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Symbols
Symbols
A Cross-sectional area of a pile, Equation Aw Area of shear reinforcement, Equation
(4-9) (7-12)
Cross-sectional area of shear wall Nominal area of the web, Equation (5-7)
boundary members or diaphragm chords Area of link stiffener web, Equation
in.2, Equations (8-2), (8-4), (8-5) (5-28), (5-31)
Area of the web cross section, = bwd,
Ab Gross area of bolt or rivet, Equations
Chapter 6
(5-18), (5-22), (5-24)
Sum of net mortared area of bed joints Ax Accidental torsion amplification factor,
above and below the test unit, Equation Equation (3-1)
(7-2)
B Width of footing, Equations (4-6), (4-7),
Ac Area of column, Equation (5-8) (4-8)
Ae Effective net area of the horizontal leg, B1 Damping coefficient used to adjust one-
Equation (5-20) second period spectral response for the
effect of viscous damping, , Equations
Ag Gross area of the horizontal leg, Equation (1-10), (1-11)
(5-19)
Gross area of cast iron column, Equation BD1 Numerical damping coefficient taken
(5-36) equal to the value of B1, as set forth in
Gross area of column, in.2, Equation (6-4) Table 1-6, at effective damping β equal to
the value of βD, Equation (9-2)
Aj Effective cross-sectional area of a beam-
column joint, in.2, in a plane parallel to BM1 Numerical damping coefficient taken
plane of reinforcement generating shear in equal to the value of B1, as set forth in
the joint calculated as specified in Table 1-6, at effective damping β equal to
Section 6.5.2.3.1, Equation (6-5) the value of βM, Equation (9-4)
An Area of net mortared/grouted section, BS Coefficient used to adjust short-period
Equations (7-1), (7-3), (7-5), (7-7), (7-9), spectral response for the effect of viscous
(7-10), (7-11), (7-13) damping, Equations (1-8), (1-9), (1-11)
Ani Area of net mortared/grouted section of C (or Cj ) Damping coefficient for viscoelastic
masonry infill, Equation (7-15) device (or device j), Equations (9-22),
(9-24), (9-29), (9-30), (9-35), (9-37)
As Area of nonprestressed tension reinforce-
ment, in.2, Tables 6-18, 6-20 C0 Modification factor to relate spectral
Area of reinforcement, Equation (7-13) displacement of an equivalent SDOF sys-
tem to the roof displacement of the build-
A′s Area of compression reinforcement, in.2, ing MDOF system, Equation (3-15)
Tables 6-18, 6-20 Damping coefficient for fluid-viscous
device, Equation (9-25)
C1 Modification factor to relate expected
maximum inelastic displacements to dis-
placements calculated for linear elastic
response, Equations (3-5), (3-6), (3-10),
(3-15), (3-19)
FEMA 356 Seismic Rehabilitation Prestandard Symbols-1
Symbols
C2 Modification factor to represent the effects DCR Demand-capacity ratio, computed in
of pinched hysteresis shape, stiffness deg- accordance with Equation (2-1) or required
radation and strength deterioration on the in Equation (2-2)
maximum displacement response,
____ Average demand-capacity ratio for a story,
Equations (3-5), (3-6), (3-10), (3-15), DCR
(3-19) computed in accordance with Equation
(2-2)
C3 Modification factor to represent increased
displacements due to p-∆ effects, Equa- DD Design displacement, in. (mm) at the cen-
tions (3-5), (3-6), (3-10), (3-15), (3-17), ter of rigidity of the isolation system in the
(3-19) direction under consideration, Equations
(9-2), (9-6), (9-8), (9-10), (9-14), (9-15),
Cb Coefficient to account for effect of nonuni- (9-18), (9-22)
form moment given in AISC (1993) LRFD
Specifications, Equation (5-9) D′D Design Earthquake target displacement, in.
(mm) at a control node located at the cen-
CFi Stage combination factors for use with ter of mass of the first floor above the
velocity-dependent energy dissipation isolation system in the direction under con-
devices as calculated by Equations (9-31) sideration, as prescribed by Equation
or (9-32) (9-10)
Cm Effective mass factor from Table 3-1, DM Maximum displacement, in. (mm) at the
Equations (3-10), (3-16) center of rigidity of the isolation system in
the direction under consideration,
Ct Numerical value for adjustment of period Equations (9-4), (9-7), (9-11), (9-16),
T, Equation (3-7) (9-17), (9-19)
Cvx Vertical distribution factor for the pseudo D′M BSE-2 target displacement, in. (mm) at a
lateral load, Equations (3-11), (3-12) control node located at the center of mass
D Generalized deformation, unitless of the first floor above the isolation system
in the direction under consideration, as
Relative displacement between two ends
prescribed by Equation (9-11)
of an energy dissipation unit, Equations
(9-1), (9-20), (9-22) Dp Relative seismic displacement that the
component must be designed to accommo-
D– Maximum negative displacement of an
date, Equations (11-8), (11-9), (11-10),
energy dissipation unit, Equations (9-21),
(11-11)
(9-23)
Dr Drift ratio for nonstructural components,
D+ Maximum positive displacement of an
Equation (11-7)
energy dissipation unit, Equations (9-21),
(9-23) DTD Total design displacement, in. (mm) of an
• element of the isolation system, including
D Relative velocity between two ends of an
both translational displacement at the
energy dissipation unit, Equations (9-22),
center of rigidity and the component of
(9-25)
torsional displacement in the direction
Dave Average displacement of an energy dissi- under consideration, as specified by
