New mathematical formula for design viscous dampers in Internal and external Scissor-Jack braces

The existing design formulas have provided significantly convenient tools to practical engineers in determining the damping coefficients of the supplemental diagonal brace, K brace, upper toggle brace, and lower toggle brace. These formulas take into account the relative vertical and horizontal deformation between the two ends of a viscous damper installed in a frame panel so that the axial deformation of the damper and thus the dissipated energy by the damper can be better captured. In this paper, a mathematical formula is proposed for the internal and external Scissor-Jack brace damper system in structure with the relative vertical and horizontal deformation between the two ends of a viscous damper.