Strengthening Open Web Steel Joists

[Qrs]

When you are strengthening an existing joist, all references say that “forces are distributed between existing member and the reinforcing member in direct proportion to their area”. This is in the “Designing with Vulcraft” document as well as the paper “Strengthening Open Web Steel Joists” by James Fischer. But why is this?

Let’s assume we have a total axial load of 14k in the bottom chord of a steel joist due to the addition of an RTU. The original design allowed for 7k of force in the bottom chord. There is a preload of 3k in the bottom chord (from existing DL). For the example, lets also assume that the existing bottom chord of the joist has an area of 0.325in^2.

The reference documents say that the amount of steel you will need for reinforcing is (14k-3k)/(7k-3k)*0.325in^2 = 0.893in^2 of reinforcing required. This is because the angle will take an additional force in direct proportion to its area: (0.325/0.893)*(14k-3k) = 4k. This 4k + the 3k of preload = 7k which is within the capacity of the original design.

But I guess my question is why does the angle take the force in proportion to its area? With an area of 0.893in^2, the reinforcing can take up to 19.25k on its own!! But we need the reinforcing to be this big not for capacity, but so that the angle is not over stressed. If we use a smaller area of reinforcing, the existing chord angle will take a greater percentage of the load and will have >7k force as originally designed.

But this doesn’t look like a problem to be. It seems to me that if the angle is overstressed it will start to yield and then the additional force will go into the reinforcing. Let’s assume we use 0.5in^2 of reinforcing. Then the angle will supposedly take (0.325/0.5)*(14k-3k)=7.15k of the additional load. Add that to the 3k of preload and you get 10.15k of load. This is over the 7k original designed. Won’t the angle start to yield and the additional force will go into the reinforcing? The reinforcing can take 10.77k on its own, so there is plenty of capacity for the additional load. Seems to me like the angle will take 7k of load as designed, and the reinforcing will pick up the slack – but that is not what literature suggests.

Can anyone help explain this to me?

Thanks.

 

[KootK]

The part of the puzzle that you're missing is this: when a member yields, it's flexural stiffness goes to zero. This means that:

1) If you reinforce a double angle top chord with a couple of round rods and the angles plastify, you're buckling capacity drops through the floor.

2) If you reinforce a double angle bottom chord with a couple of round rods and the angles plastify, your kL/r reduces dramatically and the spacing of your bottom chord bridging will be out of whack.

3) If your welds weren't designed to allow the chords and webs to reach their yield strengths, they'll fracture before you ever get those members plastified.

What you've proposed with respect to allowing yielding is possible; it just needs to be considered carefully. I've done it myself on some joists where the welds were plentiful and we reinforced the bottom chords with channels. The channels alone had kL/r values greater than the original bottom chords.

The reinforcement strategy that you've been reading about is designed to ensure that no part of the existing truss sees a load greater than it was originally designed for. It's a robust system and therefore fit for mass consumption. It's possible to take a more nuanced approach and bend a few "rules", however, if you consider the implications carefully.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Triangled]

Agreeing with KootK in item #3 above.... it's my understanding that steel joist welds are generally custom designed on a joist by joist basis and that they do not therefore necessarily develop the capacity of the web or chord, in fact likely rarely do if ever. Web #2 and web #4 may be exactly the same size member for various reasons including a lot of L1.5x1.5x.118 angle was left over from the previous project, but the welds of Web #2 and web #4 to the chords may be different due to design.

 

[spats]

I haven't read either of these documents, but it seems you're misreading it. 0.893 in^2 is the total area required, including the existing chord. The existing chord will take (0.325/total area)*11k additional load = 4K additional capacity. Solving for total A = 0.893 in^2. 0.893 - 0.325 = 0.568 in^2 of reinforcing required.

 

[woodman88]

From page 87 of the attached "Designing with Vulcraft" 2002 ed

"The following example illustrates the principles in-
volved in the reinforcement of joists. Note that the rein-
forced joist has considerably more capacity than is required
for the new loading condition. Given the unknowns associ-
ated with the reinforcement of joists, some conservatism
seemsjustified. The added capacity can be acquired at little
cost,since the incremental cost of material in the reinforce-
ment of joists is negligible. The largest portion of cost for
this type of work is for set up and labor."

It than gives an example design.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[Qrs]

Makes sense. Thanks everyone!