# Assessment of a concrete beam being strengthened by an additional steel member

Hi there (from Europe),

I am completing what should be a relatively quick assessment for the client, but I have started to second guess my self and would like some reassurance.

Essentially the job involves removing a portion of an existing 2.6m x 1.22m concrete slab in order to install a manhole (1.2m x 0.75m). I've taken the fairly rudimentary (and conservative imo) approach of simply reducing the existing slabs moment capacity by reducing it's width. For example, for assessing the moment capacity of the current slab I took a width of 1.22m, but it's reduced capacity would be based on a width of 1.22-0.75=0.47m.

With an original moment capacity (89kNm), and reduced moment capacity(37kNm), we know the difference between these two (52kNm). My idea was to simply take two Square Hollow Sections and attach them to the underside of the slab, on either side of the manhole, and size them such that each was capable of holding half the difference in moment, 26kNm.

This is a fairly simple approach but the more I think about it the more I'm beginning to reconsider and instead consider assessing the steel and concrete as a single composite section to Eurocode 4.

This is a small scheme with a low budget and I lack experience of Eurocode 4 to quickly assess this.

My question is thus: Is my approach conservative enough to safely size steel members or is there something fundamental that I am missing in composite design that makes my solution inaccurate and dangerous?

• Good question. Since steel can flex and concrete can't, I'd be nervous about this. Hopefully someone can answer... Feb 9, 2017 at 10:55
• How are you connecting the steel to the concrete? Unless they are properly connected there will be no composite action. Normally composite beams are formed by 1. putting the steel in place, 2. having shear studs on top of the beams, 3. concrete poured, which encases the shear studs. You can't do that to an existing slab. Also, how long are your SHSs? You haven't indicated any thought on this. They need to be longer than the 1.2m hole, in order for the stress to be transferred from the concrete into the SHSs. Feb 9, 2017 at 12:50
• Of course the SHS will span between the same support as that which the slab spans between (so the full 2.6m), apologies I should have been clearer. Initial thoughts are to have the SHS places very close to the bottom surface of the slab with wedge-shaped plates inserted into the gap at regular intervals to ensure that deflections in the concrete results in an immediate reaction in the steel. But I'm unsure of this hence the question. Feb 9, 2017 at 13:04

It isn't clear from your sketch whether the end supports are fixed or pinned, so I'm going to assume they were pinned. However, this is going to be a qualitative answer, so that doesn't actually matter too much.

Assuming pinned supports, the original slab was therefore basically a simply-supported beam, with no moment at the ends and positive longitudinal moment at the midspan equal to $\frac{qL^2}{8}$. Transversal moment would be effectively null.

Now, with your suggested reinforcement, you will be completely changing the slabs structural arrangement. Indeed, it would no longer be "the slab", but instead eight different slabs (for manual analytical purposes):

So, slabs S1, S3, S6 and S8 are effectively equivalent, as is S2 equal to S7, and S4 to S5. So now, when discussing the different slabs, I'll only mention slabs S1, S2 and S4, each representing all their equivalent slabs.

So, slab S1 needs to be calculated like a fixed-pinned, fixed-free slab; S2 as a fixed-fixed, pinned-free slab and (out of an abundance of caution) S4 as both a pinned-free, fixed-fixed slab and as a pinned-free, pinned-pinned slab.

The division of the unmodified strips of the original slab (S1-S2-S3 and S6-S7-S8) into three slabs may seem a bit odd. After all, this method would imply in a negative bending moment between S1 and S2 even though they are actually the same slab with no beam beneath them. But that is in fact correct, since S4 will now resist any rotation around the S1-S2 interface. Meanwhile, between S1 and S4 there is now the reinforcing beam, which adds stiffness to that interface.

So, if you want to be very conservative, you should calculate the slab with all its loading as if it were originally constructed with that hole and see what is the required steel reinforcement (rebar) in both the longitudinal and transversal directions. Check to see whether the built slab satisfies all of these requirements. If it does, you're fine. If it doesn't, then the slab itself may need to be reinforced, and simply adding steel beams may not be enough.

Indeed, my concern is with the negative reinforcement that will be necessary in the slab. The positive will probably be fine since you are effectively reducing the effective span of each span area and whatever load is transferred from S4 and S5 will go to the beams and not the neighboring slabs. The original slab was probably not designed with any significant negative reinforcement, so I would not be surprised if a problem occurs there, especially on the S1-S4 edge, where you're dealing with negative transversal reinforcement which is probably almost nonexistent in the original slab.

An argument could be made that considering the entirety of the load when calculating the reinforcement would be excessive. After all, some portion of the self-weight and dead load will probably be unmolested by the hole (for instance, whichever part of the load which already goes from S1 to S3) and therefore shouldn't be considered when calculating the new configuration. This would be especially important when considering the effect of the beams, since if the slab doesn't redistribute much load to them, they won't be of much use. However, the hole is so massive (my drawing is more to scale than your sketch) that considering a full redistribution of loads seems entirely reasonable to me.

Another question is how to fix the beams to the slab in such a way as to certify that they will indeed work in tandem. As @AndyT commented, this is usually done by taking special measures when the slab is poured. Obviously, in this case that is not possible. My suggestion would therefore be to use anchor bolts. This, however, would not be possible with SHS profiles since you wouldn't be able to access the bolts along the beam's span. You'd therefore need to change to L-, T- or I-shapes.

However, as described above, you may need to add some negative reinforcement to your slab. If that is the case, then you can make a slightly larger intervention:

1. Get SHS sections with shear studs.
2. Drill two lines of large holes in the slab along each beam's span.
3. Place the SHS sections under the slab, with adequate space between the beam and the slab for the studs. Also add some shear reinforcement passing through the holes.
4. When concreting the slab with the negative reinforcement, also concrete the joint between the slab and the beam. Also add some rebar going through the shear reinforcement placed in the previous step. Given the small access, special treatment may be necessary for the concrete.

Regarding composite action, it will be minimal therefore you are doing well to ignore it.

Probably the design is adequate (except maybe for point 4 below)but i want to mention some missing elements from your analysis:

1. You are restoring the slab strength for sagging moments but not for hogging ones.
2. It is important to know when the shs members are installed. If after the hole is opened, then a verification is needed for the reduced slab under the dead loads plus any live before the shs installation.
3. Verification of deflections of the reduced slab.
4. The hole surface should probably get strengthened, particularly its corners, due to stress concentrations.