๐ Lesson 17
D5
ACI 318-19 Footing Design Workflow: Flexure, Shear, Development
A spread footing is a concrete base that spreads the weight of a structure safely into the ground, like a wide shoe for a buildingโs column.
๐ฏ Learning Objectives
- โ Calculate required footing dimensions (length, width, thickness) based on factored column loads and allowable soil bearing pressure
- โ Design flexural reinforcement for both directions using ACI 318-19 strength design provisions and strain compatibility assumptions
- โ Analyze one-way and two-way shear capacity at critical sections and verify compliance with ฯVn โฅ Vu
- โ Determine minimum and required development length for bottom reinforcement per ACI 318-19 Chapter 25
- โ Explain how footing thickness affects shear capacity, flexural demand, and constructability
๐ Why This Matters
In mining infrastructure โ such as crusher foundations, conveyor tower bases, or explosives storage bunkers โ improperly designed footings can lead to differential settlement, cracking, or catastrophic collapse under dynamic or eccentric loads. Understanding ACI 318-19โs integrated workflow ensures footings perform reliably in aggressive environments (e.g., sulfate soils, freeze-thaw cycles), directly impacting safety, operational uptime, and life-cycle cost.
๐ Core Principles
Spread footing design follows a sequential, interdependent workflow: (1) Geotechnical input defines allowable soil pressure (q_a) and determines preliminary plan dimensions; (2) Structural analysis treats the footing as a cantilever slab subjected to upward soil pressure (q_u = P_u / A); (3) Flexure governs longitudinal and transverse steel area via M_u = ฯM_n = ฯA_s f_y (d โ a/2); (4) Shear checks occur at d (one-way) and d/2 from column face (two-way), where V_u โค ฯV_c; (5) Development length l_d ensures bond capacity exceeds yield force, with modifications for concrete strength, bar size, coating, and confinement. All steps must satisfy strength (ฯ = 0.9 for flexure, 0.75 for shear) and ductility requirements per ACI 318-19 Chapters 10โ13, 22, and 25.
๐ Two-Way (Punching) Shear Capacity
Two-way shear governs footing thickness more often than flexure or one-way shear, especially for square/rectangular footings under concentric loads. The critical section is located d/2 from the column face along all sides, forming a perimeter b_o. ACI 318-19 Section 22.6.3.2 provides the nominal punching shear strength V_c.
๐ก Worked Example
Problem: Given: 24-in ร 24-in square column carrying factored load P_u = 420 kips; f'_c = 4,000 psi; footing plan = 10 ft ร 10 ft; assumed effective depth d = 22 in. Determine if d satisfies punching shear.
1.
Step 1: Compute factored soil pressure q_u = P_u / A = 420 kips / (10 ft ร 10 ft) = 4.2 ksf = 4.2 kip/ftยฒ.
2.
Step 2: Critical perimeter b_o = 4 ร (24 in + d) = 4 ร (24 + 22) = 184 in = 15.33 ft.
3.
Step 3: Compute V_u = q_u ร [A_foot โ A_column] = 4.2 ร [(10ร10) โ (2ร2)] = 4.2 ร (100 โ 4) = 403.2 kips.
4.
Step 4: Compute ฯV_c = 0.75 ร 4 ร โf'_c ร b_o ร d = 0.75 ร 4 ร โ4000 ร (184/12) ร (22/12) โ 0.75 ร 4 ร 63.25 ร 15.33 ร 1.83 โ 5,340 kip-in = 445 kips.
5.
Step 5: Compare: V_u = 403.2 kips โค ฯV_c = 445 kips โ OK. Minimum d satisfied.
Answer:
The assumed d = 22 in is adequate for punching shear. If not, increase d or footing size.
๐๏ธ Real-World Application
At the Red Dog Mine (Alaska), a 36-in-diameter steel pipe column supporting a primary crusher was founded on a 12-ft ร 12-ft ร 30-in-thick reinforced concrete footing. Soil investigation reported q_a = 3.5 ksf (siltstone bedrock). Using ACI 318-19, engineers sized the footing for P_u = 580 kips, verified punching shear at d = 26 in (ฯV_c = 628 kips > V_u = 542 kips), designed flexural steel as #8 bars @ 8 in o.c. both ways (A_s = 4.22 inยฒ > A_s,min = 2.71 inยฒ), and specified l_d = 34 in (per ACI Table 25.4.2.4) with full top/bottom lap splices due to seismic detailing requirements (IBC 2021 Seismic Design Category D).