Need to calculate bearing capacity of steel beam in residential rebuild. Best answer on the web

Posted in: darrelrussell.com edit
07 Jan 2009
  • 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.


  • 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.


  • 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


  • 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.


  • 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.


  • Very helpful,and very quick! I am so glad to have used this service.