A Douglas Fir$-$Larch No$.1$ rectangular wood beam with a span of $14$ feet is simply supported at

both ends. The beam is subjected to a uniform load of $450l\frac{b}{f}t($including the self$-$weight of the

beam$).$ The cross$-$section of the beam is $6$ inches wide by $10$ inches deep.

Material properties:

Allowable bending stress $Fb=1,200$ psi

Allowable shear stress Fv$=180$ psi

a$.$ Determine whether the beam is adequate for both bending and shear.

To do

Calculate maximum bending moment $=M=w\frac{L^2}{8}$

Solve for $S,S=b\frac{d^2}{6}$

Calculate Actual bending stress $=fb=\frac{M}{S}$ and compare to Allowable bending stress$($Fb$)$ given

Write your conclusion

Calculate maximum shear $=V=w\frac{L}{2}$

Solve for $A,A=bd$

Calculate Actual shear stress $=fv=1\mathrm{.}5\frac{V}{A}$ and compare to Allowable shear $($Fv$)$ given

Write your conclusion