Hilti Anchor Channel Tutorial Design Example #2 Page … Anchor Channel Tutorial Design Example #2...

Hilti Anchor Channel Tutorial

Design Example #2 / 29 Design provisions: ICC-ES AC232, ACI 318-11 Appendix D, ICC-ES ESR-3520 Anchor Channel: HAC-60 F hef = 5.83 in, anchor element spacing (s) = 5.91 in, channel length = 13.8 in Fixture: plate dimensions = 8.0 in x 9.5 in x 0.50 in T-bolts = two HBC-C 8.8F, diameter = M16 (16 mm) Concrete: f’c = 3500 psi, normal weight, cracked conditions, thickness (h) = 8.0 in no additional edge reinforcement, Condition B – tension, Condition B – shear no additional anchor reinforcement Loads: static, tension load = 1500 lb, shear load = 2000 lb (perpendicular to channel) assume T-bolt tolerance = +/- 0 in

1.5 in 1.5 in 5.0 in

8.0 in

13.8 in 5.0 in

2.5

in

4.5

in

2.5

in

9.5

in

A A

section A-A

8.0

in

5.83

in

5.91 in 5.91 in 0.984 in 0.984 in

fixture

anchor channel T-bolts

shear load

tension load


Design Example #2 / 29 Loads Acting on Each T-Bolt

T-Bolt N (lb) Vx (lb) Vy (lb) #1 TT-bolt = 3042 0 ST-bolt = -1000 #2 TT-bolt = 3042 0 ST-bolt = -1000

The table titled Loads Acting on Each T-Bolt shows the calculated load values acting on each T-bolt. Tension load acting on each T-bolt is designated TT-bolt and shear load acting on each T-bolt is designated ST-bolt. Loads Acting on Each Anchor Element

Anchor N (lb) V (lb) anchor element #1 Ta1,total = 1651 Sa1,total = 543 anchor element #2 Ta2,total = 2788 Sa2,total = 916 anchor element #3 Ta3,total = 1651 Sa3,total = 543

The load acting on each T-bolt is distributed to the anchor elements in the anchor channel. For this example, the T-bolt tension and shear loads have been distributed to three anchor elements. The table titled Loads Acting on Each Anchor Element shows these loads, and designates the total load acting on each anchor element as Taxx-total for tension and Saxx-total for shear loads respectively.

COMMENTS The loads acting on each T-bolt have been calculated in Design Example #1. Reference pages 1-3 in Design Example #1 to see how these loads were determined. The total load acting on each anchor element has also been calculated in Design Example #1. Reference pages 4-9 in Design Example #1 to see how these loads were determined.


Design Example #2 / 29 Tension and Shear Load Summary

Tension Failure Mode

Nominal Strength (lb)

Design Strength (lb)

Factored Load (lb)

% Utilization

Nua/φNn

COMMENTS For this example, the shear load of 2000 lb is assumed to act in the –y direction. Therefore, shear calculations use the subscript “y”. The table titled Tension and Shear Load Summary shows these subscripts for each relevant calculation parameter. The parameter “% utilization” shown in the table corresponds to the ratio: where “factored load” corresponds to the total factored load (Taxx,total or TT-bolt) and (Saxx,total or ST-bolt) acting on an anchor element in tension or shear respectively, and “design strength” corresponds to the calculated design strength for the failure mode being considered. in tension or shear respectively, Utilizations less than 100% indicate the factored load is less than the design strength, while utilizations greater than 100% indicate the factored load exceeds the design strength. Therefore, the anchor channel design is considered acceptable if all of the utilizations are less than 100%, and the combined interaction checks using these utilizations are satisfied.

steel failure: channel lips

Nsl = 11,240 anchor #2

φNsl = 8430 anchor #2

TT-bolt = 3042 anchor #2

36% anchor #2

steel failure: anchor element

Nsa = 11,240 anchor #2

φNsa = 8430 anchor #2

Ta2,total = 2788 anchor #2

33% anchor #2

steel failure: channel connection

Nsc = 11,240 anchor #2

φNsc = 8430 anchor #2


33% anchor #2

steel failure: channel bending

Ms,flex = 19,355 (in-lb)

anchor #2

φMs,flex = 16,452 (in-lb)

anchor #2

Mu,flex = 4386 (in-lb)

anchor #2

27% anchor #2

steel failure: T-bolt

Nss = 28,235 anchor #2

φNss = 18,352 anchor #2

TT-bolt = 3042 anchor #2

17% anchor #2

concrete breakout failure

Ncb = 4382 anchor #3

φNcb = 3067 anchor #3


54% anchor #3

pullout failure

Npn = 11,200 anchor #2

φNpn = 7840 anchor #2


36% anchor #2

side-face blowout Nsb = N/A

φNsb = N/A Taxx,total = N/A N/A

Shear Failure Mode

Nominal Strength (Vn)

