Masonry pilaster with wall
A reinforced concrete masonry (CMU) pilaster built into a wall, by strength design to TMS 402-22 Chapter 9 with 5.5 and the flange rules of 5.1.1. The calculation follows the load from the wall to the pilaster: the wall pressure per foot of height, the moment and shear along the height, the wall as a flange where the code allows it, axial load and flexure in each direction of bending, second-order moments, shear, the transfer between flange and pilaster, deflection and the detailing of the bars.
The masonry column calculation also has a pilaster: there the moments are entered and the flanges neglected. Use that one for a load already worked out, and this one for the wall load path and the flange.
The calculation is by strength design only, so the LRFD / ASD switch is not shown. Allowable stress design is not offered.
Edition. The design basis is TMS 402-22 / TMS 602-22. The text of the 2022 code is not on hand. Section numbers are 402-22 numbers from TMS's own cross-reference, the 2022 changes come from the TMS webinar handouts, and the wording was read in TMS 402-13 (5.1.1.2 p. C-47, 5.4 p. C-63). What remains unverified is listed under the limitations.
Inputs of the masonry pilaster #
- Pilaster and wall: nominal width along the wall and overall depth across it (wall included); the wall thickness. The pilaster is flush with one face of the wall unless you enter a projection beyond the other face. Height, end conditions (pinned; fixed base, pinned top; cantilever) and effective height, which is your input: the height for pinned ends, twice it for a cantilever, lower only where data show reliable restraint.
- Wall as a flange: 5.5 allows flanges only in running bond (5.1.1.2.1) with the intersection connected by interlocking units, steel connectors or reinforced bond beams (5.1.1.2.5). You state both; otherwise the flanges are neglected. The wall beside the pilaster is the actual flange: to a movement joint, an opening, or half way to the next pilaster. The calculation limits it to 6 times the nominal wall thickness on each side (5.1.1.2.3). A hollow or partially grouted wall counts as its two face shells only.
- Loads: the tributary width X and the portion K give wp = K w X (NCMA TEK 14-03A), acting both ways. K is your input: 1.0 when the wall spans horizontally only, otherwise from TEK 14-03A Figure 1 or your analysis. Pressures W and E are at strength level. Axial loads act at the top, with an eccentricity from the pilaster centre, positive toward the projecting face. The wall's weight on the flanges is yours to add to the axial rows.
- Reinforcement: bars in a layer on the wall side and a layer on the projecting side, at one face to bar centre distance. Compression bars count only when tied (9.3.2(e)). The grout space inputs are for the limits of 6.1.3.
- Deflection: the service factors on W and E and the limit as height / n. 143 is 0.007 h, the wall limit, applied here by your choice.
Auto-design (editor toolbar) varies nominal section (width and depth), vertical bars (size and bars per layer) and ties (size and spacing). Objectives: lowest cost index (units, grout, reinforcement); least reinforcement. Every other input is kept.
Checks performed #
| Check | Basis |
|---|---|
| Axial strength | 9.3.3.1.1 (402-13 Eqs. 9-19 / 9-20) on the net area of the pilaster and effective flange, r from that section, out of plane; bars counted when tied; φ = 0.65 |
| Axial and flexure, each direction | 9.3.2 strain compatibility: εmu = 0.0025, 0.80 f'm over a = 0.80c, Es = 29,000 ksi; the hollow cells of the flange are gaps; moments about the pilaster centre, at the levels of the largest moment and the base, for each combination with the wall pressure each way. φ by Table 9.1.4 at Pn = Pu/φ |
| Axial limit, tension-controlled and transition regions | 9.1.4.4.2: φPn ≤ 0.65 Pbal |
| Second-order moments | 9.3.4.4.3 (402-13 Eqs. 9-31 to 9-33) on the effective height, the wall procedure applied to the pilaster, as the TMS 2021 handout advises; Ieff = 0.75 In below Mcr and Icr above it, Icr with the flange in the compression zone; or not applied by your choice |
| Shear out of plane | 9.3.3.1.2 on the pilaster rectangle alone; the largest moment of the combination with its largest shear (conservative); ties when counted; φ = 0.80 |
| Shear between the flange and the pilaster | 5.1.1.2.4: the force in the overhang (the flange block at Mn × Mu/Mn, on the wider side) over two face shells or the wall thickness, along the distance from the largest moment to zero moment; Vn = 2.25 Anv √f'm, the shear equation at Mu/(Vu dv) = 1.0 with no axial load or reinforcement. The form of this check is this calculation's choice |
| Deflection under the wall load | 9.3.4.5 (402-13 Eqs. 9-29 / 9-30) for pinned ends; the elastic beam formula with In or, when cracked, Icr over the whole height for the other end conditions. Lateral load only |
| Bar size, spacing, cover | 6.1.3, 6.1.4.2 (1.5 db and 1.5 in.), 6.1.5.1 |
| Lateral ties (where bars are counted in compression) | 5.4.1.4(a), (b), and the mortar joint rule |
The key results list the wall load per foot, the section, the flanges counted, φPn and the largest factored reactions at the top and the base, to carry to the roof and footing design. The drawings (on screen, in the report and on the PDF / DXF drawing sheet) are the plan section with the effective flange, the interaction diagram for both directions of bending (not to scale) and the elevation with the wall load.
