Design Procedure

A W14x90 column in a braced frame supports a factored axial load $P_u = 400 \text{ kips}$ and a factored strong-axis moment $M_{ux} = 250 \text{ kip-ft}$ (including second-order effects). The available axial strength $\phi P_n = 1000 \text{ kips}$ and available flexural strength $\phi M_n = 574 \text{ kip-ft}$. There is no weak-axis bending ($M_{uy} = 0$).

Determine if the member is adequate based on the AISC interaction equations.

A structural engineer is designing the exterior columns of a single-story commercial building. The roof structure applies a significant gravity load.

Scenario: During a hurricane, high wind pressures act directly on the exterior walls, which transfer the load horizontally to the columns.

A multi-story steel frame building with a tall, open first floor (a "soft story") undergoes lateral displacement ($\Delta$) during a seismic event.

Scenario: The building sways laterally. The massive weight of the upper floors is now displaced horizontally from the foundation.

A W12x65 column ($F_y = 50 \text{ ksi}$) in a braced frame supports a factored axial load $P_u = 150 \text{ kips}$ and a factored strong-axis moment $M_{ux} = 120 \text{ kip-ft}$. The available axial strength $\phi_c P_n = 600 \text{ kips}$ and available flexural strength $\phi_b M_{nx} = 356 \text{ kip-ft}$. There is no weak-axis bending ($M_{uy} = 0$).

Determine if the member is adequate based on the AISC interaction equations.

A W10x49 beam-column is subjected to bi-axial bending along with an axial load. The factored loads are $P_u = 80 \text{ kips}$, $M_{ux} = 100 \text{ kip-ft}$, and $M_{uy} = 40 \text{ kip-ft}$. The capacities are $\phi_c P_n = 450 \text{ kips}$, $\phi_b M_{nx} = 227 \text{ kip-ft}$, and $\phi_b M_{ny} = 108 \text{ kip-ft}$. Evaluate the adequacy of the member.

A structural member is subjected to a factored axial tensile load $P_u = 120 \text{ kips}$ and a factored bending moment $M_{ux} = 80 \text{ kip-ft}$. The member is a W10x30.

The available axial tensile strength is $\phi_t P_n = 260 \text{ kips}$ and the available flexural strength is $\phi_b M_{nx} = 137 \text{ kip-ft}$. There is no weak-axis bending ($M_{uy} = 0$). Evaluate the adequacy of the member using the AISC interaction equations.

An engineer is checking a W12x50 column in a moment frame. The column carries a high bending moment due to lateral wind loads, but relatively low axial gravity load because it is on the top story.

The factored axial compression is $P_u = 45 \text{ kips}$, and the strong-axis bending moment is $M_{ux} = 150 \text{ kip-ft}$. The section capacities are $\phi_c P_n = 500 \text{ kips}$ and $\phi_b M_{nx} = 265 \text{ kip-ft}$.

Determine which interaction equation governs and calculate the interaction value.

A W14x99 column in a non-sway (braced) frame is subjected to a factored axial compressive load of $P_u = 600 \text{ kips}$. A first-order elastic analysis indicates the column is bent in single curvature with equal end moments of $M_1 = M_2 = 180 \text{ kip-ft}$ due to gravity loads. There are no transverse loads between supports.

The column length is $L = 14 \text{ ft}$, with effective length factor $K_1 = 1.0$. The strong axis moment of inertia is $I_x = 1110 \text{ in}^4$ and the modulus of elasticity is $E = 29000 \text{ ksi}$.

Determine the amplified moment $M_{ux}$ accounting for $P-\delta$ effects.