Masonry shear wall

A reinforced concrete masonry (CMU) shear wall loaded in its plane, designed by strength design to TMS 402-22 Chapter 9, with the prescriptive seismic reinforcement of Chapter 7 and ASCE 7-22 2.3.1 load combinations. The design section is the base of the wall: axial load with in-plane moment by strain compatibility, in-plane shear, the reinforcement limits, and the wall type the seismic design category permits.

The calculation is by strength design only, so the LRFD / ASD switch is not shown. Allowable stress design (TMS 402-22 Chapter 8) is not offered. A calculation saved with ASD is designed by strength design.

Edition. The calculation is written from TMS 402-13 / TMS 602-13 (code, commentary and specification), checked provision by provision on 2026-11-01. Section numbers below are the TMS 402-22 numbers from TMS's own cross-reference list; the 402-22 text itself is not on hand. φ, γg, the maximum reinforcement and shear friction follow 402-22 as TMS's own 2022 handouts state them; items not yet confirmed in the code are listed under the limitations.

Inputs of the masonry shear wall #

• Wall:
  • The nominal thickness: 6, 8, 10 or 12 in. units, with specified thicknesses of 5.625, 7.625, 9.625 and 11.625 in.
  • The wall length Lw and height h.
  • The grout: fully grouted, or grouted only at the reinforced cells. For a partially grouted wall the net section is the two face shells (ASTM C90 minimums: 1.0 in. for 6 in. units, 1.25 in. for the others) plus 8 in. of full thickness per grouted cell, centered on the bar. The webs are neglected, which is conservative.
• Materials:
  • f'm, entered directly or by the unit strength method from the unit strength and the mortar type (TMS 602-22 Table 2).
  • Strength design requires f'm of at least 1,500 psi (Table 4.3.1); below that the calculation is not feasible. A specified f'm above 4,000 psi is permitted, but 4,000 psi is the value used for the nominal strengths of concrete masonry, and the steps say so.
  • The unit strength method assumes ASTM C90 units sampled and tested, bed joints of 5/8 in. or less, grout to TMS 602 Article 2.2 and units at least 4 in. high (TMS 602-13 Article 1.4 B.2.b).
  • Reinforcement of Grade 60 or Grade 40.
• Vertical reinforcement:
  • The number of end bars at each end (one bar per cell, 8 in. apart) and their size.
  • The distance from the wall end to the first bar (4 in. is the center of the end cell).
  • The distributed bar size and their maximum spacing. The distributed bars are spaced evenly between the innermost end bars, at no more than that spacing.
  • Whether the compression bars are laterally tied. They are untied in the usual case, and then bars in compression are neglected, both in the axial strength and in the strain compatibility.
• Horizontal reinforcement:
  • Bond-beam bars (size and spacing), or joint reinforcement (two W1.7 wires at 8 or 16 in.), or none.
  • Joint reinforcement counts toward the prescriptive minimum of ordinary and intermediate walls but is not counted as shear reinforcement (Vns = 0).
• Loads at the base: one row per load type (D, L, Lr, S, R, W, E):
  • P is the axial compression (concentric).
  • V is the in-plane shear.
  • M is the base moment; left blank, it is V × h.
  • E is the horizontal seismic load effect as you enter it, ρQE.
  • SDS adds the vertical seismic effect Ev = 0.2SDS D (ASCE 7-22 12.4.2.2) to the 2.3.6 combinations: (1.2 + 0.2SDS)D + Eh + L + 0.15S and (0.9 − 0.2SDS)D + Eh. It is 0 by default (Eh only); a note says so while E is present.
  • The optional self-weight adds the wall weight (psf) × Lw × h to D. NCMA TEK 14-13B values for normal-weight fully grouted units are in the hint.
• Seismic detailing:
  • The shear wall type (ordinary, intermediate or special reinforced): the type you assumed for R in ASCE 7-22 Table 12.2-1.
  • The seismic design category.
  • For intermediate and special walls, whether the design uses R ≤ 1.5. That allows the exemption from the maximum reinforcement where Mu/(Vu dv) ≤ 1 (402-16 9.3.3.2.4 (to confirm against the code text: at 402-22 9.3.5.6.1)). Without it, such a wall with Mu/(Vu dv) < 1 is checked with α = 1.5.
  • The shear friction coefficient μ: 1.00 on concrete with an unfinished or intentionally roughened surface, which the drawings must then specify; 0.70 for all other conditions, prefilled (to confirm against the code text: 9.3.5.5).
  • The area crossing the base Asp. 0 takes every vertical bar, as the TMS example does; enter less when not every bar is doweled into the support.
  • The mortar type also matters in SDC D, E and F (7.4.4.2.2). It is an input only with the unit strength method; with f'm entered, the check is a reminder.

