D Value methods forces of lateral the shear force of o. M.-FAW M-F(h-W) 6.12) Combination of responses to withstand the most Without earthquake action S=YoSck+WoloSok+W.Y.S. (S=YaSor +YaSp 5.13 是 With earthquake action aS■7aS+Ψe￥S+YaSw 5.14 S-YSa +YOSm +YnSm+W.7S. S<RIYE SsR性E 516) Combination of responses S=YGSGE+YBSEM+YeSEM earthquake action S=a+Sx+Sx+w,风 S<C/Ym 66 n the shear force of the k-th column in i-th floor where Vik is the horizontal shear force induced in column k on i th story; Dik is relative shear stiffness of column k on i th story; n i k ik ik ik V D D V å= = 1 (5.7) å= n k Dik 1 is summation of relative shear stiffness of total columns on i th story. D Value methods Determine the internal forces of lateral￾force-resisting frames : Ø Determine flexural stiffness for beam and column; Ø Calculate D value; Ø Determine shear force for each column; Ø Determine the position of the point of contra-flexure in column; Ø Calculate column moments, then derive the beam moments based on equilibrium of beam to column joint, and distribution of beam stiffness / M kl = Vik h (5.11) ( ) / M ku = Vik h - h (5.12) Combination of responses Without earthquake action With earthquake action RE G GE Eh EhK Ev EvK w w wK S R S S S S S g g g g y g < / = + + + S R S S S S G GK Q Q QK w w wK < =g +y g +y g n Structures must be designed to withstand the most unfavorable combination of design loads. (1) G GE Eh Ehk S = g S + g S (5.13) (2) G GE W W Wk Eh Ehk S = g S + y g S + g S (5.14) (3) G G Q Q S = g S + g S (5.15) S R RE £ / g (5.16) • For some structures, when vertical seismic action is considered, the following combination of loads should be checked: G G E Eh Ehk Ev Evk S = g S + + g g S S Combination of responses Without earthquake action —— Displacement Check With earthquake action C/ GE EhK EvK w wK RE S S S S S S y g = + + + < GK Q QK w wK S S S S S C = + + y y <