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:

Basic Properties: Period (T), frequency (f), Stiffness (K), Damping Ratio (ζ ), 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 (α).
Effective Properties: Effective Period (Teff), Effective Frequency (feff), Effective Stiffness (Keff), Effective Linear Viscous Damping (βIeff), Effective Nonlinear Viscous Damping (βVeff), Total Effective Viscous Damping (βV+Ieff), Effective Hysteretic Damping (βHeff), and Total Effective Damping (βTot_eff).
Kinematics (D, V, A): Sd, Sv, Sar, Sat, PSv, PSa, Dres, Dres/dy, Dres/Sd.
Yielding related quantities: Dyp, Dyn, Gamma (Dinel/Del), Ductility, Pos Ductility, Neg Ductility, YE (Yield Events), Pos YE, Neg YE, Collapse.
Forces: Sfs, Sfd, Sfa, Fyp, Fyn, Cy (Fyp/W), R (Fel/Fyp), Cs (Sfs/W), Eta (Fyp/(M*PGA))
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.

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	F	Kip
Sfd	Damping Force	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, (Singed)	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)	-	-

In general, most spectral quantities correspond to the peak of a particular quantity over the full duration of the response of the single-degree-of-freedom (SDOF) system to the ground motion. For example, EK (Kinetic Energy) is the peak kinetic energy over the full response duration. There are exceptions to this however, like for-example the residual displacement (see following section "Residual Displacement").