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United StatesTMS 402/602-22

Masonry Gravity Wall (LRFD)

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Design partially- or fully-grouted reinforced CMU gravity walls to TMS 402/602-22 Strength Design. Out-of-plane shear and combined factored axial-bending interaction checks with a visual interaction diagram. Load reactions link to footing calculations.
Instantly create a new Masonry Gravity Wall (LRFD) calculation by clicking here:Create Masonry Gravity Wall (LRFD) Calculator(This link automatically opens a new project and sheet in Calcs.com.)

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Method & scope

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Choosing the right calculator

Calcs.com has three TMS 402/602-22 masonry wall calculators. They are not interchangeable.

Gravity Wall (LRFD)

This page. Out-of-plane loading on a load-bearing wall span, checked per linear foot using LRFD.

Gravity Wall (ASD)

Same out-of-plane problem using allowable stress design (TMS Chapter 8).

Shear Wall (LRFD)

In-plane lateral force-resisting walls with multi-story geometry and optional openings.
Pick Gravity Wall (LRFD) or Gravity Wall (ASD) to match your project’s design method. For in-plane shear and overturning, use Shear Wall (LRFD) instead of either gravity calculator.

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When to use this calculator

Use this calculator when you have a load-bearing CMU wall that must resist out-of-plane lateral loading in addition to gravity. It covers single-wythe running-bond walls with a continuous bottom support, checked per linear foot of wall length.
Not a shear wall calculator. In-plane shear, in-plane overturning, and in-plane seismic resistance are not considered. For lateral force-resisting masonry walls, use Masonry Shear Wall (LRFD).Anchorage and uplift are not checked. A small amount of tension can be resisted by steel reinforcement, but connection design is outside this sheet.
If your project uses ASD rather than LRFD for masonry walls, use Masonry Gravity Wall (ASD) for the same out-of-plane problem.

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Assumptions and limitations

  • Wall is load-bearing, single-wythe, and CMU is in running bond.
  • Wall is partially or fully grouted with one row of reinforcement centered in the block width.
  • Bottom support is continuous (not spanning between point supports).
  • Calculations are per linear foot of wall length. Walls shorter than 1 ft are not supported.
  • Deflection criteria are not evaluated. TMS 402-22 Chapter 9 does not include deflection provisions for LRFD masonry wall design.
  • Fully grouted walls do not apply the slenderness limit, consistent with examples in MDG 2022.
  • Stability checks for wall foundations are not conducted.
Full assumptions and limitations are listed in the Sheet Details tab within the calculator.
How to read the sheet: enter inputs first, review calculations in Detailed view, then read pass/fail in the Summary on the right.

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Calculations

After inputs are set, the calculator builds section properties, applies LRFD load combinations, and checks shear and moment-axial interaction. Open Detailed view to see intermediate steps and TMS 402/602-22 clause references for each section below.
Design Conditions
Design Conditions pulls the load combination code from project defaults (IBC 2024 / TMS 402/602-22) and confirms the design standard edition in use.
Key Properties
Key Properties computes derived section values used in the checks below: net area, moment of inertia, section modulus, radius of gyration, steel area, and Slenderness Ratio. Summary rows Factored Axial Load Demand and Design Axial Capacity (Slenderness Limit) compare compression demand to slenderness-reduced capacity. The slenderness limit applies when Fully or Partially Grouted? is set to partially grouted. Fully grouted walls skip this check per the template assumptions.
Load Combination Analysis
Load Combination Analysis expands all LRFD strength combinations and reports factored demands for moment, axial, and shear at the governing location. The finite-element beam model in the background uses Position of Supports & Braces from Bottom to build the analysis case.
Out-of-Plane Shear (TMS 402/602-22, Section 9.3.3.1.2)
Out-of-plane shear is checked in Out of Plane Shear. Nominal Masonry Shear Strength includes a 0.25 × Pu term using the minimum factored axial load across combinations. Summary rows Factored Out-of-Plane Shear Demand and Design Shear Capacity report the governing result. Bar Spacing (c/c) does not feed the shear strength calculation.
Moment-Axial Interaction (TMS 402-22, Section 9)
Combined axial and bending capacity is evaluated through Out of Plane Bending + Axial Interaction Table. The calculator builds separate tables for partially grouted and fully grouted walls per MDG 2022 Chapter 12.4.4. Strength reduction factors vary with strain compatibility:
  • Strength Reduction Factor (Compression) (φc) applies to compression-controlled behavior.
  • Strength Reduction Factor (Flexure) (φf) applies when steel strain reaches 0.005 or greater.
  • For combined loading, φ varies linearly between φc and φf based on the neutral axis depth.
The Interaction Utilization Check table reports the utilization ratio for every load combination. Summary row Interaction Governing Utilization reports the highest value across combinations.
  • Key Properties
  • Load Combination Analysis
  • Out of Plane Shear (TMS 402/602-22, Section 9.3.3.1.2.)
  • Out of Plane Bending + Axial Interaction Table (TMS 402-22, Section 9. and MDG 2022 Ch.12.4.4)

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See the exact clause

Every check in this calculator links back to its governing clause in TMS 402/602-22. Open the Formula Reference panel on any result and select the clause reference to read it. See Viewing Clauses from Inside a Calculator.

