8.2 Nonlinear static procedures (pushover analysis)
2 min read•july 25, 2024
, like , help engineers evaluate how buildings perform during earthquakes. These methods go beyond elastic limits, showing how structures yield and fail under seismic loads. They're crucial for identifying weak points and understanding .
Pushover analysis involves creating a model, applying loads, and tracking structural response. It produces a that shows how a building behaves as forces increase. While it has limitations, pushover analysis strikes a balance between simplicity and accuracy, making it a valuable tool in earthquake engineering.
Nonlinear Static Procedures: Fundamentals and Applications
Concept of pushover analysis
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- Analysis method evaluates seismic performance accounting for material and geometric nonlinearities
- Estimates structural capacity beyond elastic limit identifies weak points and
- Determines sequence of yielding and failure in structure during seismic event
- Involves key components and capacity curve generation
- Provides insights into post-yield behavior and collapse mechanisms (, )
- Commonly used in and assessment (, )
Execution of pushover analysis
- Create accurately representing geometry and connectivity
- Define and nonlinear behavior including
- Apply to account for
- Select pattern based on expected seismic response (inverted triangular, uniform)
- Incrementally increase lateral loads monitoring structural deformation
- Monitor structural response tracking formation of plastic hinges and element failures
- Interpret results through capacity curve plotting against
- Identify corresponding to different damage states (, )
- Analyze formation sequence to understand progressive collapse mechanisms
- Evaluate global and local deformation demands against (, ASCE 41)
Limitations of nonlinear static procedures
- Assumes response dominated by fundamental mode may miss (tall buildings)
- Uses constant load pattern throughout analysis neglecting load redistribution
- Neglects like damping and inertial forces
- Potentially inaccurate for structures with significant (asymmetric buildings)
- Does not account for of strength and stiffness
- Limited applicability to sensitive to higher mode effects (bridges)
- May underestimate deformation demands in some cases ()
Pushover analysis vs other methods
- simpler but less accurate for nonlinear behavior
- considers dynamic effects but limited to elastic response
- most accurate but computationally intensive ()
- Pushover analysis balances simplicity and accuracy provides insight into post-yield behavior
- Advantages include and clear visualization of failure progression
- Disadvantages include simplified dynamic effects and potential underestimation of demands
- Often used as screening tool before more detailed nonlinear dynamic analysis (FEMA P-58)
Key Terms to Review (37)
Acceptance Criteria: Acceptance criteria are the specific conditions that must be met for a structure to be considered safe and satisfactory under certain loading conditions, particularly during seismic events. These criteria help in evaluating whether the design meets safety standards and performance objectives, guiding engineers in ensuring that structures can withstand earthquakes and other forces without excessive damage or failure.
ASCE 41: ASCE 41 is a standard developed by the American Society of Civil Engineers that provides guidelines for the seismic rehabilitation of existing buildings. This standard is crucial as it outlines procedures and criteria for evaluating and retrofitting structures to improve their earthquake performance, ensuring safety and resilience against seismic events. The standard includes methods like nonlinear static procedures, which are essential for understanding how buildings respond to earthquakes and determining effective retrofit strategies.
Base Shear: Base shear is the total horizontal force that a building or structure experiences during seismic events, primarily caused by ground motion. It is crucial for understanding how a structure will respond to earthquakes, as it influences the design and analysis of structures, ensuring they can withstand seismic forces while maintaining stability.
Capacity Curve: A capacity curve is a graphical representation that illustrates the relationship between the lateral force applied to a structure and its corresponding displacement during a nonlinear static analysis, such as pushover analysis. This curve is crucial for understanding the performance of a structure under seismic loading, highlighting how it will respond to increasing levels of lateral forces and allowing engineers to identify the point of failure or limit states.
