When does a uniform load become a series of point loads? 1

[DTS419]

Most of us are familiar with the concept of designing a concrete beam for Vu @ d, that is for the shear at a distance 'd' from the face of the support. At this critical distance, the shear in a simple span beam is typically less than at the end or face of support (FOS) which results in a reduction.

Designing for this reduced shear is permitted by ACI 318-19 9.4.3.2 so long as a few conditions are met, one of them being that the beam isn't loaded "such that the shear at sections between the support and a distance 'd' from the support differs radically from the shear at distance 'd'. This commonly occurs in brackets and in beams where a concentrated load is located close to a support...". ACI does not identify how much of a difference is considered a radical difference.

Now let us consider a simply supported single span concrete beam, like a window header, that is supporting floor joists that are spaced at 16" or 24" on center. If the beam is designed using the tributary area approach, it would commonly be designed for a uniform load that would be equivalent to the series of end reactions from the floor joists. But if the beam is designed for the joist end reactions as point loads, then the possibility exists that a joist, or point load, could exist between the FOS and 'd' such that the concrete beam would need to be designed for shear at FOS rather than shear at 'd'.

So would you consider the concrete beam to be uniformly loaded by a series of joist reactions and take shear at 'd', or would you consider the series of joist reactions to be point loads?

 

[phamENG]

I'd probably look at it as a uniform load for simplicity of analysis and design, and then check shear at the face of support rather than d to ensure I captured the effect of anything inside the 'd' distance.

 

[EngDM]

I'd probably look at it as a uniform load for simplicity of analysis and design, and then check shear at the face of support rather than d to ensure I captured the effect of anything inside the 'd' distance.

This is similar to what I typically do, taking shear at face of support. I only tend to rely on the distance 'd' check when we are doing reno's on an existing condition and I'm really fighting to get it to work, OR if I have one location that would bump up my required shear reinforcing I check it with distance 'd' to see if I can save switching grade beam types.

 

[KootK]

I've seen recommendations in print to justify uniform load treatment at 5 equally spaced, similar magnitude point loads. I find that most engineers are comfortable with it down to 3 equally spaced point loads which can be mildly unconservative in some respects.

For a case like the one you've described, I feel that it's wholly appropriate to ignore the joist reactions occurring within [d] of the support. Consider:

1) Loads close to the support satisfy shear via direct strutting whereas loads further away must satisfy shear via diagonal tension.

2) The shear capacity associated with strutting is much, much, high than that associated with diagonal tension.

3) If you can collect all of the interior point loads and still satisfy diagonal tension near the support, surely adding one more of those point loads isn't going to tip the scales when you switch over to strutting. Ultimately, all of the load winds up collected and delivered through the last strut down to the support. The "d thang" is predicated on capacity growing faster than demand.

In this sense, it's a self-solving situation.

Also note that this only works if the beam is top loaded. Side loaded is a different animal.

 

[DTS419]

KootK, I agree about the strutting. In the NDS, you can ignore shear on a wood joist if it is within d from the support because of this effect. However, what do you make of ACI's exclusion of a point load between FOS and d?

 

[KootK]

Don't worry about it. It's the same thing as in the NDS and, if anything, more appropriate in concrete. ACI's exclusion is meant to preclude loads for which the logic chain that I presented above would no longer be true. Big ones.

 

[Celt83]

@Agent666 put a little test together in a blog post a bit ago:

https://engineervsheep.com/2021/what-is-the-point/

 

[DTS419]

Hmmm. KootK had me convinced to go with Vu @ d, now that blog post has me second guessing...