Problem $1[$Required$]$:

use the double angle selected tension member to resist a service dead load of $30$ kips and a service live

load of $90$ kips $.$ The member will be connnected with two lines of $\frac{7}{8}$ inch diameter bolts placed

at the workable gage distances in Table $1-7$A of the AISC steel manual. There will be more than

three bolts in each line. The member is $25$ feet long and will be connected to a $\frac{3}{8}$ inch thick

gusset plate. Use A$572$ Grade $50$ steel. Design based on LRFD$.($check block shear, terout and bearring$)$

Lood Demand

$P_v=1\mathrm{.}2D+1\mathrm{.}6L=1\mathrm{.}2({30}^k)+1\mathrm{.}6({90}^k)={180}^k$

Required $Ag$:$,Ag\frac{P_u}{del{F}_y}Ag\frac{{180}^k}{0\mathrm{.}9(50\text{k}\text{s}\text{i})}=4i{n}^2$

Required $A_e$:$,A_e\frac{P_u}{\frac{O}{F_u}}{A}_e\frac{{180}^K}{0\mathrm{.}75(65\text{k}\text{s}\text{i})}=3\mathrm{.}69i{n}^2$

Assume $U=0\mathrm{.}8($there are more than $3$ bolts$)$

Net Area $(A_n)$

Try $2L55\frac{5}{16}$

$A_g=6\mathrm{.}14i{n}^2,==1\mathrm{.}35in$

$t_f=0\mathrm{.}312sin$

$r_{\text{m}\text{i}\text{n}}=2\mathrm{.}19in$

yielding $(0\mathrm{.}9)($soksi$)(6\mathrm{.}13i{n}^2)=276K>{180}^k$

Fracture $,A_n=A_g-2n(dht)$

$=Ag-2n(dht)$

$6\mathrm{.}13-4((\frac{3}{8}+\frac{1}{16}+\frac{1}{16})(0\mathrm{.}3125)),U=\frac{3\mathrm{.}69in{?}^{(}()()2)}{4\mathrm{.}88i{n}^2}=0\mathrm{.}756$

$=4\mathrm{.}88i{n}^2$

$=1-\frac{1\mathrm{.}35}{l},l=5\mathrm{.}5$

$U=0\mathrm{.}775,l=6$

$AC=0\mathrm{.}7754\mathrm{.}88i{n}^{\text{'}}=3\mathrm{.}78i{n}^2$

check slenderness

Spacing

$2^{\frac{2}{3}}d$

$2^{\frac{2}{3}}(0\mathrm{.}94)=2\mathrm{.}5(min)$

$12t6$

$12(\frac{3}{3})6=4\mathrm{.}5$

Shear strength of Bolt

$R_n=\frac{{61\mathrm{.}3}^{*}}{20011}$

$R_v={180}^{*}$

$($A$325x,D=61\mathrm{.}3\frac{m}{?}$ boits

$Rv={180}^k,$ need $at$ leost $3$ bolts

Block shear

Agt $=$ length $of$ tension

path $f$