Collapse mechanisms: Collapse mechanisms refer to the specific ways in which a structure fails or collapses under loads, particularly during seismic events. Understanding these mechanisms is crucial as they help identify potential vulnerabilities in a building's design, enabling engineers to assess how a structure might behave under extreme conditions, such as earthquakes. By analyzing collapse mechanisms, engineers can implement design strategies that enhance structural resilience and minimize the risk of catastrophic failure during seismic activities.
Computational efficiency: Computational efficiency refers to the effectiveness of an algorithm or computational method in utilizing resources, primarily time and memory, to achieve results. In the context of nonlinear static procedures, such as pushover analysis, it highlights the importance of achieving accurate results while minimizing computational cost, thereby making it practical for real-world applications in earthquake engineering.
Cyclic degradation: Cyclic degradation refers to the process by which materials lose strength and stiffness when subjected to repeated loading and unloading cycles, often seen in structural components during seismic events. This phenomenon can lead to a significant reduction in the overall performance of a structure, impacting its ability to withstand further loading. Understanding cyclic degradation is crucial for accurately assessing a structure's response and reliability under repeated seismic forces.
Dynamic effects: Dynamic effects refer to the response of structures subjected to time-varying loads, especially during events such as earthquakes. These effects are critical in understanding how structures behave under seismic forces, which can lead to significant changes in internal forces, deformations, and ultimately structural performance. Dynamic effects become especially important when assessing the nonlinear behavior of structures during extreme loading conditions.
Eurocode 8: Eurocode 8 is a European standard that provides guidelines for the design of structures to withstand seismic actions. This code aims to improve the safety and performance of buildings in earthquake-prone regions across Europe, reflecting advancements in earthquake engineering practices and the need for uniformity in seismic design standards.
Failure mechanisms: Failure mechanisms refer to the processes or modes through which a structure fails to perform its intended function, particularly under stress or loading conditions. Understanding these mechanisms is essential for assessing structural integrity and guiding design decisions, especially in the context of analyzing how structures respond to forces such as seismic activity.
Fema 356: FEMA 356 is a guideline published by the Federal Emergency Management Agency that provides procedures for the seismic rehabilitation of buildings. It outlines the necessary methodologies for assessing existing structures and determining appropriate retrofitting techniques to improve their earthquake resilience. The document focuses on both nonlinear dynamic analysis and nonlinear static procedures, offering engineers a comprehensive framework to ensure buildings can withstand seismic forces effectively.
Gravity loads: Gravity loads refer to the forces acting on a structure due to the weight of its components and the weight of any additional materials or occupants within it. These loads are fundamental in structural design as they dictate how a structure must be supported and stabilized, particularly in the context of nonlinear static procedures, where understanding how a structure behaves under these loads is crucial for evaluating its performance during seismic events.
Higher Mode Effects: Higher mode effects refer to the impact of higher vibrational modes on the response of structures during seismic events. In the context of nonlinear static procedures, such as pushover analysis, these effects are crucial because they can significantly influence how a building behaves when subjected to lateral forces, especially in irregular or tall structures. Understanding higher mode effects is vital for accurately assessing a structure's performance and ensuring it meets safety standards during earthquakes.
Immediate Occupancy: Immediate occupancy refers to a performance objective in seismic design that ensures a structure can be occupied right after an earthquake with minimal repairs and without significant damage. This concept focuses on the safety and functionality of buildings, allowing them to be used for their intended purpose immediately after a seismic event, which is crucial for emergency response and community resilience.
Incremental loading: Incremental loading is a method used in structural analysis where loads are applied gradually, step by step, rather than all at once. This approach allows engineers to observe how structures respond to increasing loads and identify points of weakness or failure. It is particularly useful in nonlinear static procedures, where the response of the structure may change as it undergoes deformation and damage under the influence of applied forces.
Lateral Load: Lateral load refers to forces that act horizontally on a structure, typically due to wind, earthquakes, or other lateral forces. These loads are critical in the design and analysis of structures, as they can cause significant stress and deformation, impacting the overall stability and safety. Understanding lateral loads is essential for engineers to ensure that buildings and other structures can withstand these forces without experiencing catastrophic failure.
