Chapter 3 QUALITY ASSURANCE
9.2 BOLTS AND HEADED STUD ANCHORS IN CONCRETE
9.2.4 Strength Based on Calculations
9.2.4.1 Strength in Tension: The design tensile strength of the individual anchors or adequately connected groups of anchors shall be the minimum of Ps or NPc where:
1. Design tensile strength governed by steel, Ps, in pounds (N), is:
2. Design tensile strength governed by concrete failure, NPc in pounds (N) is as follows:
a. For individual anchors or groups of anchors with individual anchors spaced at least twice their embedment length apart and spaced not less than one anchor embedment length from a free edge of the concrete:
where:
As = area (in. ) of the assumed failure surface taken as a truncated cone sloping2 at 45 degrees from the head of the anchor to the concrete surface as shown in Figure 9.2.4.1a;
fNc = concrete strength (psi)--6,000 psi (41 MPa) maximum;
NPc ' N8 fc)( 2.8As)n 12
NPc ' N8 fc)( 2.8Ap % 4At) (9.2.4.1-3)
FIGURE 9.2.4.1b Truncated pyramid failure for a group of headed anchors.
N = strength reduction factor of 0.65 except that where special transverse reinforcing is provided to confine the concrete engaged by the anchor and is extended to pass through the failure surface into adjacent concrete, N is permitted to be taken as 0.85;
8 = concrete weight factor--1 for normal weight concrete, 0.85 for sand-light- weight concrete, and 0.75 for lightweight concrete.
The metric equivalent of Eq. 9.2.4.1-2 is:
where As is in mm and fN is MPa.2 c
Where any anchors are closer to a free edge of the concrete than the anchor embedment length, the design tensile strength of those anchors shall be reduced proportionately to the edge distance divided by the embedment length. For multiple edge distances less than the embedment length, use multiple reductions.
b. For anchor groups where individual anchors are spaced closer together than two embedment lengths:
where:
Ap = area (in. ) of an assumed failure surface taken as a truncated pyramid2 extending from the heads of the outside anchors in the group at 45 degrees to the concrete surface as shown in Figure 9.2.4.1b;
At = area (in. ) of the flat bottom surface of the truncated pyramid of the2 assumed concrete failure surface shown in Figure 9.2.4.1b.
NPc ' N8 fc)( 2.8Ap % 4At) 12
Vs ' ( 0.75AbFu)n
NVc ' (N800Ab8 fc))n
Concrete Structure Design Requirements
FIGURE 9.2.4.1c Pull-out failure surface for a group of headed anchors in thin section.
(9.2.4.2-1)
(9.2.4.2-2)
The metric equivalent of Eq. 9.2.4.1-3 is:
where Ap and At are in mm and fN is in MPa.2 c
If any anchors are closer to a free edge of the concrete than the anchor embedment length, the design tensile strength shall be reduced by using the reduced area Ap in the equation above.
Anchor groups shall be checked for a critical failure surface passing completely through a concrete member along the 45 degree lines as shown in Figure 9.2.4.1c with At = 0 and Ap based on the area of the sloping failure surface passing completely through the concrete member. The lowest allowable load shall govern.
9.2.4.2 Strength in Shear: The design shear strength of anchors shall be the minimum of Vs or NVc where the design shear strength governed by steel failure is Vs, in pounds (N), and the design shear strength governed by concrete failure is NVc, in pounds (N). In situations where the embedment and/or concrete edge distances are limited, reinforcement to confine concrete to preclude its premature failure shall be permitted.
a. Where anchors are loaded toward an edge with edge distance de from the back row of anchors as shown in Figure 9.2.4.2 equal to or greater than 15 anchor diameters and the distance from the front row of anchors to the edge equal to or greater than 6 anchor diameters:
NVc ' N800Ab8 fc) n 12
Vs ' ( 0.75AbFu)nb
NV ' NV)C C C
FIGURE 9.2.4.2 Shear on a group of headed an- chors.
(9.2.4.2-3)
(9.2.4.2-4)
where:
Ab = the area, in. (mm ) of the shank of the bolt or stud;2 2
Fu = the specified ultimate tensile strength (psi) of the anchor. A307 bolts or A108 studs are permitted to be assumed to have Fu of 60,000 psi (414 MPa);
n = the number of anchors;
8 = concrete weight factor--1 for normal weight concrete, 0.85 for sand-lightweight concrete, and 0.75 for lightweight concrete; and
fNc = concrete strength (psi)--6,000 psi (41 MPa) maximum.
The metric equivalent of Eq. 9.2.4.2-2 is:
where Ab is in mm and fN is in MPa.2 c
b. Where anchors are loaded toward an edge with de less than 15 anchor diameters or the front row closer to the edge than 6 anchor diameters:
NVc)
NVc) ' N12.5de1.58 fc) # 800Ab8 fc)
Cw ' 1 % b
3.5de # nb
Ct ' h
1.3de # 1.0
Cc ' 0.4 % 0.7 dc
de # 1.0
NVc) ' N12.5de1.58 fc)
2.39 # N800Ab8 fc) 12
Concrete Structure Design Requirements
(9.2.4.2-5)
(9.2.4.2-6)
(9.2.4.2-7)
(9.2.4.2-8)
where:
Ab = the area (in. ) of the shank of the bolt or stud.2
Fu = the specified ultimate tensile strength (psi) of the anchor. A307 bolts or A108 studs are permitted to be assumed to have Fu of 60,000 psi (414 MPa).
nb = the number of anchors in the back row.
= the design shear strength of an anchor in the back row:
where de = the distance from the anchor axis to the free edge (in.).
Cw = the adjustment factor for group width:
where b = the center-to-center distance of outermost anchors in the back row (see Figure 9.2.4.2) (in.) and de = the distance from the anchor axis to the free edge (in.).
Ct = the adjustment factor for member thickness:
where h = the thickness of concrete (in.) and de is as above.
Cc = the adjustment factor for member corner effects:
where dc = the distance, measured perpendicular to the load, from the free edge of the concrete to the nearest anchor in in. (see Figure 9.2.4.2) and de is as above.
The metric equivalent of Eq. 9.2.4.2-5 is:
where de is in mm, Ab is in mm and fN is in MPa.2 c
1 N
Vu
Vc # 1.0 1
N Pu
Pc # 1.0
1 N
Pu Pc
2
% Vu Vc
2
# 1.0
Pu Ps
2
% Vu Vs
2
# 1.0
Concrete Structure Design Requirements
(9.2.4.3-1a)
(9.2.4.3-1b)
(9.2.4.3-2a)
(9.2.4.3-2b)
9.2.4.3 Combined Tension and Shear: Where tension and shear act simultaneously, all of the following conditions shall be met:
where:
Pu = required tensile strength, in pounds (N), based on factored loads and Vu = required shear strength, in pounds (N), based on factored loads.
9.3 CLASSIFICATION OF SEISMIC-FORCE-RESISTING SYSTEMS: Reinforced concrete