Design Philosophy

 

DESIGN PHILOSOPHY

 

1. Working Stress Design (WSD)

Philosophy

WSD assumes the structure remains in the elastic range under service (working) loads.

 

The theory is based on Hooke's Law:

and assumes:

• Stresses are proportional to strains.
• No yielding is allowed.
• No significant redistribution of forces occurs.
• Safety is achieved by limiting stresses to a fraction of the yield strength.

 

The designer checks that:

where:

• = stress from service loads
• = material yield stress divided by a factor of safety

Characteristics

• Uses unfactored loads.
• Applies a global factor of safety to the material strength.
• Based on elastic behavior.
• Does not explicitly account for varying uncertainties in different loads.

Example

Steel yield stress:

Factor of safety:

Allowable stress:

If service load stress = 180 MPa:

✓ Design passes.

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2. Allowable Stress Design (ASD)

ASD evolved directly from WSD. In steel bridge and railway practice, ASD is essentially a refined version of WSD.

 

Philosophy

Same basic concept:

The allowable capacity is obtained by dividing nominal strength by a safety factor.

where:

• = nominal resistance
• = safety factor

 

Characteristics

• Uses service loads.
• Uses allowable stresses or allowable capacities.
• Common in older bridge specifications and some AREMA provisions.
• Easy to understand and calculate.
• Does not directly measure collapse safety.

Example

Steel girder nominal moment capacity:

Safety factor:

Allowable moment:

Service load moment:

✓ Acceptable.

 

Why ASD Was Better Than WSD

ASD allowed engineers to directly evaluate:

• Axial resistance
• Flexural resistance
• Shear resistance
• Bearing resistance
• Buckling resistance

instead of merely checking stresses.

 

 

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3. Limit States Design (LSD)

Philosophy

A structure has different possible failure conditions called limit states.

A limit state is a condition beyond which the structure no longer fulfills its intended function.

 

Examples:

Strength Failure

• Yielding
• Fracture
• Buckling
• Shear failure

Service Failure

• Excessive deflection
• Excessive vibration
• Excessive cracking

Fatigue Failure

• Repeated stress cycles

Extreme Event Failure

• Collision
• Derailment
• Earthquake

 

Fundamental Equation

or

where

• = load factor
• = load
• = resistance factor
• = nominal resistance

 

Key Principle

Loads are increased.

Resistance is reduced.

Both sides account for uncertainty.

This is much more rational than a single safety factor.

 

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4. Ultimate Limit States (ULS)

Philosophy

ULS designs for the actual strength at failure.

Instead of reducing strength only, ULS:

1. Increases loads using load factors.
2. Reduces resistance using resistance factors.

where:

• = load factor
• = load effect
• = resistance factor
• = nominal resistance

 

This is the basis of Limit States Design (LSD) used in:

• CSA S6 Canadian Highway Bridge Design Code
• AASHTO LRFD
• Modern AREMA provisions

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Example

Dead load moment:

Live load moment:

ULS combination:

Resistance:

Since:

✓ Design passes.

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5. Serviceability Limit State (SLS)

Also part of LSD. The bridge may be safe from collapse but still unusable. SLS prevents that.

 

Typical Checks

Deflection

Bridge sag under train load.

Settlement

Foundation movement.

Vibration

Passenger discomfort.

Crack Width

Concrete durability.

Track Alignment

Railway operational requirements.

 

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6. Load and Resistance Factor Design (LRFD)

LRFD is the practical implementation of LSD.

 

LRFD Equation

This is the same equation used in limit states design.

 

 

Why It Is Called LRFD

Load Factor (LF)

Apply factors to loads:

Resistance Factor (RF)

Reduce strength:

Hence:

Load and Resistance Factor Design

 

Reliability Basis of LRFD

Modern codes calibrate load and resistance factors statistically.

Suppose:

Variable	Variability
Dead Load	Low
Live Load	Medium
Wind	High
Earthquake	Very High
Steel Strength	Low
Soil Capacity	Moderate

Each variable receives a suitable factor.

This produces a consistent reliability level across different structures.

 

 

 

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Why ULS Replaced ASD/WSD

ASD assumes all uncertainties can be covered with one safety factor.

In reality:

Source of Uncertainty	Reliability
Dead load	Well known
Live load	Variable
Wind	Highly variable
Earthquake	Very uncertain
Material strength	Relatively predictable

 

LSD / ULS allows different load factors for different uncertainties.

For example:

The live load receives a larger factor because it is less predictable than dead load.

This produces a more uniform reliability level across different failure modes.

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Comparison

Item	WSD	ASD	ULS (LSD/LRFD)
Loads used	Service loads	Service loads	Factored loads
Material strength	Reduced by FS	Reduced by Ω	Reduced by φ
Design basis	Elastic stresses	Allowable stresses/capacities	Ultimate strength
Plastic behavior considered	No	Limited	Yes
Reliability based	No	Partial	Yes
Economy	Conservative	Moderate	Most efficient
Modern bridge codes	Rare	Limited use	Standard practice

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Bridge Engineering Perspective

As a bridge engineer working under CSA S6 and CN/AREMA requirements, you will mostly encounter:

 

Serviceability Limit State (SLS)

Checks:

• Deflections
• Vibration
• Crack control
• Fatigue stresses

using unfactored or lightly factored loads.

 

Ultimate Limit State (ULS)

Checks:

• Flexural resistance
• Shear resistance
• Bearing failure
• Buckling
• Foundation capacity

using factored loads and resistance factors.

 

Therefore, modern bridge design does not generally use ASD/WSD for primary strength design; it uses ULS for safety against collapse and SLS/Fatigue Limit State for operational performance. This provides a more rational and statistically calibrated level of reliability than the traditional ASD/WSD approach.