Design Strength (φVn)

Factored Load (Vua)

Utilization Vua,y/φVn

steel failure: channel lips

Vsl,y = 16,205 anchor #2

φVsl,y = 12,154 anchor #2

ST-bolt = 1000 anchor #2

8% anchor #2

steel failure: anchor element

Vsa,y = 16,250 anchor #2

φVsa,y = 12,188 anchor #2

Sa2,total = 916 anchor #2

8% anchor #2

steel failure: anchor/channel connection

Vsc,y = 16,250 anchor #2

φVsc,y = 12,188 anchor #2


8% anchor #2

steel failure: T-bolt

Vss = 16,940 anchor #2

φVss = 10,164 anchor #2

ST-bolt = 1000 anchor #2

10% anchor #2

concrete breakout failure

Vcb,y = 1213 anchor #3

φVcb,y = 849 anchor #3


64% anchor #3

concrete pryout

Vcp,y = 8804 anchor #3

φVcp,y = 6163 anchor #3


9% anchor #3

Anchor element #2 controls the anchor channel design for steel failure modes in tension and shear, as well as for pullout failure in tension. The steel failure mode design strengths (φNsl, φNsa, φNsc, φMs,flex , φNss ) and (φVsl,y, φVsa,y, φVsc,y, φVss ) are the same for each anchor element. Since the highest factored tension and shear loads act on anchor element #2, it has highest % utilization for these failure modes. The pullout failure mode design strength (φNpn) is likewise the same for each anchor element. Therefore, anchor element #2 also has highest % utilization for pullout. Anchor element #3 controls the design for concrete breakout failure in tension and shear, and for pryout failure in shear. The design strengths (φNcb, φVcb,y and φVcp,y) are dependent on the concrete geometry. Even though the highest factored load acts on anchor element #2, the design strengths and factored loads acting on anchor element #3 result in it having the highest % utilization for concrete breakout failure and pryout failure.

factored load (Nua or Vua) design strength (φNn or φVn)

Hilti Anchor Channel Tutorial Design Example #2 / 29 The calculations for steel failure modes in tension and shear, pullout in tension, and side-face blowout in tension are shown in Design Example #1. Reference the following pages in Design Example #1 for these calculations: * steel failure modes in tension (page 10 in Design Example #1). * pullout failure in tension (page 13 in Design Example #1). * side-face blowout failure in tension (page 13 in Design Example #1). * steel failure modes in shear (page 15 in Design Example #1). This design example will show calculations for concrete breakout in tension and shear, and for pryout in shear. Calculations will be made for each anchor element. The total factored loads given in the table on page 2 titled Loads Acting on Each Anchor Element will then be used to determine the % utilization for each failure mode, for each anchor element. It will be shown how anchor element #3 controls the anchor channel design for concrete breakout in tension and shear, and for pryout in shear because the design strengths and loads acting on anchor element #3 result in the highest utilization for these failure modes. Reference the figure above. It is useful in showing how the anchor element location and the concrete geometry affect the design strengths that will be calculated for each anchor element.

13.8 in 5.0 in

4.5

in

A A

section A-A

8.0

in

5.83

in

5.91 in 5.91 in 0.984 in 0.984 in

anchor element

#1 anchor element

#2

anchor element #3

anchor element

#1

anchor element

#2

Anchor element #3 controls for concrete breakout in tension and shear, and pryout in shear.

