# Nonlinear Static (Pushover) Analysis

Nonlinear static pushover analysis capabilities are provided in the Advanced  version of CSiBridge only. The nonlinear behavior occurs in discrete user-defined hinges. Currently, hinges can be introduced into frame objects only and assigned at any location along the frame object. Uncoupled moment, torsion, axial force and shear hinges are available. There is also a coupled P-M2-M3 hinge that yields based on the interaction of axial force and bending moments at the hinge location. More than one type of hinge can exist at the same location; for example, both an M3 (moment) and a V2 (shear) hinge may be assigned to the same end of a frame object. For more information about hinges, see Hinge Properties.

A pushover analysis can consist of more than one pushover load case. Each pushover load case can have a different distribution of load on the structure. For example, a typical pushover analysis might consist of three pushover load cases. The first would apply gravity load to the structure, the second would apply one distribution of lateral load over the height of the structure, and the third would apply another distribution of lateral load over the height of the structure. There are four different methods of describing the distribution of load on the structure for a pushover load case:

1. A uniform acceleration can be automatically applied. In that case, the lateral force automatically applied at each node is proportional to the mass tributary to that node.

2. A lateral force that is proportional to the product of a specified mode shape times its circular frequency squared (w2) times the mass tributary to a node can be automatically applied at each node. The user may specify the mode shape to be used in that instance.

3. An arbitrary static load pattern may be defined.

4. Any of the methods described in 1, 2 and 3 can be combined.

Several types of output can be obtained from the nonlinear static pushover analysis:

1. Base shear versus displacement at a specified control joint can be plotted.

2. Base shear versus displacement at a specified control joint can be plotted in the ADRS format where the vertical axis is spectral acceleration and the horizontal axis is spectral displacement. The demand spectra can be superimposed on that plot.

3. The sequence of hinge formation and the color-coded state of each hinge can be viewed graphically, on a step-by-step basis, for each step of the pushover.

4. The member forces can be viewed graphically, on a step-by-step basis, for each step of the analysis.

5. Tabulated values of base shear versus displacement at each point along the pushover curve, along with tabulations of the number of hinges beyond certain control points on their hinge property force-displacement curve can be viewed on the screen, printed, or saved to a file.

6. Tabulated values of the capacity spectrum (ADRS capacity and demand curves), the effective period and the effective damping can be viewed on the screen, printed, or saved to a file.

The following general sequence of steps is involved in a nonlinear static pushover analysis:

1. Define arbitrary static load patterns, if needed, for use in the pushover analysis. Note that the program also has built-in capability to define the distribution of lateral load over the height of the structure based on both uniform acceleration and mode shapes.

2. Define the pushover load cases.

3. Run the pushover analysis by selecting a static nonlinear load case on the Set Load Cases to Run form. The load case will be available only if there is at least one frame object with a hinge property assigned to it, and there is at least one pushover load case defined. If frame objects are specified to be designed by the program, this design automatically will be performed before the pushover analysis routine begins.

4. Review the pushover results.

5. If necessary, revise the model and repeat steps 1through 5.