Aisc Manual — Table 6-2

Define (LRFD): [ p = \frac98 \cdot \frac\phi_b M_nx\phi_c P_n ] But note: In Table 6-2, ( p ) is typically tabulated as: [ p = \frac98 \cdot \frac1\phi_c P_n ] Wait – check carefully: AISC Table 6-2’s ( p ) is not directly ( \frac98 \cdot \frac\phi_b M_nx\phi_c P_n ). Instead, AISC uses a normalized form:

[ M_ux \leq \phi_b M_nx - p \cdot P_u ] where ( p ) is tabulated in ( 10^-3 ) (kip-ft/kip), meaning: [ p_\textactual = \fracp_\texttable1000 \quad \textin ft ] 5. Using Table 6-2 Step-by-Step (LRFD Example) Given: W12×65, ( L_b = 10 \text ft ), ( P_u = 150 \text kips ), ( M_ux = 250 \text kip-ft ), ASTM A992 (Fy=50 ksi). aisc manual table 6-2

[ M_ux = 250 \text kip-ft > 202.75 \text kip-ft \quad \Rightarrow \textNot OK ] Define (LRFD): [ p = \frac98 \cdot \frac\phi_b

In the 16th Ed. Manual, page 6-8, the interaction equation given is: [ \fracP_u\phi_c P_n + \frac89 \cdot \fracM_ux\phi_b M_nx \leq 1.0 ] Rewriting: [ M_ux \leq \phi_b M_nx - \left( \frac98 \cdot \frac\phi_b M_nx\phi_c P_n \right) P_u ] Thus the ( p ) (in ( 10^-3 ) units) is: [ p = \frac98 \cdot \frac\phi_b M_nx\phi_c P_n \times 10^3 ] Yes – that’s correct. So ( p ) has units of (kip-ft / kip) × ( 10^3 ), or effectively ( 10^-3 ) ft × ( 10^3 ) = dimensionless? Wait, careful: [ M_ux = 250 \text kip-ft > 202

Better to derive from Table 6-2's actual printed equation:

Now, express this as: [ M_ux = \phi_b M_nx \cdot \frac98 - \frac98 \cdot \frac\phi_b M_nx\phi_c P_n \cdot P_u ]