4a. Moment Ratios

Symbols

ΣM^∗_pc = sum of the projections of the nominal flexural strengths of the columns above and below the joint
ΣM^∗_pb = sum of the projections of the expected flexural strengths of the beams at the plastic hinge locations to the column centerline, kip-in.
A_g = gross area of column, in.2 (mm2)
F_yb = specified minimum yield stress of beam, ksi (MPa)
F_yc = specified minimum yield stress of column, ksi (MPa)
M_pr = maximum probable moment at the location of the plastic hinge, as determined in accordance with AISC 358,
M_v = additional moment due to shear amplification from the location of the plastic hinge to the column centerline based on LRFD or ASD load combinations, kip-in. (N-mm)
P_r = required axial compressive strength according to Section D1.4a, kips (N)
Z_c = plastic section modulus of the column about the axis of bending, in.3 (mm3)
Z = Plastic section modulus about the axis of bending, in.³ (mm³)
α_s = LRFD-ASD force level adjustment factor 1.0 for LRFD and 1.5 for ASD

Conditions for Strong-Column and Weak-Beam (SC/WB)

For the highly ductile steel frames or reinforced concrete structural system with shearwalls and steel frames, the beam-column connections must provide the condition of the Strong-Column and Weak-Beam (SC/WB) approach depending on the earthquake direction. In beam-to-column connections, the following relationship must be fulfilled:

where ΣM_pc^* is the sum of the nominal flexural strength of the columns above and below the joint to the beam centerline with a reduction for the axial force in the column. The determination of ΣM_pc^* from the Eq (E3-2) is permitted. When the centerlines of beams in opposite direction in the same joint do not coincide, the mid-line between centerlines should be used. For the ΣM_pb^*, the sum of the expected flexural strengths of the beams at the plastic hinge locations to the column centerline. The determination of ΣM_pb^* from the Eq (E3-3) is permitted.

The nominal compressive strength, P_c, is determined as follows:

and the required axial strength is P_rc = P_uc (LRFD) or P_rc = Pac (ASD), as applicable.

In the calculation of column flexural strength capacities, the required compressive force P_ac (ASD) or P_uc (LRFD) are obtained from the load combinations, which makes these bending moment capacities the lowest in accordance with the direction of the earthquake.