Auto-design (editor toolbar) varies the nominal thickness, distributed vertical bars (size and spacing), end bars and horizontal bars. Objectives: lowest cost index (units, grout, reinforcement); least reinforcement. Every other input is kept; see Auto-design.

Checks performed #

The key results list the net area, the bar layout and the horizontal reinforcement. The drawings (on screen, in the report and on the PDF / DXF drawing sheet) are the wall elevation with the vertical bars where the calculation places them, the bond-beam bars or joint reinforcement at their spacing, the P and V arrows at the top (values by load type in the sheet notes) and the bar spacing and wall dimensions; a plan section at the wall end (detail) with the grouted cells or the full grout, the end bars and the first distributed bar, the end cover and the thickness; and the φPn–φMn interaction diagram (not to scale) with the (Mu, Pu) point of every combination and the governing one called out. CMU webs, bar splices, foundation dowels, the hooks of the shear bars and the anchorage at the top are not part of the calculation and are not drawn.

Limitations #

Not covered:

• Allowable stress design (TMS 402-22 Chapter 8).
• Out-of-plane loading, including the slender wall procedure (9.3.4).
• The special boundary element alternative to the maximum reinforcement (9.3.5.6.2): a note only.
• Unreinforced (plain) walls, clay masonry, openings, flanged or intersecting walls, masonry not laid in running bond.
• Anchorage, development and splices, grout strength (f'g ≥ f'm is assumed), the bar to grout space limits (one third of the least dimension, 4 % of the gross grout space, 6.1.3) and the horizontal reinforcement required at the top of the wall, at floor and roof levels and at openings.
• Joint reinforcement as shear reinforcement (9.3.3.7 allows it with 3/16 in. wires): it is not counted.
• The overstrength factor Ω0: enter the seismic effect you need (Emh = Ω0QE) as E. The ASD exception of 2.4.5 (0.9D for special reinforced walls in combination 10) does not apply: the wall is designed by strength design.

Simplifications:

• One bar per cell.
• Running bond.
• Each grouted cell is taken as 8 in. long, and webs are neglected in a partially grouted wall (as the TMS 402-13 commentary to its 9.3.3.5 does).
• The bar layout is symmetric.

Where this calculation is the earlier rule. Bar size: 6.1.3 has three rules for both design methods. Here only the first, and the 402-13 No. 9 limit.

Checked against TMS 402-13 on 2026-11-01. These were confirmed in TMS 402-13 / 602-13 and, as far as the TMS cross-reference and handouts show, are unchanged in the 2022 edition apart from the section number:

• Es = 29,000 ksi (4.2.2.1);
• εmu = 0.0025 and the 0.80 f'm over 0.80c stress block (9.3.2);
• φ = 0.80 for shear (9.1.4.5);
• the axial strength equations, with tied bars only (9.3.3.1.1, 9.3.2(e));
• the shear equations and the 6 / 4 Anv √f'm limits (9.3.3.1.2);
• the prescriptive reinforcement of 7.3.2.3.1 to 7.3.2.6 and the 1.25 Mn rule (7.3.2.6.1.1);
• the wall types per SDC (7.4);
• the unit strength table (TMS 602-13 Table 2).

