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Bispec Spectral Quantities
Bispec computes a large number of spectral quantities that can be plotted and examined in the Spectral Analysis dialog. They can also be exported to text files for further analysis.
In the spectral analysis window, different spectral values can be selected for plotting along the horizontal or vertical axis. This allows any two spectral quantities to be plotted against each other providing a high degree of freedom for the user to explore alternative data plotting and interpretation forms.
 
In addition to computed spectral quantities, some of the basic input properties can also be plotted such as period, mass and stiffness. This allows for example plotting any quantity vs. period (T) or stiffness (K).
 
In general, the available quantities are divided into 5 separate groups of related quantities:
  1. Basic Properties: Period (T), frequency (f), Stiffness (K), Damping Ratio (z ), Mass (M), Hardening Stiffness (Kh), Hardening Stiffness Ratio (Kh/K), Post-yield period (Tsec), P-Delta ratio (P/KL), Damping Coefficient (C), Nonlinear Damping Coefficient (Csup), and nonlinear damping exponent (alpha).
  2. Effective Properties: Effective Period (Teff), Effective Frequency (feff), Effective Stiffness (Keff), Effective Linear Viscous Damping (bIeff), Effective Nonlinear Viscous Damping (bVeff), Total Effective Viscous Damping (bV+Ieff), Effective Hysteretic Damping (bHeff), and Total Effective Damping (bTot_eff).
  3. Kinematics (D, V, A): Sd, Sv, Sar, Sat, PSv, PSa, Dres, Dres/dy, Dres/Sd.
  4. Yielding related quantities: Dyp, Dyn, Gamma (Dinel/Del), Ductility, Pos Ductility, Neg Ductility, YE (Yield Events), Pos YE, Neg YE, Collapse.
  5. Forces: Sfs, Sfd, Sfa, Fyp, Fyn, Cy (Fyp/W), R (Fel/Fyp), Cs (Sfs/W), Eta (Fyp/(M*PGA)) 
  6. Energy and Power: EI, EK, EE, EH, EHnr, ED, PI, PK, PE, PH, PHnr, PD, and DI_BB (damage index).
 

The following table lists the 61 spectral quantities and sdof properties that are available for plotting in the spectral results dialog. Each quantity is listed with its symbol, description, dimensional form and physical units. Highlighted text indicates recent changes and additions to Bispec. See the Bispec Help Manual (installed with software) for more details.



Symbol

Description

Physical Units

Unit

Basic Properties

T

Period

T

s

f

Frequency

F

Hz

K

Stiffness

F/L

Kip/in

Damping %

Damping

-

%

M

Mass

M

Kip*s2/in

Kh

Hardening Stiffness

F/L

Kip/in

Kh/K

Hardening Stiffness Ratio

-

-

Tsec

Post-yield period, corresponding to Kh

T

s

P-Delta ratio

P-Delta Ratio = P/KL, (where L is the effective height)

-

-

C

Damping Coefficient for Linear Viscous Damping (LVD)

F.t/L

Kip.s/in

Csup

Damping Coefficient for Nonlinear Viscous Damping (NLVD)

F.(t/L)α

Kip.(s/in)α

Alpha (α)

Exponent coefficient for Nonlinear Viscoud Damping (NLVD)

-

-

Effective Properties

Teff

Effective Period

T

s

feff

Effective Frequency

F

Hz

Keff

Effective Stiffness

F/L

Kip/in

βIeff %

Effective Inherent (Linear) Viscous Damping (LVD)

-

%

βVeff %

Effective Supplemental (Nonlinear) Viscous Damping (LVD)

-

%

βV+Ieff %

Total Effective Viscous Damping (LVD+NLVD)

-

%

βHeff %

Effective Hysteretic Damping

-

%

βTot_eff %

Total Effective Damping (Hysteretic + Viscous)

-

%

Kinematics (D, V, A)

Sd

Spectral Displacement

L

in

Sv

Spectral Velocity

L/t

in/s

Sar

Spectral Acceleration (Relative)

L/t2

in/s2

Sat

Spectral Acceleration (Absolute)

L/t2

in/s2

PSv

Pseudo-Spectral Velocity = Sd*(2π/T)

L/t

in/s

PSa

Pseudo-Spectral Acceleration = Sd*(2π/T)2

L/t2

in/s2

Dres

Residual Displacement at end of record (Absolute)

L

in

Dres/Dyp

Residual ductility

-

-

Dres/Sd

Dres/Sd ratio

-

-

Yielding

Dyp

Positive yield displacement

L

in

Dyn

Negative yield displacement (Signed)

L

in

Gamma (γ)

Dinel/Del: Ratio of inelastic Sd to elastic Sd

-

-

Ductility

Peak Ratio inelastic displacement to yield displacement,
computed as the larger of "Pos Ductility" and "Neg Ductility"

-

-

Pos Ductility

Positive Ductility (Dmax/Dyp)

-

-

Neg Ductility

Negative Ductility (Dmin/Dyn)

-

-

YE

Number of yielding events

-

-

Pos YE

Number of positive yield events

-

-

Neg YE

Number of negative yield events

-

-

Collapse

Collapse indicator (1: Collapse, 0: No Collapse)

-

-

Forces

Sfs

Hysteretic Force = max(fs)

F

Kip

Sfd

Damping Force = max(fd)

F

Kip

Sfa

Inertia Force = M*Sat, also equal to max(fs+fd)

F

Kip

Fyp

Positive yield force

F

Kip

Fyn

Negative yield force, (Signed)

F

Kip

Cy (Fyp/W)

Normalized Yield Capacity

-

-

R

Fel/Fyp: Ratio of elastic Sfs to Fyp

-

-

Cs (Sfs/W)

Normalized Peak Force

-

-

Eta (η)

Normalized yield strength = Fyp/(M*PGA)

-

-

Energy & Power

EI

Input Energy

F.L

Kip.in

EK

Kinetic Energy

F.L

Kip.in

EE

Elastic Energy

F.L

Kip.in

EH

Hysteretic Energy

F.L

Kip.in

EHnr

Hysteretic Non-Recoverable Energy

F.L

Kip.in

ED

Damping Energy

F.L

Kip.in

PI

Input Power

F.L/t

Kip.in/s

PK

Kinetic Power

F.L/t

Kip.in/s

PE

Elastic Power

F.L/t

Kip.in/s

PH

Hysteretic Power

F.L/t

Kip.in/s

PHnr

Hysteretic Non-Recoverable Power

F.L/t

Kip.in/s

PD

Damping Power

F.L/t

Kip.in/s

DI_BB

Damage index (Bozorgnia and Bertero)

-

-