pation unit, equal to (|D+| + |D–|)/2, Equation (9-6)
Equation (9-24)
Dclear Required clearance between a glass
component and the frame, Equation (11-9)
Symbols-2 Seismic Rehabilitation Prestandard FEMA 356
Symbols
DTM Total maximum displacement, in. (mm) of Fcr Allowable axial buckling stress, see
an element of the isolation system, Equation (5-36)
including both translational displacement
at the center of rigidity and the component FEXX Classification strength of weld metal,
of torsional displacement in the direction Chapter 5
under consideration, as specified by Fi Inertia force at floor level i, Equation
Equation (9-7) (9-27)
E Young’s modulus of elasticity, Equations Lateral load applied at floor level i,
(4-9), (5-1), (5-2), (5-17), (8-2), (8-4), Equation (3-13)
(8-5) Fmi m-th mode horizontal inertia force at floor
Ec Modulus of elasticity of concrete, psi, level i, Equation (9-34)
Equation (6-6) Fp Horizontal seismic force for design of a
Efe Expected elastic modulus of frame structural or nonstructural component and
material, ksi, Equation (7-14) its connection to the structure, Equations
(2-3), (2-4), (2-5), (2-6), (2-7)
ELoop Energy dissipated, in kip-inches (kN-mm), Component seismic design force applied
in an isolator unit during a full cycle of horizontally at the center of gravity of the
reversible load over a test displacement component or distributed according to the
range from ∆+ to ∆-, as measured by the mass distribution of the component,
area enclosed by the loop of the Equations (11-1), (11-2), (11-3), (11-4)
force-deflection curve, Equation (9-13)
Fpv Component seismic design force applied
Eme Expected elastic modulus of masonry in vertically at the center of gravity of the
compression as determined per component or distributed according to the
Section 7.3.2.4, Equation (7-14) mass distribution of the component,
Equations (11-2), (11-5), (11-6)
Es Modulus of elasticity of reinforcement,
psi, Chapter 6 Fpx Diaphragm lateral force at floor level x,
Equation (3-13)
Ese Expected elastic modulus of reinforcing
steel per Section 7.3.2.8 Fte Expected tensile strength, Equations
(5-20), (5-22), (5-24)
F Force in an energy dissipation unit,
Equations (9-1), (9-20), (9-22), (9-25) Fv Factor to adjust spectral acceleration at one
second for site class, Equation (1-8)
F– Negative force, in k, in an isolator or Design shear strength of bolts or rivets,
energy dissipation unit during a single Chapter 5
cycle of prototype testing at a displace-
ment amplitude of ∆−, Equations (9-12), Fve Unfactored nominal shear strength of bolts
(9-21), (9-23), (9-38) or rivets given in AISC(1993) LRFD
Specifications, Equation (5-18)
F+ Positive force, in k, in an isolator or energy
Fx Lateral load applied at floor level x,
dissipation unit during a single cycle of
prototype testing at a displacement Equation (3-11)
amplitude of ∆+, Equations (9-12), (9-21), Fy Specified minimum yield stress for the
(9-23), (9-38) type of steel being used, Equation (5-7)
Fa Factor to adjust spectral acceleration in the Fyb Fy of a beam, Chapter 5
short-period range for site class,
Equation (1-7) Fyc Fy of a column, Chapter 5
FEMA 356 Seismic Rehabilitation Prestandard Symbols-3
Symbols
Fye Expected yield strength, Equations (5-1) to J A coefficient used in linear procedures to
(5-8), (5-19), (5-23), (5-25), (5-31), (5-34) estimate the actual forces delivered to
force-controlled components by other
Fyf Fy of a flange, Chapter 5 (yielding) components, Equations (3-5),
(3-19)
FyLB Lower-bound yield strength, Chapter 5
K Length factor for brace; defined in AISC
G Soil Shear modulus, Equation (4-6) (1993) LRFD Specifications, Chapter 5
Shear modulus of steel, Equations (5-28),
(5-33) K’ Storage stiffness as prescribed by Equation
Modulus of rigidity of wood structural (9-23)
panels, psi, Equations (8-2), (8-4), (8-5)
K" Loss stiffness as prescribed by Equation
Gd Shear stiffness of shear wall or diaphragm (9-24)
assembly, Equations (8-1), (8-3) Kθ Rotational stiffness of a partially restrained
Gme Shear modulus of masonry as determined connection, Equations (5-15), (5-16),
per Section 7.3.2.7 (5-17)
Go Initial or maximum shear modulus, Kb Flexural stiffness, Equations (5-27), (5-29)
Equations (4-4), (4-5)
KDmax Maximum effective stiffness, in k/in., of
H Thickness of a soil layer in feet, the isolation system at the design displace-
Chapter 11 ment in the horizontal direction under
Horizontal load on footing, Chapter 4 consideration, as prescribed by Equation
(9-14)
Hrw Height of the retaining wall, Equation
(4-11) KDmin Minimum effective stiffness, in k/in. (kN/
mm), of the isolation system at the design
I Moment of inertia, Equation (6-6) displacement in the horizontal direction
Ib Moment of inertia of a beam, Equations under consideration, as prescribed by
(5-1), (5-17) Equation (9-15)
Ic Moment of inertia of a column, Equation Ke Effective stiffness of the building in the
(5-2) direction under consideration, for use with
the NSP, Equation (3-14)
Icol Moment of inertia of column section, Elastic stiffness of a link beam,
Equation (7-14) Equations (5-27), (5-30)
If Moment of inertia of most flexible frame Ki Elastic stiffness of the building in the
member confining infill panel, Chapter 7 direction under consideration, for use with
