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FEMA P-751 interior spread footing (11 × 11 ft × 26 in under 387 / 98 kips): one-way and punching shear, flexure, 9 No. 8 bars

Tool	Concrete Slab and Footing Design
Source	Building Seismic Safety Council (2012). NEHRP Recommended Seismic Provisions: Design Examples. FEMA P-751, Federal Emergency Management Agency, Washington, DC. Chapter 5, Section 5.1.2 (pp. 5-8 to 5-10) and Table 5.1-2.
Level	Undergraduate

Problem

An interior column of a seven-story steel building (W14 on a base plate, loaded area 16 in square) carries D = 387 kips and L = 98 kips to a square spread footing on medium dense sand whose net allowable bearing pressure is 4,000 psf for footings under 20 ft; f′_c = 4,000 psi, f_y = 60,000 psi. Size the footing on the service load, check a 26-in thickness for one-way shear at d and two-way shear at d/2 with the factored load 1.2D + 1.6L, and find the flexural steel at the column face against the 0.0018 minimum.

Inputs to Enter

Element: spread footing; f′_c 4,000 psi, f_y 60 ksi, φ 0.90 / 0.75 / 0.65, ρ_min 0.0018, load factors 1.2 / 1.6
Allowable bearing 4,545 psf gross with γ_c 150 pcf, γ_s 120 pcf and D_f 4 ft (the deductions 325 + 220 psf give FEMA's 4,000 psf net); c_1 = c_2 = 16 in, P_D 387 kips, P_L 100 → 98 kips, B = L = 11 ft, h 26 in, cover 3 in, No. 8 bars, 9 bars each way

Open the Concrete Slab and Footing Design tool (loaded with this example)

Answers

P = 485 kips, required area 121.25 ft², 11 × 11 ft gives 4,008 psf ≈ 4,000 (book: P_allow 484 ≈ 485 kips); P_u = 621 kips, q_u = 5.13 ksf
d = 26 − 3 − 1.5 = 21.5 in; one-way shear V_u = 5.13 (11)(58 − 21.5)/12 = 172 kips, φV_n = 0.75 (2)√4000 (132)(21.5) = 269 kips (book 172 / 269)
Two-way shear b_o = 4 (37.5) = 150 in, V_u = 621 − 5.13 (37.5/12)² = 571 kips, φV_n = 0.75 (4)√4000 (150)(21.5) = 612 kips (book 571 / 612)
M_u = 5.13 (11)(4.83)²/2 = 659.6 ft-kips; 9 No. 8: T = 427 kips, a = 0.951 in, φM_n = 0.9 (427)(21.5 − 0.476)/12 = 672.7 ft-kips (book 659 / 673); ρ = 0.00207 > 0.0018, spacing 15.6 in
Table 5.1-2 perimeter (8 × 8 ft × 18 in, 9 No. 6) and corner (6 × 6 ft × 14 in, 6 No. 5) footings reproduced to the printed digits except the corner φM_n (book 75.2 ft-kips; the bars and d = 9.5 in give 77.6)

Notes

The tool's default is an illustrative 14 × 14 in column with P_D = 150 and P_L = 100 kips on 4 ksf (4-ft embedment, 24 in thick, No. 7 bars): B = L = 8.75 ft, q_u = 4.44 ksf, φV_n 196 / 503 kips against 83.6 / 305, φM_n 416 against 279 ft-kips, l_d 41.5 in in 42.5 available. Enter the FEMA inputs above to reproduce the book. FEMA keeps d = h − 4.5 in for all three footings; the test script (615 checks) carries the book values, the development lengths of FEMA P-751 Chapters 7 and 8 and an independent numpy re-implementation in References/Slab-Footing/checks/.