Question $4-$Effective cracked stiffnesses for reinforced concrete elements

Effective stiffness is a crucial concept in modeling reinforced concrete structures, especially for seismic analysis. It accounts for the nonlinear behavior of concrete and steel, particularly when cracking occurs. Different countries and codes employ varying approaches to determine effective stiffness. While some codes use a uniform reduction factor for both beams and columns, others differentiate between the two. For instance, Eurocode $8$ applies distinct cracked stiffness modifiers for beams and columns, recognizing their different load and deformation characteristics. This nuanced approach aims to capture the complex behavior of reinforced concrete structures more accurately, leading to more reliable seismic assessments.

Figure $5$:

cracked beam sketch under bending action

a$-$ A multi$-$story column in a tall building will have a higher stiffness at the base compared to the roof, right or wrong? Explain your answer!

b$-$ Turkish standard TS $500$ entitled "Requirements for Design and Construction of Reinforced Concrete Structures" requires a reduction in the gross moment of inertia $I_g$ by $20\%$ in columns and $60\%$ reduction of Ig in beams, right or wrong? Explain your answer!

c$-$ Different standards and codes worlwide provide the same reduction factors for modifying the stiffness of reinforced concrete elements, right or wrong? Explain your answer!