Masonry Column Calculator: CMU Column Design (TMS 402)

1 · Column

Width b (x) nominal

Depth h (y) nominal

Effective height Eq. 9-11

Unbraced height times the effective length factor.

2 · Reinforcement & materials

Vertical bars

Bar size

Face to bar center d' in.

in.

Bars sit in the grouted cells, typically about 4 in. from the face.

Lateral ties

Tie spacing in.

in.

f'_m §9.1.9

psi

f_y Grade 60

ksi

Apply minimum eccentricity 0.1 × side dimension

3 · Factored loads

Strength-level (LRFD) load cases from your analysis. Leave a row at zero to skip it.

Case	P_u (k)	M_ux (k-ft)	M_uy (k-ft)	V_u (k)
1
2
3

M_ux bends about the x-axis (compression on a face of width b); M_uy bends about the y-axis. Enter magnified moments for slender columns.

How the masonry column calculator works

This free masonry column calculator checks a fully grouted, reinforced concrete masonry (CMU) column using TMS 402-16 strength design, the edition referenced by the Florida Building Code, 8th Edition (2023). Choose the column size, the vertical bars and ties, f'm and the effective height, then enter up to three factored load cases with axial load, moments about both axes and shear.

What it checks

Axial strength φP_n = 0.9 × 0.80[0.80f'_m(A_n − A_s) + f_yA_s] times the slenderness factor [1 − (h/140r)²], or (70r/h)² when h/r exceeds 99
Combined axial load and bending about each axis from a strain-compatibility interaction diagram, counting the tied compression bars
Biaxial bending with the conservative linear check M_ux/φM_nx + M_uy/φM_ny ≤ 1.0, and an optional minimum eccentricity of 0.1 times the side dimension
Shear with the masonry and tie contributions, limited to 4A_n√f'_m
Detailing: least dimension, height-to-thickness ratio, steel ratio between 0.25% and 4%, bar size and tie spacing

Method

For each load case the neutral axis is found where the φ-reduced axial strength equals the factored axial load, so the load point is checked against the φP_n–φM_n curve. Masonry compression uses the 0.80f'_m stress block with a maximum strain of 0.0025, and bars in compression are counted because the column is tied, with the displaced masonry subtracted.

Assumptions and limitations

Fully grouted rectangular column with 4 corner bars or 8 bars (corners and mid-faces).
Moments are used as entered. Second-order moment magnification for slender columns is not calculated, so enter magnified moments where it applies.
Seismic tie detailing, pilasters acting with a wall, and bearing at the top and base are not checked.

Frequently asked questions

What is the minimum size of a masonry column?

TMS 402 requires a least nominal dimension of at least 8 in. for columns, and the effective height should not exceed 25 times the least nominal dimension. The calculator checks both.

How much vertical reinforcement does a CMU column need?

The area of vertical steel must be between 0.25% and 4% of the net area, with at least four bars. The bars must be enclosed by lateral ties.

How far apart can the ties be?

Tie spacing may not exceed 16 longitudinal bar diameters, 48 tie diameters or the least column dimension. Ties are often placed in the mortar bed joints, so an 8 in. spacing only works when every limit is at least 8 in.

Does the calculator include slenderness effects?

It reduces the axial strength with the TMS slenderness factor. It does not magnify the moments, so enter second-order moments for slender columns.

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For educational and preliminary design purposes only. Always verify results with a licensed PE.