the NSP, Equation (3-14)
Ig Moment of inertia of gross concrete sec-
tion about centroidal axis, neglecting KMmax Maximum effective stiffness, in k/in., of
reinforcement, Chapter 6 the isolation system at the maximum
displacement in the horizontal direction
Ip Component performance factor; 1.0 shall under consideration, as prescribed by
be used for the Life Safety Nonstructural Equation (9-16)
Performance Level and 1.5 shall be used
for the Immediate Occupancy Nonstruc- KMmin Minimum effective stiffness, in k/in., of
tural Performance Level, Equations (11-1), the isolation system at the maximum
(11-3), (11-4), (11-5), (11-6) displacement in the horizontal direction
under consideration, as prescribed by
Equation (9-17)
Symbols-4 Seismic Rehabilitation Prestandard FEMA 356
Symbols
Ks Shear stiffness, Equations (5-27), (5-28) MCEx Expected bending strength of a member
about the x-axis, Equations (5-10),
L Length of footing in plan dimension, (5-11), (5-13), (6-1)
Equations (4-7), (4-8)
Length of pile in vertical dimension, MCEy Expected bending strength of a member
Equation (4-9) about y-axis, Equations (5-10), (5-11),
Length of member along which deforma- (5-13), (6-1)
tions are assumed to occur, Chapter 6 MCLx Lower-bound flexural strength of the
Length of wall or pier, Equations (7-4), member about the x-axis, Equation (5-12)
(7-5)
Diaphragm span, distance between shear MCLy Lower-bound flexural strength of the
walls or collectors, Equations (8-3), (8-4), member about the y-axis, Equation (5-12)
(8-5) MgCS Moment acting on the slab column strip,
Lb Length or span of beam, Equations (5-6), Chapter 6
(5-17) Mn Nominal moment strength at section,
Distance between points braced against Chapter 6
lateral displacement of the compression
flange or between points braced to prevent MnCS Nominal moment strength of the slab
twist of the cross-sections; given in AISC column strip, Chapter 6
(1993) LRFD Specifications, Equation
(5-9) MOT Total overturning moment induced on the
element by seismic forces applied at and
Linf Length of infill panel, Equations (7-17), above the level under consideration,
(7-19) Equations (3-5), (3-6)
Lp The limiting unbraced length between MPCE Expected plastic moment capacity,
points of lateral restraint for the full plastic Equation (5-6)
moment capacity to be effective; given in
AISC (1993) LRFD Specifications, MST Stabilizing moment produced by dead
Equations (5-6), (5-9) loads acting on the element, Equations
(3-5), (3-6)
Lr The limiting unbraced length between
points of lateral support beyond which MUD Design moment, Chapter 6
elastic lateral torsional buckling of the
MUDx Design bending moment about x axis for
beam is the failure mode; given in AISC
axial load PUF, kip-in., Equation (6-1)
(1993) LRFD Specifications, Equation
(5-9) MUDy Design bending moment about y axis for
M Design moment at a section, Equation axial load PUF, kip-in., Equation (6-1)
(6-4)
MUFx Bending moment in the member about the
Moment on masonry section, Equation
x-axis, calculated in accordance with
(7-11)
Section 3.4.2.1.2, Equation (5-12)
Mc Ultimate moment capacity of footing,
MUFy Bending moment in the member about the
Equation (4-8)
y-axis, calculated in accordance with
MCE Expected flexural strength of a member or Section 3.4.2.1.2, Equation (5-12)
joint, Equation (5-3), (5-4), (5-6),
Mx Bending moment in a member for the
(5-15), (5-16), (5-18), (5-22), (5-24),
x-axis, Equations (5-10), (5-11), (5-13)
(5-25), (5-26), (5-32)
FEMA 356 Seismic Rehabilitation Prestandard Symbols-5
Symbols
My Bending moment in a member for the Pi Portion of the total weight of the structure
y-axis, Equations (5-10), (5-11), (5-13) including dead, permanent live, and 25%
Yield moment strength at section, of transient live loads acting on the
Equation (6-6) columns and bearing walls within story
level i, Equation (3-2)
N Number of piles in a pile group, Equation
(4-9) Po Nominal axial load strength at zero
eccentricity, Chapter 6
— Average SPT blow count in soil within the
N
upper 100 feet of soil, calculated in PR Mean return period, Equation (1-2)
accordance with Equation (2-8)
PUF Design axial force in a member, Equations
(N1)60 Standard Penetration Test blow count (5-10), (5-11), (5-12)
normalized for an effective stress of 1 ton
per square foot and corrected to an Pye Expected yield axial strength of a member,
equivalent hammer energy efficiency of Equations (5-2), (5-4)
60%, Equation (4-5)
Q Generalized force in a component,
Nb Number of bolts or rivets, Equations Figures 2-3, 2-5, 5-1, 6-1, 7-1, 8-1
(5-18), (5-22), (5-24)
Qallow Allowable bearing load specified for the
Nu Factored axial load normal to cross-section design of deep foundations for gravity
occurring simultaneously with Vu. To be loads (dead plus live loads) in the available
taken as positive for compression, negative design documents, Equation (4-2)
for tension, and to include effects of Qc Expected bearing capacity of deep or
tension due to creep and shrinkage, shallow foundation, Equations (4-2), (4-3),
Equation (6-4) (4-7)
P Vertical load on footing, Equation (4-8) QCE Expected strength of a component or ele-
Axial force in a member, Equations (5-2), ment at the deformation level under con-
(5-4) sideration, Equations (2-1), (3-20), (5-3) to
