CELE Reinforced & Prestressed Concrete — Reinforced Concrete Fundamentals: WSD and USDConcept Map

Concept

Working Stress Design (WSD)

Sub Concepts

• Linear elastic analysis
• Modular ratio (n = Es/Ec)
• Allowable stress limits (0.45f'c for concrete)
• Service-load conditions
• Transformed section method
• Historical method (still examinable)

Relationship To Central

Traditional design method based on elastic theory and allowable stresses

Concept

Ultimate Strength Design (USD / LRFD)

Sub Concepts

• Load factoring (1.2D + 1.6L)
• Strength reduction factor (φ)
• Nominal vs design strength
• Factored loads and moments
• Limit state design
• φMn ≥ Mu design requirement

Relationship To Central

Modern NSCP 2015 method based on plastic theory and safety factors

Concept

Material Properties

Sub Concepts

• Concrete compressive strength (f'c)
• Steel yield strength (fy)
• Modulus of elasticity (Ec, Es)
• Stress-strain relationships
• 28-day cylinder strength
• Normal-weight concrete characteristics

Relationship To Central

Essential parameters for both WSD and USD calculations

Concept

Strength Reduction Factors (φ)

Sub Concepts

• Tension-controlled flexure (φ = 0.90)
• Shear and torsion (φ = 0.75)
• Spiral columns (φ = 0.75)
• Tied columns (φ = 0.65)
• Bearing on concrete (φ = 0.65)
• Plain concrete (φ = 0.60)
• Compression vs tension-controlled transition

Relationship To Central

Critical USD parameters that vary by member type and failure mode

Concept

Equivalent Stress Block and β₁

Sub Concepts

• Whitney equivalent rectangular block
• Block intensity (0.85f'c)
• Neutral axis depth (c)
• Equivalent block depth (a = β₁c)
• β₁ = 0.85 for f'c ≤ 28 MPa
• β₁ reduction formula (28 < f'c ≤ 55 MPa)
• β₁ = 0.65 for f'c ≥ 55 MPa

Relationship To Central

USD simplification for concrete compression distribution

Concept

Design Framework

Sub Concepts

• Design equations and inequalities
• Elastic vs plastic theory assumptions
• Failure mode classification
• Strain compatibility
• Equilibrium conditions
• Design adequacy verification

Relationship To Central

Systematic approach to applying either WSD or USD

Concept

NSCP 2015 Standards

Sub Concepts

• USD as primary design method
• WSD as alternate design method
• Load factor combinations
• Safety requirements
• Code provisions for all limit states

Relationship To Central

Philippine regulatory framework governing RC design

To

Material Properties

From

Working Stress Design WSD

Strength

strong

Relationship

WSD requires accurate material properties to compute elastic stresses; uses Ec for modular ratio n = Es/Ec in transformed section analysis

To

Strength Reduction Factors φ

From

Ultimate Strength Design USD

Strength

strong

Relationship

USD design inequality φMn ≥ Mu fundamentally depends on selecting the correct φ based on member type and failure mode

To

Ultimate Strength Design USD

From

Equivalent Stress Block and β₁

Strength

strong

Relationship

USD uses the Whitney equivalent rectangular block (0.85f'c intensity, depth a = β₁c) to simplify concrete compression distribution for nominal strength computation

To

Equivalent Stress Block and β₁

From

Material Properties

Strength

strong

Relationship

β₁ is determined solely by f'c; concrete modulus Ec is needed to compute strain limits and classify sections as tension- or compression-controlled

To

Design Framework

From

Strength Reduction Factors φ

Strength

strong

Relationship

The selection of φ is the critical step in applying the USD design inequality φMn ≥ Mu; depends on strain compatibility analysis

To

NSCP 2015 Standards

From

Design Framework

Strength

strong

Relationship

NSCP 2015 mandates USD as the primary method and WSD as alternate; all design frameworks must comply with these regulations

To

Design Framework

From

Working Stress Design WSD

Strength

strong

Relationship

WSD framework uses elastic equilibrium and linear strain compatibility; stress checks are made at service load level against allowable fractions of strength

To

Material Properties

From

Ultimate Strength Design USD

Strength

moderate

Relationship

USD requires material properties to determine yield strains εy and failure strain limits; used in strain compatibility to classify sections and select φ

To

Material Properties

From

Equivalent Stress Block and β₁

Strength

moderate

Relationship

The stress-block intensity 0.85f'c and the β₁ reduction are empirical factors derived from concrete material behavior; β₁ varies with f'c strength level

To

Strength Reduction Factors φ

From

NSCP 2015 Standards

Strength

strong

Relationship

NSCP 2015 specifies the exact numerical values of φ for each member type and failure mode to be used in USD design

To

Ultimate Strength Design USD

From

Working Stress Design WSD

Strength

moderate

Relationship

Both methods are applied to the same reinforced concrete elements but use fundamentally different safety philosophies: WSD uses allowable stress limits; USD uses load factors and strength reduction

To

Equivalent Stress Block and β₁

From

Design Framework

Strength

strong

Relationship

The equivalent rectangular stress block is the mathematical tool that enables the design framework for USD; its geometry (height a = β₁c) must be correctly computed