CELE Reinforced & Prestressed Concrete — Reinforced Concrete ColumnsConcept Map

Concept

Axial Capacity & Design

Sub Concepts

• Pure Axial Nominal Strength (P₀)
• Concrete Contribution
• Steel Contribution
• Design Axial Load Limits
• Tied vs Spiral Reduction Factors

Relationship To Central

Core strength calculation method for columns under compression

Concept

Reinforcement Requirements

Sub Concepts

• Longitudinal Steel Ratio (ρg)
• Minimum and Maximum Limits
• Spiral Reinforcement Ratio (ρs)
• Minimum Number of Bars
• Tie Design and Spacing

Relationship To Central

Steel ratio and arrangement rules that govern column detailing

Concept

Axial-Moment Interaction

Sub Concepts

• Interaction Diagram Construction
• Balanced Point (Pb, Mb)
• Compression-Controlled Failure
• Tension-Controlled Failure
• Nominal and Design Strength Curves

Relationship To Central

Design methodology accounting for combined compression and bending

Concept

Slenderness Effects

Sub Concepts

• Slenderness Ratio (kℓu/r)
• Short vs Slender Column Limits
• P-delta and P-Delta Effects
• Moment Magnification Method
• Braced and Unbraced Frames

Relationship To Central

Modifications to capacity for long, slender columns prone to buckling

Concept

Column Types & Classification

Sub Concepts

• Tied Columns
• Spiral Columns
• Circular vs Rectangular
• Ductility Comparison
• Reduction Factor (φ) Variation

Relationship To Central

Categorization based on transverse reinforcement and behavior

Concept

Design Standards & Codes

Sub Concepts

• NSCP 2015 (National Structural Code of the Philippines)
• ACI 318 (American Concrete Institute)
• RA 544 (Licensure Law for Civil Engineers)
• Capacity Reduction Factors
• Safety Margins and Load Factors

Relationship To Central

Regulatory framework governing column design in the Philippines

Concept

Material Properties

Sub Concepts

• Concrete Compressive Strength (f'c)
• Steel Yield Strength (fy)
• Spiral Yield Strength (fyt)
• Design vs Nominal Strengths
• Material Partial Safety Factors

Relationship To Central

Concrete and steel characteristics affecting column strength

To

Pure Axial Strength Po

From

Axial Capacity Design

Strength

strong

Relationship

Po is calculated as the sum of concrete and steel contributions; the foundation for design axial limits

To

Design Limits (Tied vs Spiral)

From

Pure Axial Strength Po

Strength

strong

Relationship

Design axial capacity is obtained by applying reduction factors and caps to Po; tied columns use lower cap (0.80) and phi (0.65) than spiral

To

Reinforcement Requirements

From

Column Types

Strength

strong

Relationship

Tied columns require minimum 4 bars and transverse ties; spiral columns require minimum 6 bars and continuous spiral with specified ratio

To

Longitudinal Steel Ratio

From

Reinforcement Requirements

Strength

strong

Relationship

Steel ratio (ρg = Ast/Ag) is bounded between 1% and 8%; affects load capacity and constructability

To

Spiral Ratio

From

Reinforcement Requirements

Strength

strong

Relationship

Spiral columns must satisfy minimum ratio ρs based on core geometry and material strengths; provides lateral confinement

To

Axial-Moment Interaction

From

Axial Capacity Design

Strength

strong

Relationship

Pure axial capacity (Po) establishes the top point of interaction diagram; real columns carry combined P and M

To

Balanced Point

From

Axial-Moment Interaction

Strength

strong

Relationship

Balanced point (Pb, Mb) is the maximum moment capacity; marks transition between compression-controlled and tension-controlled regions

To

Compression-Controlled Failure

From

Balanced Point

Strength

strong

Relationship

Above balanced point, concrete crushes at strain 0.003 while steel is below yield; brittle behavior with phi = 0.65

To

Tension-Controlled Failure

From

Balanced Point

Strength

strong

Relationship

Below balanced point, steel yields while concrete is in compression; ductile behavior with phi = 0.90

To

Short vs Slender Column Limits

From

Slenderness Effects

Strength

strong

Relationship

Slenderness ratio (kℓu/r) determines if column is short (ignore P-delta) or slender (apply moment magnification)

To

Moment Magnification Method

From

Slenderness Effects

Strength

strong

Relationship

Slender columns require amplification of applied moment using magnifier delta m to account for P-delta and P-Delta effects

To

Axial-Moment Interaction

From

Moment Magnification Method

Strength

strong

Relationship

Magnified moment replaces applied moment in interaction diagram check; critical for slender column design

To

Pure Axial Strength Po

From

Material Properties

Strength

strong

Relationship

Po depends on f'c (concrete) and fy (steel); design strengths determined from specified values and partial factors

To

Spiral Ratio

From

Material Properties

Strength

moderate

Relationship

Spiral ratio formula includes f'c and fyt (yield of spiral steel, capped at 700 MPa per code)

To

Axial Capacity Design

From

Design Standards & Codes

Strength

strong

Relationship

NSCP 2015 and ACI 318 specify formulas for Po, reduction factors, and design limits for tied and spiral columns

To

Reinforcement Requirements

From

Design Standards & Codes

Strength

strong

Relationship

Code prescribes minimum and maximum steel ratios, tie/spiral spacing, and minimum bar requirements based on section type

To

Slenderness Effects

From

Design Standards & Codes

Strength

strong

Relationship

Code defines slenderness limits for braced/unbraced frames and prescribes moment magnification methodology

To

Axial Capacity Design

From

Column Types

Strength

strong

Relationship

Tied columns use phi = 0.65 and cap = 0.80; spiral columns use phi = 0.75 and cap = 0.85; reflected in design limits

To

Axial Capacity Design

From

Longitudinal Steel Ratio

Strength

moderate

Relationship

Higher Ast increases the steel contribution term (fy × Ast) in Po; limited by practical and code constraints

To

Column Types

From

Tied vs Spiral Reduction Factors

Strength

strong

Relationship

Spiral columns are more ductile and efficient, justifying higher phi factor (0.75 vs 0.65) and cap factor (0.85 vs 0.80)