs would work together, but maybe not to 200% of the original load.

Definitely not 200% of the original load. You lose the bending capacity of the vertical walls at the location of maximum moment. Unless I am mistaken, the only way to regain it is to cut a section out of the continuous member and weld some additional plates aligning with the two walls of the added pieces.

That type of continuity could be achieved with open sections, but there is no good way to do it with square tubing. It is a bad design idea and the OP should recognize it.

 

[BAretired]

It would be nice if the OP would acknowledge the responses to date.