Report - PEER - University of California, Berkeley

end work-point to work-point). And ψ is the angle between the horizontal beam andthe brace. Thus, if θ mi is the target drift of the i th story calculated from the targetdisplacement profile, then the story ductility can be computed from:µi= θmi/ θ(2)yiAfter calculating all the story ductilities from Eq. 2, the average of all storyductilities is taken as the system ductility. Second, the beam framing into the bracesare designed by capacity design principle. This requires the consideration of thehorizontal brace force components as beam axial loads and the flexural demandresulted from a vertical unbalanced concentrated force of 0.1 Ω h P y sin ψ actingupward at the center of the beam span as depicted in the free body diagram Fig. 2.Noted that P y is the nominal tensile yield strength of brace, the factor of 0.1 considersthe 10% difference between the peak compressive and tensile strengths, and Ω hrepresents the effects of strain hardening. Applying LRFD specifications:P /( φ u cPn) ≥0. 2 : ( ) 8 ⎡⎛P ⎞ ⎤P / / ⎢ 1⎥ ≤ 1.9⎜⎟0uφcPn+ Mu− φbM(3)n⎣⎝Pe⎠ ⎦2where Pn= FcrAg, π EIP e= , φ 0.75( tension)or 0.85( compression)( kl) 2 c=, φb= 0. 9Note that the bottom beam flange is not laterally braced except by transverse beams atthe center point of span. Accordingly, P n and M n in Eq. 3 are conservatively computed(without considering the effects of the concrete slab) from an unbraced length of 3.5m for the capacity design of left beam segment shown in Fig. 2.cos φ *(C+T)/2 cos φ *(C+T)/2TcosφCcosφsin φ *(C-T)/2 sin φT*(C-T)/2CφT sin φC sin φUnbalanced vertical concentrated force=(C-T) sinφ≅ ( β − 1) Ω P sinφFigure 2. Free body diagram of a beam supporting the BRBs.The final selections of structural members are given in Table 1.Table 1. Selection of member sizes and gradesMember Beam Sizes and Core Cross Sectional Area of Braces (A572 GR50)Location 1FL 2FL 3FLBeam (mm) H456×201×10×17 H450×200×9×14 H400×200×8×13Brace (cm 2 ) 30 25 15Dimension of Columns (A572 Gr.50) unit : mm CFTs: C1: Tube: 350×9, C2: Pipe: 400×400×9hy248