Question

Considering modular ratio as 13, grade of concrete as M20 and grade of steel as 415, what is the ratio of balanced depth of neutral axis as per working stress method to the balanced depth of neutral axis as per limit state method?

• A. $\frac{12}{7}$
• B. $\frac{11}{3}$
• C. $\frac{7}{12}$
• D. $\frac{3}{11}$

Answer 1

The correct option is C $\frac{7}{12}$

$\begin{array}{cc}& \text{As per working stress method balanced depth of}\\ & \text{neutral axis is given by}\\ x_c& =\left(\frac{mc}{t+mc}\right)\times d\\ & \text{For M20 concrete,}c=7N/m{m}^2\text{and for}\\ Fe415,t& =230N/m{m}^2\\ \therefore x_c& =\left(\frac{13\times 7}{230+13\times 7}\right)\times d\\ \Rightarrow x_c& =0.28d\\ & \text{As per limit state method, for}Fe415\\ x_{u,lim}& =0.48d\\ \therefore \frac{x_c}{x_{u,lim}}& =\frac{0.28d}{0.48d}\\ \Rightarrow \frac{x_c}{x-u,lim}& =\frac{7}{12}\end{array}$