Pc Lower bound of vertical compressive (5-8), (5-18), (5-22), (5-24), (5-25), (5-26),
strength for wall or pier, Equations (7-7), (5-30), (5-31), (5-32), (5-34), (5-35), (7-3),
(7-4), (7-15)
(7-13)
QCEb Expected bending strength of the beam,
PCE Expected axial strength of a member or
joint, Equations (5-19), (5-20), (5-21), Equation (5-14)
(5-26) QCL Lower-bound estimate of the strength of a
Expected gravity compressive force, component or element at the deformation
Equations (7-1), (7-4) level under consideration, Equations
(3-21), (5-36), (6-5), (7-5) to (7-8), (7-13),
PCL Lower-bound axial strength of column,
(7-21)
Equations (5-10), (5-11), (5-12), (5-36)
Lower bound axial compressive force due QCLc Lower-bound strength of the connection,
to gravity loads specified in Equation (3-4) Equation (5-14)
PEY Probability of exceedance in Y years, QD Design action due to dead load, Equations
expressed as a decimal, Equation (1-2) (3-3), (3-4)
PI Plasticity Index for soil, determined as the QE Design action due to design earthequake
difference in water content of soil at the loads, Equations (3-18), (3-19)
liquid limit and plastic limit,
Section 1.6.1.4.1
Symbols-6 Seismic Rehabilitation Prestandard FEMA 356
Symbols
QG Design action due to gravity loads, SXS Spectral response acceleration parameter
Equation (3-3), (3-4), (3-18), (3-19) at short periods for the selected Earthquake
Hazard Level and damping, adjusted for
QL Design action due to live load, Equations site class, and determined in accordance
(3-3), (3-4) with Section 1.6.1.4 or 1.6.2.1,
QS Design action due to snow load, Equations Equation (1-4), (1-8), (1-9), (1-11), (1-13),
(3-3), (3-4) (1-14), (1-15), (1-16), (4-11), (11-1),
(11-3), (11-4), (11-5), (11-6)
QUD Deformation-controlled design action due
to gravity and earthquake loads, T Fundamental period of the building in the
Equations (2-1), (3-18), (3-20) direction under consideration, seconds,
Equations (1-8), (1-10), (3-7), (3-8),
QUF Force-controlled design action due to grav- (3-9), (3-10), (9-29)
ity and earthquake loads, Equations (3-19), Tensile load in column, Equation (5-13)
(3-21))
T0 Period at which the constant acceleration
Qy Yield strength of a component, region of the design response spectrum
Figures 2-3, 2-5 begins at a value = 0.2TS, Equations (1-8),
Substitute yield strength, Figure 2-5 (1-12)
Q′y
TCE Expected tensile strength of column com-
R Ratio of the elastic-strength demand to the puted in accordance with Equation (5-8)
yield-strength coefficient, Equations
(3-15), (3-16), (3-17) TD Effective period, in seconds, of the
seismic-isolated structure at the design
ROT Response modification factor for overturn- displacement in the direction under
ing moment MOT, Equation (3-6) consideration, as prescribed by Equation
(9-3)
Rp Component response modification factor
from Table 11-2, Equation (11-3)) Te Effective fundamental period of the
building in the direction under consider-
S1 Spectral response acceleration parameter ation, for use with the NSP, Equations
at a one-second period, obtained from (3-14), (3-15), (3-17)
response acceleration maps, Equations Effective fundamental period, in seconds,
(1-1), (1-3), (1-5) of the building structure above the
Sa Spectral response acceleration, g, isolation interface on a fixed base in the
Equations (1-8), (1-9), (1-10), (3-10), direction under consideration, Equations
(3-15), (3-16) (9-10), (9-11)
Sn Distance between nth pile and axis of rota- Ti Elastic fundamental period of the building
tion of a pile group, Equation (4-10) in the direction under consideration, for
use with the NSP, Equation (3-14)
SS Spectral response acceleration parameter
at short periods, obtained from response TM Effective period, in seconds, of the seis-
acceleration maps, Equations (1-1), mic-isolated structure at the maximum dis-
(1-3), (1-7) placement in the direction under
consideration, as prescribed by Equation
SX1 Spectral response acceleration parameter (9-5)
at a one-second period for any earthquake
hazard level and any damping, adjusted for Tm m-th mode period of the rehabilitated
site class, Equations (1-5), (1-10), (1-11), building including the stiffness of the
(1-13), (1-14), (1-15), (1-16) velocity-dependent devices, Equation
(9-35)
FEMA 356 Seismic Rehabilitation Prestandard Symbols-7
Symbols
TS Period at which the constant acceleration Vi The total calculated lateral shear force in
region of the design response spectrum the direction under consideration in an
transitions to the constant velocity region, element or at story i due to earthquake
Equations (1-8), (1-9), (1-10), (1-11), response to the selected ground shaking
(1-12), (1-13), (3-10), (3-15) level, as indicated by the selected linear
analysis procedure, Equations (2-2), (3-2)
Tss Secant fundamental period of a rehabili-
tated building calculated using Equation Vine Expected shear strength of infill panel,
(3-14) but replacing the effective stiffness Equation (7-15)
(Ke) with the secant stiffness (Ks) at the
VmL Lower bound shear strength provided by
target displacement, Equation (9-37)
masonry, Equations (7-8), (7-11)
V Pseudo lateral load, Equations (3-10),
Vn Nominal shear strength at section,
(3-11)
Equation (6-5)
Design shear force at section, Equation
