Reinforced masonry wall
A masonry wall carries two things at once: the axial load from above, and the out-of-plane bending from wind. Both produce compression on the same face, so the check is an interaction rather than either one alone — and slenderness is what makes it bite, because the allowable axial stress falls with (h/r)².
| Check | Value | Allowable |
|---|---|---|
| Wall thickness | 8 in | — |
| Unsupported height | 10.0 ft | — |
| Radius of gyration | 2.31 in | t/√12 |
| Slenderness h/r | 52 | 99 |
| Allowable axial Fa | 323 psi | 0.25 f’m [1 − (h/140r)²] |
| Applied axial fa | 125 psi | P/t |
| Out-of-plane moment | 3750 in·lb | w h²/8 |
| Section modulus | 128 in³ | t²/6 per foot |
| Bending fb | 29 psi | 495 psi |
| Interaction | 0.45 | 1.00 |
| Steel required | 0.043 in²/ft | 0.083 provided |
Axial uses 39% of its allowable and bending 6%, for a combined 45%.
h/r, r = t/√12 · Capped at 99.
0.25 f’m [1 − (h/140r)²] · TMS 402 §8.3.4.
fb = M/S, S = t²/6 · Per foot of wall.
fa/Fa + fb/Fb ≤ 1 · Both on the same face.
A clear path from inputs to results.
A masonry wall carries two things at once: the axial load from above, and the out-of-plane bending from wind. Both produce compression on the same face, so the check is an interaction rather than either one alone.
How to use
- Choose the wall thickness and the unsupported height.
- Set the masonry strength and the axial load per foot.
- Enter the wind pressure and the vertical reinforcement.
- Read the interaction and whether the wall passes.
The formula
Reference: TMS 402-16 §8.3.4 for axial compression and §8.3.3 for flexural compression, allowable-stress design.
Worked example
An 8 in wall, 10 ft high, 25 psf wind
- 8 in nominal thickness, 10 ft unsupported height.
- f’m 1,500 psi, 1,000 lb/ft axial.
- 25 psf wind, #3 bars at 16 in.
- 1
The radius of gyration is 8/√12 = 2.31 in, so h/r = 51.96.
- 2
The allowable axial stress is 0.25 × 1,500 × (1 − (51.96/140)²) = 323 psi.
- 3
The applied axial stress is 1,000/8 = 125 psi.
- 4
The wind moment is 25 × 100/8 = 312.5 ft·lb, giving 29.3 psi of bending.
- 5
The interaction is 125/323 + 29.3/495 = 0.45, so the wall passes comfortably.
h/r 52 · interaction 0.45 · passes.
Interpreting the result
Slenderness is the governing variable, not strength. Doubling the height raises the moment fourfold and cuts the allowable axial stress by more than half, so the interaction roughly quadruples — which is why an intermediate bond beam or a thicker wall is usually the fix rather than more steel.
Assumptions & limitations
- Simply supported top and bottom, concentrically loaded.
- Solidly grouted reinforced concrete masonry.
- Out-of-plane wind as a uniform load.
- No shear check, no in-plane load and no seismic detailing.
Frequently asked questions
What is the 99 limit?
TMS 402 caps the slenderness ratio at 99 for an axially loaded member. Beyond that the wall is not permitted regardless of the stress calculation.
Do I need to check both faces?
Only if the load is eccentric. With a concentric axial load and out-of-plane wind, the windward face goes into tension and the leeward into compression, and the compression check governs.
Does grouting matter?
Enormously. A partially grouted wall has less than half the effective area and a much lower section modulus, and the calculation is quite different.
Why does the allowable stress fall with h/r squared?
Because it is a second-order effect: the wall deflects, the load becomes eccentric, and the extra moment grows with the square of the slenderness.
How much steel is typical?
#4 at 48 in or #5 at 48 in for a lightly loaded wall; closer spacing where the wind moment is high or the wall is tall.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.