Hilti Anchor Channel Tutorial Design Example #2 / 29 Nominal concrete breakout strength in tension for anchor element #1 Ncb,1 = Nb,1 ψs,N,1 ψed,N,1 ψco,N,1 ψc,N,1 ψcp,N,1 ESR-3520 Equation (6) Calculate the basic concrete breakout strength in tension (Nb,1). Nb,1 = 24 λ αch,N f’c hef

1.5 ESR-3520 Equation (7)

λ = 1.0 (normal weight concrete) HAC-60F channel: hef = 5.83 in ESR-3520 Table 8-1 f’c = 3500 psi αch,N = → αch,N = 0.971 ESR-3520 Equation (8) Nb,1 = (24) (1.0) (0.971) (3500)0.5 (5.83)1.5 → Nb,1 = 19,407 lb Calculate the modification factor for anchor influence (ψs,N,1). ψs,N,1 = ESR-3520 Equation (10) si = spacing between each anchor element = 5.91 in sxx,1 = distance of each influencing anchor element from anchor element #1 s2,1 = distance from anchor element #2 to anchor element #1 = 5.91 in s3,1 = distance from anchor element #3 to anchor element #1 = 11.82 in scr,N = critical anchor spacing for tension loading (hef = 5.83 in) scr,N = (2) 2.8 - → scr,N = 20.20 in ESR-3520 Equation (11) Na

ua,1 = tension load on anchor element #1 (Ta1,total) =1651 lb (see p. 2) Na

ua,2 = tension load on anchor element #2 (Ta2,total) = 2788 lb (see p. 2) Na

ua,3 = tension load on anchor element #3 (Ta3,total) = 1651 lb (see p. 2) influence of anchor element #2 on anchor element #1: = 1.01 influence of anchor element #3 on anchor element #1: = 0.267 ψs,N,1 = → ψs,N,1 = 0.439

COMMENTS The parameter αch,N is a factor that is used to account for the influence of the channel size on the concrete breakout capacity in tension. The value 7.1 is a constant. ESR-3520 Table 8-1 provides minimum effective embedment depth values (hef,min) for each anchor channel size. The hef,min value given for an HAC-60F channel will be used for hef in this example. The value calculated for concrete breakout strength in tension (Ncb) is based on the location of the anchor element being considered. The parameter ψs,N is a modification factor that is calculated to account for the influence of anchor elements located within the distance scr,N from the anchor element being considered. Reference ESR-3520 Equation (10) for more information on how to calculate ψs,N. The parameter scr,N corresponds to the maximum distance that is assumed with respect to the influence of an anchor element on the anchor element being considered. Any anchor elements that are within scr,N from the anchor element being considered are assumed to have an influence on that anchor element. Reference ESR-3520 Equation (11) for more information on how to calculate scr,N.

hef 0.15

7.1

si 1.5

scr,N

Naua,i

Naua,1 1 +

1

n+1 i=2

1 -

5.91 in 1.5

20.20 in

2788 lbi 1651 lb

1 -

11.82 in 1.5

20.20 in

1651 lbi 1651 lb

1 -

1 + (1.01 + 0.267)

1

anchor element #2

scr,N scr,N

si si anchor element #3

1.3 hef 7.1 (hef)

anchor element #1

Σ

Hilti Anchor Channel Tutorial Design Example #2 / 29 Calculate the modification factor for edge influence (ψed,N,1). ψed,N,1 = ESR-3520 Equation (13) where ca1 = 4.5 in (reference page 1) ccr,N = (0.5)(scr,N) = 10.10 in ESR-3520 Equation (14) where scr,N = 20.20 in (reference page 5) ∴ψed,N,1 = = 0.668 Calculate the modification factor for corner influence (ψco,N,1). ψco,N,1 = ESR-3520 Equation (16) ccr,N = 10.10 in ca2,(+x) = 5.00 in + 0.984 in + 5.91 in + 5.91 in = 17.8 in (reference page 1) ca2,(-x) = ∞ (reference page 1) ca2(+x) and ca2(-x) > ccr,N → ψco,N,1 = 1.0 ESR-3520 Equation (15) Calculate the modification factor for cracked/uncracked concrete (ψc,N,1). Cracked concrete conditions → ψc,N,1 = 1.0. Note: if uncracked concrete conditions are assumed, ψc,N,1 = 1.25. Calculate the modification factor for splitting (ψcp,N,1). Cracked concrete conditions → ψcp,N,1 = 1.0. Note: if uncracked concrete conditions are assumed: ψcp,N,1 = max if ca,min or ccr,N < cac ESR-3520 Equation (18) ca,min = the smallest fixed edge distance from the anchor element being considered cac = edge distance required to preclude splitting in uncracked concrete without supplementary reinforcement. cac values are given in ESR-3520 Table 8-4.

