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A509.2.1 Determination of the Effective Stiffness
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A509.2.1.1 General
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  

A509.2.1.2 Effective Stiffness of Infills
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.
A509.2.1.3 Model of Infill
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.
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