A contractor has in her construction yard $212$ Douglas$-$Fir wooden planks with

allowable bending stress $F_b=1250$psi. She also has $3"$ Extra Strong steel pipes for

bearers and posts with a yield stress of $36$ksi. She is hiring you to design a heavy$-$duty

scaffold to use on one of her projects.

a$)$ Design the maximum spacing between the posts so as not to exceed the allowable

stress in the wooden planks. $($F$\text{'}$b$=1250$ psi and $S_x=4\mathrm{.}5i{n}^3)$

b$)$ Design the maximum length an interior bearer could be so as not to exceed the

allowable bending stress.$($Fb$=9000$psi and a section modulus $S_x=2\mathrm{.}23i{n}^3)$

c$)$ Using the maximum spacing computed in a$)$ and the maximum possible bearer

length computed in b$),$ check if the bottom posts can carry five levels of

scaffolding.

i$.$ Assume that each level is $12$ feet in height and check for buckling and

combined loads.

ii$.$ The posts are A$36$ steel and the minimum required factor of safety $($F$.$O$.$S$)$

is $4$ for both buckling and combined loads.

iii. Assume $F_y=36,000$psi,$A=3\mathrm{.}03i{n}^2,I=3\mathrm{.}89i{n}^4,S=2\mathrm{.}23i{n}^3,r=1\mathrm{.}14"$

iv$.$ Assume the eccentricity between the center of the bearer and the center of

the post is $3".$