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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 force-displacement relationship of the element or system. The secant stiffness shall be measured as the slope from the origin to the intersection of the force-displacement relationship at the assumed displacement. The force-displacement relationship shall be determined by a nonlinear analysis. The force-displacement 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 A5-5, A5-6 and A5-7. The estimates shall be revised if the ratio used exceeds the ratio calculated by more than 20 percent. (Equation A5-5)

where: (Equation A5-6) 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 force-displacement relationship of the frame-infill system from the frame-only 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 beam-column joints. The secant stiffness of the force-displacement 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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