Modeling Diaphragms in 2D Models with Linear and Nonlinear Elements

Transcription

1 Modeling Diaphrags in 2D Models with Linear and Nonlinear Eleents Vesna Terzic UC Berkeley October 2011

2 Introduction to the proble (1) Floor diaphrag need to be axially rigid to assure proper distribution of seisic forces to all lateral force resisting eleents (coluns and walls) Coon odeling approach for frae structures is to represent the structural coponents (beas and coluns) by line eleents located at the original eber centerlines and having crosssectional properties equal to those of coponents Coon way to odel the effect of a rigid diaphrag at a floor level is by iposing rigid constraints on all nodes of that floor level and thus enforcing the sae lateral displaceents of all nodes at the floor level These constrains enforce condition of zero axial strain on eleents (i.e., eleent centerline) that are part of that floor level

3 Introduction to the proble (2) For sections where the neutral axis does not shift as a consequence of bending in the bea, axial strains at eleent s centerlines are zero, and thus rigid constraints can be applied to odel a rigid diaphrag (e.g. steel sections, elastic aterials) For nonlinear-bea colun eleents with RC fiber section where the neutral axis shifts due to bending in the bea axial strains at eleent s centerlines are no longer zero. Thus, rigid constraints that enforce condition of zero axial strain on eleents will change the response of the frae

4 Case study The effect of rigid constraints on a force-based bea-colun eleent will be deonstrated on a portal frae considering three different types of sections: Elastic steel section Nonlinear steel section Nonlinear concrete section Force-based bea-colun eleent is chosen for this case study as it is the ost widely used for odeling frae eleents. However, all of conclusions derived fro this study hold for displaceent-based bea-colun eleent.

5 Exaple: portal frae Two types of analysis: Pushover (up to displaceent of 5 in.) Tie history analysis P (180) P (180) RC sections Colun Bea H 3 (3) (1) (2) Steel sections Colun: W14x257 Bea: W24x68

6 Materials Elastic steel section: Elastic aterial Nonlinear steel section: Steel02 aterial Nonlinear concrete section: Concrete01 for core and cover and Steel02 for reinforceent Concrete01 Stress Es Steel02 Stress Elastic Fy b Es Strain Strain

7 Constraints The rigid constraints are iposed using equaldof coand in OpenSees # $asternode $slavenode $dof equaldof

8 Elastic steel fiber cross-section: Pushover analysis H/2 3 4 H/2 tieseries Linear 1 pattern Plain 2 1 { load load } Maxiu displaceent: 5.0 in Constraints deforation of the bea force in the bea Bending oents in the bea Shear forces in the coluns No Yes

9 Elastic steel fiber cross-section: Tie history analysis 3 4 tieseries Path 2 -dt filepath A10000.acc -factor $G pattern UniforExcitation 2 1 -accel 2 Maxiu displaceent: 5.3 in Constraints deforation of the bea force in the bea Bending oents in the bea Shear forces in the coluns No Yes

10 Nonlinear steel fiber cross-section: Pushover analysis H/2 3 4 H/2 tieseries Linear 1 pattern Plain 2 1 { load load } Maxiu displaceent: 5.0 in Constraints deforation of the bea force in the bea Bending oents in the bea Shear forces in the coluns No Yes e

11 Nonlinear steel fiber cross-section: Tie history analysis 3 4 tieseries Path 2 -dt filepath A10000.acc -factor $G pattern UniforExcitation 2 1 -accel 2 Maxiu displaceent: 4.0 in Constraints deforation of the bea force in the bea Bending oents in the bea Shear forces in the coluns No Yes e

12 Nonlinear RC fiber cross-section: Pushover analysis H/2 3 4 H/2 tieseries Linear 1 pattern Plain 2 1 { load load } Maxiu displaceent: 5.0 in Constraints deforation of the bea force in the bea Bending oents in the bea Shear forces in the coluns No Yes

13 Nonlinear RC fiber cross-section: Tie history analysis 3 4 tieseries Path 2 -dt filepath A10000.acc -factor $G pattern UniforExcitation 2 1 -accel 2 Constr. Max. disp at nodes 3 & 4 deforation of the bea force in the bea Bending oents in the bea Shear forces in the coluns No Yes

14 Nonlinear RC fiber cross-section: Tie history analysis 3 4 tieseries Path 2 -dt filepath A10000.acc -factor $G pattern UniforExcitation 2 1 -accel 2 All eleents have the sae (rectangular 16x24) cross-section Constr. Max. disp at nodes 3 & 4 deforation of the bea force in the bea Bending oents in the bea Shear forces in the coluns No Yes

15 Suary and conclusions To odel the effect of a diaphrag on a 2D frae rigid constraints can be used for elastic and steel eleents Presence of rigid constraints in concrete nonlinear eleents will induce unrealistic axial force and possibly change banding oents in the bea and shear forces in the coluns. Concrete eleents have very high axial stiffness (solid sections) and as such ay be capable of transferring the seisic forces to coluns. However, this has to be checked for each specific odel.