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What it calculates

US structural engineers and engineering designers designing reinforced CMU gravity walls subject to wind and out-of-plane seismic loads to TMS 402/602-22. Checks out-of-plane shear (Section 9.3.3.1.2) and combined factored axial-bending interaction across ASCE 7 load combinations. Load reactions link to footing calculations so structural changes propagate downstream. Automate LRFD load combinations and moment-axial interaction checks for partially and fully grouted walls, with out-of-plane shear and bending per TMS 402/602-22.

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Calculation method

Masonry and reinforcement properties
Material inputs define the design basis: CMU block size (6” to 12”), masonry type (clay or concrete), specified compressive strength f’m, unit weight, and mortar type. Grout condition, partial or full, determines the effective cross-section for capacity calculations. Partial grouting uses net area and net moment of inertia at the reinforced cell spacing; full grouting uses the gross section. Reinforcement is a single centered layer with user-specified grade and spacing.
Load combination analysis
Factored axial gravity loads (1.2D, 1.2D + 1.6L, etc.) and out-of-plane lateral demands from wind or seismic are assembled into the governing ASCE 7 strength-level combinations. The calculator applies factored loads per unit width of wall and identifies the combination that produces the maximum demand for each check. Dynamic load linking allows axial demands to propagate from connected beam or column calculations.
Out-of-plane shear (TMS 402/602-22, Section 9.3.3.1.2)
Factored shear demand Vu from out-of-plane lateral loads is checked against the design shear strength: phi * Vn ≥ Vu, with phi = 0.80 Nominal shear strength Vn is computed from masonry shear resistance based on f’m, net area, and axial load. Horizontal reinforcement contributes to Vs when provided. In-plane shear is not checked, this calculator covers gravity walls only.
Out-of-plane bending and axial interaction (TMS 402-22, Section 9, MDG 2022 Ch.12.4.4)
A phi-Pn vs. phi-Mn interaction diagram is generated using a rectangular equivalent stress block (depth a = 0.80c) with neutral axis from strain compatibility. The factored demand point (Pu, Mu) must lie within the design capacity envelope: utilization = Mu / phi-Mn (at Pu) ≤ 1.0 The interaction diagram is plotted for the full range of axial loads, and demand points from all governing load combinations are shown against the envelope. Deflection checks are not included, Chapter 9 of TMS 402-22 does not contain deflection limits for LRFD masonry walls. The fully grouted wall model does not apply the slenderness limit per MDG 2022 examples.

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How to use it

1

Inputs

Work through the input sections in order. Geometry, reinforcement, and loads drive all downstream checks.
1

Masonry Properties

These inputs feed wall geometry, material strength, and support conditions in Key Properties, self-weight, slenderness, and the interaction diagram.
  • Concrete Masonry Unit Size: nominal block width (6”, 8”, 10”, or 12”). Section properties follow CMU-TEC-002-23.
  • Height of Wall: clear span between supports. Sloped walls are not supported.
  • Specified Compressive Strength: design compressive strength of the masonry assembly, typically 1500 to 2500 psi.
  • Density of Concrete Masonry Block and Grout Density: feed the Self-Weight output in Key Properties.
  • Fully or Partially Grouted?: switches between partially and fully grouted section properties, interaction tables, and whether the slenderness limit appears in Summary.
  • Position of Supports & Braces from Bottom: support types and heights from the bottom of the wall. Used by the beam analysis model in Load Combination Analysis. Masonry Properties inputs showing CMU size, wall height, compressive strength, grout type, and support positions
2

Reinforcement Properties

Reinforcement is assumed in a single centered row.
  • Reinforcement Grade, Bar Size, and Bar Spacing (c/c): feed steel area and moment capacity in Out of Plane Bending + Axial Interaction Table. Default spacing is six times the nominal block width. The calculator may flag spacings that do not align with the block module.
  • Consider Compression Reinforcement?: toggles whether tied compression steel is included in Design Axial Capacity (Slenderness Limit) per TMS 402/602-22 Section 5.4.1.4. Reinforcement Properties inputs showing bar grade, size, spacing, and compression reinforcement option
3

