Masonry Wall Calculator
Quick answer: A 20 ft tall, 8-inch nominal CMU wall (f'm = 2,000 psi) with #5 bars at 40 inches on center, fully grouted, can resist approximately 20 psf out-of-plane lateral pressure under TMS 402. The governing limit state is typically out-of-plane bending at mid-height. An ungrouted 8-inch wall has roughly 30-40% of the capacity of a fully grouted wall with reinforcement.
Use the free calculator below to check compression, out-of-plane bending, and shear capacity for reinforced and unreinforced CMU walls per TMS 402.
Typical CMU Wall Properties
| Nominal Size | Actual Width (in) | f'm Range (psi) | Common Use |
|---|---|---|---|
| 6-inch | 5.625 | 1,500-2,500 | Non-structural partitions |
| 8-inch | 7.625 | 1,500-3,000 | Load-bearing walls, most common |
| 10-inch | 9.625 | 1,500-3,000 | Higher axial loads, taller walls |
| 12-inch | 11.625 | 1,500-3,000 | Basement walls, high axial loads |
Key Design Checks Per TMS 402
1. Axial compression: Pn = 0.80 x f'm x Ag (unreinforced) or strain compatibility (reinforced). Slenderness ratio h/t is checked; if h/t > 30 for unreinforced or h/t > 99 for reinforced walls, moment magnification is required.
2. Out-of-plane bending: The wall is modeled as simply supported between floor levels. For reinforced walls, moment capacity comes from the internal couple between masonry compression and rebar tension (phi-Mn = phi x As x fy x (d - a/2), where a = As x fy / (0.80 x f'm x b)). For unreinforced walls, no tension is allowed in the masonry.
3. Shear: phi-Vn = phi x (Vms + Vmv), where Vms is masonry shear contribution and Vmv is reinforcement contribution. Shear typically does not govern for out-of-plane design unless the wall is very short or heavily loaded.
Quick Worked Example
Wall: 20 ft tall, 8-inch CMU, fully grouted, f'm = 2,000 psi Reinforcement: #5 bars at 40 in O.C. (As = 0.31 in^2 per bar, spacing b = 40 in) Axial load: P = 500 lb/ft (dead load from above) Lateral pressure: 20 psf wind
Effective d = 7.625/2 = 3.8 in (bar at center of wall) a = As x fy / (0.80 x f'm x b) = 0.31 x 60,000 / (0.80 x 2,000 x 40) = 0.29 in phi-Mn per bar spacing = 0.9 x 0.31 x 60,000 x (3.8 - 0.29/2) = 62,900 in-lb per 40 in width Mu from wind = w x L^2 / 8 = 20 x 20^2 / 8 x (40/12) = 33,333 in-lb per 40 in width
Demand/capacity = 33,333 / 62,900 = 0.53 -- PASS
How the Calculator Works
The calculator uses strain compatibility for reinforced masonry (iterates neutral axis depth, computes internal forces) and cracked-section analysis for unreinforced masonry. Slenderness effects are included via the moment magnifier per TMS 402 Section 9.3.
TMS 402 Design Formulas — Detailed Reference
Axial compression capacity
Unreinforced masonry (TMS 402 §9.2.3):
Pn = 0.80 × f'm × An × (1 - (h/140r)²)
Where:
f'm = specified masonry compressive strength (psi)
An = net cross-sectional area (in²)
h = wall height between lateral supports (in)
r = radius of gyration of net section
Reinforced masonry (TMS 402 §9.3.2):
Pn = φ × [0.80 × f'm × (An - As) + fy × As]
With slenderness reduction for h/r > 99:
Use moment magnifier δs = Cm / (1 - Pu/(φ × Pe))
Out-of-plane bending capacity
Reinforced masonry (TMS 402 §9.3.3):
φMn = φ × As × fy × (d - a/2)
Where:
As = reinforcement area per bar spacing
fy = yield strength of reinforcement (psi)
d = effective depth from compression face to rebar center
a = As × fy / (0.80 × f'm × b)
b = bar spacing (in)
φ = 0.90 (tension-controlled)
Check: φMn ≥ Mu from applied lateral loads
Shear capacity
φVn = φ × (Vms + Vmv)
Masonry contribution:
Vms = 2.45 × √(f'm) × b × d (simplified)
Reinforcement contribution (horizontal steel):
Vmv = 0.5 × (Av/s) × fy × d
Where:
b = width of section (bar spacing)
d = effective depth
Av = area of horizontal shear reinforcement
s = spacing of horizontal reinforcement
f'm Values by Unit Strength and Mortar Type
The specified masonry compressive strength f'm can be determined from the unit strength method per TMS 602 Table 3.
