An A36 steel plate ($F_y = 36$ ksi, $F_u = 58$ ksi) is used as a tension member. The plate has a width of 8 inches and a thickness of 0.5 inches. It is connected to a gusset plate using a single line of three 3/4-inch diameter bolts.

Calculate the nominal tensile strength based on gross yielding ($P_{ny}$) and net section fracture ($P_{nf}$). According to AISC specifications, the effective hole diameter for calculating the net area is the nominal bolt diameter plus 1/8 inch (to account for the standard hole clearance and damage from punching/drilling).

A W8x31 wide-flange steel shape is used as a column in a single-story building. The column is 15 feet long and is pinned at both ends ($K = 1.0$).

The properties of the W8x31 section are: Gross Area ($A_g$) = 9.13 $in^2$ Moment of Inertia about the strong axis ($I_x$) = 110 $in^4$ Moment of Inertia about the weak axis ($I_y$) = 37.1 $in^4$ Modulus of Elasticity for structural steel ($E$) = 29,000 ksi.

Determine the critical Euler buckling load ($P_{cr}$) for this column. Does it buckle about its strong axis ($x-x$) or weak axis ($y-y$)?

Two 3/8-inch thick steel plates ($F_y = 50$ ksi, $F_u = 65$ ksi) are connected by a single 7/8-inch diameter high-strength bolt. The bolt is located exactly 1.5 inches from the edge of the plate (measured from the center of the hole to the edge).

Determine the nominal bearing strength ($R_n$) of the plate at the bolt hole. The AISC specification states that if deformation at the bolt hole at service load is a design consideration, the bearing strength is given by: $R_n = 1.2 \cdot L_c \cdot t \cdot F_u \le 2.4 \cdot d \cdot t \cdot F_u$

Where $L_c$ is the clear distance (in inches) between the edge of the hole and the edge of the adjacent material, $d$ is the nominal bolt diameter, and $t$ is the plate thickness.