# Column-Beam Moment Ratio Check for SMF per AISC 341-16 with ideCAD

How does ideCAD control the Column-Beam Moment Ratio according to AISC 341-16?

• Moment ratio is automatically controlled and reported in accordance with AISC 341-16 §E3.

Symbols

ΣMpc = sum of the projections of the nominal flexural strengths of the columns above and below the joint
ΣMpb = sum of the projections of the expected flexural strengths of the beams at the plastic hinge locations to the column centerline, kip-in.
Ag = gross area of column, in.2 (mm2)
Fyb = specified minimum yield stress of beam, ksi (MPa)
Fyc = specified minimum yield stress of column, ksi (MPa)
Mpr = maximum probable moment at the location of the plastic hinge, as determined in accordance with AISC 358,
Mv = 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)
Pc = the nominal compressive strength
Pr = required axial compressive strength according to Section D1.4a, kips (N)
Zc = 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)
αs = 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 systems 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 directions 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 ΣMpb* from the Eq (E3-3) is permitted.

The equation given below determines the nominal compressive strength, Pc.

The required axial strength is Prc = Puc (LRFD) or Prc = Pac (ASD), as applicable.

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

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