Q1: If A_c, A_sc and A are areas of concrete, longitudinal steel and section of a R.C.C. column and m and σ_c are the modular ratio and maximum stress in the configuration of concrete, the strength of column is

ANS:D - all the above.

1. σcAc + mσcAsc: This expression represents the total strength of the R.C.C. column by considering the contributions from both the concrete and longitudinal steel reinforcement.
   • σcAc: This term represents the contribution of the concrete to the strength of the column. Here, σc is the maximum stress in the concrete, and Ac is the cross-sectional area of the concrete.
   • mσcAsc: This term represents the contribution of the longitudinal steel reinforcement to the strength of the column. Here, σc is again the maximum stress in the concrete, Asc is the cross-sectional area of the longitudinal steel, and m is the modular ratio which accounts for the difference in modulus of elasticity between concrete and steel.
2. σc(A - Asc) + mσcAsc: This expression incorrectly subtracts the area of longitudinal steel from the total area of the column, which is not an accurate representation of the strength of the column. The strength of the column is not simply the contribution of the concrete minus the contribution of the longitudinal steel.
3. σc[A + (m - 1)Asc]: This expression applies the modular ratio to the area of the longitudinal steel, which is not standard practice. The modular ratio accounts for the difference in modulus of elasticity between concrete and steel, but it is not directly applied to the area of steel. This option does not accurately represent the strength of the column.