Problem $3$

The connection below employs SAE grade $5$ bolts $(Sp=82$ksi,$E=200$GPa $).$ They connect two plates of $1020$ steel $($Young$\text{'}$s modulus $210$ GPa $)$ with equal thickness. Load Fis $5400$ lb $,$ while load P is $2000$ lb $.$ Both forces are applied at the center of their corresponding sides. The bolts have been $75\%$ preloaded. Find the safety factor for the bolts if:

a$)$ The friction coefficient between the plates is $0.$

b$)$ The friction coefficient between the plates is $0\mathrm{.}15.$

Answers:

A$)$ FOS $=1\mathrm{.}2($normal stress is $62\mathrm{.}3$ksi, shear stress is $16\mathrm{.}3$ksi$)$

B$)$ FOS $=1\mathrm{.}32($normal stress is $62\mathrm{.}3$ksi, shear stress is zero due to friction$)$