Prestressed masonry wall
An unreinforced, post-tensioned concrete masonry wall per foot of wall, spanning vertically and pinned at the top and bottom, under out-of-plane lateral load and axial load. The basis is Chapter 10 of the TMS code, read as TMS 402-13: the 402-22 chapter is not on disk, so it is marked (to confirm against the code text). Service stresses by Chapter 8, moment strength by the chapter's own equations, as the code requires both.
Inputs of the prestressed masonry wall #
- Wall: height, specified thickness, face shell, and the net section per foot (An, In, Sn, r) from CMHA CMU-TEC-002 for your bedding. 8 in. CMU with full mortar bedding is prefilled.
- Masonry: f'm, and f'mi, the strength when stressed. Em. The allowable flexural tension from Table 8.2.4.2 for your mortar: 33 psi prefilled, Type M or S portland cement lime, hollow units, normal to bed joints. The 402-22 table may read lower: read it when it arrives.
- Tendons: bonded or unbonded; laterally restrained or unrestrained; spacing, area, fpy, fpu.
- Forces per tendon: jacking, after transfer, and effective after all losses. These are entered because the code leaves the loss calculation to you (10.3.4). The Commentary's ranges for concrete masonry are 5 to 10 % at transfer and 30 to 35 % in total. The check says if you fall far outside them.
- Anchorage bearing area.
- Loads: axial dead and live at the top, an eccentricity, and the lateral load at the strength level (ASCE 7-22 W or E). It is used at 0.6 in service and 1.0 at strength.
Auto-design varies the tendon spacing, widest first. The tendon, its forces and the wall are kept.
Checks performed #
| Check | Basis |
|---|---|
| Tendon stress at jacking, after transfer, at anchorages | 10.3.1, 10.3.2, 10.3.3 |
| Axial and flexure after losses, and axial at transfer on f'mi with the 20 % increase | 8.2.4 Eq. 8-14; 10.4.1.2 |
| No net tension under prestress and dead load; net tension under lateral load at most Table 8.2.4.2 | 10.4.1.3; 8.2.4.2 |
| Buckling, P at most Pe/4, prestress counted only with unrestrained tendons | 10.4.2; Eqs. 8-15, 8-19 |
| Moment strength: φ = 0.80, a from 0.80 f'm, Eq. 10-3 for unbonded tendons, d limited for unrestrained | 10.4.3 |
| a/d at most 0.38; compression block within the face shell on hollow walls | 10.4.3.6; Commentary |
| Out-of-plane shear with the effective prestress in the axial force | 10.6.1, 9.2.6 |
| Anchorage bearing at jacking, 0.50 f'mi | 10.8.4 |
Limitations of the prestressed masonry wall #
- Walls pinned top and bottom, tendons concentric, one lateral load case with the load combinations stated. No cantilevers, no in-plane shear wall design, no mild reinforcement, no clay masonry losses.
- First-order moments. The chapter says the factored moment shall include the moment from relative lateral displacement (10.4.3.1): on a tall wall add it yourself. Deflection, camber and time effects (10.7) are not computed.
- Anchorage zone bursting (10.8.3), bond beams, corrosion protection (10.9) are stated, not designed.
- Code numbers are 402-13's. The 402-22 chapter and the Masonry Designers' Guide Examples 13-4 are to be read when bought.
Verification examples #
Verification status: 12 values compared in 1 example (1 published, 0 hand calculations from the cited equations): 12 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.
| Source | What |
|---|---|
| CMHA TEK 14-20A, Design Example, pp. 4-5 | Wall weight at midheight 234 lb/ft, M 270 lb-ft/ft, the tendon stress limits, Ppi 2,850 and Ppf 1,800 lb/ft, fb 37, fa 49, fai 74 psi, fb - fa = -12 psi |
That example is to 402-02, whose moment strength rule has since changed, so its strength figures are not compared. No published example of the moment strength or the unity check at the current rules was available: those are by hand from the equations. Treat this as a checked implementation of the chapter's equations, not a type verified end to end.