The plastic rotation demand is calculated with the yield rotation calculated using the displaced axis rotation and the moment-curvature analysis when performing the linear performance analysis.
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ICONS
E = Concrete modulus of elasticity
h = Section height
I = Moment of inertia
L p = Plastic hinge length
l c = Element net opening
M y = Effective yield moment
M yi = Effective yield momentat i end
M yj = Effective yield moment at j end
Δ = Element translation between nodes
ϕ y = Flow curvature
ϕ t = Total curvature
θ p =Plastic rotation demand
θ i = i joint rotation
θ j = j node rotation
θ y = flow rotation
θ yi = flow rotation at end i
θ yj = flow rotation at end j
θ k = displaced axis rotation
θ ki = displaced axis rotation at end i
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In the above equation , ki is the axis rotation of the element at the i end and is calculated from Equation (15A.1) . The value of ki is obtained by subtracting Δ / l c from the value obtained by dividing the translation between the element nodes by the element net span, and the rotation value of the node i . In this way , the value of θ ki is obtained with the values obtained as a result of the linear calculation.
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The θ yi value given in Equation (15A.2) is the yield rotation for frame elements and is calculated from Equation (15A.3) . In these equations, M yi and M yj are the effective yield moments at the ends i and j, respectively, and are calculated by the moment-curvature relationship derived from the section material model and the reinforcement layout. EI is the flexural stiffness of the unbroken section and is calculated from the section geometry.
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Evaluation and Design According to Strain of existing buildings as seen (ŞGDT) in determining the approach to seismic performance and linear calculation method used plastic rotation demand θ p , the value is calculated by the approximate expression obtained in a linear method. In this case, when the nonlinear seismic analysis methods applied plastic made by plastic hinge rotation θ p θ obtained by the linear method with p value to show affinity to a specific order but it will be the same.
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