Axial Strength of a Reinforced Concrete Wall

Axial Strength of a Reinforced Concrete Wall

Reference: Reinforced Concrete Walls

Draft - Comments Welcome

For an example, let's go back to the lesson on Calculated Footing Width (here), except that let's place a basement under the structure in the example. The Main level floor and superstructure above will frame on top of the wall, and the height of the wall from top to footing will be 8'-4". Let's assume a 4 in. basement slab, but not count the slab to reduce the wall height. Let's specify 3000 psi concrete and Gr. 60 deformed reinforcement, size # 4 or # 5, whichever works out best. Let's place the steel in the center of the wall, and we will assume that the wall is also adequately designed by whatever means (buttresses, returns, etc., but not dealt with here) to resist any lateral earth pressures.

From the earlier example the following information is obtained.

Total loads to top of foundation:

DL = 518 plf

SL = 520 plf SL

LL = 800 plf LL

Now let's add in the weight of the wall itself.

... ω _DL = 150 pcf (8/12 ft x 8.33 ft) = 833 plf.

So,

Total DL is 518 + 833 = 1351 plf.

There are two load combinations that we should look at ...

U = 1.2 D + 1.6 L + 0.5 S ... and ... 1.2 D + 1.0 L + 1.6 S

... and the design factored load will be the greater of these.

So,

U = 1.2 (1351) + 1.6 (800) + 0.5 (520) = 3161 plf

U = 1.2 (1351) + 1.0 (800) + 1.6 (520) = 3253 plf

So, our design factored load is 3253 plf.

Now let's see how strong our wall is. Let's use k = 1.00 assuming top and bottom of the wall supported to resist translation but not rotation.

... φ P _nw = 0.55 φ f '_c A_g [1 - (k l_c / 32 h)²] = 0.55 (0.70) 3000 psi (12 in. x 8 in.) [1 - (1.0 x 8.33 x 12 in. / 32 x 8 in.)²] = 93,975 lb (per foot of wall).

The strength of the wall (94,000 plf) way exceeds the load (3250 plf) on the wall. So much so, that unless other issues are involved, I don't even do this calc check.

I suppose you could argue ... `Yeah, but it's just a residential structure!' Yeah, go ahead and argue that. And I'll add some more stories, maybe even make some of the superstructure walls out of solid concrete ... and as long as the load is axial, and essentially centric, we are still way strong.

References

Reinforced Concrete Walls, Jeff Filler, Associated Content

Calculated Footing Width for a Residential Foundation, Jeff Filler, Associated Content.

Building Code Requirements for Structural Concrete, ACI 318, American Concrete Institute, P.O. Box 9094, Farmington hills, Michigan, 48333.