*Draft – Comments Welcome*

**1. Introduction**

Walls. Reinforced concrete walls are cool. If I build my next house it will be out of concrete. (Well, maybe I have also said that about other materials.) Reinforced concrete walls are strong. They are bulletproof. With some insulation (say an ICF system) they have great thermal properties. In this lesson we will look at `just how strong’ are reinforced concrete walls.

In the context of this lesson, and a good portion of the course, when I say (just) `wall’ I am referring to a reinforced concrete wall with the minimum reinforcement specified in Chapter 14 of the ACI 318 Code. In some cases we will need *more* than the minimum reinforcement specified by Chapter 14, such as what I call the `one-way’ basement retaining wall (here). But we can also construct other types of basement walls (lesson here) with the Chapter 14 minimum amounts, as long as we don’t require the wall to span too great of distances as it retains earth backfill and thus resists the lateral earth pressures.

We are going to see that if we load the wall axially (in the plane of the wall) … that the wall is hugely strong. The most common type of such axial loading is the use of a (vertical) wall to carry (downward) gravity loads, say from roof, floors, decks, and the weight of the wall itself. And as long as we keep the load(s) centered in the wall. Once the loads get (way) off-center, or if we load the wall laterally (all or some component of the loads perpendicular to the plane of the wall), then the wall is loaded in flexure (bending) and it must act as a one-way slab, beam, or two-way slab. In these cases where the wall is subject to flexural loading we may need more reinforcement. And there is the case where we may building (`hide’) a column in a wall, and as such require more reinforcement.

Sometimes you might hear me say “UBC Walls” … and what I am referring to are (these) walls with the ACI Ch. 14 min. amounts of steel.

Here goes …

**2. Minimum Reinforcement**

… ρ min, walls, H.S. = 0.0020 for # 5 and smaller, Grade 60 or higher rebar

… ρ min, walls, V.S. = 0.0012 for # 5 and smaller, Grade 60 or higher rebar

Other rebar (# 6 and larger or less than Gr. 60):

… ρ min. = 0.0025 for H.S. … and … ρ min. . = 0.0015 for V.S.

These ratios are based on gross area;

… ρ = as / (s h) …

where,

… as is the area of a single bar,

… s = bar spacing, and

… h = wall thickness.

**3. Openings**

Ch. 14 of the ACI 318 Code (prescriptively) requires that there be 2 # 5 bars around all (window and door) openings. And that these bars shall extend at least 24 in. past the opening corners.

Also, if the concrete above an opening acts as a lintel, or header, additional reinforcement may be necessary. (Lintel design will be in a later lesson.)

**4. Layers of Reinforcement**

The ACI 318 Code also requires for walls greater than 10 in. thick (except basement walls) that the reinforcement be placed in two mats or layers parallel with the wall faces. (See ACI 318 Sec. 14.3.4).

**5. Maximum Spacing**

The ACI Code also specifies a maximum *spacing* of horizontal and vertical bars of the lesser of:

… three times the wall thickness,

or

… 18 in.

And I tend to space *basement* wall reinforcement not greater than the above, though sometimes I feel somewhat alone in that practice.

**6. Wall Strength**

I love this next equation (though I seldom have to use it).

The axial compressive strength of a reinforced concrete wall is given by the following equation (subject to the limitations following the equation):

… φ P nw = 0.55 φ f ‘c Ag [1 – (k lc / 32 h)2], …

where,

… φ = strength reduction factor; in this application = 0.70;

P nw = the `nominal’ (theoretical, perfect world’) compressive strength of the wall;

(And where thus … φ P nw … is the `factored strength’.)

0.55 = a number (that we may or may not talk more about later);

… f ‘c = the specified 28-day compressive strength of the concrete;

Ag = the gross area … b times h …

… k is kind of an effective length (height) factor, as follows:

0.8 for walls with either top or bottom restrained against rotation;

1.0 for walls unrestrained against rotation at both ends; and

2.0 for walls not braced against lateral translation.

lc = is the wall height (height between support or brace points);

h = wall thickness;

and,

… [1 – (k lc / 32 h)2] … looks like it accounts for slenderness and reduces the strength to account for potential buckling of the wall.

Note: if we are using the wall to resist a `line load’ then we generally deal on a `per foot of wall’ basis. In this case Ag = 12 in. times h. If we are using the wall to resist concentrated loads, say reaction from a girder, or from joists, or a concentrated load from a column (or something) above, the length of wall to be used may not exceed the center-to-center spacing of the loads nor the bearing width of the load plus four times the wall thickness.

**Limitations** …

The above equation may only be used under the following conditions:

The resultant of the axial load acts in the middle third of the wall.

The wall thickness may not be less than 1/25th the wall length or height; nor may it be less than 4 in. thick (7-1/2 in. thick for exterior basement and foundation walls).

**7. Basement Retaining Walls**

By analysis it can be shown that walls with the `minimum reinforcement’ described above are also capable of resisting significant lateral loads, and as such, may be used as basement retaining walls. (See the lesson on Basement Walls … here).

**8. Example: So, How Strong is Strong?**

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 number crunching is … here.

**9. References**

Design of a One-Way Reinforced Concrete Basement Retaining Wall, Jeff Filler, Associated Content.

Design of Concrete Basement 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.

Axial Strength of a Reinforced Concrete Wall, Jeff Filler, Associated Content