32.11. Pushover Analysis and Capacity Spectrum Method

Static nonlinear analysis technique. Applies lateral loads incrementally until target displacement or collapse.

Pushover analysis is a method used to evaluate the structural performance of buildings, particularly under seismic loads. This technique applies horizontal forces to a structure in a step-wise manner. These forces are increased until the structure reaches a defined target displacement or begins to fail. This approach allows engineers to observe how the building behaves under varying loads, identifying points of weakness and potential failure modes.

Imagine a child pushing a swing. Initially, the swing moves back and forth easily. However, as the child pushes harder and more frequently, the swing begins to move in more extreme arcs. Eventually, if pushed too hard, the swing may break or fail to function as intended. Similarly, in pushover analysis, engineers gradually apply increasing loads to see how the building can handle stress until it can no longer maintain its structural integrity.

Base shear vs top displacement. Reflects structural stiffness degradation.

The capacity curve is a graphical representation that shows the relationship between the base shear (the total horizontal force acting at the foundation) and the top displacement (the amount the building moves or sways at the top). As the structure is pushed and subjected to increasing loads, this curve illustrates how the building's stiffness may degrade due to yielding of materials or other factors. Understanding this curve is crucial for assessing how much load the structure can withstand before failure.

Consider a rubber band. When you slightly stretch it, it easily returns to its original shape. As you stretch it more and more, it can start to lose its elasticity and won’t return to the same length. If you stretch it too far, it will snap. The capacity curve is like observing how much force you can apply to the rubber band before it either deforms or breaks.

Intersection of demand and capacity curves. Used in performance-based design.

In the context of pushover analysis, the performance point is a critical intersection on the graph where the capacity curve meets the demand curve. The demand curve represents the expected loads during an earthquake, while the capacity curve shows how much load the structure can withstand. The performance point signifies the maximum load the structure can handle before significant damage occurs. This point is essential in performance-based design, as it helps engineers ensure that buildings can withstand specific levels of seismic activity.

Think of a shelf that holds a collection of books. The strength of the shelf (capacity) can be represented by how heavy the books are. If you keep adding books (demand), there will be a point where the shelf will bend or break. The performance point is the moment when the weight of the books matches the shelf's limit. Engineers want to ensure that the weight of the books (earthquake forces) does not exceed the shelf's limit.

Valid mainly for low- to mid-rise buildings. Assumes invariant mode shapes.

While pushover analysis is a valuable method, it has limitations. Primarily, it is most effective for low- to mid-rise buildings, where the assumptions made about structural behavior are more likely to hold true. One major assumption is that the mode shapes (the way a building vibrates) do not change during the analysis, which may not be true in large, complex structures. Therefore, while it can provide useful insights, results should be interpreted with caution, especially in tall or irregular structures.

Consider a team of runners in a relay race. If the team is made up of people of similar heights and builds, they might perform well based on their training and practice. However, if one member suddenly changes to a much taller or shorter runner, the dynamics change, and the team's performance may suffer. Similarly, pushover analysis assumes uniformity in how buildings respond to loads, which may not be accurate for all structures.

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