A W10x49 steel column ($F_y = 50$ ksi) is supported by a concrete pier ($f'_c = 3$ ksi). The pier dimensions exactly match the required base plate dimensions ($A_1 = A_2$). The column carries an LRFD factored axial load $P_u = 300 \text{ kips}$. Determine the minimum required area ($A_1$) for the base plate.

The same W10x49 column carrying $P_u = 300 \text{ kips}$ is now supported by a massive concrete spread footing where the concrete support area $A_2$ is significantly larger than $A_1$. Assume the maximum confinement multiplier applies. Determine the new minimum required area ($A_1$).

A base plate is sized at $B = 14 \text{ in}$ and $N = 14 \text{ in}$ to support a W10x49 column ($d = 10.0 \text{ in}$, $b_f = 10.0 \text{ in}$). The factored load is $P_u = 300 \text{ kips}$. The plate is A36 steel ($F_y = 36 \text{ ksi}$). Calculate the required plate thickness, $t_p$.

Determine the required LRFD nominal tensile strength ($P_n$) of an anchor rod. The factored uplift force on the column is $T_u = 120 \text{ kips}$. There are 4 anchor rods in the base plate layout, and the load is distributed equally among them. Assume the threads are included in the shear plane (though this is pure tension).

A fully welded moment connection is used to connect a W18x50 beam to a W14x90 column flange. The factored bending moment at the connection is $M_u = 240 \text{ kip}\cdot\text{ft}$. The depth of the beam is $d = 18.0 \text{ in}$, and the flange thickness is $t_f = 0.570 \text{ in}$. Calculate the required factored force ($P_{uf}$) that the top flange weld must resist in tension.

A contractor is setting a massive W14x311 column on a concrete foundation for a heavy industrial facility. The concrete foundation is rarely perfectly level, and the heavy base plate (3 inches thick) must be set to an exact elevation. How is this practically achieved?

A rigid frame building is designed to resist extreme lateral wind loads. The calculated lateral shear force at the base of the column exceeds the combined shear capacity of the anchor rods and the friction between the base plate and the grout.

A tall slender column is subjected to a large lateral wind load, creating a significant overturning moment at the base plate in addition to its axial load.

A base plate ($N = 20 \text{ in}$, $B = 20 \text{ in}$) is subjected to an axial load $P_u = 400 \text{ kips}$ and a small overturning moment $M_u = 1000 \text{ kip}\cdot\text{in}$. Assume the eccentricity is small ($e \le N/6$). Calculate the maximum bearing pressure on the concrete.

A moment connection transfers a flange tension force of $P_{uf} = 165 \text{ kips}$ into the column. The column is a W14x90 ($d_c = 14.0 \text{ in}$, $t_w = 0.440 \text{ in}$, $k_{des} = 1.31 \text{ in}$). The specified yield stress of the column is $F_{yc} = 50 \text{ ksi}$. Determine if the column web yields locally under this concentrated force. Assume the force is applied at a distance greater than the column depth from the column end.

Calculate the LRFD nominal shear strength ($\phi_v R_n$) of a single 1-inch diameter ASTM F1554 Grade 36 anchor rod. The threads are included in the shear plane.

A shear lug measuring 10 inches wide by 3 inches deep (embedded into the grout/concrete) is used to transfer a lateral shear force of $V_u = 80 \text{ kips}$. The foundation concrete has $f'_c = 4 \text{ ksi}$. Check if the bearing pressure on the concrete face of the lug is acceptable.

A base plate ($N = 20 \text{ in}$, $B = 20 \text{ in}$) is subjected to an axial load $P_u = 200 \text{ kips}$ and a large overturning moment $M_u = 1200 \text{ kip}\cdot\text{in}$. Assume the eccentricity is large ($e > N/6$). Calculate the maximum bearing pressure on the concrete.

A column base must resist an axial load of $P_u = 150 \text{ kips}$ and a lateral shear force of $V_u = 40 \text{ kips}$. The coefficient of friction between the steel base plate and concrete is $\mu = 0.40$. Determine if friction alone is sufficient, or if a shear lug is required.