(6-4) Vo Shear strength of slab at critical section,
Shear on masonry section, Equation (7-11) Chapter 6
V* Modified equivalent base shear, Chapter 9 Vpz Panel zone shear, Chapter 5
Vb The total lateral seismic design force or Vr Expected shear strength of wall or pier
shear on elements of the isolation system based on rocking shear, Equation (7-4)
or elements below the isolation system, as
prescribed by Equation (9-8) Vs Nominal shear strength provided by shear
reinforcement, Chapter 6
Vbjs Expected shear strength of wall or pier The total lateral seismic design force or
based on bed-joint sliding shear stress, see shear on elements above the isolation
Equation (7-3) system, as prescribed by Section 9.2.4.4.2,
Equation (9-9)
Vc Nominal shear strength provided by
concrete, Equation (6-4) VsL Lower bound shear strength provided by
shear reinforcement, Equations (7-8),
VCE Expected shear strength of a member, (7-12)
Equations (5-11), (5-31), (5-32),
(5-34) Vt Base shear in the building at the target
displacement, Chapter 3
VCL Lower bound shear strength, Equations
(7-8), (7-9), (7-10) Vtc Lower bound shear strength based on toe
compressive stress for wall or pier,
Vdt Lower bound shear strength based on Chapter 7
diagonal tension stress for wall or pier,
Chapter 7 Vtest Test load at first movement of a masonry
unit, Equation (7-2)
Vfre Expected story shear strength of the bare
steel frame taken as the shear cpacity of Vu Factored shear force at section, Chapter 6
the column, Chapter 7
Vy Yield strength of the building in the direc-
Vg Shear acting on slab critical section due to tion under consideration, for use with the
gravity loads, Chapter 6 NSP, Equation (3-16)
Vya Nominal shear strength of a member modi-
fied by the axial load magnitude, Chapter 5
Symbols-8 Seismic Rehabilitation Prestandard FEMA 356
Symbols
W Weight of a component, calculated as a Parameter used to measure deformation
specified in this standard, Chapter 2. capacity in component load-deformation
Effective seismic weight of a building curves, Figures 2-3, 5-1, 6-1
including total dead load and applicable Clear width of wall between columns,
portions of other gravity loads listed in Equations (5-33), (5-34)
Section 3.3.1.3.1, Equations (3-10), (3-16) Equivalent width of infill strut,
The total seismic dead load in kips (kN). Equations (7-14), (7-16), (7-17), (7-18),
For design of the isolation system, W is the (7-19)
total seismic dead-load weight of the
a′ Parameter used to measure deformation
structure above the isolation interface,
capacity in component load-deformation
Equations (9-3), (9-5)
curve, Figure 2-5
WD Energy dissipated in a building or element
thereof or energy dissipation device during ap Component amplification factor from
a full cycle of displacement, Equations Table 11-2, Equation (11-3)
(9-24), (9-39) b Parameter used to measure deformation
Wj Work done by an energy dissipating capacity in component load-deformation
device, j, in one complete cycle corre- curves, Figures 2-3, 5-1, 6-1
sponding to floor displacement, Equations Shear wall length or width, Equations
(9-26), (9-28), (9-29), (9-36), (9-37) (8-1), (8-2)
Diaphragm width, Equations (8-4), (8-5)
Wk Maximum strain energy in a frame as cal- The shortest plan dimension of the rehabil-
culated by Equation (9-27) itated building, in ft. (mm), measured
Wmj Work done by device j in one complete perpendicular to d, Equations (9-6), (9-7)
cycle corresponding to modal floor ba Connection dimension, Equations (5-22),
displacements δmi Equation (9-33) (5-23)
Wmk Maximum strain energy in the frame in the bbf Beam flange width in Equations for Beam-
m-th mode determined using Equation Column Connections in Sections 5.5.2.4.2
(9-34) and 5.5.2.4.3
Wp Component operating weight, bcf Column flange width in Equations for
Equations (11-1), (11-3), (11-4), (11-5), Beam-Column Connections in
(11-6) Sections 5.5.2.4.2 and 5.5.2.4.3
X Height of upper support attachment at bf Flange width, Tables 5-5, 5-6, 5-7
level x as measured from grade, see
Equation (11-7) bp Width of rectangular glass, Equation
(11-9)
Y Time period in years corresponding to a
mean return period and probability of bt Connection dimension, Equations (5-24),
exceedance, Equation (1-2) (5-25)
Height of lower support attachment at bw Web width, in., Equation (6-4)
level y as measured from grade, see
Equation (11-7) c Parameter used to measure residual
Z Plastic section modulus, Equations (5-1), strength, Figures 2-3, 5-1, 6-1, 7-1, 8-1
(5-2), (5-3), (5-4), (5-6)
Z’ Adjusted resistance for mechanical
fastener, Chapter 8
FEMA 356 Seismic Rehabilitation Prestandard Symbols-9
Symbols
c1 Size of rectangular or equivalent rectangu- e Length of EBF link beam, Equations
lar column, capital, or bracket measured in (5-28), (5-29), (5-30), (5-32)
the direction of the span for which Parameter used to measure deformation
moments are being determined, in, capacity, Figures 2-3, 5-1, 6-1, 7-1, 8-1
Section 6.5.4.3 Actual eccentricity, ft. (mm), measured in
Clearance (gap) between vertical glass plan between the center of mass of the
edges and the frame, Equation (11-9) structure above the isolation interface and
the center of rigidity of the isolation
c2 Clearance (gap) between horizontal glass system, plus accidental eccentricity, ft.
