Stiffening a W-beam with a T of different strength

[amecENG]

When welding a WT stiffener to the bottom of a W beam you get two different elastic section modulus: one for the top flange and one for the very bottom flange.

I am trying to stiffen a simply supported W beam with a yield strength of 240MPa with a WT with a yield strength of 350MPa.

Is it too conservative to use the lower 240MPa strength for the top flange or should I use a ratio of the yield strengths?

 

[frv]

I usually just use the lower value. Conservative? Yes. Overly so? I don't think so.

 

[csd72]

There will be two different stresses. The top flange of the existing will be fully restrained I assume and must be checked using the original stress (i.e. the 240.

The bottom with the welded T needs to be checked against the new stress in the new section and the old stress in the bottom of the old section.

If the T is of greater stiffness than the original then this can sometimes make a difference, if not then the highest stress will be in the original section and this wont really make any difference.

 

[rb1957]

what's difficulat with calc'ing the right stresses, using the "rule of mixtures" .. ie transforming the section to a consistent E ?

 

[csd72]

Are we talking stresses or youngs modulus? Youngs modulus doesnt change that much between different strengths of carbon steel.

 

[amecENG]

I was talking about stress not Young's modulus.

The Tee section is nearly as deep as the original member. But the flange thickness of the Tee is thicker and hence I am calculating different elastic section modulus for the top and bottom regions.

When I am selecting a Tee I am calculating the moment resistance from the elastic section modulus of the compression zone (i.e. top) with the grade of steel of the top member (i.e. 240MPa).

Am I correct in using the elastic section modulus of the compression zone?

 

[csd72]

You need to check both values for S that you calculate. If you use the distance from the neutral axis (NA) to the top of the section then this is the section modulus that you use for the top and then check the resulting stress for the grade 240 steel.

Use the distance from the NA to the bottom to calculate the stress in the bottom of the section and compare this stress to the allowable stress of the grade 350 steel.

Depending on the location of the NA you may also have a maximum stress in the bottom of the grade 240 steel that also needs to be checked.

Is it a simply supported beam or do you have moment reversal?

 

[BAretired]

It is not too conservative to use 240 MPa for the top flange, because that is what it is. You are entitled to use 350 MPa for the bottom flange of the Tee.

The value of E is the same for both steels, so there is no "transformed" section.

BA

 

[spats]

You're going to find that the top flange stress will control because you are lowering the neutral axis. If you add enough WT to make the top flange work, you'll see that the WT is not nearly fully stressed, and doesn't need to be a higher yield than the W beam.

 

[Lion06]

spats nailed it. The top will always control, especially if you don't jack out any of the existing stresses.

 

[WillisV]

If you are using LRFD methods existing stresses should not matter for strength design...

(

http://www.modernsteel.com/steelinterchange_details.php?id=972)

 

[Lion06]

The only comment I would make with that is that you should still do a stress check to ensure that service loads don't cause yielding at the top with superposition of stresses.

What I've found to be true is that for unsymmetrical sections Z/S can get very high. I remember being shocked at the difference in capacity for a composite beam comparing the 9th ed. to the 13th ed.. This is all because "Z" (if you want to call it that for a composit beam, please don't let the point of my post be lost in the detail of using the term "Z" for a composite section). If Z/S is greater than your combined load factor you will get yielding under service loads. This is especially true when the least critically stressed portion of the section (the bottom in this case) has a higher yield strength or when you consider superposition of elastic stresses.

I'm not saying the ultimate moment is affected, because it isn't, but it is possible that the section experiences yielding under service loads and I think it's a check worth doing.

 

[WillisV]

Lion06 - I agree that it is good engineering judgment to hold members such as this to the elastic range under service loads as you suggest, but it is not an actual code requirement, and you could just take the inelasticity into account for deflection checking (perhaps easier said than done).

Note that it is possible, though not likely, to yield even a regular rolled W-shape composite beams with high dead to live load ratios as some shape factors are as high as 1.3, and as far as I am aware no "canned" software will perform this check for LRFD design.

 

[a2mfk]

Don't forget a lot of this may be moot if lateral-torsional buckling controls... Is your compression flange braced?

 

[Brad805]

This is a case where the material cost is really not that important unless you have a great number of them to do. The actual install time, and prep work is 80% of the battle. I would focus a lot of the attention on the connection design.

Brad