July 6, 2020

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

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

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

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

Check pullout

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

Check pullout

≔n2 Two most critically loaded studs

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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.

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