Masonry wall at openings
The strip of a reinforced concrete masonry wall beside one or two openings, spanning vertically out of plane and carrying the load of the openings, by strength design to TMS 402-22: flexure with axial load, the moment magnifier, axial strength, shear and service deflection. The wall away from the openings is the masonry wall out-of-plane calculation; the lintel over the opening is the masonry lintel.
The calculation is by strength design only, so the LRFD / ASD switch is not shown.
Edition. The design basis is TMS 402-22 / TMS 602-22. The text of the 2022 code is not on hand. Section numbers come from TMS's cross-reference, the changes from the TMS handouts of 2022, and the wording was read in TMS 402-13. Only Eq. 9-28 is a confirmed 402-22 equation number here.
Inputs of the masonry wall at openings #
- Wall and openings: the height between supports, simply supported top and bottom; a parapet; the strip width; the opening on each side, half of which loads the strip; sill and head.
- Wind on the openings: on by default. A door or window passes the wind to the masonry beside it, so wind loads the whole tributary width over the whole height. Seismic comes from the masonry's own mass, so beside the openings it loads the strip only (FEMA P-1051 13.1.6.2). Whether a given door or window passes the wind on is your judgment.
- Parapet reduces the moment: off by default. A parapet's load is added to the top reaction, but its cantilever moment is not taken off the moment in the span unless you say so.
- Section: thickness, face shell, grouting, f'm, bars per layer, one layer at the centre or one at each face. With a layer at each face, the layer near the compression face is not counted unless you ask for it, then only while it is in tension (bars not tied, 9.3.2(e)). The published examples leave it out.
- Loads: by load type, w the axial load per foot of wall over the whole tributary width at the top, e its distance from the wall centre line, p the out-of-plane pressure. The wall's weight is per wall area; openings weigh nothing.
Auto-design (editor toolbar) varies bar size, bars per layer and thickness. Objective: the least reinforcement, then the thinnest wall. Strip and openings are kept.
Checks performed #
| Check | Basis |
|---|---|
| Moments and reactions | Statics on the load pieces, simply supported. The moment from the eccentric load at the top is added in the direction of the lateral load |
| Flexure with axial load | 9.3.2 strain compatibility about the wall centre line; φ of Table 9.1.4 at Pn = Pu/φ; checked at the largest moment and at the door head of every combination |
| Moment magnifier | 9.3.4.4.3: ψ = 1/(1 − Pu/Pe), Ieff = 0.75 In below Mcr, otherwise Icr by Eq. 9-28 when the neutral axis is in the face shell or the wall is grouted |
| Axial strength | 9.3.3.1.1 with h/r; bars not counted, not tied |
| Axial limit | 9.1.4.4.2 |
| Shear | 9.3.4.3, 9.3.3.1.2 with Mu/(Vu dv) = 1.0, axial load not counted, on the larger reaction |
| Service deflection | 9.3.4.5: 0.007 h, ASD combinations; the curvature with the uncracked section to Mcr and the cracked beyond it, integrated along the height (for a uniform load this is the code's two-part equation), times ψ |
| Compressed width | 5.1.2: per bar at most the spacing, 6 t and 72 in. |
| Bars | 6.1.3, 6.1.4 |
The drawings are the wall elevation to the middle of each opening, and the plan section of the strip.
Limitations #
- Strength design only.
- The strip's section is used over the whole height. Above and below an opening the wall is wider, which this ignores: conservative, by a margin the FEMA example shows at the largest moment (95.6 kip-ft on the bay "does not control").
- Openings at the same height on each side, one sill and one head. Different openings: use the worse, or enter the wider one on both sides and judge the result.
- Simply supported top and bottom. No fixed base.
- Lintel and its bearing, bond beams, splices and in-plane forces are separate calculations. Prescriptive seismic bars at openings are not checked (to confirm against the code text: TMS 402-22 7.4.3.1).
Verification examples #
Verification status: 22 values compared in 5 examples (3 published, 2 hand calculations from the cited equations): 15 within tolerance, 7 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, both of the same building: TMS webinar "SD Walls Axial and Out-of-Plane Loads", Feb. 2021, Guide Example 6.3.3.12, pp. 23-26 (402-16): reactions, first-order moment, Pu, ψ, Mu, Mn with one layer and with two, φMn, the 1.2D + Ev + Eh combination. FEMA P-1051 13.1.6.3, pp. 13-28 to 13-35 (402-13): axial load, Mn and φMn at the door head.
Differences recorded on the Verification page: Icr and so Pe (402-22 Eq. 9-28 against the older form); the deflection, where both published checks use the cracked section throughout and the handout puts the upper load over the whole height, as "quick checks"; a rounded load in FEMA (1,178 printed as 1,200 plf); FEMA's Mn at the door head adds Pu where the handout and ILX use Pu/φ, 1.5 % apart. FEMA's Mu at the door head comes from a P-delta frame run with the wider wall above, and is not compared with the magnifier as a verification value. FEMA's C = 184.1 kips is not its own T + P = 186.1 kips; its Mn is within tolerance of either.
Hand calculations: no opening equals w h²/8; an unloaded opening. All published examples are older than 402-22.