Lateral load pattern: A lateral load pattern refers to the distribution of forces that act horizontally on a structure during events such as earthquakes or strong winds. These loads are critical in evaluating a structure's response to seismic events, as they help determine how the building will sway and deform under stress. The choice of lateral load pattern can significantly influence the results of nonlinear static procedures, like pushover analysis, which assesses how structures perform beyond their elastic limits.
Life safety: Life safety refers to the measures and design strategies implemented to protect occupants during an emergency, particularly in the event of an earthquake. It focuses on ensuring that structures can withstand seismic forces while allowing for safe evacuation and minimizing the risk of injury or loss of life. This concept is crucial for establishing performance objectives and design criteria for buildings, as well as influencing the development of innovative materials and structural systems.
Linear dynamic analysis: Linear dynamic analysis is a method used to evaluate the response of structures under dynamic loads, assuming that the material behavior remains within the linear elastic range. This analysis helps in predicting how a structure will respond to various loading conditions, like earthquakes, by utilizing mathematical models and simplified equations. It provides insights into the structural performance without accounting for potential material nonlinearity that may occur under extreme conditions.
Linear static analysis: Linear static analysis is a method used to evaluate the structural response of a system under static loads, assuming that material behavior is linear and elastic. This approach simplifies the analysis by not considering the effects of dynamic loads, such as those from earthquakes, which can be critical for structures like shear walls and diaphragms. By applying this analysis, engineers can identify potential weaknesses in structures, allowing for effective design and assessment techniques.
Long-period structures: Long-period structures are buildings or infrastructures that have a natural period of vibration greater than one second, making them more susceptible to lower-frequency seismic waves during an earthquake. These structures tend to sway more compared to shorter buildings, which can lead to larger displacements and forces acting on the structure during seismic events. Understanding their behavior is essential when using nonlinear static procedures to ensure they can withstand such dynamic loads effectively.
Material Properties: Material properties refer to the physical and mechanical characteristics of materials that define their behavior under various conditions, especially when subjected to forces like seismic activity. These properties influence how materials respond to stress, strain, and deformation, which is crucial when assessing the stability and safety of structures during earthquakes. Understanding these properties is essential for engineers to design buildings and infrastructure that can withstand seismic waves and mitigate structural failures.
Near-fault ground motions: Near-fault ground motions are seismic waves that occur in close proximity to a fault during an earthquake, typically characterized by strong shaking and unique ground motion patterns. These motions can significantly impact structures due to the high levels of acceleration and velocity they produce, which are often not adequately represented in traditional seismic design procedures. Understanding these motions is essential for evaluating the performance of buildings and other infrastructures in earthquake-prone areas.
Nonlinear dynamic analysis: Nonlinear dynamic analysis refers to the evaluation of structural response under time-varying loads, particularly seismic forces, considering the inelastic behavior of materials and structural components. This approach captures the complex interactions between a structure and seismic waves, allowing engineers to assess performance beyond elastic limits. It connects to various essential concepts, such as the incremental dynamic analysis method, which systematically evaluates a structure's response over increasing ground motion intensities, and detailing requirements that ensure ductile behavior during extreme loading events.
Nonlinear static procedures: Nonlinear static procedures are analytical methods used to evaluate the seismic performance of structures by applying lateral forces in a controlled manner, typically through a pushover analysis. These procedures account for the material and geometric nonlinearities of a structure, providing insight into how it will respond under earthquake loading. This approach helps engineers assess the capacity of a structure, identify potential weak points, and improve its overall design for better safety during seismic events.
P-delta effects: P-delta effects refer to the additional moments and forces in a structure that arise due to the displacement of the structure's center of mass during lateral loading, such as during an earthquake. This effect occurs when the lateral displacements cause vertical loads to create secondary moments, which can lead to increased demand on structural elements and affect their stability. Understanding p-delta effects is crucial for accurately analyzing structural performance, especially when using nonlinear static procedures and when designing supplemental damping devices.