COMMENTS The parameters ca1 and ca2 correspond to the distance from the center of the anchor element being considered to a fixed edge. ca1 is measured perpendicular to the anchor channel longitudinal axis, and is considered when calculating the modification factor for edge influence (ψed,N). ca2 is measured parallel to the anchor channel longitudinal axis, and is considered when calculating the modification factor for corner influence (ψco,N). Since the calculated value for concrete breakout in tension (Ncb) is dependent on the concrete geometry, it is important to note that values for ca1 and ca2 must be taken with respect to the relevant edge distances from the anchor element being considered. The parameter ccr,N corresponds to the maximum edge distance that is assumed with respect to values for ca1 and ca2. Any ca1 or ca2 value less than ccr,N must be considered when calculating ψed,N and ψco,N. If more than one ca1 value is less than ccr,N, the smallest ca1 value will be used to calculate ψed,N. If more than one ca2 value is less than ccr,N, ψco,N will be calculated for each ca2 value and the product of these ψco,N values will be used to calculate the nominal concrete breakout strength in tension (Ncb). Concrete is typically assumed to be cracked under normal service load conditions. If uncracked concrete conditions are assumed, an increase in Ncb is permitted via the modification factor ψc,N ; however, a decrease in capacity may also result via the modification factor for splitting ψcp,N .

ca1

ca2(+x)

#2 #1 #3

ca1 0.5

ccr,N

4.5 in 0.5

10.10 in

ca2(+x) 0.5

ccr,N

ca,min ccr,N

cac cac

:

ca2(-x)

x

y

ca2(-x) 0.5

ccr,N

Hilti Anchor Channel Tutorial Design Example #2 / 29 Nominal concrete breakout strength in tension for anchor element #1 Ncb,1 = Nb,1 ψs,N,1 ψed,N,1 ψco,N,1 ψc,N,1 ψcp,N,1 ESR-3520 Equation (6)

Nb,1 = 19,407 lb (reference page 5) ψs,N,1 = 0.439 (reference page 5) ψed,N,1 = 0.668 (reference page 6) ψco,N,1 = 1.0 (reference page 6) ψc,N,1 = 1.0 (reference page 6) ψcp,N,1 = 1.0 (reference page 6) Ncb,1 = (19,407 lb) (0.439) (0.668) (1.0) (1.0) (1.0) → Ncb,1 = 5691 lb

COMMENTS The calculated value for Ncb,1 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φNcb,1). Design strengths for this example are summarized in the table on page 13 titled Summary for Concrete Breakout in Tension. The calculated φNcb,1 value for anchor element #1 will be checked against the factored load acting on anchor element #1 (Ta1,total) to obtain the % utilization (Ta1,total / φNcb1). The anchor element with the highest % utilization will control the design with respect to concrete breakout failure in tension.

Hilti Anchor Channel Tutorial Design Example #2 / 29 Nominal concrete breakout strength in tension for Anchor Element #2 Ncb,2 = Nb,2 ψs,N,2 ψed,N,2 ψco,N,2 ψc,N,2 ψcp,N,2 ESR-3520 Equation (6) Calculate the basic concrete breakout strength in tension (Nb,2). Nb,2 = 24 λ αch,N f’c hef






COMMENTS The value calculated for concrete breakout strength in tension (Ncb) is based on the location of the anchor element being considered. The basic concrete breakout strength in tension (Nb) is not dependent on the anchor element being considered or the concrete geometry. Therefore, the calculated value for Nb will be the same for each anchor element. The parameter ψs,N will be dependent on the anchor element being considered and the concrete geometry. Reference ESR-3520 Equation (10) for more information on how to calculate ψs,N. The parameter scr,N corresponds to the maximum distance that is assumed with respect to the influence of an anchor element on the anchor element being considered. Any anchor elements that are within scr,N from the anchor element being considered are assumed to have an influence on that anchor element. The calculated value for scr,N will be the same for each anchor element; however, the number of anchor elements within the distance scr,N from the anchor element being considered may not always be the same. Reference ESR-3520 Equation (11) for more information on how to calculate scr,N.

hef 0.15

7.1

si 1.5

scr,N

Naua,i

Naua,2 1 +

1

Σ n+1 i=2

1 -

5.91 in 1.5

20.20 in

1651 lbi 2788 lb

1 -

5.91 in 1.5

20.20 in

1651 lbi 2788 lb

1 -

1 + (0.352 + 0.352)

