Effect of Joint Flexibility on Seismic Performance of a Reinforced Concrete Ductile Moment-Resisting Frame

Table 1

Design details of beam-column joints.

Frames	Frame PF4			Frame PF8			PF4-noJH	PF8-noJH	PF4-R	PF8-R
	Interior joint	Exterior joint	Knee joint	Interior joint	Exterior joint	Knee joint	All joints	All joints	All joints	All joints
Development length provided, (mm)	500 (20)	445	445	600 (24)	545	545	All joint details are the same as those of frame PF4	All joint details are the same as those of frame PF8	All joint details are the same as those of frame PF4	All joint details are the same as those of frame PF8
Development length required—ACI 318	20	483	483	20	483	483
Development length required—ACI 352	20.5	376	376	20.5	376	376
Ratio of column capacity to beam moment capacity,	1.5	−2.3 + 3.9	−1.2 + 2.0	2.1	−3.2 + 5.5	−1.6 + 2.8
Ratio of joint shear capacity to shear demand	1.3	1.6	1.1	1.7	2.1	1.4
Joint shear stress level,	0.97	0.62	0.62	0.73	0.47	0.47
Joint shear reinforcement ratio in a single layer, (%)	0.81	0.81	0.81	0.76	0.76	0.76	W/o joint hoop	W/o joint hoop	W/rigid joint	W/rigid joint
Total joint shear reinforcement ratio, (%)	0.6	0.6	0.6	0.66	0.66	0.66

The modulus of elasticity is  = 25 GPa and  = 200 GPa for concrete and steel, respectively. The uniaxial cylinder compressive strength of the concrete is  = 28.2 MPa. The yield strength of the longitudinal reinforcing bars is  = 431 MPa, and the yield stress of the stirrups, ties, and joint hoops is  = 387 MPa. Five layers of 4-D10 tie bars are placed in the joints of Frame PF4, whereas seven layers of 4-D10 tie bars are installed in those of Frame PF8. Thus, the area of a layer of 4-D10 is 285.32 mm², which is greater than the requirement of ACI 318-19: 216.2 mm² at 80 mm spacing and 192.5 mm² at 70 mm spacing. The flexural strength of the column is calculated at an axial load ratio of 0.1 . Positive and negative signs indicate hogging and sagging moments of the beam end section, respectively.