RC Footing Analysis & Design
| Limit State | Demand | Capacity (Allowable) | Utilization | Status |
|---|
* L-Dir bars are placed at the bottom. B-Dir bars sit on top of L-Dir bars. Required As is governed by flexure or code minimums (e.g. 0.0018).
| Material | Qty | Unit |
|---|
The design of reinforced concrete isolated footings requires satisfying multiple distinct structural limit states to ensure both geotechnical stability and material strength. Below is an outline of the exact governing mathematical mechanics utilized by this tool:
1. Soil Bearing Pressure & The Kern Limit ($e \le L/6$)
The footing pad must distribute the axial load ($P$) and overturning moment ($M$) safely into the soil without exceeding the allowable bearing capacity ($q_a$). The base pressure distribution is calculated using the elastic flexural formula: $q = \frac{P}{A} \pm \frac{M}{S}$.
- Inside the Kern: If the eccentricities ($e_L$, $e_B$) are within the biaxial kern limit ($\frac{e_L}{L} + \frac{e_B}{B} \le \frac{1}{6}$), the entire footing base remains in compression.
$$q_{max,min} = \frac{P}{LB} \left( 1 \pm \frac{6e_L}{L} \pm \frac{6e_B}{B} \right)$$
- Outside the Kern (Partial Uplift): If the kern is exceeded, the footing experiences partial uplift. Soil cannot resist tension, forming a triangular or polyhedral stress block. The tool uses exact 1D uplift equations or applies an approximate magnification approach for biaxial double-uplift scenarios.
2. Governing Shear Limit States
- One-Way (Beam) Shear: The critical section is evaluated across the entire width of the footing at a distance $d$ from the column face.
$$\text{ACI / IS / BS / GB: } V_c \approx 0.17 \sqrt{f'_c} \, b_w d$$ $$\text{Eurocode 2: } V_{Rd,c} = \max \left[ C_{Rd,c} \, k \, (100 \rho_l f_{ck})^{1/3} , v_{min} \right] b_w d$$
- Two-Way (Punching) Shear: This limit state evaluates the risk of the column "punching" straight through the pad. The critical control perimeter ($b_o$) is located at $d/2$ from the column face for ACI/IS/BS codes, and $2d$ (with rounded corners) for Eurocode (EN 1992-1-1).
$$\text{ACI / IS / BS / GB: } V_c \approx \min\left(0.33, 0.17\left(1+\frac{2}{\beta}\right), 0.083\left(\frac{\alpha_s d}{b_o} + 2\right)\right) \sqrt{f'_c} \, b_o d$$ $$\text{Eurocode 2: } V_{Rd,c} = \max \left[ C_{Rd,c} \, k \, (100 \rho_l f_{ck})^{1/3} , v_{min} \right] u_1 d$$
3. Flexural Reinforcement (Bending)
The footing acts as an inverted cantilever beam fixed at the column interface, loaded upward by soil pressure. The tool uses the Independent Strip Method, evaluating Biaxial Moments by designing orthogonal 1D flexural strips. The bottom reinforcing mat must be sized to resist this flexure, subject to strict code-prescribed minimums.
Typical Allowable Bearing Capacities (Best Practice Reference)
Note: Values provided below are for preliminary conceptual sizing only. Always refer to a site-specific geotechnical investigation report for formal foundation design.
| Soil Classification | Material Description | Presumptive $q_a$ (kPa) | Presumptive $q_a$ (ksf) |
|---|---|---|---|
| Hard Rock | Massive bedrock (Granite, Basalt) | 3,000 - 10,000 | 60 - 200 |
| Gravel | Dense, well-graded gravel / sandy gravel | 300 - 600 | 6 - 12 |
| Sand | Medium to dense coarse sand | 150 - 300 | 3 - 6 |
| Stiff Clay | Firm, cohesive clay | 100 - 200 | 2 - 4 |
| Soft Clay / Silt | High compressibility, low strength | < 75 | < 1.5 |
- ACI 318: Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute.
- EN 1992-1-1 (Eurocode 2): Design of concrete structures - Part 1-1: General rules and rules for buildings. European Committee for Standardization.
- SS EN 1992-1-1: Singapore National Annex to Eurocode 2. Enterprise Singapore.
- IS 456: Plain and Reinforced Concrete - Code of Practice. Bureau of Indian Standards.
- BS 8110-1: Structural use of concrete. Code of practice for design and construction. British Standards Institution.
- GB 50010: Code for design of concrete structures. Ministry of Housing and Urban-Rural Development of the PRC.
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