Limitations #
Not covered:
- Allowable stress design (Chapter 8).
- The wall panel between pilasters and its horizontal reinforcement (masonry wall calculation); the K factor itself.
- Bending along the wall, in-plane forces, the seismic rules of Chapter 7.
- Bars in the flanges and a flange in flexural tension: 5.1.1.2.3(c) permits 0.75 times the height, but no bars in it are counted and the masonry takes no tension.
- Connections at the top and base, anchor bolts, splices and development, bearing (masonry bearing calculation), clay masonry.
Simplifications:
- Uncracked properties (In, Mcr) are those of the pilaster rectangle, flanges neglected: a lower cracking moment, conservative.
- Axial loads act at the top. The self-weight is the pilaster rectangle's and acts at its centre.
- The moment gradient is not used to reduce the magnifier. Deflection takes the lateral load only, not the eccentric axial load or P-delta.
Still to verify in TMS 402-22 / 602-22 (marked (to confirm against the code text) in the check references):
- the wording of 5.5 and 5.1.1.2: the 402-22 flange numbers are carried from 402-13 through the cross-reference;
- what 5.1.1.2.4 requires for the interface, and whether the shear equation at Mu/(Vu dv) = 1.0 is the intended form;
- the equation numbers other than Eq. 9-28, which is used here with the axial load not credited.
Verification examples #
Verification status: 36 values compared in 9 examples (4 published, 5 hand calculations from the cited equations): 35 within tolerance, 1 recorded deviations. Code basis: written from an older edition, with the differences noted. Not yet compared line by line with the target edition.
All published examples are older than the 2022 code. None has a flanged masonry pilaster: no free published flanged example was found, so the flanged results rest on hand calculations, solved in the test by a separate equilibrium loop.
| Example | Values compared | Published | ILX |
|---|---|---|---|
| TMS webinar Oct. 2017, pilaster, pp. 14-15 (402-16) | wp, Pu at the top, top moment, level of the largest moment, Mu, Pu at that level | 0.416 kip/ft; 0.54 kips; 3.1 kip-in; 143.7 in.; 361 kip-in; 2.7 kips | Agree within 1 %. The example's required As = 0.57 in.² is not compared: this calculation checks given bars |
| NCMA TEK 14-03A pp. 2-3 | wp, moment, shear, fixed base and pinned top | 328 lb/ft; 5,900 lb-ft; 2,460 lb | Agree within 1 %. K = 0.91 read from the TEK's chart and entered |
| FEMA P-1051 13.1.6, pp. 13-22 to 13-24 (402-13) | wu, Mu, In, Mcr, c, Icr, service moment, deflection parts, total | 0.407 kip/ft; 39,886 lb-ft; 4,967; 103,633 lb-in; 2.64; 1,337.1; 335,042 lb-in; 0.136 + 1.131 = 1.267 in. | Agree within 1 % |
| FEMA P-1051 13.1.6 | φMn | 520,059 lb-in | About 2 % higher: a recorded deviation. The example uses the two tension bars, and ILX solves both layers, the second also in tension |
| TMS night school 2021, column, pp. 10-11 (402-16) | r, Pn, Mn at Pn = 102.6 kips | 4.51 in.; 337.7 kips; 82.62 kip-ft | Agree within 1 %. Nominal values: the published φ = 0.90 is 402-16; 402-22 Table 9.1.4 gives 0.65 there |
| Hand calculations | Flange in compression with the block in the face shell and past it; projecting face in compression; flange transfer; net area, r, Pn | Agree |
A note on FEMA P-1051 13.1.6. The example takes 20 ft of wall for a pilaster with pilasters at 40 ft on center. By TEK 14-03A wp = K w X with X the center-to-center span, which would be 40 ft. The tributary width is your input here, and the 20 ft is entered as printed to compare the example. Enter the width your framing carries.
Not verified: any flanged pilaster against a published example, and any value written to the 2022 code. Masonry Designers' Guide 2022 examples 12.4-7 and 11.4-6 are paid.