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LIST OF ABBREVIATIONS

𝐴 : Pipe cross section area

𝐢 : Global viscous damping matrix which accounts for all inherent velocity dependent energy dissipating mechanisms in the structure other than the inelastic hysteretic energy dissipated by the structural members

𝐷 : Pipe outer diameter

𝑑 : Longitudinal displacement related to single pipes and MCSD

𝐸 : Young Modulus

𝐸

!

: Tangential Modulus

𝐹 : External Axial load acting unidirectional on single pipes and on MCSD

𝐹

!

𝑑 : Vector of global nonlinear forces at time t generated by the hysteretic characteristics of structural elements

𝐹

!

: Vector of global static loads applied to the structure prior to and maintained during the seismic excitation

𝐺 : Shear Modulus

𝐿 : Pipe length

π‘š : Number of half waves in longitudinal direction

𝑀 : Global mass matrix

𝑛 : Number of half waves in circumferential direction

𝑁 : Axial force acting unidirectional on single pipes and on MCSD 𝑝 : Contact pressure between pipes surfaces

𝑃

!"#$

: Critical load of single pipe

π‘Ÿ : Vector coupling the directions of the ground motion input with the directions of the DOFs of the structure

𝑅 : Pipe outer radius

π‘Ÿ : Pipe inner radius

𝑑 : Pipe thickness

𝐽 : Inertia moment of the cross section

𝐾

!

: Elastic Stiffness

𝐾

!"

: Elastoplastic Stiffness

𝑀 : Pipe Surface Radii displacement

π‘₯

!

: Resulting penetration between pipes surfaces

𝑋 𝑑 , 𝑋 𝑑 , 𝑋 𝑑 :Respectively the vectors of global acceleration, velocities and displacement relative to the moving base at time t

𝑋

!

𝑑 : Horizontal acceleration of the ground at time t

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𝜎 : Stress

𝜎

!

: Stress acting in longitudinal direction 𝜎

!

: Stress acting in radii direction

𝜎

!

: Stress acting in angular direction

πœ€ : Strain

πœ€

!

: Strain acting in longitudinal direction πœ€

!

: Strain acting in radii direction

πœ€

!

: Strain acting in angular direction

πœƒ : Orientation angle of a surface piece with origin the gravity point of the cross section

πœ‘ : Orientation angle of the longitudinal slot with origin the gravity point of the cross section

𝜏 : Shear Stress

𝜈 : Poisson Ratio

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Riferimenti

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