Reinforced CMU Shear Wall In-Plane Shear (TMS 402 ASD)
The allowable in-plane shear of a reinforced masonry shear wall, fully or partially grouted (gamma_g 0.75).
Example
You enter
- Masonry strength f'm (psi) 1500
- Net wall thickness (in) 7.625
- Shear depth dv, wall length (in) 96
- Sustained axial load P (lb) 20000
- Shear-span ratio M/(V dv) 0.5
- Horizontal bar area Av (in², 0 = none) 0.2
- Horizontal bar spacing s (in) 48
- Allowable steel stress Fs (psi) 32000
You get
- An (in²) 732
- Masonry term Fvm 67.3 psi
- Reinforcement term Fvs 8.7 psi
- Combined Fv (vs cap) 76.1 psi (cap 103.3 psi)
- Fv max 103.28
- Allowable in-plane shear Va 55.7 kip
Checked against published worked examples from: The Masonry Society, ASD Night School.
Details, formula, and sources
ScopeThe masonry term Fvm = 0.5 x ((4.0 - 1.75 M/(V dv)) sqrt(f'm)) + 0.25 P/An that grows with axial compression and shrinks with slenderness, the horizontal-steel term Fvs = 0.5 Av Fs dv/(An s), and the combined stress against the shear-span-graded 3-to-2 sqrt(f'm) cap, times the net area for the allowable force. An 8 in by 8 ft wall under 20 kip of axial with #4 horizontals at 48 in carries 76 psi and 55.7 kip -- the capacity the seismic base-shear demand is checked against. A special reinforced shear wall takes 1/4 in place of 1/2 on the masonry term. Sustained axial only; special-reinforced detailing is separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
Formula or tableFvm = c x ((4.0 - 1.75 x M/(V dv)) x sqrt(f'm)) + 0.25 x (P/An), c = 1/2 (1/4 for a special reinforced shear wall); Fvs = 0.5 x (Av Fs dv)/(An s); Fv = (Fvm + Fvs) gamma_g, capped at 3 sqrt(f'm) gamma_g (M/(V dv) <= 0.25) grading to 2 sqrt(f'm) gamma_g (>= 1.0), gamma_g = 1.0 fully / 0.75 partially grouted; Va = Fv An.
Source and editionTMS 402-16 allowable-stress in-plane shear provisions, as compiled in the Masonry Designers' Guide and CMHA TEK 14-07C, by name.
Free accessCMHA TEK notes on shear-wall allowable-stress design are free public CMHA technical notes; the Fvm / Fvs arithmetic is public.
What governsEstimate. AHJ and licensed professional govern.
API field namesfm_psi, b_in, dv_in, p_lb, mvd, av_in2, s_in, fs_psi, an_in2, fvm, fvs, fv, fv_max, va_kip
- Two contributions plus a cap the masonry diagonal-tension term (raised by axial compression, lowered by slenderness) plus the horizontal-steel term, with the combined stress capped on the shear-span-graded 3-to-2 sqrt(f'm) lineTMS 402-16
- Sustained axial only P is the sustained compression acting with the shear; do not count live load that may be absent when the lateral force arrivesTMS 402-16 / Masonry Designers' Guide
- Grouting and wall class gamma_g 1.0 fully grouted / 0.75 partially grouted on Fv and its cap; Fvm leads with 1/4 for a special reinforced shear wall, 1/2 otherwiseTMS 402-16 8.3.5.1
- Detailing separate special-reinforced shear-wall detailing, minimum reinforcement ratios, and the shear-friction base check are separate code requirementsTMS 402-16