## L

FIGURE 4.40 Key dimensions of a radius cut reduced beam section.

An optimal RBS is one in which the moment at the face of the column will be minimized. To achieve this condition, the following procedure is recommended (Gross et al. 1999):

• Compute the RBS plastic section modulus using the equation

where Zb is the plastic section modulus of the full beam cross-section, c is the depth of cut as shown in Figure 4.40, and d, tf, tw are the beam depth, beam flange thickness, and web thickness, respectively.

Compute z, the ratio of moment at the face of the column to plastic moment of the connecting beam, from the equation

ZRBS wL'sc

Zb 2ZbFyf

where sc is given in Equation 4.155 and shown in Figure 4.40, L' is the beam span between critical plastic sections (see Figure 4.40), ZRBS and Zb are defined in Equation 4.156, wis the magnitude of the uniformly distributed load on the beam, and Fyf is the beam flange yield strength.

• If z < 1.05, then the RBS dimensions are satisfactory. Otherwise, use RBS cutouts in both the top and bottom flanges, or consider using other types of moment connections (Gross et al. 1999).

Experimental studies (Uang and Fan 1999; Engelhardt et al. 2000; Gilton et al. 2000; Yu et al. 2000) of a number of radius cut RBS with or without the presence of a concrete slab have shown that the connections perform satisfactorily and exhibit sufficient ductility under cyclic loading. However, the use of RBS beams in a moment resistant frame tends to cause an overall reduction in frame stiffness of around 4 to 7% (Grubbs 1997). If the increase in frame drift due to this reduction in frame stiffness is appreciable, proper allowances must be made in the analysis and design of the frame.

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