// CODE SNIPPET
A509.2 PseudoNonlinear Dynamic Analysis Procedure
JUMP TO FULL CODE CHAPTER
Structures shall be analyzed for seismic forces acting concurrently on the orthogonal axes of the structure. The effects of the loading on two orthogonal axes shall be combined by SRSS methods. The analysis shall include all torsional effects. Accidental torsional effects need not be considered.
The effective stiffness of concrete and masonry elements or systems shall be calculated as the secant stiffness of the element or system with due consideration of the effects of tensile cracking and compression strain. The secant stiffness shall be taken from the forcedisplacement relationship of the element or system. The secant stiffness shall be measured as the slope from the origin to the intersection of the forcedisplacement relationship at the assumed displacement. The forcedisplacement relationship shall be determined by a nonlinear analysis. The forcedisplacement analysis shall include the calculation of the displacement at which strength degradation begins.
Exception: The initial effective moment of inertia of beams and columns in shear wall or infilled frame buildings may be estimated using Table A508.1. The ratio of effective moment of inertia used for the beams and for the columns shall be verified by Equations A55, A56 and A57. The estimates shall be revised if the ratio used exceeds the ratio calculated by more than 20 percent.
where:
Exception: The initial effective moment of inertia of beams and columns in shear wall or infilled frame buildings may be estimated using Table A508.1. The ratio of effective moment of inertia used for the beams and for the columns shall be verified by Equations A55, A56 and A57. The estimates shall be revised if the ratio used exceeds the ratio calculated by more than 20 percent.
 (Equation A55) 
where:
 (Equation A56) 
and  

The effective stiffness of an infill shall be determined from a nonlinear analysis of the infill and the confining frame. The effect of the infill on the stiffness of the system shall be determined by differentiating the forcedisplacement relationship of the frameinfill system from the frameonly system.
The mathematical model of an infilled frame structure shall include the stiffness effects of the infill as a pair of diagonals in the bays of the frame. The diagonals shall be considered as having concrete properties and only axial loads. Their lines of action shall intersect the beamcolumn joints. The secant stiffness of the forcedisplacement relationship, calculated as prescribed in Section A509.2.1.2, shall be used to determine the effective area of the diagonals. The effective stiffness of the frame shall be determined as specified in Section A509.2.1.1. Other procedures that provide the same effective stiffness for the combination of infill and frame may be used when approved by the building official.
The pseudononlinear dynamic analysis is an iterative response spectrum analysis procedure using effective stiffness as the stiffness of the structural components. The response spectrum analysis shall use the peak dynamic response of all modes having a significant contribution to total structural response. Peak modal responses are calculated using the ordinates of the appropriate response spectrum curve that corresponds to the modal periods. Maximum modal contributions are combined in a statistical manner to obtain an approximate total structural response.
The effective stiffnesses shall be determined by an iterative method. The mathematical model using assumed effective stiffnesses shall be used to calculate dynamic displacements. The effective stiffness of all concrete and masonry elements shall be modified to represent the secant stiffness obtained from the nonlinear forcedisplacement analysis of the element or system at the calculated displacement. A reanalysis of the mathematical model shall be made using the adjusted effective stiffness of existing and supplemental elements and systems until closure of the iterative process is obtained. A difference of 10 percent from the effective stiffness used and that recalculated may be assumed to constitute closure of the iterative process.
The effective stiffnesses shall be determined by an iterative method. The mathematical model using assumed effective stiffnesses shall be used to calculate dynamic displacements. The effective stiffness of all concrete and masonry elements shall be modified to represent the secant stiffness obtained from the nonlinear forcedisplacement analysis of the element or system at the calculated displacement. A reanalysis of the mathematical model shall be made using the adjusted effective stiffness of existing and supplemental elements and systems until closure of the iterative process is obtained. A difference of 10 percent from the effective stiffness used and that recalculated may be assumed to constitute closure of the iterative process.
At least 90 percent of the participating mass of the structure is included in the calculation of response for each principal horizontal direction.
The peak displacements for each mode shall be combined by recognized methods. Modal interaction effects of threedimensional models shall be considered when combining modal maxima.
Related Code Sections
A509.2 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings, PseudoNonlinear Dynamic Analysis Procedure
nonlinear dynamic analysis is an iterative response spectrum analysis procedure using effective stiffness as the stiffness of the structural components. The ...
2010 Existing Building Code of NY > A5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings > A509 Tier 3 Analysis Procedure > A509.2 PseudoNonlinear Dynamic Analysis Procedure
A509.2.1.1 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings, General
at the assumed displacement. The forcedisplacement relationship shall be determined by a nonlinear analysis. The forcedisplacement analysis shall ...
2010 Existing Building Code of NY > A5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings > A509 Tier 3 Analysis Procedure > A509.2 PseudoNonlinear Dynamic Analysis Procedure > A509.2.1 Determination of the Effective Stiffness > A509.2.1.1 General
A509.2.1.3 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings, Model of Infill
the effective area of the diagonals. The effective stiffness of the frame shall be determined as specified in Section A509.2.1.1. Other procedures that provide ...
2010 Existing Building Code of NY > A5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings > A509 Tier 3 Analysis Procedure > A509.2 PseudoNonlinear Dynamic Analysis Procedure > A509.2.1 Determination of the Effective Stiffness > A509.2.1.3 Model of Infill
Section A509 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings, Tier 3 Analysis Procedure
The pseudononlinear dynamic analysis is an iterative response spectrum analysis procedure using effective stiffness ...
2010 Existing Building Code of NY > A5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings > A509 Tier 3 Analysis Procedure
Section A507 Earthquake Hazard Reduction in Existing Concrete Buildings, Tier 3 Analysis Procedure
A Tier 3 evaluation shall be performed using the Nonlinear Static Procedure or Nonlinear Dynamic Procedure of Section 10.3.1.2.2 of ASCE 41. The ...
Existing Building Code 2015 of New York State > A5 Earthquake Hazard Reduction in Existing Concrete Buildings > A507 Tier 3 Analysis Procedure