14.2 Load combinations and limit states design

Load combinations and limit states design are crucial concepts in structural engineering. They ensure structures can withstand various forces while remaining safe and functional. This approach considers both ultimate failure scenarios and everyday performance, balancing strength and serviceability.

Engineers use load factors to account for uncertainties in different load types. They also apply resistance factors to material strengths. This method, known as Load and Resistance Factor Design (LRFD), provides a more nuanced approach to structural safety than older methods.

Design Approaches

Limit States and Load Factor Design

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• Limit states design identifies critical conditions where a structure may fail to perform its intended function
• Load and resistance factor design (LRFD) applies separate factors to loads and resistances to account for uncertainties
• LRFD uses probability theory to determine appropriate safety factors for different limit states
• Reliability index measures the probability of failure for a given design, with higher values indicating greater reliability

Allowable Stress Design

• Allowable stress design (ASD) ensures stresses in structural elements remain below allowable limits
• ASD applies a single factor of safety to the material strength to determine allowable stress
• Compares calculated stresses from applied loads to allowable stresses
• ASD historically used in steel and timber design, now largely replaced by LRFD in modern codes

Limit States

Ultimate Limit States

• Ultimate limit states (ULS) involve structural failure or collapse
• ULS includes yielding of materials, fracture, buckling, and overturning
• Design for ULS ensures sufficient strength and stability to resist maximum expected loads
• ULS calculations typically use factored loads and reduced material strengths

Serviceability Limit States

• Serviceability limit states (SLS) relate to performance under normal use conditions
• SLS includes excessive deflections, vibrations, and cracking
• Design for SLS ensures structure remains functional and comfortable for occupants
• SLS calculations often use unfactored loads and nominal material properties

Load Considerations

Load Combinations and Factors

• Load combinations account for different load types acting simultaneously on a structure
• Dead loads (permanent) and live loads (variable) combined with environmental loads (wind, snow, earthquake)
• Load factors amplify individual loads to account for uncertainties and variability
• Load factors typically greater than 1.0 for critical loads, less than 1.0 for stabilizing loads
• Common load combinations include 1.2D + 1.6L for gravity loads, 1.2D + 1.0W + 0.5L for wind loads

Resistance Factors and Safety

• Resistance factors reduce nominal strength of materials or components
• Factors account for uncertainties in material properties, fabrication, and installation
• Resistance factors typically less than 1.0, varying by material and failure mode
• Structural design satisfies equation: Factored Resistance ≥ Factored Loads
• $\phi R_n \geq \sum \gamma_i Q_i$ where $\phi$ is resistance factor, $R_n$ is nominal resistance, $\gamma_i$ are load factors, and $Q_i$ are load effects