Concrete Expansion Anchor Design

ACI 318-19 Ch. 17 (strength design) · ESR product data: KB-TZ2, Strong-Bolt® 2, Power-Stud®+ SD2

Post-Installed Expansion Anchor — Design Calculation

ACI 318-19 Chapter 17 strength design · product data per ICC-ES evaluation report (see Section 1)
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1 · Design parameters input echo & ESR reference

2 · Installation & geometry checks ESR tables; ACI 17.9

3 · Tension design strength ACI 17.6, 17.10

Failure modeCalculationφNn (lb)

4 · Shear design strength ACI 17.7, 17.10

Failure modeCalculationφVn (lb)

5 · Governing strengths, interaction & demand check ACI 17.8

6 · Notes & assumptions

  1. Strength design per ACI 318-19 Chapter 17 as modified by the governing ICC-ES evaluation report: Hilti KB-TZ2 — ESR-4266; Simpson Strong-Bolt® 2 — ESR-3037; DeWALT Power-Stud®+ SD2 — ESR-2502. Carbon-steel anchor versions only; stainless variants carry different values in the same reports. Confirm you are using the current edition of each report before final issue.
  2. Product data (Nsa, Vsa, Vsa,eq, Np, k, cac, cmin, smin, hmin, kcp, φ) transcribed from the ESR design tables; the user must verify against the current report edition before final issue. Where an ESR lists multiple cmin/smin boundary pairs, the smallest values are used as absolute floors and intermediate combinations require interpolation per the ESR figure.
  3. Tension modes: steel (n·φNsa, 17.6.1), group concrete breakout Ncbg per 17.6.2 = (ANc/ANco)·ψec,N·ψed,N·ψc,N·ψcp,N·Nb, with ψec,N = 1/(1 + e′N/1.5hef) (17.6.2.3), ψed,N (17.6.2.4), ψc,N = 1.0 with kcr/kuncr per ESR, ψcp,N (17.6.2.6); and pullout n·φNpn (17.6.3, with (f′c/2500)n normalization; "n/a" in the ESR means pullout need not be evaluated). Nb = k·λa√f′c·hef1.5 (17.6.2.2).
  4. Shear modes: steel (n·φVsa; Vsa,eq for seismic, 17.7.1), concrete breakout toward the front edge Vcbg per 17.7.2 = (AVc/AVco)·ψec,V·ψed,V·ψc,V·ψh,V·Vb, with ψec,V = 1/(1 + e′V/1.5ca1) (17.7.2.3) and ℓe ≤ min(hef, 8da); and pryout Vcpg = kcp·Ncbg per 17.7.3. Shear parallel to an edge (2× factor, 17.7.2.1(c)) and corner cases must be examined separately where applicable.
  5. Seismic option applies the 0.75 factor of ACI 17.10.5.4 to non-steel tension modes and substitutes Np,eq/Vsa,eq. The designer remains responsible for satisfying one of the 17.10.5.3 options (ductile yielding, anchor reinforcement, overstrength Ω0, etc.) and SDC-specific restrictions (e.g., 1/4″ Strong-Bolt 2 and SD2 anchors are limited to SDC A–B / uncracked use per their reports).
  6. λa = 0.8λ per ESR §4.1.12 for lightweight concrete. f′c is capped at 8,000 psi per ACI 17.3.1; ESR scope is 2,500–8,500 psi.
  7. 3-D actions & moments. Applied N, Vx, Vy, Mx, My, Mz are distributed to individual anchors by a rigid-plate elastic model: Ti = N/n + Mxyi/Σy² + Myxi/Σx² (anchors with Ti ≤ 0 are assumed unloaded — compression carried by concrete bearing, not the anchors; no prying or base-plate flexibility is considered). Steel and pullout are checked against the most-loaded anchor Tmax; concrete breakout is evaluated for the group of net-tension anchors with the projected area ANc formed from those anchors only and a biaxial ψec,N = [1/(1+e′Nx/1.5hef)][1/(1+e′Ny/1.5hef)] from the tension-resultant offset (ACI 17.6.2.3). Torsion Mz adds Vi = Mzri/J (J = Σ(x²+y²)) vectorially to direct shear; the worst |Vi| governs steel, the self-equilibrating torsion does not change the group's net shear toward an edge but is carried into ψec,V (17.7.2.3) via e′V = Mz/V. This elastic, tension-only method is standard and conservative; large moments may warrant an iterative neutral-axis (AISC DG-1) check.
  8. Breakout projection. ANc and AVc use the ACI 318-19 CCD square idealization (ANco = 9hef², AVco = 4.5ca1²), computed as the true union of each anchor's 1.5hef influence square clipped at all adjacent edges, so corners and multiple close edges are captured. The rounded cones in the figure depict the physical ~35° failure surface for clarity only; the governing design areas are the squares. The narrow-member limit on hef (ACI 17.6.2.1.2, h′ef = max(ca,max/1.5, smax/3)) is applied automatically when anchors lie within 1.5hef of three or more edges; shear parallel to an edge (17.7.2.1(c)) and true corner breakout interaction should be confirmed by hand for skewed groups.
  9. Base-plate design, standoff bending of the anchor, concrete splitting under sustained tension (17.6.5), and fatigue/shock loading are outside scope. Anchors must be installed per the ESR (drill bit per ANSI B212.15, hole cleaning, Tinst) with periodic special inspection per IBC 1705.3.
  10. This tool assists a qualified design professional and does not replace engineering judgment, the governing ESR, or code review.