Reinforced CMU Wall Axial Compression (TMS 402 ASD)
The allowable concentric axial load of a reinforced masonry wall or column: 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 tile. A design aid, not a substitute for the engineer of record's stamped design.
Formula and source
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.
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