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Q: Need to calculate bearing capacity of steel beam in residential rebuild. ( Answered ,   0 Comments )
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 Subject: Need to calculate bearing capacity of steel beam in residential rebuild. Category: Science Asked by: cpopetz-ga List Price: \$50.00 Posted: 18 Jul 2006 09:31 PDT Expires: 17 Aug 2006 09:31 PDT Question ID: 747389
 ```I am adding a second story to my house, and need to know if the existing steel beam under the first floor, which is supporting the one load bearing wall, can bear the weight of a second story. The roof is bearing on the exterior walls, so it is not a factor. I am looking at two floors with live loads of 30 psf and dead loads of 20 psf, plus one 2nd floor ceiling with no live load and a dead load of 10 psf. (The ceiling joists are not roofing members, and thus are bearing on the wall.) The existing steel beam is an old-style S-flange, namely an S 7x20 (Ixx=42.4, Iyy=3.17). It joists are 22' long, so that's a tributary span of 11'. The beam is 24' and is supported at 12' with a column on a concrete slab. I need to know how to calculate (a) the load that beam is bearing with one floor, (b) what it bears with the second floor and extra ceiling, and (c) whether the beam is strong enough to handle that. I'd love to know the actual equations for these things, so I can do this calculation next time on my own, and so when I present this to the the building inspector I know what I'm talking about.```
 ```Hello cpopetz, you seem to have done a very good job of describing your problem. I think we can get some answers. (a) the load that beam is bearing with one floor NOTE: What you have here is a continuous beam with two equal spans. However, to make things a little easier we can consider it as a simple beam. The answer will be a little conservative, but that is probably good and these formulas are not 100% accurate anyway. The beam formulas for this loading are: M (maximum bending moment) = wl^2/8 D (deflection @ center of span) = 5wl^4/384 EI NOTE: Maximum deflection is limited to D = l/360 = 12 x 12 / 360 = 0.40 in w (load per foot) = (30 + 20 + 10)psf x 11' = 660 lb per ft l (beam span) = 12 ft Where E is a constant for steel = 30,000,000 psi And I is the moment of inertia Solving for M: M = 660 x 12^2 / 8 = 11,880 ft lb = 142,560 in lb The allowable bending stress for structural steel (s) = 0.55 x 36,000 psi = 19,800 psi The section modulus of the required beam (S) = M/s = 142,560/19,800 = 7.2 in^3 Now we must calculate the required I (moment of inertia): Solving for I in the above formula for deflection we get: I = 5wl^4/384 ED = (5 x 660 x 12^4 / 384 x 30,000,000 x 0.40) x 1728 NOTE: 1728 is a conversion factor to get the proper units for I I = 25.66 in^4 This tells us what we already know, that the existing beam was more than adequate. (b) what it bears with the second floor and extra ceiling The only difference in these calcs is that we now add in another 30 + 20 psf. So, w now becomes: 110 x 11' = 1210 lb per ft Solving for M: M = 1210 x 12^2 / 8 = 21,780 ft lb = 261,360 in lb The allowable bending stress for structural steel (s) = 0.55 x 36,000 psi = 19,800 psi The section modulus of the required beam (S) = M/s = 261,360/19,800 = 13.2 in^3 Now we must calculate the required I (moment of inertia): Solving for I in the above formula for deflection we get: I = 5wl^4/384 ED = (5 x 1210 x 12^4 / 384 x 30,000,000 x 0.40) x 1728 NOTE: 1728 is a conversion factor to get the proper units for I I = 47.04 in^4 (c) whether the beam is strong enough to handle that I checked your numbers for the existing S 7x20 and you are exactly right. So, we are comparing our calculated required value of 47.04 in^4 to 42.4 in^4. I would say that your existing beam is adequate. I have a beam program that will handle the actual end conditions that you have. I will check out the beam using that program and let you know what results I get. If there is any of what I have posted that you don't understand, please ask for a clarification. Back with you soon, Redhoss``` Clarification of Answer by redhoss-ga on 18 Jul 2006 11:44 PDT ```I just ran your beam on the software and got: Maximum moment = 200,096 in lb Deflection = 0.31 inch Since we are allowed 0.4 inch, I believe your existing beam is adequate. The only area your building inspector might question is the column footing. This would get a little sticky since you probably don't know the footing size. I would argue that the footing was designed to support a fully loaded beam. It seems that the beam was designed with the possibility of adding a second floor. Please let me know if you have further questions.``` Request for Answer Clarification by cpopetz-ga on 18 Jul 2006 12:48 PDT ```Thanks so much! That all makes sense to me. The inspector is also concerned about the column itself. (He hasn't seen it yet, he's going by my descriptions.) There are actually two columns, although they are placed so close together that I have assumed one was used to install the other, or that one was installed after the other for some reason (though since the steel beam isn't likely to sag, I can't imagine the reason.) Anway, the column at 12' looks like a cast concrete pier, 6" diameter octagonal, with two peices of rebar running vertical in it. It's on a 24" square pad, but I don't know how deep. The column 1 foot away from it is a telescoping steel column, on another 24" square pad. Both columns are in good shape, on rust on the steel, no cracking/crumbling on the concrete. Any thoughts on this? I realize this is a lot more vague than the previous question.``` Clarification of Answer by redhoss-ga on 18 Jul 2006 15:07 PDT ```Thanks for the tip, five stars, and kind words. Without some very specific info on the columns I don't think anyone can give you anything other than an educated guess. It sounds to me like the contractor that did the original job was well advised. I would suspect that the columns and footings are well designed. Other than this, I don't know what to say.```
 cpopetz-ga rated this answer: and gave an additional tip of: \$10.00 `Very helpful,and very quick! I am so glad to have used this service.`