Report - PEER - University of California, Berkeley

3.3.2 B-modeThe equilibrium condition for the free body for B-mode are given by Eq. (11) for horizontaldirection and moment around the center of the beam-column joint by Eq. (12),where sign (±) stand for (-) for closing and (+) for opening respectively.– T 2T 3– + C ± N = 0(free body BD: x-direction) (11)1--jD( T2 2– T 3)C C+ --- ⎛D– ---------- ⎞2 ⎝ b cσ c⎠ ± LV 0(free body BD: moment) (12)=σ B3.4 Failure Criteria of Materials3.4.1 ConcreteIt is assumed that diagonal cracks transfers no tensile force across the crack. Resultantforces in compression are transferred by compressive reinforcement and/or across concretecracks. In J-mode, each direction of principle stress on the critical section isassumed parallel to the diagonal direction of the joint panel. On the critical sections,distribution of the concrete stress is assumed as a rectangular stress block, where theconcrete stress is σ c and 85% of concrete compressive strength , typical value forflexural analysis.3.4.2 Reinforcing SteelTensile force is transmitted by the longitudinal bars. Thus it is assumed that they donot exceed the yielding force. The typical restrictive conditions are given by Eq. (13).T 3where, Σa t: total cross section area of tensile reinforcements, and f y: tensile yieldpoint of longitudinal reinforcement. Joint shear reinforcing bars are assumed that theyare concentrated at the mid-height of the joint and always equal to the yielding forceand given by Eq. (14),T 5≤ Σa tf y=p wb c( jD)f sywhere, p w : joint shear reinforcement ratio, f sy : tensile yield point of joint reinforcement.In the analysis below, longitudinal bars in beam and columns are assumed perfectlyanchored for the simplicity.3.5 Ultimate StrengthUnder closing moment, the value of T 1 , T 2 ; the resultant forces in longitudinal bars incompression are assumed to be zero. Then, five unknown variables V, T 4 , C 1 , C 2 , andC 3 are determined as a function of T 3 by solving the simultaneous equations from (1)(13)(14)463