Unreinforced masonry wall
A one-foot strip of a concrete masonry wall or partition without reinforcement, spanning out of plane, loadbearing or not. The design keeps it uncracked: TMS 402-22 8.2 by allowable stress or 9.2 by strength, with the switch in the toolbar. Reinforced walls are the masonry wall out-of-plane calculation.
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 and the free sample of the Masonry Designers' Guide 2022, which also confirms 8.2.6.2 and a value of Table 8.2.4.2; the wording was read in TMS 402-13. No 402-22 equation number is confirmed here: they are written as 402-13 numbers. The bed joint shear rows of the 2022 tables are the 402-13 values (to confirm against the code text).
Inputs of the unreinforced wall #
- Span: vertically (supported top and bottom, or a cantilever from the base) or horizontally between supports. A horizontal span uses tension parallel to the bed joints, gets no credit from axial load, and needs running bond.
- Section: thickness; hollow units on face shell bedding, grouted at a spacing or fully; or solid units. The net section is at a bed joint: face shells only where hollow. Partial grouting interpolates the table by the share of grouted cells. Webs per unit and web thickness set the area for shear on the webs.
- Wall weight: an input, counted as resisting tension. Enter what the wall weighs with its grout.
- Check low dead load with a live lateral load: on by default. ASCE 7 has no combination for a live lateral load with dead load resisting; the MDG-2022 example takes 0.6D. This adds 0.6D + L in allowable stress and 0.9D + 1.6L in strength. Off uses the ASCE 7 combinations only, which credits the full dead load. Your judgment.
- Use the lowest bed joint shear stress: off by default. The Guide's example takes the table's lowest value for out-of-plane sliding; off uses the row for the bond and grouting.
- Loads: w the axial load per foot at the top, e from the wall centre line, p the out-of-plane pressure. Interior partitions: at least 5 psf (ASCE 7-22 4.3.4).
- Deflection limit: span divided by the number entered; IBC Table 1604.3 by finish.
Auto-design (editor toolbar) varies thickness, grouting and grouted cell spacing. Objective: the thinnest wall, then the least grout. The wall weight is kept, so a heavier wall gets no credit until you enter it.
Checks performed #
| Check | Allowable stress | Strength |
|---|---|---|
| Flexural tension | M/Sn − P/An against Table 8.2.4.2, 8.2.4.2 | ψ Mu/Sn − Pu/An against φ fr of Table 9.1.9.1, 9.2.4.1, φ = 0.60 |
| Compression | fa/Fa + fb/Fb ≤ 1, 8.2.4.1 (402-13 Eq. 8-14) | Pu/An + ψ Mu/Sn ≤ φ 0.80 f'm, 9.2.4.1 |
| Axial | P ≤ Pe/4 with the load's actual eccentricity (Eqs. 8-15, 8-19) | φ Pn, 9.2.4.2 (Eqs. 9-11, 9-12) |
| Moment magnifier | None in the code | ψ of 9.2.4.3, 1.0 at h/r up to 45 |
| Axial tension | Not permitted, 8.2.5 | Not permitted, 9.2.5 |
| Shear on the webs | 3/2 V/A ≤ 1.5 √f'm and 120 psi, 8.2.6 | 3.8 A √f'm and 300 A, 9.2.6 |
| Shear on the bed joint | 3/2 V/An ≤ 37 or 60 psi + 0.45 Nv/An, or 15 psi, Table 8.2.6.2 | 56 or 90 An + 0.45 Nu, or 23 An, Table 9.2.6.1 |
| Deflection | Uncracked, against your limit | Same |
Stresses are checked at 41 stations along the height in every combination, so the wall's weight changing with height is captured. A cantilever takes an effective height of twice its height.
The drawings are the wall along its span and the wall at a bed joint.
Limitations #
- Out of plane only. In-plane shear wall action is not covered here.
- Chapter 15 of 402-22, prescriptive partition walls, is new and only its contents are on hand: its height and length limits and anchorage rules are not checked. This calculation is the engineered route of the MDG example.
- Concrete masonry. Clay masonry has a different modulus; AAC has its own chapter.
- Masonry not laid in running bond spanning horizontally needs a continuous grout section, which is not modelled, so it is refused.
- Parapets add weight; their own bending is not checked.
- Stresses from restraint of movement are controlled by joints (8.2.2 commentary), not calculated.
- φ of 0.60 and the numbers of the shear tables are 402-13 values (to confirm against the code text).
Verification examples #
Verification status: 28 values compared in 6 examples (1 published, 5 hand calculations from the cited equations): 28 within tolerance, 0 recorded deviations. Thin: only 1 published example. Code basis: written from an older edition, with the differences noted. Not yet compared line by line with the target edition.
Published: Masonry Designers' Guide 2022, Example 11.3-1 (sample pp. 4-5; written to 402-22): section properties, stresses, allowable stresses and both shear limit states of a 12 ft hollow partition. The Guide checks midheight and gets 9.6 psi net tension. The wall's weight falls with height, so the largest net tension is a little higher up, 9.9 psi at 6.9 ft; ILX reports that, within the tolerance on the printed value. The margin against 12 psi is about the same.
Hand calculations: the same wall by strength design, bed joint strength, a grouted cantilever, a loadbearing wall's Fa, Fb, Pe and Pn, a horizontal span. There is no free published strength example of an unreinforced wall: MDG 12.3-1 to 12.3-3 are in the paid Guide.