Moment of Resistance of the Section:

Let $M_r$ be the moment of resistance to Section

Let $M_w$ and $M_s$ be moments resistance of wood and steel.

Let the wooden joist be b units & d units deep.

Let each steel plate be 't' unit thick and d units deep.

Let $f_w$ and $f_s$ be the extreme stress in wood and steel.

$M_r =M_w + M_s$ where M- moment, p- bending stress, I-inertia, y-depth of neutral axis.

$\frac{M}{I}=\frac{p}{y}$

$M=\frac{pI}{y}$

$M_r=\frac{f_w*I_w}{y_w}+\frac{f_s*I_s}{y_s}$

=$f_w*\frac{bd^3}{12}*\frac{1}{\frac{d}{2}}+f_s*\frac{2t*d^3}{12}*\frac{1}{\frac{d}{2}}$

$\frac{1}{6}*f_w*bd^2+2*\frac{1}{6}*(f_w*m)td^2$

($m=\frac{f_s}{f_w}$ where m-modular ratio)

$M_r=\frac{1}{6}f_w(b+2mt)d^2$

Hence the moment of the resistance of the section is the same as that of a wooden member of breadth b+m(2t) and depth d.

This rectangular section b+m(2t) units wide and d units deep is called the equivalent wooden section.

The moment of resistance of the flitched beam section may, therefore, be determined by considering the equivalent wooden section. In some cases however the moments of resistance of the individual components may also be computed and the total moment of resistance may be determined.

• Hence the moment of the resistance of the section is the same as that of a wooden member of breadth b+m(2t) and depth d.
• This rectangular section b+m(2t) units wide and d units deep is called the equivalent wooden section.
• The moment of resistance of the flitched beam section may, therefore, be determined by considering the equivalent wooden section. In some cases however the moments of resistance of the individual components may also be computed and the total moment of resistance may be determined.