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Steel-Plate Composite (SC) Wall Against Hard-Missile Impact — Three-Step Method

Local-damage design of a concrete-filled double steel-plate (SC) wall, transcribed cell-for-cell from Purdue's official design spreadsheets (doi:10.4231/TRXQ-7482, CC0): the original three-step method of Bruhl, Varma & Johnson (2015) and the modified method of Kim & Varma (2020). (1) Concrete perforation velocity, (2) residual velocity with the dislodged concrete plug, (3) rear faceplate thickness, × 1.25 (AISC N690 N9.1.6c). The rear plate prevents scabbing, so perforation governs.

Missile

Mass M kg

Diameter d m

Impact velocity V₀ m/s

Nose

Method

α_p

SC wall

Wall thickness t_sc m

Faceplate t_p (each) mm

f′c MPa

Plate f_y MPa

High-strength / UHPC (f′c above calibration)

Results

β = T_c/(α_pd) · plug angle θ · σ_s—

Step 2: concrete perforation velocity V_p · method—

Concrete plug mass · residual velocity V_r—

Step 3: calculated t_p — original · modified—

Required faceplate (×1.25, ≥ 6.35 mm) vs provided—

SourceSeo & Varma (2021), Purdue University Research Repository, doi:10.4231/TRXQ-7482 (CC0) — the formulas of both spreadsheets are implemented exactly; verified against the spreadsheets' own cached results (50 of 50 points: required t_p = 1.000 in at the official perforation velocity).

MethodV_p from Degen + modified NDRC with a factor on penetration (1.45 original; K_sc = 2.073 − 0.661K + 0.688α_pd/T_c + 0.835x_c/T_c modified); plug angle θ = 45°/(T_c/d)^1/3; V_r = √[W/(W + W_cp)·(V₀² − V_p²)]; t_p = 0.72·m·V_r²/(2πa²σ_s), σ_s = 5.1F_y + 101 ksi (t_p ≥ 0.25 in) or 3.9F_y + 64 ksi.

CautionIn the modified method the plate demand is not monotonic in velocity: once penetration × K_sc reaches the faceplate the method returns no plate demand. The tool then uses the original method. An earlier version of this tool (v473), reconstructed from a partly unreadable open paper, required 2.5–3 times thinner plates than the official method — it has been replaced.

UHPCThe formulas are calibrated for normal-strength concrete. Above the limit the calculation uses the limit strength by default (no credit for high-strength or UHPC). Evidence is regime-dependent: shallow-impact tests (same projectile, 41–162 MPa) show penetration falling as f′c^−0.43, faster than the f′c^−0.25 of NDRC, so NDRC is conservative there; one deep-penetration UHPC data set (160 MPa) shows the opposite and remains unresolved.

DBA / BDBAThe original method carries a statistical factor β = 1.45 giving 95% confidence over a 58-test database — for design-basis events. The modified method is a 50% best estimate for beyond-design-basis evaluation (Kim 2018, Purdue dissertation, §7.6). Large-scale check (KHNP tests, Kim 2018 Table 7-5: 150 mm, 40–80 kg missiles, 240–480 mm walls): the original method's design velocities are reproduced within 1%.

TestsPurdue/KAERI tests (Kim et al. 2021, 10 shots): 0 unconservative predictions with both methods; stopped shots predicted as perforated — original 5 of 8, modified 2 of 8 (their documented conservatism). SMiRT-22 hurricane pipe missile (287 lb, 6.6 in, 308 ft/s; 12 in + 2 × 0.25 in): V_p 343 ft/s — stopped, as published.

Preliminary calculation tool. Final design requires the full text of the referenced standard (see the sources on this page) and review by a licensed PE.