Seismic Notations

The unit dimensions used with the items covered by the symbols shall be consistent throughout except where specifically noted. Notation presented in this section applies only to the seismic requirements in this standard as indicated.

Ach = cross-sectional area (in.2 ormm2) of a structural member measured out-to-out of transverse reinforcement

A0 = area of the load-carrying foundation (ft2 or m2)

Ash = total cross-sectional area of hoop reinforcement (in.2 or mm2), including supplementary cross-ties, having a spacing of sh and crossing a section with a core dimension of hc

Avd = required area of leg (in.2 or mm2) of diagonal reinforcement

Ax = torsional amplification factor (Section 12.8.4.3)

ai = the acceleration at level i obtained from a modal analysis (Section 13.3.1)

ap = the amplification factor related to the response of a system or component as affected by the type of seismic attachment, determined in Section 13.3.1

bp = the width of the rectangular glass panel

Cd = deflection amplification factor as given in Tables 12.2-1, 15.4-1, or 15.4-2

Cs = seismic response coefficient determined in Section 12.8.1.1 and 19.3.1 (dimensionless)

CT = building period coefficient in Section 12.8.2.1

Cvx = vertical distribution factor as determined in Section 12.8.3

c = distance from the neutral axis of a flexural member to the fiber of maximum compressive strain (in. or mm)

D = the effect of dead load

Dclear = relative horizontal (drift) displacement, measured over the height of the glass panel under consideration, which causes initial glass-to-frame contact. For rectangular glass panels within a rectangular wall frame, Dclear is set forth in Section 13.5.9.1

Dp = relative seismic displacement that a component must be designed to accommodate as defined in Section 13.3.2

Ds = the total depth of stratum in Eq. 19.2-12 (ft or m)

dC = The total thickness of cohesive soil layers in the top 100 ft (30 m); see Section 20.4.3 (ft or m)

di = The thickness of any soil or rock layer i (between0 and 100 ft [30 m]); see Section 20.4.1 (ft or m)

dS = The total thickness of cohesionless soil layers in the top 100 ft (30 m); see Section 20.4.2 (ft or m)

E = effect of horizontal and vertical earthquakeinduced forces (Section 12.4)

Fa = short-period site coefficient (at 0.2 s-period); see Section 11.4.3

Fi , Fn, Fx = portion of the seismic base shear, V, induced at Level i , n, or x, respectively, as determined in Section 12.8.3

Fp = the seismic force acting on a component of a structure as determined in Section 13.3.1

Fv = long-period site coefficient (at 1.0 s-period); see Section 11.4.3

f 'c = specified compressive strength of concrete used in design

f 's = ultimate tensile strength (psi or MPa) of the bolt, stud, or insert leg wires. For A307 bolts or A108 studs, it is permitted to be assumed to be 60,000 psi (415 MPa).

fy = specified yield strength of reinforcement (psi or MPa)

fyh = specified yield strength of the special lateral reinforcement (psi or kPa)

G = γv2 so/g = the average shear modulus for the soils beneath the foundation at large strain levels (psf or Pa)

G0 = γv2 so/g = the average shear modulus for the soils beneath the foundation at small strain levels (psf or Pa)

g = acceleration due to gravity

H = thickness of soil

h = height of a shear wall measured as the maximum clear height from top of foundation to bottom of diaphragm framing above, or the maximum clear
height from top of diaphragm to bottom of diaphragm framing above

h = average roof height of structure with respect to the base; see Chapter 13

¯h = effective height of the building as determined in Section 19.2.1.1 or 19.3.1 (ft or m)

hc = core dimension of a component measured to the outside of the special lateral reinforcement (in. or mm)

hi , hn, hx = the height above the base to Level i , n, or x, respectively

h p = the height of the rectangular glass panel

hsx = the story height below Level x = (hx − hx−1)

I = the importance factor in Section 11.5.1

I0 = the static moment of inertia of the load-carrying foundation; see Section 19.2.1.1 (in.4 or mm4)

Ip = the component importance factor as prescribed in Section 13.3.1

i = the building level referred to by the subscript i ;

i = 1 designates the first level above the base

Kp = the stiffness of the component or attachment, Section 13.6.2

Ky = the lateral stiffness of the foundation as defined in Section 19.2.1.1 (lb/in. or N/m)

Kθ = the rocking stiffness of the foundation as defined in Section 19.2.1.1 (ft-lb/degree or N-m/rad)

KL/r = the lateral slenderness ratio of a compression member measured in terms of its effective length,

KL, and the least radius of gyration of the member cross section, r

k = distribution exponent given in Section 12.8.3

¯k = stiffness of the building as determined in Section 19.2.1.1 (lb/ft or N/m)

L = overall length of the building (ft or m) at the base in the direction being analyzed

L0 = overall length of the side of the foundation in the direction being analyzed, Section 19.2.1.2 (ft or m)

M0, M01 = the overturning moment at the foundation-soil interface as determined in Sections 19.2.3 and 19.3.2 (ft-lb or N-m)

Mt = torsional moment resulting from eccentricity between the locations of center of mass and the center of rigidity (Section 12.8.4.1)

Mta = accidental torsional moment as determined in Section 12.8.4.2

m = a subscript denoting the mode of vibration under consideration; that is, m = 1 for the fundamental mode

N = standard penetration resistance, ASTM 1586

N = number of stories (Section 12.8.2.1)

¯N = Average field standard penetration resistance for the top 100 ft (30 m); see Sections 20.3.3 and 20.4.2

¯N ch = average standard penetration resistance for cohesionless soil layers for the top 100 ft (30 m); see Sections 20.3.3 and 20.4.2

