Pushover Load Analysis
Typically the first pushover load case is used to apply gravity load and then subsequent lateral pushover load cases are specified to start from the final conditions of the gravity pushover. Pushover load cases can be force controlled, that is, pushed to a certain defined force level, or they can be displacement controlled, that is, pushed to a specified displacement. Typically a gravity load pushover is force controlled and lateral pushovers are displacement controlled. ETABS allows the distribution of lateral force used in the pushover to be based on a uniform acceleration in a specified direction, a specified mode shape, or a user-defined static load case.
Figure 2: Frame Hinge Property input in Etabs
Run the basic static analysis and,
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ϵ u= 0.003+0.002(b/z)+0.2.ρs
The moment and curvature is noted at this instance.
For each extreme compression strain varying from zero to ultimate strain, moment curvature relationship is established.
The moment curvature curves is converted into idealized bilinear curves
Figure 7: Stress blocks at different extreme compression fibre strain
Figure 8: Moment curvature curve
2.6.5 Moment-Rotation relations:
The input of nonlinearity in the modelling of hinge location is the moment rotation values. The moment curvature found out from the program has to be converted into moment rotation relationship. The total rotation of the element at the ultimate moment is equal to the sum of rotation of element at the yielding moment and plastic rotation. θu = θy + θp θy and θp are yield and plastic rotations calculated from yield and ultimate curvatures as shown below.
The yield rotation can be calculated using slope deflection equations. The yield rotation is given as
Plastic rotation of the section
Where =Ultimate curvature
=Yield curvature
=0.8*k1*k3*(z/d)*c (from ATC
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These documents define force-deformation criteria for hinges used in pushover analysis. As shown in Figure 2 , five points labeled A, B, C, D, and E are used to define the force deflection behavior of the hinge and three points labeled IO, LS and CP are used to define the acceptance criteria for the hinge. (IO, LS and CP stand for Immediate Occupancy, Life Safety and Collapse Prevention respectively.) The values assigned to each of these points vary depending on the type of member as well as many other parameters defined in the ATC-40 and FEMA-273
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