Reinforced CMU Wall Out-of-Plane Flexure (TMS 402 ASD)

Fully grouted CMU wall by the working-stress cracked transformed-section method: the modular ratio n = Es/(900 f'm), the neutral-axis and lever-arm coefficients k and j, the steel-governed Ms = As Fs j d against the masonry-governed Mm = 0.5 Fb k j b d^2, and whichever is less governs. An 8 in wall with #5 bars at 24 in on 2,000 psi masonry carries 1,428 lb-ft per foot, steel-governed -- the textbook lightly-reinforced outcome; tighten the bars to 16 in and the masonry compression block takes over at 1,924. Cracked section, pure flexure, no axial interaction or one-third increase. A design aid, not a substitute for the engineer of record's stamped design.

n = Es/Em (Em = 900 f'm); rho = As/(b d); k = sqrt(2 rho n + (rho n)^2) - rho n; j = 1 - k/3; Ms = As Fs j d; Mm = 0.5 Fb k j b d^2 (Fb = 0.45 f'm); Ma = min(Ms, Mm).

TMS 402-16 (Building Code Requirements for Masonry Structures, ACI 530 / ASCE 5) allowable-stress-design cracked transformed-section flexure, as compiled in the Masonry Designers' Guide and CMHA TEK 14-07C, by name.

CMHA TEK 14-07C (Allowable Stress Design of Concrete Masonry) is a free public CMHA technical note; the k / j working-stress arithmetic is public and printed in every masonry-design text.

Estimate. AHJ and licensed professional govern.

Field names used by the API: fm_psi, as_in2, d_in, b_in, fs_psi, n_ratio, k, j, ms_ftlb, mm_ftlb, ma_ftlb

• Cracked working-stress section singly reinforced, fully grouted, cracked transformed section in near-pure flexure; the axial interaction and the slender-wall P-delta method are separate analysesTMS 402-16 / CMHA TEK 14-07C
• Allowable stresses Fs = 32,000 psi (Grade 60) and Fb = 0.45 f'm, with Em = 900 f'm for concrete masonry; editable for other grades and materialsTMS 402-16
• Governing mode reported the lesser of the steel- and masonry-governed moments governs; adding steel past the balance point stops paying off once Mm < MsMasonry Designers' Guide