Front matter for Anchorage Design for Petrochemical and Other Industrial Facilities

Other Titles of Interest

Petrochemical Energy Committee

Task Committee on Anchorage Design

Notation

A_{bearing_anc}

Assumed bearing area of a compression strut on an anchor in a strut-and-tie model for shear, in.² (mm²)

A_brg

Net bearing area of the head, bearing nut, or bearing plate of a stud or anchor, in.² (mm²)

A_d

Nominal area of an anchor, in.² (mm²)

A_Nc

Projected concrete failure area of a single anchor or a group of anchors for the calculation of strength in tension, in.² (mm²)

A_Nco

Projected concrete failure area of a single anchor for the calculation of strength in tension if not limited by edge distance or spacing, in.² (mm²)

AP

Anchor plate

A_p

Pedestal area, in.² (mm²)

A_req

Bearing area required for a shear lug, in.² (mm²)

A_s

Area of nonprestressed longitudinal tension reinforcement, in.² (mm²)

A_se,N

Effective cross-sectional area of an anchor in tension, in.² (mm²)

A_se,V

Effective cross-sectional area of an anchor in shear, in.² (mm²)

A_{se_tie}

Area of one leg of tie reinforcement, in.² (mm²)

A_st

Minimum required area of longitudinal nonprestressed reinforcement, in.² (mm²)

A_Vc

Projected concrete failure area of a single anchor, a group of anchors, or a shear lug for the calculation of the strength in shear, in.² (mm²)

A_Vco

Projected concrete failure area of a single anchor, for the calculation of the strength in shear, if not limited by corner influences, spacing, or member thickness, in.² (mm²)

A_w

Area of a weld, in.² (mm²)

b₁

Pedestal dimension in one direction, in. (mm)

b₂

Pedestal dimension in the direction perpendicular to b₁, in. (mm)

C

Cover distance to the top of a rebar, in. (mm)

C_d

Ratio of deflection of a vertical vessel owing to deflection from elastic analysis to total deflection

c_a,max

Maximum distance from the center of an anchor shaft to the edge of concrete, in. (mm)

c_a,min

Minimum distance from the center of an anchor shaft to the edge of concrete, in. (mm)

c_a1

Distance from the center of an anchor shaft to the edge of concrete in one direction, in. (mm). If shear is applied to the anchor, c_a1 is taken in the direction of the applied shear. If tension is applied to the anchor, c_a1 is the minimum edge distance.

c_a2

Distance from the center of an anchor shaft to the edge of concrete in the direction perpendicular to c_a1, in. (mm)

c_a3

Distance from the center of an anchor shaft to the edge of the effective tensile stress area toward the center of an octagon-shaped concrete pedestal, in. (mm). See Example 2.

c_a4

Distance from the center of an anchor shaft to the edge of the effective tensile stress area opposite to c_a2 of an octagon-shaped concrete pedestal, in. (mm). See Example 2.

D

Vertical dead load, lbs (N); diameter of a pipe or weld, in. (mm)

D_bc

Bolt circle diameter, in. (mm)

D_p

Face-to-face dimension of a pedestal, ft (m)

d

Depth of a column in. (mm)

d_a

Outside diameter of the anchor or the shaft diameter of the headed stud, headed bolt, or hooked bolt, in. (mm)

d_actual

Actual distance between an anchor and reinforcing bars under consideration, in. (mm)

d_b

Nominal diameter of a rebar, in. (mm)

d_max

Maximum distance between an anchor and reinforcing bars where the reinforcing bars can be considered to be effective for resisting anchor tension, in. (mm)

d_s

Diameter of a sleeve shell, in. (mm)

d_tie

Nominal diameter of a tie reinforcement bar, in. (mm)

E_sh

Coefficient for shrinkage, in./in. (mm/mm)

E_v

Vertical component of a seismic load, kips (kN)

EA_{bearing_rebar}

Assumed bearing area of a compression strut on a reinforcing bar in a strut-and-tie model for a shear, in.² (mm²)

F

Side-face blowout force, kips (kN)

F_c

Compression force at anchors, kips (kN)

