Transformed Sections and Cracked Moment of Inertia

[@PremKumar-ky7gl]

Thank you very much sir, this is a great work. Thanks alot

[@liamjackson1509]

Sir, please let me know the derivation how it becomes nAs and significance of modular ratio n....

[@StructuresProfH]

Reinforced concrete is a composite of concrete and steel. When we examine the stiffness of the section, for example when computing deflections, we are generally interested in the elastic modulus E multiplied by the moment of inertia I. However, we have two material with different modulus: steel Es and concrete Ec… so what do we use? To get around this, I can convert (or transform) my steel into an equivalent area of concrete. Steel has a higher modulus than concrete, and we represent this with the ratio n = Es/Ec. The transformed area nAs is the steel area converted into a larger area of concrete such that the total stiffness is unchanged. Using this transformed area, I can treat my section as though it’s 100% concrete, meaning I can now find a moment of inertia I with modulus Ec using traditional, single-material beam bending theory.