edges and the frame, Equation (11-9) (mm), taken as 5% of the maximum build-
d Depth of soil sample for calculation of ing dimension perpendicular to the direc-
effective vertical stress, Equation (4-5) tion of force under consideration,
Parameter used to measure deformation Equations (9-6), (9-7)
capacity, Figures 2-3, 5-1, 6-1, 7-1, 8-1 en Nail deformation at yield load per nail for
Distance from extreme compression fiber wood structural panel sheathing,
to centroid of tension reinforcement, in., Equations (8-2), (8-4), (8-5)
Equation (6-4)
The longest plan dimension of the rehabili- f1 Fundamental frequency of the building,
tated building, in ft. (mm), Equations Equation (9-24)
(9-6), (9-7)
fa Axial compressive stress due to gravity
da Elongation of anchorage at end of wall loads specified in Equations (3-3), (7-5),
determined by anchorage details and load (7-6)
magnitude, Equation (8-1)
fae Expected vertical compressive stress,
Deflection at yield of tie-down anchorage Chapter 7
or deflection at load level to anchorage at
end of wall determined by anchorage fc Compressive strength of concrete, psi,
details and dead load, in., Equation (8-2) Equations (6-4), (6-5)
db Overall beam depth, Equations (5-7), f ′dt Lower bound masonry diagonal tension
(5-8), (5-21), (5-22), (5-23), (5-24), (5-25), strength, Equation (7-5)
(5-26), (5-29)
Nominal diameter of bar, in., Equation f ′m Lower bound masonry compressive
(6-3) strength, Equations (7-6), (7-7), (7-9),
(7-10), (7-11), (7-13), (7-21)
dbg Depth of the bolt group, Table 5-5
fme Expected compressive strength of masonry
dc Column depth, Equation (5-5) as determined in Section 7.3.2.3
di Depth, in feet, of a layer of soils having fpc Average compressive stress in concrete
similar properties, and located within 100 due to effective prestress force only (after
feet of the surface, Equations (1-6), (1-7) allowance for all prestress losses),
Chapter 6
dv Length of component in the direction of
shear force, Equations (7-11), (7-12) fs Stress in reinforcement, psi, Equations
(6-2), (6-3)
dw Depth to ground-water level, Equation
(4-5) f ′t Lower bound masonry tensile strength,
Chapter 7
dz Overall panel zone depth between continu-
ity plates, Chapter 5 fte Expected masonry flexural tensile strength
as determined in Section 7.3.2.5
Symbols-10 Seismic Rehabilitation Prestandard FEMA 356
Symbols
fvie Expected shear strength of masonry infill, hn Height to roof level, ft, Equation (3-7)
Equation (7-15)
hp Height of rectangular glass, Equation
fy Yield strength of tension reinforcement, (11-9)
Equations (6-2), (6-3)
Lower bound of yield strength of reinforc- hx Height from base to floor level x, ft,
ing steel, Equations (7-12), (7-13) Equations (3-12), (9-9)
fye Expected yield strength of reinforcing steel k Exponent used for determining the vertical
as determined in Section 7.3.2.8 distribution of lateral forces, Equation
(3-12)
g Acceleration of gravity (386.1 in./sec.2, or Coefficient used for calculation of column
9,807 mm/sec2 for SI units), Equations shear strength, Chapter 6
(3-15), (9-2), (9-3), (9-4), (9-5), (9-30)
k1 Distance from the center of the split tee
h Average story height above and below a stem to the edge of the split tee flange fil-
beam-column joint, Equation (5-17) let, Equation (5-25)
Clear height of wall between beams, keff Effective stiffness of an isolator unit, as
Equations (5-33), (5-35) prescribed by Equation (9-12), or an
Distance from inside of compression energy dissipation unit, as prescribed by
flange to inside of tension flange, Equation Equations (9-23) or (9-38)
(5-7)
Height of member along which deforma- kh Horizontal seismic coefficient in soil act-
tions are measured, Chapter 6 ing on retaining wall, Equation (4-11)
Overall thickness of member, in,
ksr Winkler spring stiffness in overturning
Equation (6-4)
(rotation) for pile group, expressed as
Height of a column, pilaster, or wall, moment/unit rotation, Equation (4-10)
Chapter 7
Shear wall height, Equations (8-1), (8-2) ksv Winkler spring stiffness in vertical direc-
Average roof elevation of structure, tion, expressed as force/unit displacement/
relative to grade elevation, Equation (11-3) unit area, Equation (4-6)
Pile group axial spring stiffness expressed
hc Assumed web depth for stability, as force/unit displacement, Equation (4-9)
Chapter 5
Gross cross-sectional dimension of column kv Shear buckling coefficient, Chapter 5
core measured in the direction of joint
shear, in, Chapter 6 kvn Axial stiffness of nth pile in a pile group,
Equation (4-10)
hcol Height of column between beam center-
lines, Equation (7-14) lb Length of beam, Equation (5-1)
Provided length of straight development,
heff Effective height of wall or pier compo- lap splice, or standard hook, in., Equation
nents under consideration, Equations (7-4), (6-2)
(7-5), (7-6)
lbeff Assumed distance to infill strut reaction
hi Height from the base of a building to floor point for beams, Equation (7-18)
level i, Equations (3-12), (9-9)
Height of story i between two floors at lc Length of column, Equations (5-2), (5-36)
common points of reference, Equation
(3-2) lceff Assumed distance to infill strut reaction
point for columns, Equation (7-16)
hinf Height of infill panel, Equations (7-14),
(7-17), (7-19), (7-20), (7-21)
FEMA 356 Seismic Rehabilitation Prestandard Symbols-11
Symbols
ld Required length of development for a rinf Diagonal length of infill panel, Equation
straight bar, in., Equation (6-2) (7-14)
le Length of embedment of reinforcement, s Spacing of shear reinforcement, Equation
in., Equation (6-3) (7-12)
lp Length of plastic hinge used for calcula- si Minimum separation distance between
tion of inelastic deformation capacity, in., adjacent buildings at level i, Equation
Equation (6-6) (2-8)
lw Length of entire wall or a segment of wall su Undrained shear strength of soil, pounds/
considered in the direction of shear force, ft.2, Chapter 1
in., Chapter 6
— Average value of the undrained soil shear
su
m Modification factor used in the acceptance strength in the upper 100 feet of soil, cal-
criteria of deformation-controlled compo- culated in accordance with Equation (1-6),
nents or elements, indicating the available pounds/ft.2
ductility of a component action, Equations
(3-20), (5-9) t Effective thickness of wood structural
panel or plywood for shear, in., Equations
me Effective m-factor, Equation (5-9) (8-2), (8-4), (8-5)
mt Value of m-factor for the column in ten- ta Thickness of angle, Equations (5-21),
sion, Equation (5-13) (5-23)
mx Value of m for bending about x-axis of a tbf Thickness of beam flange, Chapter 5
member, Equations (5-10), (5-11),
(5-13), (6-1) tbw Thickness of beam web, Chapter 5
my Value of m for bending about y-axis of a tcf Thickness of column flange, Chapter 5
member, Equations (5-10), (5-11),
(5-13), (6-1) tcw Thickness of column web, Chapter 5
n Total number of stories in a vertical seis- tf Thickness of flange, Equations (5-25),
mic framing, Equations (3-12), (3-13) (5-29)
pD+L Expected gravity stress at test location, tinf Thickness of infill panel, Equations (7-14),
Equation (7-2) (7-20), (7-21)
q Vertical bearing pressure, Equation (4-8) tp Thickness of panel zone including doubler
qallow Allowable bearing pressure specified in plates, Equation (5-5)
the available design documents for the Thickness of flange plate, Equation (5-26)
design of shallow foundations for gravity ts Thickness of split tee stem, Equations
loads (dead plus live loads), Equation (4-1) (5-24), (5-25)
qc Expected bearing capacity of shallow tw Thickness of web, Equations (5-7), (5-29)
foundation expressed in load per unit area, Thickness of plate wall, Equation (5-33)
Equations (4-1), (4-3), (4-7), (4-8)
Thickness of wall web, in., Chapter 6
qin Expected transverse strength of an infill
tz Thickness of panel zone (doubler plates
panel, Equation (7-21)
not necessarily included), Chapter 5
r Governing radius of gyration, Equation
v Maximum shear in the direction under
(5-36)
consideration, Equation (8-5)
Symbols-12 Seismic Rehabilitation Prestandard FEMA 356
Symbols
vme Expected masonry shear strength, ∆− Negative displacement amplitude, in.
