Structures’ response: - Linear (constant stiffness) - Nonlinear (variable stiffness) →Structural Analysis Approaches: - Linear static (ELF) ((least accurate; least complex) p ) - Linear dynamic (response spectra) - Nonlinear static (pushover) - Nonlinear dynamic (time history) (most accurate; most complex)
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Pushover analysis: Applying a force distribution to the structure in an incremental fashion while monitoring the occurrence of nonlinear behavior and plotting the base shear (Vb) versus control node displacement (uN).
compromise the simplicity of linear static approaches and accuracy of nonlinear dynamic methods.
1- Nonlinearity sources: - Geometrical (P-Delta effects) (consider or not: codes) - Material (too many material’s behavior models) 2- Nonlinearity modeling: - Concentrated
- Distributed
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Plastic hinge properties: - running section analysis and coming up with M-φ curves
Plastic hinge properties: - using codes’ tabulated properties
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3- Lateral load pattern: - a single concentrated force at the top (good for one-story buildings) - in proportion to the standard code procedure: Fx wxhx / wxhx V
- in proportion to the product of story masses and predominant mode shape of the elastic model of the structure Fx wxx / wxx V
4- Control node: - For common buildings, the control node could be selected as roof (top) story node h l i is i stoppedd when h the h structure reaches: h - Pushover analysis pre-defined displacement or ultimate capacity
5- Gravity loads should be applied prior to the application of lateral loads
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6- Check at performance point : The global response of the structure and individual component deformations are compared to limits in li ht off the th specific ifi performance f l off the th system t light goals
Using SAP2000 for Pushover Analysis We will use the same frame (elastic beams), just modify dead loads:
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1- Run Modal Analysis
(1 )
1 .0 0 .7 5 9 0 .3 4 5
Select lateral load pattern:
Fx
1 0 0 0 759 345
k ip s
2- Lateral Load Case
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3- Modify Dead Load Case
3- Define Push Load Case
1 2
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3- Define Push Load Case
1
2
4- Assign Plastic Hinges Select column elements:
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4- Assign Plastic Hinges
4- Assign Plastic Hinges Select beam elements:
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5- Run
6- Results Output Display displacement:
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6- Results Output Display pushover curve:
7- Checking Hinges Status Looking for 0.5 ft roof displacement:
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7- Checking Hinges Status
At 0.5 ft roof displacement: the performance level of the system is Collapse Prevention (CP)
