There are a number of different ways to increase the axial/flexural strength of a concrete wall. Any engineer who has designed lateral force resisting systems for concrete buildings has no doubt spent a lot of time assessing the optimum means of increasing the resistance of a wall panel or wall core to flexure. Geometric constraints presented by the architect are likely to influence the decision made.

We here in the RAM Structural System development group have been running a number of test cases through the **RAM Concrete Shear Wall **Design module as of late. One scenario that was created did a good job of illustrating the impacts of strengthening a simple wall for axial-flexural loads by different methods. We therefore felt it was worth sharing this information with colleagues who find this a topic of interest. The configurations and design results are documented below. Note that we are in no way endorsing one means of strengthening over any other, as the parameters involved in making this decision are obviously far more extensive than what is considered below.

The specific test at hand is a parametric study of axial-flexural design results for a simple planar concrete wall 15 feet in length and 50 feet in height. The wall stack as analyzed in RAM Frame is shown in elevation below, with the applied seismic story forces shown at each level.

The walls at each level are loaded with a 1500 plf dead load and an 800 plf live load (no reduction). __All design checks done in each example are performed at the base of the wall stack, and the reinforcing shown for each scenario below is the reinforcing used at the lowest level.__ Each scenario below results in an axial-flexural interaction value between 0.97 and 1.01 for all cases. Thus, each scenario has roughly equal axial-flexural strength.

**Scenario 1: The control case**

Wall thickness = 16"

f'_{c} = 4,000 psi, f_{y} = 60 ksi

Reinforce wall panel with (2) #9@8" oc vert

δ_{ROOF} = 1.482"

Axial/Flexure Interaction Value = 0.991

c = 2.30 ft > c_{LIMIT} = 2.04 ft, **therefore 1.15' S.B.E. required**

**A**_{s} **= 46.0 in ^{2}**

**V**

_{conc}= 7.41 cy

**Scenario 2:** **Bundle steel at wall ends**

Wall thickness = 16"

f'_{c }= 4,000 psi, f_{y} = 60 ksi

Reinforce wall panel with (4) rows of (3) #9@4" oc vert at each end, with (2) #6@18" oc vert balance

δ_{ROOF} = 1.482"

Axial/Flexure Interaction Value = 0.973

c = 1.84 ft < c_{LIMIT} = 2.04 ft, **therefore no S.B.E. required**

**A**_{s}** = 31.0 in ^{2}**

**V**

_{conc}= 7.41 cy

**Scenario 3**: **Use higher concrete strength**

Wall thickness = 16"

f'_{c} = 6,000 psi at lowest two levels, 4,000 psi above, f_{y} = 60 ksi

Reinforce wall panel with (2) #8@9" oc vert

δ_{ROOF} = 1.260"

Axial/Flexure Interaction Value = 0.998

c = 1.78 ft < c_{LIMIT} = 2.40 ft, therefore no S.B.E. required

**A**_{s}** = 33.2 in ^{2}**

**V**

_{conc}= 7.41 cy

**Scenario 4: Use even higher concrete strength**

Wall thickness = 16"

f'_{c} = 8,000 psi at lowest two levels, 4,000 psi above, f_{y} = 60 ksi

Reinforce wall panel with (2) #8@10" oc vert

δ_{ROOF} = 1.048"

Axial/Flexure Interaction Value = 1.007

c = 1.57 ft < c_{LIMIT }= 2.88 ft, therefore no S.B.E. required

**A**_{s}** = 30.0 in ^{2}**

**V**

_{conc}= 7.41 cy

**Scenario 5: Increase wall thickness**

Wall thickness = 20"

f'_{c} = 4,000 psi, f_{y} = 60 ksi

Reinforce wall panel with (2) #9@10" oc vert

δ_{ROOF} = 1.185"

Axial/Flexure Interaction Value = 0.978

c = 1.88 ft < c_{LIMIT} = 2.54 ft, therefore no S.B.E. required

**A**_{s} **= 38.0 in ^{2}**

**V**

_{conc}= 9.26 cy

**Scenario 6: Decrease wall thickness, use flanges at each end of panel**

Wall thickness = 10"

Flange dimensions: 10" x 2'-0"

f'_{c} = 4,000 psi, f_{y }= 60 ksi

Reinforce wall panel with (1) #6@18" oc vert in web, (11) #9 in each flange

δ_{ROOF} = 1.383"

Axial/Flexure Interaction Value = 0.974

c = 1.31 ft < c_{LIMIT} = 2.31 ft, therefore no S.B.E. required

**A**_{s}** = 25.4 in ^{2}**

**V**

_{conc}= 5.35 cy