Flange Check for Point Load

[j19]

I want to check the top flange of a floor beam for local bending due to the point load from a floor joist. The beam is in the center of a bay so that there are joists attaching to the beam on both sides of the web. The joists are in line with each other so they do not extend across the web but stop so that there is a ¼” gap between the ends of the joists. See the attached sketch. I started to use ’05 AISC equation J10-1 (even though the loading is in compression) but I think it would only be applicable if the load is continuous across the beam web rather than point loads on each side of the web. The flange capacity is easy to calculate if I consider that ½ the beam flange as fixed at the web with three sides free, but I think that may be too conservative. I could easily oversize the flange of this one beam but I want to make this check a part of my standard procedures for floor beams. Can anyone point me towards something that might be more accurate?

Thanks.

 

[rb1957]

simplest would be to consider the flange as a cantilever, width ? as wide as the joist would be conservative, as wide as the joist + twice the width of one side of the flange (draw a 45deg line from the intersection of the joist cap and the flange to the base of the flange) doesn't sound unreasonable.

 

[BAretired]

You could use a yield line analysis. See attached sketch for yield line locations.

BA

 

[j19]

Thanks BA. Why wouldn't the positive and negative yield lines be the same?

 

[BAretired]

The negative yield lines result from negative moment (tension on top). The positive yield lines from positive moment (tension on the bottom).

BA

 

[bootlegend]

I believe Modern Steel Construction (Dec 1999, you can look it up on the MSC site) replied to someone's similar question a few years ago. I think it was the bottom flange bending capacity for an underhung crane beam. They calculated an effective width at the web based on the load spreading out at 30 degrees each side and checked it as a cantilever beam. Of course you'll get more out of BA's yield line procedure if you can get it programmed so you don't have to calculate it for every joist.

 

[msquared48]

Just put in a bearing stiffener and forget it.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[ToadJones]

Unless the loads are very light, I agree with Mike.
Its a very simple check and like Boot said, easy to make a spreadsheet.

 

[nutte]

Put in a bearing stiffener under each joist? That's a lot of stiffeners. Is anybody doing this? I've not seen it done that way.

 

[ToadJones]

you wont see it much.
Run your checks for flange bending.

 

[JoshPlumSE]

It's not a bad idea to take a look at what that load would do using yield line theory...especially for a critical structure/connection. To me, however, this is more like a one time calculation that you do to prove to yourself that typical joist seats are going to work fine.

I'm not sure that other folks are really looking at it those connections so closely. At least, not for each and every project. After all, if this were a common failure mechanism, I'd think the joist references would talk about it. And, I don't recall seeing a discussion of this anywhere.

Personally, I'd start out using section J10. The joist seats are going to spread that load out over the flanges a decent amount. So, it really is an over simplification to treat that load as a point load.

 

[AVak]

You could always stagger the joists to aloow the seats to extend over the beam web. This should eliminate the localized flange bending problem.

Adam Vakiener, P.E.

 

[msquared48]

Is this a short header beam seeing a large load from a deep open web joist? Usually OWJ's bearing on steel beams do not have this problem.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[BAretired]

Extending the joist shoe across the beam web does not help unless the shoe is designed for moment, which it usually is not. The gap between joist ends is only 1/4" now, so in effect the joist shoe overlaps part of the web and fillet.

The beam flange is usually more than capable of supporting a joist reaction. This can easily be checked by the Yield Line method in a couple of minutes, so why not just do it?

BA

 

[gobsmacked]

Yield line theory gives an upper bound to the strength. You need to consider all possible yield line patterns, including the one attached, which could well be more critical.

 

[dhengr]

I’d run a FEA on this mother. Don’t forget to consider that the combined stresses in the flange will be different at max. beam moment locations than at other locations, and different at +Mmax and at -Mmax. The residual stresses in the flange/web/radius region should be included in that analysis. And, this is the same region where piping is most likely to occur if it exists. And, don’t forget to consider that both the beam flange and the joist seat have some twist angle tolerance as delivered and this will concentrate the joist loading out at the tip of the flange at a single point, not over some area. I see several Ph.D. theses here, and a whole new section in the next AISC code edition.

 

[BAretired]

gobsmacked,

It is true that the yield line method provides an upper bound solution and it is important to find the correct yield line pattern. I would agree that your yield line pattern is possible if the load is considered a point load at the middle of the bearing area of the joist shoe.

I have added to your sketch as shown attached. The red lines represent negative yield line...the green represent positive yield lines. The width of joist shoe is dimension 'c'.

If there are any other potential yield lines, they too should be considered.

BA

 

[BAretired]

dhengr,

You are correct that flexural stress in the flange plays a role in this, so some conservatism is warranted. I think that the load is best considered as uniform over the bearing area of the shoe, but that could be argued.

You are absolutely right about the potential for a few Ph.D. theses. Funny thing is...I don't think too many engineers calculate this effect because they assume that the flange is more than adequate and most of the time, they are right.

BA

 

[BAretired]

gobsmacked,

you are correct in your critical yield line pattern as shown in the attachment. In hindsight, it should have been apparent to me.

These calculations are based on a plate having a unit moment resistance, m. The value 'm' is the factored moment resistance per inch which, for a stress relieved plate is the same in every direction, namely [φ]*t^2/4 where [φ] is 0.9 and t is plate thickness. R in the attachment is the factored joist reaction which is considered uniformly distributed in the crossed rectangle. The arrows indicate the slope of sections between yield lines with unit deflection assumed along side 'c'. R deflects 0.5 units.

If the joist reaction is located at a point of high flexural stress in the flange, m(parallel) remains the same but m(normal) should be reduced an amount reflecting the axial stress in the flange.

Finally, to allow for potential corner effects, m required should be increased by 10%.

BA