Reinforced CMU Wall Axial Compression (TMS 402 ASD)
The allowable concentric axial load of a reinforced masonry wall or column.
Example
You enter
- Masonry strength f'm (psi) 2000
- Net area An (in²) 91.5
- Vertical steel Ast, tied (in², 0 = untied) 0.155
- Effective height h (in) 144
- Radius of gyration r (in) 2.201
- Allowable steel stress Fs (psi) 32000
You get
- Slenderness h/r 65.4 (short/intermediate branch)
- Material capacity 0.25 f'm An + 0.65 Ast Fs 48974 lb
- Slenderness factor R 0.7816
- Allowable axial Pa 38.3 kip
Details, formula, and sources
The material capacity 0.25 f'm An + 0.65 Ast Fs (the steel term for laterally tied bars) times the slenderness factor -- 1 - (h/140r)^2 up to h/r = 99 and the Euler-type (70r/h)^2 beyond, the two branches meeting continuously. A one-foot strip of a 12 ft, 8 in grouted wall with #5 verticals at 24 in carries 38.3 kip; stretch it to 24 ft and the slender branch cuts it to 14.0 kip, the buckling penalty that forces thickness or a brace. Pure axial; the moment interaction pairs with the flexure check. A design aid, not a substitute for the engineer of record's stamped design.
Pa = (0.25 f'm An + 0.65 Ast Fs) x R; R = 1 - (h/(140 r))^2 for h/r <= 99, R = (70 r / h)^2 for h/r > 99 (branches meet at h/r = 99).
TMS 402-16 (ACI 530 / ASCE 5) allowable-stress axial-compression provisions for reinforced masonry, as compiled in the Masonry Designers' Guide and CMHA TEK 14-07C, by name.
CMHA TEK notes on ASD axial design are free public CMHA technical notes; the two-branch slenderness arithmetic is public.
Estimate. AHJ and licensed professional govern.
Field names used by the API: fm_psi, an_in2, ast_in2, h_in, r_in, fs_psi, hr, p0_lb, r_factor, pa_kip
- Two-branch slenderness the 1 - (h/140r)^2 short/intermediate parabola and the (70r/h)^2 slender (Euler-type) branch meet continuously at h/r = 99TMS 402-16
- Tied bars for the steel term 0.65 Ast Fs counts only laterally tied vertical reinforcement; an untied wall conservatively takes 0.25 f'm An x R aloneTMS 402-16 / Masonry Designers' Guide
- Concentric only pure axial with no moment interaction; eccentric or combined loading runs through the unity check with the flexure tileTMS 402-16