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The basic seismic analysis procedure uses response spectra that are representative of, but substantially reduced from, the anticipated ground motions. As a result, at the MCER level of ground shaking, structural elements are expected to yield, buckle , or otherwise behave inelastically. In the standard, such design forces are computed by dividing the forces that would be generated in a structure behaving elastically when subjected to the design earthquake ground motion by the response modification coefficient, R, and this design ground motion is taken as two-thirds of the MCER ground motion.
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The energy dissipation resulting from hysteretic behavior can be measured as the area enclosed by the force–deformation curve of the structure as it experiences several cycles of excitation. Some structures have far more energy dissipation capacity than others. The extent of energy dissipation capacity available depends largely on the amount of stiffness and strength degradation the structure undergoes as it experiences repeated cycles of inelastic deformation. Fig. C12.1-2 shows representative load deformation curves for two simple substructures, such as a beam–column assembly in a frame. Hysteretic curve (a) in the figure represents the behavior of substructures that have been detailed for ductile behavior. The substructure can maintain almost all of its strength and stiffness over several large cycles of inelastic deformation. The resulting force–deformation “loops” are quite wide and open, resulting in a large amount of energy dissipation. Hysteretic curve (b) represents the behavior of a substructure that has much less energy dissipation than that for the substructure (a) but has a greater change in response period. The structural response is determined by a combination of energy dissipation and period modification.
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In this equation D , Resistance Redundancy Factor 's is shown. With this coefficient, it is expressed that the yield strength is excessive compared to the design strength.
The concept of ductility is mainly determined by the difference between the temporal displacement and permanent displacement regions in the stress-strain curve of the materials. For example, the following curve obtained in the base section as a result of the static cyclic loading test (push - pull) on a reinforced concrete cantilever column shows the typical nonlinear strength-displacement behavior.
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Under the effect of an earthquake, structural elements behave similar to the curve above. In order to design the structure ductile, this displacement capability, which the elements can do, is used. For example, the behavior shown with the dashed line in the figure below represents a building with a brittle design and the continuous line symbolizes the ductile building.
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The basis of the calculation method used for Design Based on Strength is the ductile behavior of the carrier system and the reduction of earthquake loads. As you will see in the curve below, the nonlinear behavior of the structure is translated into a conjugate linear system. The assumption is based on the assumption that the area under both curves is equal, that is, the building can absorb equal energy.
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Sae represents the elastic spectral acceleration and m represents the weight of the structure.
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Yield Strength Reduction Coefficient R y (µk, T) , according to the rule of equal displacement
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For structural systems with high rigidity, it was taken in TBDY 2018 as follows:
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For the section design with the bearing capacity approach in Design Based on Strength , the Earthquake Load Reduction Coefficient Ra (T ) corresponding to a certain fixed ductility capacity selected for each type of structural system is defined as follows ;
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As a result, the Earthquake Load Reduction Coefficient R (T a ) is expressed by the following equations to be used in practice :
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