Masonry anchor bolts
Cast-in headed and bent-bar anchor bolts in grouted concrete masonry, one bolt or a rectangular group, in the side of a wall or the top of a wall or bond beam, by strength design to TMS 402-22. It checks tension, shear and the two combined, and the placement limits. The drawings show the bolt layout with the projected areas, and a section through a bolt.
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. The equations were read in TMS 402-13 (6.2, 9.1.6), masonry crushing with 1,750 and the 5/3 interaction in the TMS 402-16 handout of March 2018, and steel from the specified tensile strength in the TMS 402-22 handout of October 2022. φ for steel from fu is not printed in anything on hand: 0.75 in tension is read back from Example 9.3-6a of the Masonry Designers' Guide 2022, and 0.65 in shear is an inference. Both are marked (to confirm against the code text) in the report.
Inputs of the masonry anchor bolts #
- Bolts: side or top of a wall; headed or bent bar; diameter 1/2 to 1 in.; steel by ASTM grade or entered fu and fy; embedment from the masonry surface to the bearing surface of the head or of the bent end; bolts along the wall and rows, up to 6 × 6.
- Masonry: wall thickness, f'm, grout, the length and height of masonry to the free edges, openings or movement joints that stop the cones, and the distance of the first bolt from the left end and the near edge. In the top of a wall the near edge is the near face and the wall thickness closes the other side.
- Open cells: the part of each bolt's cone over open cells, cores or head joints is deducted (6.3.2, 6.3.3). The module has no cell layout: measure this area and enter it. Zero means the masonry is grouted over the whole cone.
- Loads: tension and shear on the group by load type, shared equally by the bolts. The direction of the shear sets the edge distance for shear breakout.
- Offset shear: a ledger's load acts away from the wall. Enter the offset and a moment arm and the tension from that moment is added. The arm is your judgment; TEK 12-03C takes 5/6 of the distance from the bolt to the edge of the ledger. An arm of 0 adds nothing.
- Seismic anchorage: on by default. Combinations with E take the factor (2.0) on each force whose strength is not governed by steel, as ASCE 7 requires for anchorage of seismic-force-resisting masonry to diaphragms and chords (to confirm against the code text: ASCE 7-22 14.4.5). IBC 1613 excludes ASCE 7 Chapter 14, and anchorage of nonstructural components takes the overstrength factor of 13.4.2.2 instead, so the choice is yours.
Auto-design (editor toolbar) varies bolt diameter, embedment and bolts along the wall. Objective: the least bolt steel. Spacing, edge distances, f'm and loads are kept; if more bolts do not fit the masonry, that candidate is dropped.
Checks performed #
| Check | Basis |
|---|---|
| Tension per bolt | 9.1.6.3.1: the least of masonry breakout 4 Apt √f'm (φ = 0.50), steel Ab fu (Eq. 9-2, φ = 0.75 (to confirm against the code text)), and for a bent bar pullout 1.5 f'm eb db + 300 π (lb + eb + db) db (φ = 0.65) |
| Apt | 6.3.2: a circle of radius lb, cut by the masonry edges; overlapping circles share their area so no masonry counts twice; a group of overlapping bolts shares the group's area equally (Commentary), the least group governs |
| Shear per bolt | 9.1.6.3.2: the least of masonry breakout 4 Apv √f'm, crushing 1,750 (f'm Ab)^(1/4), pryout 8 Apt √f'm (all φ = 0.50), steel 0.6 Ab fu (Eq. 9-7, φ = 0.65 (to confirm against the code text)) |
| Apv | 6.3.3, 6.3.7: half a circle of radius lbe on the free edge the shear acts toward, each row of bolts with its own lbe, cut by the masonry at that edge; the row with the least area governs |
| Combined | 9.1.6.3.3: (baf/φBan)^(5/3) + (bvf/φBvn)^(5/3) ≤ 1.0 (to confirm against the code text: 402-16 exponent, kept in 402-22) |
| Placement | 6.3.1 clear distance at least the bolt diameter and 1 in.; 6.3.6 effective embedment at least 4 db and 2 in. |
| Grout around the bolt | Top of a wall: face shell + grout + half the head to each face. Side of a wall: embedment at most wall − face shell − grout − head (TMS handout, March 2018, from 6.3.1) |
The drawings (on screen, in the report and on the PDF / DXF drawing sheet) are the layout on the masonry surface with the dashed projected areas, and a section at a bolt. Edge distances too long to fit in the view are in the sheet notes.
Limitations #
- Strength design only; allowable stress design is planned with the other masonry ASD versions.
- Post-installed anchors and anchors found by test (9.1.6.2) are not covered.
- The forces are shared equally. Moment on the group, other than the offset shear, is not distributed: work out the tension on the worst bolt and enter it as an equivalent group force.
- Apv for several rows takes each row alone; the code gives no rule for rows behind each other.
- The ledger or plate and the wall under the bolt forces are not checked.
Verification examples #
Verification status: 36 values compared in 12 examples (8 published, 4 hand calculations from the cited equations): 32 within tolerance, 4 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: Masonry Designers' Guide 2022 free sample, Examples 9.3-6 and 9.3-6a (written to 402-22): Apt, breakout and the steel design strength. TMS webinar Anchor Bolt Design, March 2018 (402-16), pp. 22, 24-25, 29, 41-42, 51-54: bent bar, headed, near an edge, shear, combined with E. CMHA TEK 12-03C pp. 4-5 (2013 code), strength part.
Two differences are deliberate and recorded on the Verification page. The 2018 handout's steel values use a 36 ksi yield; 402-22 uses the specified tensile strength. TEK 12-03C's crushing uses 1,050, the 402-13 coefficient; 402-16 raised it to 1,750. TEK's page prints 90.00 in.² in its equations where its text gives 90.99 in.²; its results follow 90.99.
Hand calculations from the equations: shear breakout with overlapping half circles, the limit on fu, the seismic factor, a corner bolt. Anything that depends on a (to confirm against the code text) above (φ of the steel, the exponent, the crushing coefficient) waits for the 2022 code text.