Performance points: Performance points are specific indicators used in structural engineering to assess the expected performance of a building or structure under various loading conditions, particularly seismic loads. They serve as benchmarks in nonlinear static procedures, allowing engineers to evaluate how a structure will respond during an earthquake by identifying key points on a load-displacement curve that correspond to different levels of structural performance, such as elastic, yielding, and ultimate failure.
Performance-based seismic design: Performance-based seismic design is an approach that focuses on evaluating and ensuring a structure's performance during seismic events, based on defined performance objectives. This method takes into account the expected behavior of a building under various earthquake scenarios, allowing for the consideration of factors like damage limitation and occupant safety rather than merely meeting code requirements. It emphasizes understanding how structures respond to seismic forces, which helps engineers make informed decisions about design and retrofitting.
Plastic hinge: A plastic hinge is a localized region in a structural element where yielding occurs due to applied loads, allowing for rotation and redistribution of moments without significant increase in overall load. This concept is crucial in understanding how structures behave under extreme conditions, such as seismic events, as it helps to predict failure mechanisms and enhance ductility in design.
Pushover analysis: Pushover analysis is a nonlinear static analysis method used to evaluate the seismic performance of structures by applying a gradual lateral load until failure occurs. This technique helps engineers understand how a structure will respond to seismic forces, identifying potential weaknesses and assessing ductility, which is essential for effective seismic design.
Roof displacement: Roof displacement refers to the horizontal movement experienced at the roof level of a structure during seismic events. This term is crucial for understanding how buildings respond to earthquakes, as it directly affects the overall stability and integrity of a structure. Accurately measuring and analyzing roof displacement is essential in assessing the performance of buildings under seismic loads and informs the design and retrofitting processes necessary for earthquake resilience.
Shear failure: Shear failure refers to the failure of a structural element due to shear stress exceeding the material's shear strength. This type of failure is often critical in the context of structural integrity during seismic events, where lateral forces can cause significant displacement and stress in materials. Understanding shear failure is essential for analyzing past structural failures and for implementing effective design strategies, particularly in nonlinear static analysis methods like pushover analysis.
Soft story: A soft story refers to a building design feature characterized by a ground floor that is significantly more flexible than the upper floors, often due to large openings like windows or garage doors. This design can compromise the structural integrity of the building during an earthquake, making it more vulnerable to damage or collapse. Understanding soft stories is crucial in assessing building performance under seismic loads, especially when using nonlinear static procedures such as pushover analysis.
Stress-strain relationships: Stress-strain relationships describe how materials deform under applied loads, illustrating the relationship between stress (force per unit area) and strain (deformation) in materials. This relationship is crucial for understanding material behavior during loading conditions, particularly in nonlinear static procedures like pushover analysis, where the actual response of structures to seismic forces is assessed, beyond the linear elastic range.
Structural model: A structural model is a mathematical representation that describes the behavior and characteristics of a physical structure under various loads and conditions. It serves as a crucial tool in analyzing how structures respond to forces such as gravity, wind, and seismic activity, allowing engineers to predict performance and ensure safety. In the context of nonlinear static procedures like pushover analysis, a structural model helps assess how a building will behave as it is pushed beyond its elastic limits, providing insights into potential failure modes and design improvements.
Time-History Analysis: Time-history analysis is a method used in earthquake engineering to assess the dynamic response of structures to seismic events by applying recorded ground motion data over time. This approach allows engineers to capture the effects of varying intensity and frequency of seismic forces on structures, providing insights into their behavior during actual earthquake scenarios.
Torsional response: Torsional response refers to the twisting or rotational movement of a structure when subjected to lateral loads, such as those from earthquakes. This phenomenon can significantly affect the structural performance and stability during seismic events, as different parts of the structure may experience varying degrees of motion, leading to potential damage. Understanding torsional response is crucial when analyzing structures using nonlinear static procedures, as it helps in predicting how a building will behave under seismic forces.