Homework #$21$

$10$ Points

A C$10$X$15\mathrm{.}3$ steel channel $($textbook Table A$4)$ is bolted to a $1/2"$ thick gusset plate with six $(6)3/4"$ diameter A$325-$N high strength bolts and $13/16"$ diameter standard size holes.

All connected steel material is ASTM A$36($Fy$=36$ ksi, Fu$=58$ ksi$)$

Determine the maximum allowable tensile load, $P,$ for this connection.

Hint: The allowable load $P$ is based on the minimum value of the following four $(4)$ conditions:

$(1)$ bolt shear

$(2)$ bearing failure at bolt holes of the connected steel member

$(3)$ tensile rupture of net area of connected steel member

$(4)$ tensile yielding of gross area of connected steel member.

Allowable bearing stress $=Fp=(1\mathrm{.}2)(Fu)=(1\mathrm{.}2)(58)=69\mathrm{.}6$KSI

Allowable tensile rupture stress $=Ft=(0\mathrm{.}5)(Fu)=(0\mathrm{.}5)(58)=29$KSI

Allowable tensile yield strength of A$36$ steel $=(0\mathrm{.}6)(Fy)=(0\mathrm{.}6)(36)=22$KSI