CELE Reinforced & Prestressed Concrete — Reinforced Concrete Footings, Bond and DevelopmentConcept Map

Concept

Footing Sizing and Bearing Capacity

Sub Concepts

• Service Load Analysis
• Allowable Soil Bearing Pressure (qa)
• Required Footing Area Calculation
• Factored Load Determination
• Net Design Pressure (qu)
• Square vs Rectangular Footings

Relationship To Central

Foundation for all structural design; establishes footing plan dimensions based on soil capacity

Concept

Two-Way Punching Shear

Sub Concepts

• Critical Perimeter bo Determination
• Punching Shear Capacity Vc Formula
• Punching Demand Calculation
• Reduction Factor Application (φ = 0.75)
• Perimeter Location at d/2 from Column Face
• Stress Distribution Pattern

Relationship To Central

Critical shear check preventing column breakthrough; governs footing thickness

Concept

One-Way Beam Shear

Sub Concepts

• Critical Section Location (distance d from column face)
• Beam Shear Capacity Formula
• Full Width Shear Transfer
• Relation to Footing Depth
• Concrete Strength Influence

Relationship To Central

Secondary shear check across footing width; ensures diagonal cracking resistance

Concept

Flexural Design

Sub Concepts

• Critical Moment Section Location
• Cantilever Moment Calculation (Mu = qu·B·ℓ²/2)
• Projecting Length ℓ Definition
• Steel Area Calculation (As)
• Reinforcement Distribution Across Width
• Moment Arm and Internal Couple

Relationship To Central

Determines main reinforcement quantity; based on cantilever moment at column face

Concept

Development Length and Bond

Sub Concepts

• Tension Development Length (ℓd) Formula
• Bar Diameter Classification (≤20 mm vs >20 mm)
• Modification Factors (ψt, ψe)
• Concrete Strength and Density Effects (λ)
• Clear Spacing and Cover Requirements
• Standard Hooks (90° and 180°)
• Minimum Development Length (300 mm floor)
• Favorable vs Unfavorable Conditions

Relationship To Central

Ensures reinforcement develops full yield strength; critical for load transfer

Concept

NSCP 2015 and ACI 318 Provisions

Sub Concepts

• Load Factor Applications
• Resistance Factors (φ values)
• Material Strength Specifications
• Development Length Tables and Formulas
• Shear Capacity Expressions
• Bond and Anchorage Requirements

Relationship To Central

Regulatory framework governing all design calculations and safety factors

Concept

Reinforcement Detailing and Anchorage

Sub Concepts

• Straight Bar Development
• Hooked Bar Anchorage
• Bar Spacing Rules
• Concrete Cover Minimums
• Stirrup Placement and Spacing
• Bend Diameter Limitations
• Lap Splicing Fundamentals

Relationship To Central

Practical implementation ensuring bars function as designed

To

Net Design Pressure qu

From

Footing Sizing

Strength

strong

Relationship

Sizing determines footing area; area directly used to calculate qu for all subsequent checks

To

One-Way Beam Shear

From

Two-Way Punching Shear

Strength

strong

Relationship

Both use same design pressure qu and footing depth d; punching typically governs, so often controls thickness choice

To

Flexural Design

From

One-Way Beam Shear

Strength

strong

Relationship

Once footing depth d is set by shear, it becomes input for flexural moment arm and steel stress calculation

To

Development Length

From

Flexural Design

Strength

strong

Relationship

Flexure determines required steel area As; reinforcement quantity/size directly determines ℓd required

To

Reinforcement Detailing

From

Development Length

Strength

strong

Relationship

Computed ℓd governs bar placement (straight or hooked) and final footing drawing dimensions

To

Two-Way Punching Shear

From

Critical Perimeter bo

Strength

strong

Relationship

Perimeter is defined geometric input to punching capacity formula Vc = 0.33√fc·bo·d

To

Flexural Design

From

Cantilever Moment Calculation

Strength

strong

Relationship

Cantilever load distribution and projecting length ℓ determine moment Mu = qu·B·ℓ²/2

To

Development Length Formula

From

Bar Diameter Classification

Strength

strong

Relationship

Bar size (≤20 mm vs >20 mm) determines coefficient (2.1 vs 1.7) in ℓd calculation

To

Development Length Modification

From

Spacing and Cover Requirements

Strength

strong

Relationship

Favorable spacing (≥db) and cover (≥db) allow use of normal ψ factors; unfavorable requires adjustment

To

All Design Checks

From

NSCP 2015 Provisions

Strength

strong

Relationship

NSCP provides load factors, resistance factors φ, capacity formulas, and development tables governing entire design

To

Two-Way and One-Way Shear

From

Concrete Strength fc

Strength

moderate

Relationship

Shear capacity Vc is proportional to √fc; higher strength improves capacity

To

Punching Perimeter bo

From

Footing Thickness d

Strength

strong

Relationship

bo = 4(c+d); larger d increases critical perimeter and improves capacity

To

Moment Arm jd

From

Footing Thickness d

Strength

moderate

Relationship

Larger d increases internal lever arm, reducing required steel area As for same moment

To

Development Length

From

Steel Yield Strength fy

Strength

strong

Relationship

ℓd is proportional to fy; higher strength steel requires longer development

To

Development Length

From

Hooked Anchorage

Strength

moderate

Relationship

Standard hooks (90°/180°) achieve full development in shorter length than straight bars; alternative where space is limited

To

Shear and Flexure Demands

From

Footing Bearing Pressure

Strength

strong

Relationship

Service-load bearing check sizes footing; factored bearing pressure qu drives all structural demands

To

Moment and Punching

From

Column Size and Location

Strength

strong

Relationship

Larger column increases critical perimeter bo; asymmetric placement changes cantilever length ℓ and moment distribution

To

Development Length

From

Modification Factor ψt

Strength

moderate

Relationship

Top bar position (ψt = 1.3) increases ℓd; affects bar placement strategy in footing

To

Footing Load Transfer

From

Bond and Anchorage

Strength

strong

Relationship

Proper development ensures bars can transfer column load into concrete; failure → loss of footing strength

To

Capacity Check φVc

From

Demand Calculation Vu

Strength

strong

Relationship

Shear adequacy requires Vu ≤ φVc; controls iteration to find minimum acceptable footing depth