Determine the nominal gross yielding strength and the LRFD design strength of an ASTM A36 ($F_y = 36 \text{ ksi}$, $F_u = 58 \text{ ksi}$) steel plate measuring $1/2 \times 6 \text{ inches}$.

Given:

• Steel: A36 ($F_y = 36 \text{ ksi}$)
• Plate dimensions: $t = 0.5 \text{ in}$, $w = 6 \text{ in}$

The same $1/2 \times 6 \text{ inch}$ A36 plate from Example 1 is connected at its ends by two $3/4\text{-inch}$ diameter bolts in a single line across the width. Determine the LRFD design strength based on net section fracture. Assume $U = 1.0$.

Given:

• Steel: A36 ($F_u = 58 \text{ ksi}$)
• $A_g = 3.0 \text{ in}^2$, $t = 0.5 \text{ in}$
• Bolt diameter: $d_{bolt} = 3/4 \text{ in}$
• $U = 1.0$

A $3/8\text{-inch}$ thick steel plate ($F_u = 65 \text{ ksi}$) is 10 inches wide and has three $7/8\text{-inch}$ bolts arranged in a staggered pattern. The holes are spaced longitudinally (pitch $s$) by 2.0 inches and transversely (gage $g$) by 3.0 inches. Determine the controlling net width and net area.

Given:

• $t = 0.375 \text{ in}$, $w_g = 10 \text{ in}$, $F_u = 65 \text{ ksi}$
• $d_{bolt} = 7/8 \text{ in}$
• $s = 2.0 \text{ in}$, $g = 3.0 \text{ in}$

An L$6\times 4\times 1/2$ angle ($A_g = 4.75 \text{ in}^2$, $\bar{x} = 0.981 \text{ in}$ from the long leg face) is connected only by its $6\text{-inch}$ long leg to a gusset plate using a welded connection. The length of the longitudinal welds is $L = 5.0 \text{ in}$. Determine the effective net area.

Given:

• $A_g = 4.75 \text{ in}^2$, $\bar{x} = 0.981 \text{ in}$
• Weld length $L = 5.0 \text{ in}$

Determine the LRFD block shear design strength for a $1/2\text{-inch}$ thick A36 plate ($F_y=36\text{ ksi}, F_u=58\text{ ksi}$) connected by two $3/4\text{-inch}$ bolts in a single line. The bolts are centered, with an edge distance of $1.5 \text{ in}$ and a spacing of $3.0 \text{ in}$.

Given:

• $t = 0.5 \text{ in}$, $d_h = 7/8 \text{ in}$
• Shear path length: $L_v = 1.5 + 3.0 = 4.5 \text{ in}$
• Tension path width (half plate width): $w_t = 3.0 \text{ in}$

Check the tear-out strength of the end bolt in the previous example. The bolt has a $1.5\text{-inch}$ edge distance to the center of the hole.

Given:

• $L_{edge} = 1.5 \text{ in}$ to hole center.
• Hole diameter $d_h = 7/8 \text{ in}$. Bolt diameter $d = 3/4 \text{ in}$.
• $t = 0.5 \text{ in}$, $F_u = 58 \text{ ksi}$.

Select the lightest single angle (A36 steel, $F_y=36\text{ ksi}, F_u=58\text{ ksi}$) to carry a dead load of $20\text{ kips}$ and a live load of $60\text{ kips}$. Assume the effective net area $A_e = 0.75 A_g$ for initial sizing.

Given:

• $P_D = 20 \text{ kips}$, $P_L = 60 \text{ kips}$

Check if a single angle L$4\times 4\times 1/4$ ($r_z = 0.795 \text{ in}$) used as a tension bracing member is acceptable if its unbraced length is 18 feet.

Given:

• $r_{min} = r_z = 0.795 \text{ in}$
• $L = 18 \text{ ft}$