Equation (7-1) (mm), of an isolator or energy dissipation
Expected masonry bed-joint sliding shear unit during a cycle of prototype testing,
strength, Equation (7-3) Equations (9-12), (9-13), (9-38)
vte Average bed-joint shear strength, Equation ∆+ Positive displacement amplitude, in. (mm),
(7-1) of an isolator or energy dissipation unit
during a cycle of prototype testing,
vto Bed-joint shear stress from single test, Equations (9-12), (9-13), (9-38)
Equation (7-2)
∆ave Average displacement of an energy dissi-
vy Shear at yield in the direction under pation unit during a cycle of prototype
consideration in lb./ft., Equations (8-1),
testing, equal to (|∆+| + |∆−|)/2, Equation
(8-2), (8-3), (8-4), (8-5)
(9-39)
w Water content of soil, calculated as the
∆d Diaphragm deformation, Equations (3-8),
ratio of the weight of water in a unit
(3-9)
volume of soil to the weight of soil in the
unit volume, expressed as a percentage, ∆eff Differentiated displacement between the
Section 1.6.1.4.1 top and bottom of the wall or pier compo-
Length of connection member, see nents under consideration over a height,
Equations (5-23), (5-25) heff, Figure 7-1
wi Portion of the effective seismic weight ∆fallout Relative seismic displacement (drift)
corresponding to floor level i, Equations causing glass fallout from the curtain wall,
(3-12), (3-13), (9-9) storefront, or partition, as determined in
wx Portion of the effective seismic weight accordance with an approved engineering
corresponding to floor level x, Equations analysis method, Equations (11-10),
(3-12), (3-13), (9-9) (11-11)
wz Width of panel zone between column ∆i Inter-story displacement (drift) of story i
flanges, Chapter 5 divided by the story height, Chapter 5
x Elevation in structure of component ∆i1 Estimated lateral deflection of building 1
relative to grade elevation, Equation (11-3) relative to the ground at level i,
Equation (2-8)
y The distance, in ft. (mm), between the
center of rigidity of the isolation system ∆i2 Estimated lateral deflection of building 2
rigidity and the element of interest, relative to the ground at level i,
measured perpendicular to the direction of Equation (2-8)
seismic loading under consideration, ∆inf Deflection of infill panel at mid-length
Equations (9-6), (9-7) when subjected to transverse loads,
∆ Generalized deformation, Figures 2-3, 2-5, Equation (7-20)
5-1, 6-1, 8-1 ∆p Additional earth pressure on retaining wall
Total elastic and plastic displacement, due to earthquake shaking, Equation
Chapter 5 (4-11)
Calculated deflection of diaphragm, wall,
or bracing element, in. ∆w Average in-plane wall displacement,
Equation (3-8)
FEMA 356 Seismic Rehabilitation Prestandard Symbols-13
Symbols
∆y Generalized yield deformation, unitless, Σ|F -M|max Sum, for all isolator units, of the maximum
Figure 5-1 absolute value of force, in kips (kN), at a
Calculated deflection of diaphragm, shear negative displacement equal to DM,
wall, or bracing element at yield, see Equation (9-16)
Equations (8-1), (8-2), (8-3), (8-4), (8-5)
Σ|F -M|min Sum, for all isolator units, of the minimum
Σ(∆ cX) Sum of individual chord-splice slip values absolute value of force, in kips (kN), at a
on both sides of the diaphragm, each negative displacement equal to DM,
multiplied by its distance to the nearest Equation (9-17)
support, Equations (8-4), (8-5)
α Ratio of post-yield stiffness to effective
ΣED Total energy dissipated, in in-kips, in the stiffness, Equation (3-17)
isolation system during a full cycle of Factor equal to 0.5 for fixed-free cantile-
response at the design displacement, DD, vered shear wall, or 1.0 for fixed-fixed
Equation (9-18) pier, Equation (7-4)
ΣEM Total energy dissipated, in in-kips, in the Velocity exponent for a fluid viscous
isolation system during a full cycle of device in Equation (9-25)
response at the maximum displacement,
β Modal damping ratio, Table 1-6
DM, Equation (9-19)
Factor to adjust fundamental period of the
building, Equation (3-7)
Σ|F+D|max Sum, for all isolator units, of the maximum
absolute value of force, in kips (kN), at a Ratio of expected frame strength, vfre, to
positive displacement equal to DD, expected infill strength, vine, Chapter 7
Equation (9-14) Damping inherent in the building frame
(typically equal to 0.05), Equations (9-26),
Σ|F+D|min Sum, for all isolator units, of the minimum (9-28), (9-30)
absolute value of force, in kips (kN), at a
positive displacement equal to DD, βb Equivalent viscous damping of a bilinear
Equation (9-15) system, Chapter 9
Σ|F+M|max Sum, for all isolator units, of the maximum βD Effective damping of the isolation system
absolute value of force, in kips (kN), at a at the design displacement, as prescribed
positive displacement equal to DM, by Equation (9-18))
Equation (9-16) βeff Effective damping of isolator unit, as
prescribed by Equation (9-13), or an
Σ|F+ M|min Sum, for all isolator units, of the minimum
