Load Combinations in Allowable Stress Design

Introduction

In our concrete house design, where we sized the perimeter footing (here), we used the full Snow load, full Dead load, and full Live load design values. The building codes generally recognize that using the full values added together is probably unnecessarily conservative. Stated another way, the probability that the `events' associated with the design loads have an unnecessarily low chance of ever happing all at the same time. As such, the codes allow us some reduction (relief, benefit, whatever you want to call it) when such so-called `variable' loads occur simultaneously.

Load Combinations

In Allowable Stress Design (ASD) we deal with `service loads'. The International Building Code (IBC) provides the following:

"IBC 1605.3.1.1 (Basic Load Combinations) ... Load Reduction. It is permitted to multiply the combined effect of two or more variable loads by 0.75 and add to the effect of dead load. The combined load ... shall not be less than the sum of the effects of dead load and any one of the variable loads."

I interpret this to mean, for example ...

... the probability that the full design Snow load and the full design Live load will occur at the same time is really pretty low, unnecessarily low ... but not the probability that three-fourths of each may occur simultaneously.

So, we need to investigate the following (with regard to gravity loads) ...

D

D + L

D + S

D + 0.75 (L + S)

... and choose the larger value.

Note: the Code does not prevent us from using the full values ... D + L + S ... but recognizes it may be unnecessary ... and will produce larger structural members than necessary.

Example

Back to our example footing calculation. We determine the footing width using ASD ... so, from before (here), ...

Loads to the bearing soil including 12 x 30 footing ...

D = 2672 plf

S = 760 plf

L = 320 plf

We added them to get Total Load ... 3752 plf. And from that we found that the 30 x 11 footing was barely big enough (or not).

Now let's look at Load Combinations per ... 1605.3.1.1.

D = 2672 plf ... yeah, this certainly could happen ... empty house in summer.

D + S = 2672 + 760 = 3432 plf ... empty house during particularly bad winter.

D + L = 2672 + 320 = 2292 plf ... big summer party.

D + 0.75 (S + L) = 2672 + 0.75 (760 + 320) = 3482 plf.

We need to design for the `worst' of the above (largest number), so ...

... 3482 plf.

Note that this is less than the 3752 value used earlier. The 3452 plf could / should result in a smaller footing???

Let's see.

Try 11 x 28 footing ...

Footing weight = 11/12 x 28/12 x 150 = 321 plf.

So, the total Dead load, including footing ... is 2672 - 344 (for the 11 x 30) + 321 = 2649 plf ... a difference of 23 lb.

So, the controlling combined load will be 3482 - 23 = 3459 plf.

The applied soil pressure is ... f_p = 3459 plf / (28/12 ft) = 1482 plf.

So, is f_p = 1482 plf ≤ F_p = 1500 psf? ... Yes!

Not only have shown that the 11 x 30 footing is good, but by using the provided load combinations we have shown that a footing of 11 x 28 is good.

Conclusion (for now)

We have gone to a fair amount of work to show that we can shave off a couple inches of footing width. Depending on the size of the structure it may or may not `be worth our while' to do so. In situations where our Live load is larger, relatively, there would be more benefit. In our concrete house, where a good chunk of the load is Dead load, the above load combination `hair splitting' provides less benefit. Also, if we split hairs too close in the footing design, we preclude any design changes later on (after the foundation is poured) that increase the total Dead load.

Next we will talk about Load Factors.

References

International Building Code, International Code Council, 4051 West Flossmoor Road, Country Club Hills, IL 60478.