A reinforced concrete beam 230 mm wide is to carry load 40 KN/m. The beam is simply supported on a span of 8 m. Design a section when: - 1. Depth is not restricted. - 2. Effective depth is restricted to 500 mm -

Use $M_{20}$ grade of concrete $F_{e415}$ grade of steel

Case 1: Depth is not restricted

$B.M=\frac{wl^2}{8}=\frac{40{\times}8^2}{8}=320KNm \\ M_u=1.5{\times}320=480KNm \\ B=230 \ mm \\ M_{u \max}=0.138 f_ckbd^2 \\ 480{\times}10^2=0.138{\times}20{\times}230{\times}d^2 \\ d=869.56 \ mm \\ Ast_x=\frac{0.5f_ckbd}{f_y}{\times}\bigg(1-\sqrt{1-\frac{4.6M_u}{f_ckbd^2}}\bigg) \\ \frac{0.5{\times}20{\times}230{\times}869.5}{415}{\times}\bigg(1-\sqrt{1-\frac{4.6{\times}480{\times}10^6}{20{\times}230{\times}869.5}}\bigg) \\ Ast_x=1907.13 \ mm^2 \\ Provide \ 4-25 \ mm \ {\phi} \\ Ast_p=1963 \ mm^2$

Case 2:-Effective depth is restricted to 500 …