F_cor

Factor to modify the side-face blowout near a corner

F_EXX

Electrode classification number, ksi (MPa)

F_W

Nominal strength of weld metal per unit area, ksi (MPa)

F_r

Maximum horizontal dynamic force, kips (kN)

F_t

Tension force at anchors, kips (kN)

F_y

Specified yield strength of structural steel, psi (kPa)

${f^{\prime }}_c$

Specified compressive strength of concrete, psi (kPa)

f_cc,200

Concrete compressive strength based on a 200-mm cube, psi (kPa)

f_ce

Effective compressive strength of concrete in a strut or nodal zone (Strut-and-Tie Model [STM]), psi (kPa)

f_t

Desired tensile stress in anchor owing to tensioning, psi (kPa)

f_uta

Specified tensile strength of anchor steel, psi (kPa)

f_w

Weld stress, ksi (MPa)

f_y

Specified yield strength of reinforcement, psi (kPa)

f_ya

Specified yield strength of anchor steel, psi (kPa)

G

Grout thickness, in. (mm)

H

Height of the pipe used for a shear lug, in.; the height of a vertical vessel, in. (mm)

h

Distance from the center of a seismic load on a vertical vessel to the bottom of the vertical vessel base plate, in. (mm)

h_ef

Effective embedment depth of an anchor, in. (mm)

${h^{\prime }}_e$

Minimum nut-sleeve clearance, in. (mm)

${h^{\prime }}_{ef}$

Limiting value of h_ef when anchors are located less than 1.5 h_ef from three or more edges, in. (mm)

h_s

Height of a sleeve, in. (mm)

I

Importance factor

k_c

Coefficient for basic concrete breakout strength in tension

L

Length of an anchor, in. (mm); the length of a weld, Figure 5-5, in. (mm)

LA

Lever arm between the centroid of tension loads on anchors and the centroid of the compression load, in. (mm)

L_g

Grip dimension of an anchor bolt, in. (mm)

L_stretch

Anchor stretch length (the distance between the top and the bottom nuts on the anchor), in. (mm)

L_t

Thread length at the bottom of an anchor, in. (mm)

l_d

Development length in the tension of reinforcement, in. (mm)

l_da

Available development length of reinforcement, in. (mm)

l_dh

Development length in the tension of reinforcement with a standard hook, in. (mm)

l_dha

Available development length of a hairpin, in. (mm)

l_e

Load-bearing length of an anchor for shear, in. (mm)

M_n

Nominal flexural strength, k-in. (kN-mm)

M_u

Factored overturning moment, k-ft (kN-m)

$M_u^E$

Factored overturning moment at the vessel base owing to the seismic effect acting alone, k-ft (kNm)

N_arf

Tension to be taken by anchor reinforcement, lb (N)

N_b

Basic concrete breakout strength in the tension of a single anchor in cracked concrete, lb (N)

N_cb

Nominal concrete breakout strength in the tension of a single anchor, lb (N)

N_cbg

Nominal concrete breakout strength in the tension of a group of anchors, lb (N)

N_dse

Controlling tension for ductile steel element failure, lb (N)

N_n

Nominal strength in tension, lb (N)

N_p

Pullout strength in the tension of a single anchor in cracked concrete, lb (N)

N_pn

Nominal pullout strength in the tension of a single anchor owing to the crushing of concrete under an anchor head, lb (N)

N_sa

Nominal strength of a single anchor or a group of anchors in tension as governed by the steel strength, lb (N)

N_sb

Side-face blowout strength of a single anchor, lb (N)

N_sbg

Side-face blowout strength of a group of anchors, lb (N)

N_u

Factored axial normal to cross-section occurring simultaneously with Vu or Tu; to be taken as a positive for the compression applied and negative for tension, lb (N)

N_ua

Factored tensile force applied to an anchor or a group of anchors, lb (N)

n or n_a

Number of anchors

n_layers

Required number of layers of ties to resist the resultant of the radial horizontal component of diagonal concrete struts (assumed to be similar to side-face blowout force)

n_t

Anchor threads per in. (mm)

$P_u^E$

Factored compression force at the top of a pedestal owing to the seismic effect acting alone (including the vertical component of a seismic load acting upward), lb (N)