absolute value of force, in kips (kN), at a energy dissipation unit, as prescribed by
positive displacement equal to DM, Equation (9-39); also used for the effective
damping of the building, as prescribed by
Equation (9-17) Equations (9-26), (9-28), (9-30), (9-31),
Σ|F -D|max Sum, for all isolator units, of the maximum (9-32), (9-36)
absolute value of force, in kips (kN), at a βeff-m Effective damping in m-th mode
negative displacement equal to DD, prescribed by Equation (9-33)
Equation (9-14)
βM Effective damping of the isolation system
Σ|F -D|min Sum, for all isolator units, of the minimum at the maximum displacement, as
absolute value of force, in kips (kN), at a prescribed by Equation (9-19))
negative displacement equal to DD,
Equation (9-15) βm m-th mode damping in the building frame,
Equation (9-33)
Symbols-14 Seismic Rehabilitation Prestandard FEMA 356
Symbols
γ Unit weight, weight/unit volume (pounds/ θ Generalized deformation, radians,
ft3 or N/m3), Equation (4-4) Figures 5-1, 6-1
Coefficient for calculation of joint shear Angle between infill diagonal and horizon-
strength, Equation (6-5) tal axis, tanθ = hinf/Linf, radians, see
Equation (7-14)
γf Fraction of unbalanced moment trans-
ferred by flexure at slab-column θb Angle between lower edge of compressive
connections, Chapter 6 strut and beam, radians, Equations (7-18),
(7-19)
γt Total unit weight of soil, Equations (4-5),
(4-11) θc Angle between lower edge of compressive
strut and column, radians, Equations
γw Unit weight of water, Equation (4-5)
(7-16), (7-17)
δi Lateral drift in story i, in the direction θi Stability coefficient indicative of the
under consideration, at its center of stability of a structure under gravity loads
rigidity, using the same units as for mea- and earthquake-induced deflection,
suring hi, Equation (3-2) Equation (3-2)
Displacement at floor i, Equations (9-26), Inter-story drift ratio, radians, Chapter 5
(9-27)
θj Angle of inclination of energy dissipation
δmi m-th mode horizontal displacement at floor device, Equation (9-30)
i, Equation (9-34)
θy Generalized yield deformation, radians,
δmrj m-th relative displacement between the Figure 5-1
ends of device j along its axis, Yield rotation, radians, Equations (5-1),
Equation (9-35) (5-2), (5-30), (5-35), (6-6)
δrj Relative displacement between the ends of κ A knowledge factor used to reduce
energy dissipating device j along the axis component strength based on the level of
of the device, Equations (9-29), (9-37) knowledge obtained for individual compo-
δt Target displacement, Figure 3-1 nents during data collection, Equations
(3-20), (3-21), (6-1)
δxA Deflection at level x of Building A, λ Correction factor related to unit weight of
determined by an elastic analysis as concrete, Equation (6-5)
defined in Chapter 3, Equations (11-7),
(11-8) λ1 Coefficient used to determine equivalent
width of infill strut, Equation (7-14)
δxB Deflection at level x of Building B, deter-
mined by an elastic analysis as defined in λ2 Infill slenderness factor, Equation (7-21)
Chapter 3, Equation (11-8)
λp Limiting slenderness parameter for
δyA Deflection at level y of Building A, deter- compact element, Chapter 5
mined by an elastic analysis as defined in
Chapter 3, Equation (11-7) λr Limiting slenderness parameter for
noncompact element, Chapter 5
η Displacement multiplier, greater than 1.0,
to account for the effects of torsion, µ Coefficient of shear friction, Chapter 6
Equation (3-1)
ν Poisson’s ratio of soil, Equation (4-4)
FEMA 356 Seismic Rehabilitation Prestandard Symbols-15
Symbols
νs Shear wave velocity in soil, in feet/sec.,
Section 1.6.1.4.1
Shear wave velocity at low strains,
Equation (4-4)
__ Average value of the soil shear wave
vs
velocity in the upper 100 feet of soil,
calculated in accordance with Equation
(1-6), feet/sec.
ρ Ratio of non-prestressed tension reinforce-
ment, Chapter 6
ρbal Reinforcement ratio producing balanced
strain conditions, Chapter 6
ρg Ratio of area of total wall or pier vertical
plus horizontal reinforcement to area of
wall or pier cross-section, Chapter 7
ρlp Yield deformation of a link beam,
Chapter 5
ρn Ratio of distributed shear reinforcement in
a plane perpendicular to the direction of
the applied shear, Chapter 6
ρ′ Ratio of non-prestressed compression
reinforcement, Chapter 6
ρ′′ Reinforcement ratio for transverse joint
reinforcement, Chapter 6
σ Standard deviation of the variation of the
material strengths, Chapter 2
σ′o Effective vertical stress, Equation (4-5)
φ Strength reduction factor
φi Modal displacement of floor i, see
Equation (9-30)
φrj Relative modal displacement in horizontal
direction of energy dissipation device j,
Equation (9-30)
χ A factor to calculate horizontal seismic
force, Fp, Equations (2-6), (2-7)
ω1 Fundamental angular frequency equal to
2πf1, Equation (9-24)
Symbols-16 Seismic Rehabilitation Prestandard FEMA 356
