Anchor Bolt Design for Shear and Tension UMESH J. KHAROD
When column base plates are subject to both uplift and very large shear loads, two independent systems are normally used to resist tension in the anchor bolts and shear at the level of the base plate: (1) the length of embedment and the diameter of the anchor bolts are determined on the basis of uplift tension and (2) a shear key is welded to the column base plate to resist re sist shear. shea r. If very large shear loads do not accompany the uplift, the anchor bolts can be designed to resist both shear and tension, without using a shear key, as in the following example.
Figure 2
Solution:
EXAMPLE
Shear:
Given: Design anchor bolts for a column base plate for an uplift of 100 kips, and a shear load of 40 kips due to wind or seismic loading. Use 4 anchor bolts. (See Fig. 1.)
See Fig. 2. f' c = 3.0 ksi F p = 0.25 f' c = 0.75 ksi l s = 12 D (assumed) D (assumed) Ac = (l s D) D) = 12 D
2
Concrete resistance for shear: 2
S = = ½ F p Ac = 6 F p D = (6 × 0.75) D = 4.5 D
2
2 1/ 2
1/ 2
S 10 ∴ D = = = 49.1 4.5 4.5
in.
Use D Use D = = 2 in. Figure 1
l s = 12 D = D = 24 in. Tension: 3/2 1/2 For plain bars, u = 4.75 × 10− ( f' c) / D D For D For D = = 2: 3/2 1/2 u = 4.75 × 10− (3.0) /2 = 0.13 ksi ∴use u = 0.13 ksi T = u(π D) D) l t t T 25 = = 30.61 in. l t = u (π D) 0.13(π × 2.0) l = = (l s + l t t ) = (24 + 30.61) = 54.61 in. Use l = = 4 ft-6 in.
Design Des ign Data: Dat a: Load Load per anchor bolt is as follows: 100/4 = 25 kips 40/4 = 10 kips
Umesh J. Kharod is Project Engineer, MikroPul Corp., Summit, New Jers ey.
22 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Check Bolt Stresses: (a) A g =
D2 4
π
= 3.141in. 2 2
At = 0.75 A g = 2.356 in. (AISC Spec. Sect. 1.5.2.1, with n = 7) Figure 3
For A307 bolts, F y = 33 ksi; F v = 0.3 F y = 10 ksi Fnfnb = F t = 0.6 F y = 20 ksi (b)
NOMENCLATURE
S 10 f v = = 3.188 ksi A g = 3.141 T 25 = 10.16 ksi = At 2.356 F t = 28.0 – 1.6 f v = 22.90 ksi ≤ 20 ksi (AISC Spec. f t =
Sect. 1.6.3)
∴ Use F t or F b = 20 ksi (c) See Fig. 3. Bending moment due to shear S at the level of top of grout = m. m = (S × 1.0) = (10 × 1.0) = 10 kip-in. f b
=
m (π / 32) D
3
=
10.0 (π / 32) × 2.0
3
= 12.73 ksi
(1/1.33) ( f t + f b) = (1/1.33) (10.61 + 12.73) o.k. = 17.55 ksi < F t = 20 ksi
F y F v F t F b Ac D A g At F p f' c
= = = = = = = = = =
l s
=
l t
=
l u f v f t n
= = = = =
Yield stress of anchor bolt material, ksi Allowable shear stress in anchor bolt, ksi Allowable tensile stress in anchor bolt, ksi Allowable bending stress in anchor bolt, ksi 2 Area of concrete in compression, in. Diameter of anchor bolt, in. 2 Gross area of anchor bolt, in. 2 Tensile stress area of anchor bolt, in. Allowable bearing stress on concrete, ksi Specified compressive strength of concrete at the end of 28 days, ksi Length of anchor bolt required for resisting shear force on bolt, in. Length of anchor bolt required for resisting tensile force on bolt, in. Total length of embedment required, in. Allowable bond stress of concrete, ksi Actual shear stress in anchor bolt, ksi Actual tensile stress in anchor bolt, ksi Number of threads per inch for anchor bolt
23 FIRST QUARTER / 1980
