Seismic wall anchorage
The anchorage of a concrete, masonry or other structural wall to a flexible or rigid diaphragm by ASCE/SEI 7-22 12.11: the out-of-plane wall force, the anchorage force with ka and its minimums, the optional reduction below the roof, the force per anchor with the 1.4 factor for steel elements, the continuous crosstie force and the subdiaphragm ratio and shear, each checked against the design strength you enter.
Inputs of the wall anchorage #
- Seismic hazard: SDS, the risk category (Ie of Table 1.5-2) and the seismic design category (SDC A: only the general anchorage of 1.4.4, 0.2 times the wall weight but not less than 5 psf; SDC C to F: the additional requirements of 12.11.2.2 for concrete and masonry walls).
- Wall: concrete or masonry, or other (wood, cold-formed steel); its weight Ww (psf); the wall height from the support below to the anchor and from the anchor to the support above (0 at the roof) and the parapet. The weight tributary to the anchor is Ww × (half the height below + half the height above + the parapet) per foot of wall.
- Diaphragm and anchor level: flexible (12.3.1.1 or 12.3.1.3) with its span Lf between the vertical elements that support it laterally in the direction considered, or rigid / semirigid (ka = 1.0); the diaphragm material (wood and metal deck have their own rules); the anchor at the roof or below it; and, below the roof of a structure with no flexible diaphragms, the option to apply (1 + 2z/h)/3 with the anchor height z and the roof height h (your choice: C12.11.2 notes that 1.0 may be more appropriate where the wall cantilevers above its highest support).
- Anchors: the spacing s, the element checked (a steel element of the anchorage system such as a strap, hold-down or bracket takes the 1.4 factor of 12.11.2.2.2; an anchor bolt or reinforcing bar does not) and the design strength of one anchor (LRFD φRn or ASD Rn/Ω, from the product report, ACI 318 Chapter 17 or the NDS).
- Crossties and subdiaphragm: the continuous crosstie spacing (0 = not calculated), whether the crosstie elements are steel (× 1.4), its design strength (0 = force reported only), the subdiaphragm depth perpendicular to the wall (0 = none) and its design unit shear (0 = shear reported only).
Auto-design (editor toolbar) varies the anchor spacing (8 ft down to 1 ft, framing multiples) and, where crossties are calculated, the subdiaphragm depth (8 to 40 ft). Objective: fewest anchors. The anchor strength, the crosstie spacing, the wall and the diaphragm are kept; see Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Out-of-plane wall force | Fp = 0.4 SDS Ie Ww, not less than 0.10 Ww (12.11.1) |
| Anchorage force | Fp = 0.4 SDS ka Ie Wp (Eq. 12.11-1), ka = 1.0 + Lf/100 ≤ 2.0 at a flexible diaphragm, 1.0 otherwise (Eq. 12.11-2), not less than 0.2 ka Ie Wp nor 5 psf × the tributary area (12.11.2.1); with the reduction (1 + 2z/h)/3, not less than the 12.11.1 force, 0.2 Wp or 5 psf × area; SDC A: 0.2 Wp ≥ 5 psf (1.4.4) |
| Anchor | Fp × s (× 1.4 for a steel element in SDC C to F at a concrete or masonry wall, 12.11.2.2.2; × 0.7 for ASD) against the design strength entered |
| Anchor spacing | Over 4 ft: the wall is designed to bend between the anchors (12.11.2.1), an advisory |
| Continuous crosstie | Fp × crosstie spacing (× 1.4 steel, × 0.7 ASD) against the strength entered, or reported (12.11.2.2.1) |
| Subdiaphragm | Length-to-width ratio = crosstie spacing / depth ≤ 2.5 (12.11.2.2.1, SDC C to F, concrete or masonry walls); unit shear Fp (spacing / 2) / depth against the strength entered, or reported |
| Additional requirements | 12.11.2.2.1 to 12.11.2.2.7 named for SDC C to F (wood: no toenails, nails in withdrawal or cross-grain bending; metal deck not the crosstie; embedded straps; eccentric anchorage; pilasters) |
The drawings show the wall section at the anchor (heights, parapet, tributary height, the diaphragm, the anchorage force and the anchor spacing and force) and, where crossties are calculated, the partial diaphragm plan along the wall (anchors, continuous crossties, the subdiaphragm with its ratio and shear). The wall thickness is schematic.
Limitations #
- The anchor, crosstie and subdiaphragm strengths are entered: the device, its embedment, the splices and the sheathing and nailing are designed elsewhere (the concrete anchor and wood diaphragm calculations, product data).
- The wall spanning between anchors over 4 ft apart, eccentric or skewed anchorage (12.11.2.2.6) and pilasters (12.11.2.2.7) are named, not calculated.
- The forces are strength level (E) with ASD at 0.7 E; the simplified procedure of 12.14.7.5 (no Ie) is not offered.
- Nonstructural walls are designed by Chapter 13 (use the nonstructural components calculation), except the anchorage of concrete or masonry walls to flexible diaphragms, which Table 13.5-1 note b sends back to 12.11.2.
Verification examples #
Verification status: 28 values compared in 12 examples (8 published, 4 hand calculations from the cited equations): 27 within tolerance, 1 recorded deviations. Code basis: the provisions it uses were read in the target edition.
FEMA P-1051 (2015 NEHRP Provisions Design Examples) is written to ASCE 7-10, whose 12.11.1 and Eqs. 12.11-1 / 12.11-2 are unchanged in 7-22. FEMA P-1051 does not apply the 1.4 steel factor to its tie device; the values below are compared before that factor.
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| 14.2-SIDE | Masonry warehouse, 8 in. CMU side walls (65 psf), wood roof, Lf = 200 ft, SDS 1.43 (pp. 14-47 to 14-51) | ka 3.0 → 2.0, 1.14 Wp, 1.19 klf, 4.76 kips per anchor at 4 ft, crosstie 23.8 kips at 20 ft, subdiaphragm 0.595 klf | same |
| 14.2-END | End walls, 12 in. CMU (103 psf), Lf = 100 ft (pp. 14-53 to 14-55) | 1.89 klf, 7.56 kips, crosstie 37.8 kips, minimum subdiaphragm depth 8 ft, 2.36 klf (8 ft) and 1.18 klf (16 ft) | same |
| 11.1-PLANK-D | Five-story masonry, topped plank (rigid), SDC D (p. 11-31) | 208 plf, 0.83 kips at 4 ft | same |
| 11.1-PLANK-C | Untopped plank, SDC C, SDS 0.37 (p. 11-15) | 61.6 plf | 61.6 plf by Eq. 12.11-1; the 12.11.2.1 minimum 0.2 ka Ie Wp governs at 83.2 plf (a documented deviation) |
| 13.1 / 13.2 | Out-of-plane wall forces (pp. 13-10, 13-73, 13-85) | 37 psf; 4.3 psf with the 4.5 psf minimum governing; 7.1 psf | same |
Hand calculations: the 0.2 ka Ie Wp minimum (83.2 plf), the reduction below the roof with the 12.11.1 floor (factor 0.467, 0.24 klf), a steel strap in ASD (0.7 × 1.4 × 0.48 klf × 6 ft = 2.82 kips) and SDC A (30 plf by the 5 psf minimum), all exact.