Tool for analysis of Isolated footing subjected to axial load and high biaxial moments

Rigorous Biaxial Footing Analyzer (All 5 Analytical Cases)

Design Load Inputs & Geometry

Footing Length L (m) Footing Width B (m) Axial Structural Load P (kN) Moment Mx (kNm, about X-Axis) Moment My (kNm, about Y-Axis)

Geotechnical & Stability Parameters

Allowable SBC q_all (kN/m²) Coefficient of Friction μ Factored Horizontal Load H (kN) Footing Thickness t (m) Column Size Along X (m) Column Size Along Y (m)

Current Execution Matrix Preview

Run computation to verify active stress blocks.

Structural Engineering Calculation Document

RIGID SHALLOW FOOTING BIAXIAL PRESSURE REPORT (ALL 5 GEOMETRIC CASES)

Generation Date:

1. Input Geometric Bounds & Vector Loading

2. Stress Block Case Evaluation Framework

3. Soil Pressure Structural Response Matrix

4. Soil-Structure Separation Vector Diagram

The engineering map below outlines the precise boundary coordinates of the Neutral Axis and associated zero-pressure uplift regions.

5. Compliance Summary & Professional Validation Sign-Off

• The internal calculation engine checks soil-structure lift-off for all five biaxial loading cases.
• Peak edge bearing pressure p_max must remain within allowable SBC limits.
• Reinforcement enhancement is required if uplift or severe stress concentration develops.

6. Stability & Geotechnical Validation

Prepared By: Structural Engineer

Approved By: Principal Structural Engineer

Footing Mechanics Analysis Engine

User Documentation & Mathematical Reference Guide

1. System Overview

The provided JavaScript analysis module evaluates the soil-structure interaction behavior of a rigid rectangular shallow foundation subjected to axial load ($P$) and biaxial flexure ($M_x, M_y$). It evaluates structural eccentricity ratios, segments the structural response into one of five critical contact mechanics zones, checks geotechnical limits, and renders a live, scaled engineering diagram via an HTML5 canvas.

2. Expected Input Fields

The calculation engine binds data from your HTML template via document.getElementById(). Ensure the following IDs match your input fields exactly:

Element ID	Parameter Name	Engineering Description	Expected Unit
L	Footing Length	Dimension parallel to the X-axis (Must be > 0)	meters (m)
B	Footing Width	Dimension parallel to the Y-axis (Must be > 0)	meters (m)
P	Axial Load	Vertical concentric structural load (Must be > 0)	kiloNewtons (kN)
Mx	Moment X	Overturning moment rotating around the X-axis	kN·m
My	Moment Y	Overturning moment rotating around the Y-axis	kN·m
qall	SBC	Allowable Safe Bearing Capacity of the underlying stratum	kN/m²
mu	Friction Coefficient ($\mu$)	Interface sliding friction factor between concrete and soil	dimensionless
H	Horizontal Load	Lateral shear forces driving sliding tendencies	kiloNewtons (kN)
t	Footing Thickness	Total depth/thickness of concrete structural raft slab	meters (m)
cx	Column Width (X)	Structural base column size in the X-direction	meters (m)
cy	Column Depth (Y)	Structural base column size in the Y-direction	meters (m)

3. Structural Contact Mechanics & Case Zonation

Eccentricities are mapped into ratio benchmarks ($r_x = \frac{|M_y|/P}{L}$ and $r_y = \frac{|M_x|/P}{B}$). The algorithm processes the foundation behavior using five distinct kinematic conditions:

Case I: Full Compression ($r_x \le \frac{1}{6}$ AND $r_y \le \frac{1}{6}$)

Behavior: The resultant load stays perfectly within the traditional "Kern" or middle-third bounds. Zero uplift occurs across the envelope.

Governing Equation: $$q = \frac{P}{A} \pm \frac{6M_x}{LB^2} \pm \frac{6M_y}{BL^2}$$

Case II: One-Way Lift-Off Along Length ($r_x > \frac{1}{6}$ AND $r_y \le \frac{1}{6}$)

Behavior: Excessive longitudinal eccentricity induces local heel separation. The Neutral Axis runs cleanly parallel to the footing width.

Effective Length ($L_{eff}$): $\alpha \cdot L$, where $\alpha = 1.5 - 3r_x$

Case III: One-Way Lift-Off Along Width ($r_y > \frac{1}{6}$ AND $r_x \le \frac{1}{6}$)

Behavior: Excessive lateral eccentricity induces side separation. The Neutral Axis runs parallel to the footing length.

Effective Width ($B_{eff}$): $\beta \cdot B$, where $\beta = 1.5 - 3r_y$

Case IV: Pentagonal Compression Zone ($r_x > \frac{1}{6}$, $r_y > \frac{1}{6}$, and $r_x, r_y < 0.5$)

Behavior: Significant biaxial bending causes a single localized corner of the footing to lift off the soil stratum. The effective bearing footprint shifts into a pentagonal layout.

Case V: Triangular Compression Block (Severe Biaxial Overturning)

Behavior: High over-turning moment triggers severe global tilt. Only an isolated triangular wedge remains under active structural compression.

4. Automated Geotechnical Safety Frameworks

The code processes and yields key stability triggers inside the target #screenReadout wrapper element:

• Allowable SBC Validation: Compares peak pressure ($q_{max}$) against user-provided qall. Flags an explicit, colored EXCEEDS ALLOWABLE SBC alert if structural stresses exceed capacities.
• Factor of Safety (FOS) Calculations: Evaluates safety ratios against lateral sliding structural failures ($\frac{\mu \cdot P}{H}$) and mechanical overturning actions ($\frac{\text{Resisting Moment}}{\text{Overturning Moment}}$).
• Punching Shear Assessment: Calculates uniform out-of-plane continuous column punching boundary forces using critical perimeter tracking formulas: $$2 \cdot ((c_x + t) + (c_y + t))$$ Striking thresholds exceeding 1000 kN/m² throws an immediate CRITICAL PUNCHING SHEAR warning.

Critical Structural Warnings Triggered by the Engine:

• HIGH DIFFERENTIAL SETTLEMENT RISK: Automatically triggers if your effective compressed structural bearing contact space falls below 70%.
• HEAVY TOP REINFORCEMENT REQUIRED: Triggers if tension/uplift is present, or if soil bearing utilization crosses beyond 85%.

5. Dynamic Blueprint Visualization Canvas

The module includes a secondary renderer function named renderEngineeringBlueprint() which handles real-time scaling and context vector drawing on an HTML canvas element tagged with id="blueprintCanvas".

Visual Map Indicators Generated on Canvas:

• Sky Blue Boundaries: The nominal footprint boundaries of your structural base concrete footing.
• Shaded Inner Polygon: The verified region under active structural compression.
• Red Dashed Line: The computed Neutral Axis line separating compression zones from soil lift-off regions.
• Green Vector Line: Vector highlighting resultant load path displacement showing eccentricity coordinates relative to structural center point.