| name | masonry-structures |
| description | Masonry structural design — compressive strength f'm (from unit + mortar per TMS 402), allowable stress vs. strength design, unreinforced masonry (URM) axial and flexural design, reinforced masonry beam and wall, slender wall design (P-delta, moment magnification), pilaster design, empirical design provisions, masonry shear wall in-plane and out-of-plane, seismic detailing (SDC A–F), masonry prism testing, mortar types (M/S/N/O), grout, ASTM C90 CMU, TMS 402/602 (formerly ACI 530/ASCE 5). |
| metadata | {"priority":7,"promptSignals":{"phrases":["masonry","CMU","masonry wall","unreinforced masonry","TMS 402"],"minScore":3}} |
Masonry Structural Design — Complete Skill
Masonry Materials
Compressive Strength f'm
Unit + mortar combination (TMS 402 Table 4.2.2.1.1 — unit strength method):
f'm from tables based on net area compressive strength of CMU and mortar type
Example: 12.5 MPa (1800 psi) CMU unit + Type S mortar → f'm = 12.5 MPa (1800 psi) net area
Units: f'm commonly 10–25 MPa (1500–3000 psi) for reinforced CMU
Prism testing (TMS 602 Section 1.4B):
Test 3 prism sets at 28 days → f'm = average of prism tests × correction factor for h/t ratio
H/t correction factor: h/t = 2 → factor 1.0; h/t = 5 → factor 1.30
Prism test more accurate; use when f'm > 20 MPa or code requires verification
Mortar types (ASTM C270):
| Type | Proportions (cement:lime:sand) | f'm_mortar [MPa] | Use |
|---|
| M | 1 : 1/4 : 3–3.75 | 17.2 | Below grade, exterior |
| S | 1 : 1/2 : 4–4.5 | 12.4 | General; MSJC preferred |
| N | 1 : 1 : 5–6 | 5.2 | Interior; above grade |
| O | 1 : 2 : 8–9 | 2.4 | Interior non-load-bearing |
Grout (ASTM C476):
Fine grout (slump 200–280 mm): cells ≤ 50×75 mm; coarse grout: cells ≥ 75×100 mm
f'g (grout compressive strength) ≥ 1.5 × f'm and ≥ 17 MPa
Allowable Stress Design (ASD) — TMS 402
Unreinforced Masonry (URM)
Allowable compressive stress (axial):
F_a = 0.25 × f'm × [1 − (h/(140 × r))²] [for h/r ≤ 99]
F_a = 0.25 × f'm × (70 × r/h)² [for h/r > 99; Euler-like slenderness]
Where: h = effective height [mm]; r = radius of gyration = t/√12 for solid rectangular section
Allowable flexural compression:
F_b = 0.33 × f'm [extreme fiber in compression]
Allowable tension (URM, perpendicular to bed joint):
F_t (flexural tension): per TMS 402 Table 8.2.4.2 (varies by mortar type and direction)
Type S mortar, running bond, perpendicular to bed joint: F_t = 0.207 MPa (30 psi)
Type S mortar, stack bond: F_t = 0.103 MPa (15 psi)
Combined axial + bending (URM):
fa/F_a + fb/F_b ≤ 1.0 [interaction formula; fa = actual compressive stress; fb = actual bending stress]
Also check: net tension = fb − fa ≤ F_t (no tension zone)
Reinforced Masonry (RM)
Reinforcement limits:
ρ_min = 0.0013 (horizontal and vertical combined for shear walls)
ρ_max = limited by 3εy/(εmu + 3εy) balanced reinforcement (SDC D–F per TMS 402)
ε_mu = 0.003 (masonry ultimate strain)
Flexural design (RM beam or wall):
Mu ≤ ϕ × Mn [ϕ = 0.9 for flexure]
Mn = As × fy × (d − a/2) [a = As×fy/(0.80×f'm×b); Whitney stress block adaptation for masonry]
Depth of stress block: a = T/(0.80 × f'm × b) [T = As × fy]
Shear design (RM):
Vu ≤ ϕ × Vn [ϕ = 0.80 for shear]
Vn = Vm + Vs [Vm = masonry shear contribution; Vs = steel shear contribution]
Vm = [4/3 × √(f'm) − 0.45 × (Nuz/An)] × An × Cd [MPa; Nuz = factored axial; An = net area; Cd = shear coefficient from M/(Vd)]
Slender Wall Design
P-Delta Effects
Slender wall criterion: h/t > 30 (must use moment magnification)
Moment magnification method (TMS 402 Section 9.3):
M_u,total = M_u,0 + P_u × Δ_s [where Δ_s = lateral deflection under factored loads]
Deflection at mid-height:
For Mu < Mcr: Δ_s = 5 × M_u,total × h²/(48 × E_m × I_eff)
For Mu > Mcr: Δ_s = 5 × M_cr × h²/(48 × E_m × I_n) + 5 × (M_u − M_cr) × h²/(48 × E_m × I_cr)
Cracking moment:
M_cr = S_n × (f'r + P_u/A_n) [S_n = net section modulus; f'r = modulus of rupture]