1

anchor element #2

scr,N scr,N si si

anchor element #3

1.3 hef 7.1 (hef)

anchor element #1

Hilti Anchor Channel Tutorial Design Example #2 / 29 Calculate the modification factor for edge influence (ψed,N,2). ψed,N,2 = ESR-3520 Equation (13) where ca1 = 4.5 in (reference page 1) ccr,N = (0.5)(scr,N) = 10.10 in ESR-3520 Equation (14) where scr,N = 20.20 in (reference page 8) ∴ψed,N,2 = = 0.668 Calculate the modification factor for corner influence (ψco,N,2). ψco,N,2 = ESR-3520 Equation (16) ccr,N = 10.10 in ca2(+x) = 5.00 in + 0.984 in + 5.91 in = 11.89 in (reference page 1) ca2(-x) = ∞ (reference page 1) ca2(+x) and ca2(-x) > ccr,N → ψco,N,2 = 1.0 ESR-3520 Equation (15) Calculate the modification factor for cracked/uncracked concrete (ψc,N,2). Cracked concrete conditions → ψc,N,2 = 1.0. Note: if uncracked concrete conditions are assumed, ψc,N,2 = 1.25. Calculate the modification factor for splitting (ψcp,N,2). Cracked concrete conditions → ψcp,N,2 = 1.0. Note: if uncracked concrete conditions are assumed: ψcp,N,2 = max if ca,min or ccr,N < cac ESR-3520 Equation (18) ca,min = the smallest fixed edge distance from the anchor element being considered cac = edge distance required to preclude splitting in uncracked concrete without supplementary reinforcement. cac values are given in ESR-3520 Table 8-4.


ca1

ca2(+x)

#2 #1 #3

ca1 0.5

ccr,N

4.5 in 0.5

10.10 in

ca2(+x) 0.5

ccr,N

ca,min ccr,N

cac cac

:

ca2(-x)

x

y

ca2(-x) 0.5

ccr,N


Nb,2 = 19,407 lb (reference page 8) ψs,N,2 = 0.587 (reference page 8) ψed,N,2 = 0.668 (reference page 9) ψco,N,2 = 1.0 (reference page 9) ψc,N,2 = 1.0 (reference page 9) ψcp,N,2 = 1.0 (reference page 9) Ncb,2 = (19,407 lb) (0.587) (0.668) (1.0) (1.0) (1.0) → Ncb,2 = 7610 lb

COMMENTS The calculated value for Ncb,2 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φNcb,2). Design strengths for this example are summarized in the table on page 13 titled Summary for Concrete Breakout in Tension. The calculated φNcb,2 value for anchor element #2 will be checked against the factored load acting on anchor element #2 (Ta2,total) to obtain the % utilization (Ta2,total / φNcb2). The anchor element with the highest % utilization will control the design with respect to concrete breakout failure in tension.

Hilti Anchor Channel Tutorial Design Example #2 / 29 Nominal concrete breakout strength in tension for Anchor Element #3 Ncb,3 = Nb,3 ψs,N,3 ψed,N,3 ψco,N,3 ψc,N,3 ψcp,N,3 ESR-3520 Equation (6) Calculate the basic concrete breakout strength in tension (Nb,3). Nb,3 = 24 λ αch,N f’c hef






COMMENTS The value calculated for concrete breakout strength in tension (Ncb) is based on the location of the anchor element being considered. The basic concrete breakout strength in tension (Nb) is not dependent on the anchor element being considered or the concrete geometry. Therefore, the calculated value for Nb will be the same for each anchor element. The parameter ψs,N will be dependent on the anchor element being considered and the concrete geometry. Reference ESR-3520 Equation (10) for more information on how to calculate ψs,N. The parameter scr,N corresponds to the maximum distance that is assumed with respect to the influence of an anchor element on the anchor element being considered. Any anchor elements that are within scr,N from the anchor element being considered are assumed to have an influence on that anchor element. The calculated value for scr,N will be the same for each anchor element; however, the number of anchor elements within the distance scr,N from the anchor element being considered may not always be the same. Reference ESR-3520 Equation (11) for more information on how to calculate scr,N.

hef 0.15

7.1

si 1.5

scr,N

Naua,i

Naua,3

1

Σ n+1 i=2

1 -

11.82 in 1.5

20.20 in

1651 lbi 1651 lb

1 -

5.91 in 1.5

20.2 in

2788 lbi 1651 lb

1 -

1 + (0.267 + 1.01)