The check corrected:

• the 1.25 Mn requirement, now the lesser of the two values;
• f'm above 4,000 psi, now capped instead of rejected;
• the α of squat walls (Mu/(Vu dv) < 1), now 1.5;
• the boundary element screen, now on Ag with all the conditions of 9.3.5.6.2.1.

It also added two checks: the end bar within 8 in. of the end, and the mortar in SDC D to F.

Still to verify in TMS 402-22 / 602-22 (the text is not on hand; marked (to confirm against the code text) in the code and the check references):

• the section numbers, which come from TMS's cross-reference, and the 402-22 equation numbers, confirmed only for Eq. 9-15;
• the α rule, the R ≤ 1.5 exemption and the axial load of the maximum reinforcement at 9.3.5.6.1;
• shear friction at 9.3.5.5: the formulas are from TMS's 2022 handout; the μ conditions, what counts in Asp and φ = 0.80 are not confirmed;
• the 4,000 psi upper limit of f'm;
• that TMS 602-22 Table 2 kept the 2013 values;
• the ASTM C90 face-shell thicknesses, which TMS 402 does not give;
• the ordinary wall height limit of ASCE 7-22 Table 12.2-1;
• the NCMA wall weights.

Verification examples #

Verification status: 75 values compared in 20 examples (9 published, 11 hand calculations from the cited equations): 64 within tolerance, 11 recorded deviations. Code basis: written from an older edition, with the differences noted. Not yet compared line by line with the target edition.

Published examples (golden tests in backend/tests/test_verify_masonry_wall.py):

• FEMA P-1051 (NEHRP Recommended Seismic Provisions: Design Examples, 2015 edition, Chapter 13, TMS 402-13), Section 13.2.4.5: Wall D of the five-story building in SDC B. 8 in. CMU partially grouted, Lw = 32 ft 8 in., story height 8 ft 8 in., f'm = 2,000 psi, #4 bars in the end cells and at 8 ft, 0.07 in.²/ft of horizontal steel (entered as #3 at 18.86 in.), Pu = 0.86D. Free from FEMA.
• The Masonry Society, webinar handout Design of Masonry Shear Walls (R. Bennett, 2018, TMS 402-16), Examples SD-1 to SD-3: a 2 ft pier and a 16 ft × 10 ft partially grouted wall, SDS = 0.5, wall weight 45 psf. Free from TMS.

Documented deviation TMS402-22-GG-WALL: these examples predate 402-22 and use γg = 0.75; ILX uses 0.70, so its partially grouted shear values are 6.7 % lower. FEMA's maximum reinforcement check (FEMA-13.2-DUC) is on an ordinary wall, where 402-22 deleted the limit: it is entered as intermediate, which reaches the same α = 1.5 rule. TMS SD-3 now fails the special wall shear for 1.25 Mn at 1.04, from the same γg.

Documented deviation (docs/verification/deviations.json, TMS-SD-EQT): in SD-2 and SD-3 the handout draws the interaction diagram and checks the maximum reinforcement with an equivalent (averaged) thickness of the partially grouted wall. ILX takes the face shells plus the grouted cells, as the FEMA example does. The handout's 0.9 Pn at the maximum-reinforcement strain is 323 / 364 kips (ILX 354 / 393 kips), and SD-2 is stressed to 94 % of its flexural design strength (ILX 89 %).

The hand calculations in closed form (MW-1 to MW-5) check the remaining paths. The base case (MW-1) is:

• 8 in. CMU, f'm = 2,000 psi, Lw = h = 8 ft;
• one #5 bar 4 in. from each end;
• #4 bond beams at 48 in.;
• E: V = 20 kips at the top.

MW-5 evaluates the closed-form maximum reinforcement equation printed in the TMS 402-13 commentary (9.3.3.5, p. C-139).

Not yet compared with a published example: the axial strength of 9.3.3.1.1 (402-13 Eqs. 9-19 / 9-20) on its own, and a published TMS 402-22 example. The examples above use earlier editions (402-13 and 402-16); the φ, γg and maximum reinforcement rules of 402-22 are hand calculations from TMS's 2022 handouts.