CMU unit strength vs f'm (Type S mortar)
| CMU Unit Strength (psi) | f'm (Type S Mortar) | f'm (Type N Mortar) |
|---|---|---|
| 1,900 | 1,500 | 1,350 |
| 2,800 | 2,000 | 1,800 |
| 3,750 | 2,500 | 2,250 |
| 4,800 | 3,000 | 2,700 |
| 5,600 | 3,500 | 3,150 |
| 6,500 | 4,000 | 3,600 |
Mortar types and their applications
| Mortar Type | Compressive Strength (psi) | Workability | Best Use |
|---|---|---|---|
| M | 2,500 | Low | High-load, below-grade, foundation |
| S | 1,800 | Medium | Structural walls, lateral load resistance |
| N | 750 | High | Non-load-bearing partitions, above-grade |
| O | 350 | Very high | Interior non-structural, tuck pointing |
Type S is the standard for structural CMU walls. Type M is used for below-grade and foundation walls.
Reinforcement Requirements for CMU Walls
Minimum reinforcement per TMS 402
| Seismic Design Category | Min Vertical Bar | Max Spacing (in) | Min Horizontal | Max Spacing (in) |
|---|---|---|---|---|
| A, B | #4 at 120" | 120 | #4 at 120" | 120 |
| C | #4 at 48" | 48 | #4 at 48" | 48 |
| D | #4 at 48" | 48 | #4 at 48" | 48 |
| E, F | #4 at 24" | 24 | #4 at 24" | 24 |
Standard reinforcement configurations
| Wall Size | Bar Size | Spacing (in) | As per ft (in²) | d (in) | Typical Use |
|---|---|---|---|---|---|
| 8" | #4 | 48 | 0.10 | 3.81 | Light lateral |
| 8" | #5 | 48 | 0.15 | 3.81 | Moderate lateral |
| 8" | #5 | 24 | 0.31 | 3.81 | High lateral / SDC D |
| 8" | #6 | 24 | 0.44 | 3.81 | Very high lateral |
| 10" | #5 | 48 | 0.15 | 4.81 | Higher axial loads |
| 10" | #6 | 24 | 0.44 | 4.81 | Shear walls |
| 12" | #6 | 24 | 0.44 | 5.81 | Basement walls |
| 12" | #7 | 24 | 0.60 | 5.81 | High axial + lateral |
Note: d values assume bar centered in wall. For bars offset toward the tension face, d increases.
Maximum reinforcement ratio
ρmax = 0.025 × f'm / fy (TMS 402)
For f'm = 2,000 psi, fy = 60,000 psi:
ρmax = 0.025 × 2000 / 60000 = 0.000833
For 8" wall (b = 7.625 in) at 48" spacing:
As_max = 0.000833 × 7.625 × 48 = 0.305 in² → #5 at 48" = 0.31 in² (near limit)
Grouting Requirements
Grout placement methods
| Method | Grout Pour Height | Grout Consistency | Cleanout Required |
|---|---|---|---|
| Low-lift | Up to 5 ft | Fine grout, slump 8-11 in | No |
| High-lift | 5 to 24 ft | Coarse grout, slump 8-11 in | Yes (for >5 ft) |
Grout strength requirements
f'g (grout compressive strength) must equal or exceed f'm.
Typical: f'g = 3,000 to 5,000 psi
Grout must fill all cells containing reinforcement.
For partially grouted walls, only reinforced cells are grouted.
For fully grouted walls, all cells are filled.
Minimum grout space dimensions per TMS 602 Table 7:
For bar #5 and smaller: 2" × 3" clear grout space
For bar #6 to #8: 2.5" × 3" clear grout space
For bar #9 and larger: 3" × 3" clear grout space
Frequently Asked Questions
What is f'm and how is it determined? f'm is the specified compressive strength of masonry, analogous to f'c for concrete. It depends on the CMU unit strength, mortar type, and grout strength. It is verified by prism testing (ASTM C1314) or can be estimated from unit strength and mortar type tables in TMS 602. Typical f'm values for structural CMU range from 1,500 to 3,000 psi.
When is grouted reinforced masonry required? Reinforced masonry is required when the wall must resist significant lateral loads (wind, seismic), when the wall is tall and slender, or when the seismic design category requires special reinforced masonry shear walls. Even in low-seismic areas, reinforcement is commonly added at corners, jambs, and bond beams for crack control and structural integrity.