f'r = 0.633 MPa (100 psi) normal weight CMU, Type S mortar, in plane with bed joint
Effective stiffness:
I_n = net cross-section moment of inertia [per meter of wall; CMU hollow]
I_cr = cracked section; transformed area with Es/Em ratio n = Es/Em [Em = 900 × f'm for clay; 700 × f'm for concrete masonry]
P-delta iteration:
- Assume Δ_s = 0; compute Mu = M_u,0
- Compute Δ_s from above formulas
- Recompute Mu = M_u,0 + P_u × Δ_s
- Iterate until convergence (typically 2–3 cycles)
Shear Walls
In-Plane Shear (Lateral Load Resistance)
Masonry shear wall design:
h_w/l_w = wall height / wall length; aspect ratio governs behavior:
h_w/l_w ≤ 0.5: flexurally stiff; shear governs; squat wall
h_w/l_w > 1.5: flexure governs; slender wall; need sufficient flexural reinforcement
Chord reinforcement (overturning):
T = M_u/l_w − P_u/2 [tension at boundary; P_u = factored gravity; M_u = factored moment from lateral]
A_s,chord = T/(ϕ × fy) [ϕ = 0.9]
Collector / diaphragm connection:
Force transferred from diaphragm to wall through shear friction or embedded anchor
V_friction = μ × Ac × f'c (grouted interface) [conservative; or anchor bolt design per TMS 402 Section 9.1.6]
Out-of-Plane Pressure (Wind/Seismic)
Tributary width loading:
w = lateral pressure [kN/m²] × tributary width [m] = linear load [kN/m]
Moment: M_u = 0.1 × w × h² (two-way if surrounded; propped cantilever; or simple span per boundary conditions)
Design as slender wall (above) or short wall if h/t ≤ 30
Seismic Design Requirements (TMS 402)
Seismic Design Category (SDC) requirements:
| SDC | Requirements |
|---|
| A, B | Empirical design allowed (h/t limits); prescriptive |
| C | Engineered masonry; special reinforcement at openings |
| D, E | Reinforced masonry; minimum ρ = 0.0013 each direction |
| F | Special reinforced masonry (SRM); max bar spacing 600 mm each way |
Masonry detailing for high SDC:
Max spacing of vertical reinforcement: 600 mm (SDC D–F)
Horizontal reinforcement: bond beams at max 1200 mm spacing; continuous; lap = 48 × d_b
No URM for SDC D–F (except parapets ≤ 1200 mm); SRM required
Empirical Design (Low-Rise, Low-Seismic)
Empirical method permitted when:
SDC A or B; wind speed ≤ 44 m/s; building ≤ 3 stories; h ≤ 11 m
Wall thickness limits:
Bearing walls: t_min = h/14 [h = unsupported height; minimum absolute: 150 mm for 1 story]
Parapet: t_min = h_parapet/3 and ≥ 200 mm
Lateral support requirement:
Maximum h/t for exterior walls: 18 (solid); 16 (hollow); or 20 (hollow with grout + reinf.)
If exceeded: must add pilasters, cross walls, or design as structural element
Standards
| Standard | Scope |
|---|
| TMS 402-22 | Building code requirements for masonry structures |
| TMS 602-22 | Specification for masonry structures |
| ASTM C90 | Loadbearing concrete masonry units (CMU) |
| ASTM C270 | Mortar for unit masonry |
| ASTM C476 | Grout for masonry |
| ASTM C1019 | Sampling and testing of grout |
| ASCE 7-22 | Loads for masonry design reference |
| IBC 2021 | Adopts TMS 402/602 by reference |
Output
Provide: material properties (f'm [MPa]: from unit strength table or prism test; mortar type; grout f'g [MPa]; Em = 700×f'm [MPa] for CMU), wall geometry (thickness t [mm]; height h [mm]; h/t slenderness; reinforcement: vertical d_b @ spacing [mm]; horizontal d_b @ spacing [mm]), loading (P_u [kN/m] axial; Mu [kN·m/m] from wind/seismic/eccentric; Vu [kN/m] in-plane or out-of-plane), slender wall P-delta (Mcr [kN·m]; M_u,0 [kN·m]; iterate Δ_s [mm]; final Mu [kN·m]; ≤ Mn?), design check (Mn = As×fy×(d−a/2) [kN·m]; ϕMn ≥ Mu?; Vn = Vm+Vs [kN/m]; ϕVn ≥ Vu?; axial: fa/Fa+fb/Fb ≤ 1.0 for URM), seismic (SDC; min ρ = 0.0013?; bar spacing ≤ 600 mm?; boundary elements?; chord reinforcement at openings [mm²]), empirical check (h/t ≤ 18 for exterior?; if SDC A/B empirical allowed), and applicable standard (TMS 402 for design; TMS 602 for specification; ASTM C90 for CMU material; ASCE 7 for loads).