Loads

Enter unfactored (nominal) loads. The calculator applies LRFD load factors automatically.
  • Default Load Eccentricity: default axial eccentricity for bending, taken as one sixth of the block depth. Override per load in the Axial, Shear, & Moment Loads table.
  • Axial, Shear, & Moment Loads: line loads per foot of wall. Enter unfactored (nominal) loads; the calculator applies LRFD load factors in Load Combination Analysis. Each row can set its own eccentricity and load types (D, L, W, E, and others).
  • Lateral Distributed Loads: area loads converted to line loads using tributary width. Default wind entries populate from project defaults when available. Specify different tributary widths at the start and end of a load to enter triangular distributions.
Default Load Eccentricity applies to new rows in Axial, Shear, & Moment Loads. Each row has its own Eccentricity column that overrides the default for that load.
Loads inputs showing default eccentricity, axial/shear/moment load table, lateral distributed loads, and self-weight toggle
2

Results

The Summary panel on the right collects governing pass/fail outcomes. The Out of Plane Bending + Axial Interaction Diagram at the top of the sheet plots the moment-axial capacity envelope alongside each load combination.Summary panel showing factored moment, axial, and shear demands with design capacities, governing load combination, and interaction utilization

Out-of-plane moment

Factored Out-of-Plane Moment Demand vs Maximum Design Moment Capacity

Axial compression

Factored Axial Load Demand vs Design Axial Capacity (Slenderness Limit)

Out-of-plane shear

Factored Out-of-Plane Shear Demand vs Design Shear Capacity

Interaction

Interaction Governing Utilization and Governing Load Combination
Green badges indicate passing utilization; red badges flag a governing failure. Values above 1.0 on Interaction Governing Utilization indicate failure.
Switch to Detailed using the toggle at the top of the calculator to see every intermediate step and the relevant TMS 402-22 clause for each check.
Reading the interaction diagramThe Out of Plane Bending + Axial Interaction Diagram plots the moment-axial capacity envelope for your wall section. Each LRFD load combination appears as a point. Points inside the envelope correspond to passing combinations in Interaction Utilization Check.Out of plane bending and axial interaction diagram showing load combination points inside the partially grouted capacity envelopePartially grouted and fully grouted walls use separate interaction tables and diagrams. The diagram updates when you change Fully or Partially Grouted?.
A reinforced CMU gravity wall carries vertical loads while resisting out-of-plane forces from wind or seismic pressure. This calculator checks moment, axial, and shear capacity using factored load combinations per TMS 402/602-22 LRFD provisions. It supports partially and fully grouted single-wythe walls and plots a moment-axial interaction diagram for each design.
This calculator follows TMS 402/602-22 Chapter 9 (LRFD) and MDG 2022 Chapter 12.4.4 for interaction tables.

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Troubleshooting

Check the validation message next to the field. Common causes include bar spacings that are not practical multiples of the block module and compressive strength values outside the supported range.
Open Out of Plane Bending + Axial Interaction Table in Detailed view to see utilization per load combination. Check whether Eccentricity on individual load rows or Fully or Partially Grouted? is driving the result. Summary row Governing Load Combination identifies which combination controls.
Open that check in Detailed view to see which inputs feed the calculation. Summary rows link to the governing section. Use the input list above to find the corresponding fields in the sheet.

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Common questions

Strength Design (LRFD) per TMS 402/602-22 Chapter 9. Factored loads from ASCE 7 load combinations are checked against design strengths (phi times nominal capacity) for out-of-plane shear and combined axial-bending.
CMU block size, masonry type (clay or concrete), specified compressive strength (f’m), unit weight, grout condition (partial or full), bar size and spacing, wall height, boundary conditions, factored axial gravity loads, and out-of-plane wind or seismic distributed loads.
Out-of-plane shear (TMS 402/602-22, Section 9.3.3.1.2) and combined factored axial-bending interaction per TMS 402-22 Section 9 and MDG 2022 Ch.12.4.4. Results include an interaction diagram plotting factored demand points against the design capacity envelope.
Yes, partial and full grouting are both supported. Net section properties are computed from the actual grouted cross-section for each configuration. The fully grouted wall model does not apply the slenderness limit per MDG 2022 examples.
LRFD uses factored loads (1.2D + 1.6L, 1.2D + 1.0W + L, etc.) compared against design strengths (phi times Pn or Mn). ASD uses unfactored loads against allowable stresses. For masonry, LRFD checks are in TMS 402-22 Chapter 9 and ASD checks are in Chapter 8.
Yes, factored axial reactions at the wall base can be linked directly to footing calculations in the same project. When gravity loads change in a connected beam or column, the wall’s axial demand and the footing below both update automatically.