How does masonry wall slenderness affect capacity? Tall, thin masonry walls are susceptible to P-delta effects that amplify the out-of-plane moment. TMS 402 addresses this through the slenderness ratio h/t and provides moment magnification factors or requires second-order analysis for walls exceeding certain h/t limits. For unreinforced masonry, the allowable slenderness is more restrictive than for reinforced masonry.
What is the difference between clay brick and concrete masonry unit (CMU) walls? Clay brick masonry (ASTM C216) uses fired clay units with typical compressive strengths of 8,000-14,000 psi, while CMU (ASTM C90) uses concrete units with typical strengths of 1,900-4,800 psi. Brick walls are typically 4 inches nominal width (veneer) or 8 inches (structural), while CMU walls range from 6 to 12 inches. Brick masonry uses Type N or S mortar and does not require grouting for most applications. CMU is more commonly used for load-bearing structural walls because it is easier to reinforce and grout, and the larger cell size accommodates vertical reinforcement and electrical conduit.
When are movement joints required in masonry walls? Masonry expands and contracts due to temperature changes, moisture absorption (clay brick expands over time, CMU shrinks), and elastic shortening under load. TMS 402 requires vertical expansion joints in clay brick walls at 20-25 ft spacing and vertical control joints in CMU walls at 20-25 ft spacing. Control joints in CMU are typically tooled or scored at locations of stress concentration: near corners, at changes in wall height, and at openings. Without movement joints, cracking is virtually guaranteed. The joint width is typically 3/8 to 3/4 inch and is filled with backer rod and sealant.
What are common CMU wall assemblies for different applications? Single-wythe solid grouted CMU is the most common assembly for load-bearing walls (8-inch or 12-inch, fully grouted with #4 or #5 bars at 24-48 inches). Double-wythe (cavity wall) assemblies use an outer brick veneer with an inner CMU backup, separated by a 2-inch cavity with wall ties and insulation. Partially grouted walls grout only the cells containing reinforcement, saving material but requiring careful design for the ungrouted cells. For below-grade basement walls, 12-inch CMU with waterproofing membrane on the exterior and #5 bars at 24 inches is standard. Multi-wythe grouted composite walls combine two wythes of CMU grouted solid for high-load bearing wall applications.
How does TMS 402 differ from ACI 530? ACI 530 (Building Code Requirements for Masonry Structures) was the predecessor standard that was re-designated as TMS 402 in 2013. They are the same standard under different sponsorship. The technical content is identical; only the designation changed. Some older references and building codes still cite ACI 530, but the current standard is TMS 402-22 (2022 edition). The corresponding specification for masonry construction is TMS 602 (formerly ACI 530.1).
What is the difference between running bond and stack bond masonry? Running bond (each course offset by half a unit length) is the standard pattern and provides better structural integrity through overlapping units. Stack bond (all joints aligned vertically) is used for aesthetic reasons but has lower structural capacity because the vertical joints create a plane of weakness. TMS 402 requires minimum horizontal reinforcement (typically #9 gauge joint reinforcement at 16 inches on center) for stack bond walls to compensate for the lack of structural interlock. Running bond does not have this additional requirement.
What is the effective depth d for a reinforced CMU wall? The effective depth d is the distance from the extreme compression face to the center of the reinforcement. For a standard 8-inch CMU wall (7.625 inches actual), d = 7.625/2 = 3.81 inches when the bar is centered in the wall. If the bar is placed in the face shell closer to the tension side (common practice for optimized design), d can increase to 5-6 inches, significantly increasing the moment capacity. However, centered reinforcement is most common because it works for wind from either direction and simplifies construction. For 10-inch and 12-inch walls, d increases proportionally to the wall thickness.
What is the minimum f'm required for structural CMU walls? TMS 402 does not specify a minimum f'm for structural walls; the designer selects f'm based on the required capacity. However, most building codes require f'm of at least 1,500 psi for load-bearing masonry. Typical values: f'm = 1,500 psi for non-critical walls, 2,000 psi for standard load-bearing walls, and 2,500-3,000 psi for heavily loaded or seismic-resisting shear walls. The f'm is verified through prism testing per ASTM C1314 during construction, or by the unit strength method using TMS 602 tables that correlate CMU unit strength and mortar type to f'm.
Related pages
- Shear wall calculator
- Retaining wall calculator
- Concrete beam-column calculator
- Load combinations (ASCE 7-16)
- Tools directory
- How to verify calculator results
- Disclaimer (educational use only)
- Load combinations calculator
- Wind load calculator
- Seismic load calculator
Disclaimer (educational use only)
This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.
All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.
The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.