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Global Response of RC Slabs and Walls to Hard-Missile Impact — Energy Balance

Overall (flexural) response of a reinforced-concrete slab or wall struck by a hard missile, by the NRC-accepted energy-balance method of BC-TOP-9A: plastic-impact energy, yield-line resistance, required ductility ratio against the ACI 349-13 Appendix F limit, and a punching-versus-flexure check. Use it after the local-damage check (penetration, scabbing, perforation).

Missile

Mass M kg

Impact velocity m/s

Contact diameter m

Missile type

Slab / wall

Thickness T m

Short span a m

Long span b m

Edge support

f′c MPa

f_y MPa

ρ (tension face)

ρ′ (compression face)

Cover to steel centroid m

Results

Effective mass M_e · impact energy E_s—

Resistance R_m · elastic deflection x_e—

Required ductility μ_r vs allowed μ_d—

Max. deflection · punching V_n vs R_m—

MethodE_s = M²V²/[2(M + M_e)], M_e = (D + T)²ρ_cT; R_m = 2π(m_u⁺ + m_u⁻); x_e = α R_m a²/D_p with I_a = (I_g + I_c)/2; μ_r = E_s/(R_mx_e) + ½ (BC-TOP-9A Rev. 2, 1974). μ_d = 0.05/(ρ − ρ′) ≤ 10 (ACI 349-13 F.3.3).

Verified(1) BC-TOP-9A worked example E.3 reproduced exactly (μ_r = 3.30), also by an independent RK4 solution. (2) Zineddin & Krauthammer (2007) drop-weight slab tests: across the full input uncertainty the predicted deflection is 1.9–29 times the measured — always on the safe side, often strongly so.

LimitsNot for soft missiles (IRIS B1: ~25 × over-prediction). Early-impact contact forces can exceed R_m several times, so the punching comparison covers only the global flexural phase; local damage must be checked separately.

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.