P_u

Normal factored compression force, lb (N)

p

Bearing pressure on the head of an anchor, psi (kPa)

r

Radius, in. (mm)

S_p

Face dimension of an octagonal pedestal, ft (m)

S_x

Section modulus of a weld, in.³ (mm³)

s

Center-to-center spacing of anchors, reinforcement, or other items in one direction, in. (mm)

s₁

Center-to-center spacing of anchors in one direction, in. (mm)

s₂

Center-to-center spacing of anchors in the direction perpendicular to s₁, in. (mm)

T, T₁

Tensile force on a tie, lb (N)

$T_u^E$

Factored tension design load from load combinations that include an overstrength factor of 2.5 applied to seismic loads (per anchor), lb (N)

T₂

Tensile force on a hairpin, lb (N)

t

Wall thickness of a pipe; the thickness of a weld, in. (mm)

t_f

Flange thickness

V_b

Basic concrete breakout strength in the shear of a single anchor in a cracked section, lb (N)

V_cb

Nominal concrete breakout strength in the shear of a single anchor or a shear lug, lb (N)

V_cbg

Nominal concrete breakout strength in the shear of a group of anchors, lb (N)

V_cp

Nominal concrete pryout strength of a single anchor, lb (N)

V_dse

Controlling shear for ductile steel element failure, lb (N)

V_f

Resisting friction force, lb (N)

V_n

Nominal shear strength, lb (N)

V_sa

Nominal strength in the shear of a single anchor or a group of anchors as governed by the steel strength, lb (N)

V_u

Factored shear force at a section, lb (N)

V_ua

Factored shear force applied to a single anchor, a group of anchors, or a shear lug, lb (N)

W_a

Equipment weight at an anchor location, lb (N)

W_e

Vessel empty weight, lb (N)

W_o

Vessel operating weight, lb (N)

Z

Plastic section modulus, in.³ (mm³)

z

Vertical hairpin concrete cover + 0.5d_b, in. (mm); also, the internal lever arm between the centroid of anchors in tension and the centroid of a compression force on foundation, in. (mm)

α

Ratio of F to N_ua

β_n

Factor to account for the effect of the anchorage of ties on the effective compressive strength of a nodal zone

Δ_A

Amplified displacement at the top of a vertical vessel, in. (mm)

Δ_a

Amount of stretch in an anchor, in. (mm)

Δ_ie

Inelastic portion of displacement at the top of a vertical vessel, in. (mm)

Δ_s

Deflection at the top of a vertical vessel from elastic analysis, in. (mm)

λ

Modification factor related to the unit weight of concrete

λ_p

Limiting slenderness parameter for a compact element

μ

Coefficient of friction

φ

Strength reduction factor

Strength reduction factor, tension loads

φ_V

Strength reduction factor, shear loads

φ_b

Resistance factor for flexure (structural steel)

φ_s

Strength reduction factor used for anchor reinforcement design

φ_v

Resistance factor for shear (structural steel)

Ψ_c,P

Factor used to modify the pullout strength of anchors based on the presence or absence of cracks in concrete

Ψ_c,V

Factor used to modify the shear strength of anchors based on the presence or absence of cracks in concrete and the presence or absence of supplementary reinforcement

Ψ_c,N

Factor used to modify the tensile strength of anchors based on the presence or absence of cracks in concrete

Ψ_cp,N

Factor used to modify the tensile strength of post-installed anchors intended for use in uncracked concrete without supplementary reinforcement

Ψ_e

Factor used to modify the development length because of reinforcement coating

Ψ_ec,N

Factor used to modify the tensile strength of anchors based on the eccentricity of applied loads

Ψ_ec,V

Factor used to modify the shear strength of anchors based on the eccentricity of applied loads

Ψ_ed,N

Factor used to modify the tensile strength of anchors based on proximity to the edges of a concrete member

Ψ_ed,V

Factor used to modify the shear strength of anchors based on proximity to the edges of a concrete member

Ψ_m,N

Modification factor for an overturning moment

Ψ_t

Factor used to modify the development length based on the reinforcement location

Ω_o

Seismic overstress factor