Ni = Standard penetration resistance of any soil or rock layer i (between 0 and 100 ft [30 m]); see Section 20.4.2

n = designation for the level that is uppermost in the main portion of the building

Px = total unfactored vertical design load at and above Level x, for use in Section 12.8.7

PI = plasticity index, ASTM D4318

QE = effect of horizontal seismic (earthquake-induced)
forces

R = response modification coefficient as given in
Tables 12.2-1, 12.14-1, 15.4-1, or 15.4-2

Rp = component response modification factor as defined in Section 13.3.1

r = a characteristic length of the foundation as defined in Section 19.2.1.2.

ra = characteristic foundation length as defined by Eq. 19.2-7 (ft or m)

rm = characteristic foundation length as defined by Eq. 19.2-8 (ft or m)

SS = mapped MCE, 5 percent damped, spectral response acceleration parameter at short periods as defined in Section 11.4.1

S1 = mapped MCE, 5 percent damped, spectral response acceleration parameter at a period of 1 s as defined in Section 11.4.1

SaM = the site-specific MCE spectral response acceleration at any period

SDS = design, 5 percent damped, spectral response acceleration parameter at short periods as defined in Section 11.4.4

SD1 = design, 5 percent damped, spectral response acceleration parameter at a period of 1 s as defined in Section 11.4.4

SMS = the MCE, 5 percent damped, spectral response acceleration at short periods adjusted for site class effects as defined in Section 11.4.3

SM1 = the MCE, 5 percent damped, spectral response acceleration at a period of 1 s adjusted for site class effects as defined in Section 11.4.3

su = undrained shear strength; see Section 20.4.3

¯su = average undrained shear strength in top 100 ft (30 m); see Sections 20.3.3 and 20.4.3, ASTM D2166 or ASTM D2850

sui = undrained shear strength of any cohesive soil layer i (between 0 and 100 ft [30 m]); see Section 20.4.3

sh = spacing of special lateral reinforcement (in. or mm)

T = the fundamental period of the building

˜T ˜T1 = the effective fundamental period (s) of the building as determined in Sections 19.2.1.1 and 19.3.1

Ta = approximate fundamental period of the building as determined in Section 12.8.2

TL = long-period transition period as defined in Section 11.4.5

Tp = fundamental period of the component and its attachment, Section 13.6.2

T0 = 0.2SD1/SDS

TS = SD1/SDS

T4 = net tension in steel cable due to dead load, prestress, live load, and seismic load (Section 14.1.7)

V = total design lateral force or shear at the base

Vt = design value of the seismic base shear as determined in Section 12.9.4

Vx = seismic design shear in story x as determined in Section 12.8.4 or 12.9.4

˜V = reduced base shear accounting for the effects of soil structure interaction as determined in Section 19.3.1

V1 = portion of the reduced base shear, ˜V , contributed by the fundamental mode, Section 19.3 (kip or kN)

V = reduction in V as determined in Section 19.3.1 (kip or kN)

V1 = reduction in V1 as determined in Section 19.3.1 (kip or kN)

vs = shear wave velocity at small shear strains (equal to 10−3 percent strain or less); see Section 20.4.1 (ft/s or m/s)

¯vs = average shearwave velocity at small shear strains in top 100 ft (30 m); see Sections 20.3.3 and 20.4.1

vsi = the shear wave velocity of any soil or rock layer i (between 0 and 100 ft [30 m]); see Section 20.4.1

vso = average shear wave velocity for the soils beneath the foundation at small strain levels, Section 19.2.1.1 (ft/s or m/s)

W = effective seismic weight of the building as defined in Section 12.7.2. For calculation of seismic-isolated building period, W is the total effective seismic weight of the building as defined in Sections 19.2 and 19.3 (kip or kN)

¯W = effective seismic weight of the building as defined in Sections 19.2 and 19.3 (kip or kN)

Wc = gravity load of a component of the building

Wp = component operating weight (lb or N)

w = moisture content (in percent), ASTM D2216

wi,wn,wx = portion of W that is located at or assigned to Level i , n, or x, respectively

x = level under consideration, 1 designates the first level above the base

z = height in structure of point of attachment of component with respect to the base; see Section 13.3.1

β = ratio of shear demand to shear capacity for the story between Level x and x − 1

¯β = fraction of critical damping for the coupled structure-foundation system, determined in Section 19.2.1

β0 = foundation damping factor as specified in Section 19.2.1.2

γ = average unit weight of soil (lb/ft3 or N/m3)

 = design story drift as determined in Section 12.8.6

fallout = the relative seismic displacement (drift) at which glass fallout from the curtain wall, storefront, or partition occurs

a = allowable story drift as specified in Section 12.12.1

δmax = maximum displacement at Level x, considering torsion, Section 12.8.4.3

δavg = the average of the displacements at the extreme points of the structure at Level x, Section 12.8.4.3

δx = deflection of Level x at the center of the mass at and above Level x, Eq. 12.8-15

δxe = deflection of Level x at the center of the mass at and above Level x determined by an elastic analysis, Section 12.8-6

δxm = modal deflection of Level x at the center of the mass at and above Level x as determined by Section 19.3.2

˜δ x ,˜δx1 = deflection of Level x at the center of the mass at and above Level x, Eqs. 19.2-13 and 19.3-3 (in. or mm)

θ = stability coefficient for P-delta effects as determined in Section 12.8.7

ρ = a redundancy factor based on the extent of structural redundancy present in a building as defined in Section 12.3.4

ρs = spiral reinforcement ratio for precast, prestressed piles in Sections 14.2.7.1.6 and 14.2.7.2.6

λ = time effect factor

0 = overstrength factor as defined in Tables 12.2-1, 5.4-1, and 15.3-1