Using SAP2000 Software Package inUsing SAP2000 Software Package in Earthquake Engineering (Part II: Pushover)

k /fSame frame but different loading

QD = 4.5 kips/ft

QD = 10.5 kips/ft

Q 10 5 ki /fQD = 10.5 kips/ft

Loads on structures:- Static (e.g. self-weight)Static (e.g. self weight)- Dynamic (e.g. earthquake)

Structures’ response:Structures response:- Linear (constant stiffness)- Nonlinear (variable stiffness)

→Structural Analysis Approaches:Linear static (ELF)- Linear static (ELF)(least accurate; least complex)

- Linear dynamic (response spectra)Linear dynamic (response spectra)- Nonlinear static (pushover)- Nonlinear dynamic (time history)y ( y)

(most accurate; most complex)

Pushover analysis:A l i f di ib if di ib i h iApplying a force distributionforce distribution to the structure in an incremental fashion while monitoring the occurrence of nonlinear behaviornonlinear behavior and plotting theoccurrence of nonlinear behaviornonlinear behavior and plotting the base shear (Vb) versus control nodecontrol node displacement (u )(uN).

compromise the simplicity of linear static approaches and accuracy of nonlinear dynamic methodsand accuracy of nonlinear dynamic methods.

1- Nonlinearity sources: Geometrical (P Delta effects)- Geometrical (P-Delta effects)(consider or not: codes)

- MaterialMaterial(too many material’s behavior models)

2- Nonlinearity modeling: - Concentrated - Distributed

Plastic hinge properties: running section analysis and coming up with M φ curves- running section analysis and coming up with M-φ curves

Plastic hinge properties: - using codes’ tabulated properties

3- Lateral load pattern:3- Lateral load pattern: - a single concentrated force at the top(good for one-story buildings)(good for one story buildings)

- in proportion to the standard code procedure:p p p

/x x x x xF w h w h V

- in proportion to the product of story masses and predominant mode shape of the elastic model of the structure

/x x x x xF w w V

4- Control node: - For common buildings, the control node could be selected as roof (top) story node

- Pushover analysis is stopped when the structure reaches:pre-defined displacementp porultimate capacity

5 Gravity loads should be applied prior to the5- Gravity loads should be applied prior to the application of lateral loads

6 Check at performance point :6- Check at performance point : The global response of the structure and individual component deformations are compared to limits incomponent deformations are compared to limits in light of the specific performance goals of the system

Using SAP2000 for Pushover Analysis

We will use the same frame (elastic beams), just modify dead loads:

1- Run Modal Analysis

( 1 )

1 . 00 7 5 9

( 1 ) 0 . 7 5 90 . 3 4 5

Select lateral load pattern:

1 0 0 07 5 9F k i p s

7 5 9

3 4 5xF k i p s

2- Lateral Load Case

3- Modify Dead Load Case

3- Define Push Load Case

1

2

3- Define Push Load Case

1 2

4- Assign Plastic HingesSelect column elements:Select column elements:

4- Assign Plastic Hinges

4- Assign Plastic HingesSelect beam elements:Select beam elements:

5- Run

6- Results OutputDisplay displacement:

6- Results OutputDisplay pushover curve:

7- Checking Hinges StatusLooking for 0.5 ft roof displacement:

7- Checking Hinges Status

At 0.5 ft roof displacement: the performance level p pof the system is Collapse Prevention (CP)