Mo, multiply both sides of the equation by 6/d. Since both sides of the equation are multiplied by the same term the value of the equation does not change. Cancel equal terms on the left hand side, this leaves b × d or the area on the left hand side and (6 × M)/(Fb × d) on the right side.
bd²/6 = M/Fbb × d ×
d/
6 ×
6/
d = M/Fb × 6/d ... cancel equal terms on the left side
bd = (M × 6)/(Fb × d) ... collect multiplications and divisions on the right side
I played a few more games with the algebra ... whenever you are ready for them here are a some more formulas for a simply supported beam, rectangular in cross section. Since the "Edit" function isn't enabled I'm linking to an image file; this way if there are any boo-boos I can fix them.
The units are as I prefer to use them but there are other options ... kips, kN, lb × ft, etc. I find it's easiest to kill two birds with one stone and find a value for
S which satisfies both bending and shear, then check the deflection.
Solve for
M and
V,
Fb and
Fv are found in tables.
Test drive them, have fun ...
