other:Article Title: Component-Based Model for Single-Plate Shear Connections with Pretension and Pinched Hysteresis
Article Snippet: The component-based connection model presented here makes use of the equation in Richard and Abbott (1975) , commonly referred to as the “Richard Equation.” Although the Richard Equation was originally formulated in terms of stress, strain, and elastic and plastic moduli, it can equivalently be used to express the load R in terms of deformation Δ and elastic and plastic stiffnesses as: R = ( k i − k p ) Δ ( 1 + | ( k i − k p ) Δ R n | n ) ( 1 / n ) + k p Δ , (1) where k i and k p are elastic and plastic stiffnesses, respectively, n is a shape parameter that controls the sharpness of the transition from the elastic stiffness to the plastic stiffness, and R n is a reference load, located at the projection of the plastic stiffness at a deformation of zero ( ). fig ft0 fig mode=article f1 FIG. 1 caption a4 Schematics for Richard Equation formulations used in (a) Richard and Abbott (1975) , (b) Hsieh and Deierlein (1990) , and (c) Simões et al. (2001) .
Shear:Article Title: An Empirical Component-Based Model for High-Strength Bolts at Elevated Temperatures
Article Snippet: .. Isolating the bolt component spring behavior from the model in Weigand (2016) , the transverse load-deformation behavior of the bolt, including shear and flexural effects, is modeled using the nonlinear four-parameter “Richard Equation”, which was formulated by Richard and Abbott (1975) : P ( δ ) = ( k i − k p ) ( δ − δ 0 ) ( 1 + | ( k i − k p ) ( δ − δ 0 ) r n | n ) ( 1 / n ) + k p ( δ − δ 0 ) (1) where δ is the bolt shear deformation, δ 0 is the initial bearing deformation, k i and k p are elastic and plastic stiffnesses of the bolt double-shear load-deformation response, respectively, n is a shape parameter that controls the sharpness of the transition from the elastic stiffness to the plastic stiffness, and r n is a reference load. ..
Article Title: New Component-Based Model for Single-Plate Shear Connections with Pre-tension
Article Snippet: .. The shear-plate and beam-web component springs (i.e., plate springs) are modeled using a piecewise version the Richard Equation (see Richard and Abbott (1975 )) such that: R ( Δ ) = { ( K b − − K p − ) ( Δ − Δ br − ) ( 1 + | ( K b − − K p − ) ( Δ − Δ br − ) R b − | n b − ) ( 1 n b − ) + K p − ( Δ − Δ br − ) , Δ ≤ Δ slipctr − 1 2 Δ slip ( K i − K y ) Δ ( 1 + | ( K i − K y ) Δ R y | n ) ( 1 n ) + K y Δ , Δ slipctr − 1 2 Δ slip ≤ Δ ≤ Δ slipctr ( K b + − K p + ) ( Δ − Δ br + ) ( 1 + | ( K b + − K p + ) ( Δ − Δ br + ) R b + ( T ) | n b + ) ( 1 n b + ) + K p + ( Δ − Δ br + ) , Δ ≥ Δ slipctr + 1 2 Δ slip + 1 2 Δ slip (7) where the superscripts, (·) + and (·) − , denote tensile and compressive deformations of the component spring, respectively, and the remaining parameters in Eq. (7) are defined below. (b) shows a schematic of the backbone response. ..
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