Answer to Question #274361 in Mechanical Engineering for radhe

Question

A rolled steel Joist of I-Section has flange length of 300 mm. wide and 20 mm thick with a web thickness of 20 mm. and overall depth of I-Section is 600 mm. If this beam carries a UDL of 40 KN/m over the simply supported beam of span 10 m, find the maximum stress produced in the beam.                                                                                             

Answer 1

From bending equation

$\frac{M}{I}=\frac{\sigma}{y}=\frac{E}{R}$

$\bar{y}=\frac{\sum{y_iA_i}}{\sum{A_i}}=\frac{6960000}{23200}=300mm$

$\sum F_y=0$

$R_A+R_B=400$

$\sum{M_A}=0$

$10R_B=2000\implies R_B=200$

R_A=400-200=200

Maximum moment occurs at C

${M_C}=200*5-40*5*\frac{5}{2}$

M_C=500

$I_{xx}=1.303*10^9$

$\frac{M_{max}}{I}=\frac{\sigma_{max}}{\bar{y}}$

$\sigma_{max}=\frac{M_{max}*\bar{y}}{I}$

=$\frac{500*10^3*10^3*300}{1.303*10^9}$

=115.118N/mm²