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    Calculates locally in your browser · TMS 402 allowable-stress masonry
    Masonry / walls

    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.

    VerdictPassesSteelAdequateh/r52
    Interaction
    0.45
    within unity
    Slenderness h/r
    52
    within the limit
    Allowable axial
    323 psi
    125 psi applied
    Bending stress
    29 psi
    against 495 psi allowable
    Axial, bending, and the interaction between them
    Both stresses act on the same face, so neither can be checked alone.
    0.45
    Axial, bending, and the interaction between them
    CheckValueAllowable
    Wall thickness8 in—
    Unsupported height10.0 ft—
    Radius of gyration2.31 int/√12
    Slenderness h/r5299
    Allowable axial Fa323 psi0.25 f’m [1 − (h/140r)²]
    Applied axial fa125 psiP/t
    Out-of-plane moment3750 in·lbw h²/8
    Section modulus128 in³t²/6 per foot
    Bending fb29 psi495 psi
    Interaction0.451.00
    Steel required0.043 in²/ft0.083 provided

    Axial uses 39% of its allowable and bending 6%, for a combined 45%.

    Inspect the model
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    Interaction against wall height
    Falls away steeply: the allowable axial stress drops with (h/r)², so height hurts twice.
    Interaction against wall height0.0000.2020.4050.6070.8101.018 ft8 ft10 ft10 ft12 ft12 ft14 ft14 ft16 ft16 ft18 ft18 ft20 ft20 ftInteraction
    Axial against bending
    Which term dominates depends on the wall — a tall thin wall is bending-governed, a short one axial.
    Axial against bending0.0009.1218.2527.3736.4945.6238.66AxialAxial5.92BendingBendingShare of allowable
    Canonical equations
    The exact relationships implemented by this engine.

    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.

    engineering methodology

    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.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Choose the wall thickness and the unsupported height.
    2. Set the masonry strength and the axial load per foot.
    3. Enter the wind pressure and the vertical reinforcement.
    4. Read the interaction and whether the wall passes.

    The formula

    faFa+fbFb≤1\frac{f_a}{F_a} + \frac{f_b}{F_b} \le 1

    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

    Inputs
    • 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.
    Calculation path
    1. 1

      The radius of gyration is 8/√12 = 2.31 in, so h/r = 51.96.

    2. 2

      The allowable axial stress is 0.25 × 1,500 × (1 − (51.96/140)²) = 323 psi.

    3. 3

      The applied axial stress is 1,000/8 = 125 psi.

    4. 4

      The wind moment is 25 × 100/8 = 312.5 ft·lb, giving 29.3 psi of bending.

    5. 5

      The interaction is 125/323 + 29.3/495 = 0.45, so the wall passes comfortably.

    Result

    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.