21.1 Determine the required embedment, hef, for a 5/8 in. diameter hex head bolt away
from edges in 4000 psi cracked concrete with no supplemental reinforcement and carrying
a sustained dead load of 6000 lbs, Figure P21.1. Given: fy= 36 ksi, futa = 58 ksi,
ASe,N=0.226, and Abrg=0.454 in2. (
h
ef
=4 in.)
Given:
≔f’c4000 psi ≔P6.0kip
≔futa 58000 psi
≔ASeN 0.226 in2≔Abrg 0.454 in2
≔ψcP 1.0 ≔ψcN 1.0
≔Nua =⋅1.4 P 8.4 kip
Check steel capacity
cP Abrg 8f‘
c10.9 kip =hef
3.5
⎢
⎥
7.5
⎢
⎥
21.2 An insert with four -1/2 in. diameter headed studs is embedded 4 in. into an uncracked concrete
panel well away from any edges, Figure P21..2 The material strength is f’c = 5000 psi and the stud
yield strength is fy = 51,000 psi. Determine the tensile design load for the insert. (Nu=21.7 kip)
≔f’c5000 psi ≔fy51 ksi ≔da0.50 in
≔futa =⋅1.9 fy96.9 ksi ≔n4
≔ψcN 1.2 ≔ϕ0.75 ≔kc24 in.5
≔hef 4in ≔s4in ≔λa1.0
Steel Strength
π
20.2 in2
Solutions Chapter 21
21.3 An insert with four –1/2 in. diameter headed studs is embedded 4 in. into an uncracked
concrete panel with the center of the insert 6 in. from any edges, Figure P21.3. The material
strength is f’c = 5000 psi and the stud yield strength is fy = 51,000 psi. Determine the shear
design load for the insert.
ca1
f’c5000psi fya 51000psi futa 1.9fya 96900 psi
λ1.0 normal weight concrete
ϕ0.65 kc24 per Code
AVco
Check Pryout
kcp 2 Stud embedment >2“
Ncpg 30.6kip from Example 1
Solutions Chapter 21
21.4 An insert with four – 1/2 in. diameter headed studs is embedded 4 in. into an uncracked
concrete panel near a corner, Figure P21.4. The material strength is f’c = 5000 psi and the stud
yield strength is fy = 51,000 psi. Determine the tensile design load for the insert.
f’c5000psi fya 51000psi futa 1.9fya 96900 psi
2″ 2″
16″
λ1.0 normal weight concrete
ϕ0.75 kc24
ANco
Pullout capacity Abrg
π
41in()
20.5in()
2
Np8Abrg f’c
23.6 kip
21.5 The attachment shown in Figure 21.5 carries a factored load of 18 kips loaded
concentrically on the attachment. Given that the four headed studs are 1/2 in. in diameter,
have a specified yield stress of 51 ksi, and are welded to a 3/8 in plate, determine hef for the
attachment. The concrete may be considered cracked, f’c= 4000 psi, and the attachment is
away from any edge.
≔f’c4000 psi ≔fy51 ksi ≔da0.50 in
≔futa =⋅1.9 fy96.9 ksi ≔n4
≔Nu18.0 kip ≔ϕ0.75 ≔kc24 in.5
≔ψcN 1.0 ≔s4in ≔λa1.0
≔hef ,‥2in 2.5 in 6in
Check steel capacity
π
20.20 in2
4.5
5.0
5.5
6.0
⎢
⎢
⎢
⎢
⎣
⎥
⎥
⎥
⎥
⎦
19.1
21.8
24.6
27.5
⎢
⎢
⎢
⎢
⎣
⎥
⎥
⎥
⎥
⎦
Check pullout
π
⎛
2
2
⎞
21.6 The attachment shown in Figure P21.6 carries a factored load of 21.5 kips loaded
eccentricly 1/2 in. from the centerline of the attachment. Given that the four headed studs are
5/8 in diameter and have a specified yield stress of 51 ksi and are welded to a 3/8 in plate,
determine hef for the attachment. The concrete may be considered uncracked, f’c= 4000 psi,
and the attachment is away from any edge.
≔f’c4000 psi ≔fy51 ksi
≔futa =⋅1.9 fy96.9 ksi
≔Nu21.5 kip ≔ϕ0.75 ≔kc24 in.5
≔ψcN 1.25 ≔s4in ≔λa1.0
≔hef ,‥2in 2.5 in 6in
Calculate Nua
4.5
5.0
5.5
6.0
⎢
⎢
⎢
⎢
⎣
⎥
⎥
⎥
⎥
⎦
22.2
25.5
29.0
32.6
⎢
⎢
⎢
⎢
⎣
⎥
⎥
⎥
⎥
⎦
Check pullout
≔n2 Two most critically loaded studs
π
⎛
2
2
⎞
21.8 Determine the capacity of the attachment in Figure 21.18 adequate to carry a sustained
applied load using the bond stress Wcr = 1800 psi and tuncr = 2600 psi. The anchors have 10
threads per inch, are 3/4 in. diameter futa = 75000 psi steel embedded 8 inches into an exterior
concrete wall having a compressive strength of 4000 psi. The attachment is well away from
any edges, supplementary reinforcement is present and the anchors are considered category 2
– medium sensitivity and reliability. Comment on your solution.
The loads are sustained so only half the allowable bond stress from ACI 318 below is
permitted.
≔τcr ⋅1800 psi ≔τuncr ⋅2600 psi ≔nt10 ≔hef 8in
≔nV4≔nN2≔fya 55 ksi ≔da0.75 in ≔f’c⋅4000 psi
≔ecc 3 in ≔s18in ≔s26in ≔λa1.0 ≔ϕ0.65
≔ψecNa 1.0 ≔ψedNa 1.0 ≔ψcpNa 1.0
I
is based on category 2 and
supplemental reinforcement
being present.
\
values result from large edge distances and no eccentricity.
2