1

anchor element #2

scr,N scr,N

si si

anchor element #3

1.3 hef 7.1 (hef)

anchor element #1

1 +

Hilti Anchor Channel Tutorial Design Example #2 / 29 Calculate the modification factor for edge influence (ψed,N,3). ψed,N,3 = ESR-3520 Equation (13) where ca1 = 4.5 in (reference page 1) ccr,N = (0.5)(scr,N) = 10.10 in ESR-3520 Equation (14) where scr,N = 20.20 in (reference page 11) ∴ψed,N,3 = = 0.668 Calculate the modification factor for corner influence (ψco,N,3). ψco,N,3 = ESR-3520 Equation (16) ccr,N = 10.10 in ca2(+x) = 5.00 in + 0.984 in = 5.984 in (reference page 1) ca2(-x) = ∞ → = 1.0 ESR-3520 Equation (15) ψco,N,3 = ESR-3520 Equation (16) Calculate the modification factor for cracked/uncracked concrete (ψc,N,3). Cracked concrete conditions → ψc,N,3 = 1.0. Note: if uncracked concrete conditions are assumed, ψc,N,3 = 1.25. Calculate the modification factor for splitting (ψcp,N,3). Cracked concrete conditions → ψcp,N,3 = 1.0. Note: if uncracked concrete conditions are assumed: ψcp,N,3 = max if ca,min or ccr,N < cac ESR-3520 Equation (18) ca,min = the smallest fixed edge distance from the anchor element being considered cac = edge distance required to preclude splitting in uncracked concrete without supplementary reinforcement. cac values are given in ESR-3520 Table 8-4.


ca1

ca2(+x)

#2 #1 #3

ca1 0.5

ccr,N

4.5 in 0.5

10.10 in

ca2(+x) 0.5

ccr,N

ca,min ccr,N

cac cac

:

ca2(-x)

x

y

ca2(-x) 0.5

ccr,N

5.984 in 0.5

10.10 in = 0.77

ca2(-x) 0.5

ccr,N


Nb,3 = 19,407 lb (reference page 11) ψs,N,3 = 0.439 (reference page 11) ψed,N,3 = 0.668 (reference page 12) ψco,N,3 = 0.77 (reference page 12) ψc,N,3 = 1.0 (reference page 12) ψcp,N,3 = 1.0 (reference page12) Ncb,3 = (19,407 lb) (0.439) (0.668) (0.77) (1.0) (1.0) → Ncb,3 = 4382 lb

COMMENTS The calculated value for Ncb,3 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φNcb,3). Design strengths for this example are summarized in the table on this page titled Summary for Concrete Breakout in Tension. The calculated φNcb,3 value for anchor element #3 will be checked against the factored load acting on anchor element #3 (Ta3,total) to obtain the % utilization (Ta3,total / φNcb3). The anchor element with the highest % utilization will control the design with respect to concrete breakout failure in tension.

Summary for Concrete Breakout in Tension Anchor Element

Nominal Strength Ncb (lb)

Design Strength φNcb (lb)

Factored Load

Taxx,total (lb)

% Utilization Taxx,total / φNcb

COMMENTS

φ-factors for concrete breakout in tension are given in ESR-3520 Table 8-4. The concrete breakout calculations (φNcb ) were influenced by the anchor location and the concrete geometry via the modification factors ψs,N, ψed,N and ψco,N

1

Ncb,1 = 5691

φ = 0.7 φNcb,1 = 3984

Ta1,total = 1651

42%

2

Ncb,2 = 7610

φ = 0.7 φNcb,2 = 5327

Ta2,total = 2788

53%

3

Ncb,3 = 4382

φ = 0.7 φNcb,3 = 3067

Ta3,total = 1651

54% CONTROLS

Anchor element #3 has the highest % utilization with respect to concrete breakout failure in tension. It was necessary to calculate the design concrete breakout strength (φNcb) relative to anchor elements #1, #2 and #3; and then determine the % utilization (Taxx,total / φNcb) based on the factored load acting on that element. Once the % utilization for all three anchor elements was calculated, a comparison could be made to determine which anchor element had the highest % utilization. Anchor element #3 had the highest % utilization (54%), thereby controlling the design with respect to concrete breakout failure in tension. ICC-ES AC232 provisions for anchor channel systems require the design strengths (φNN and φVN) for tension and shear respectively to be calculated for each possible failure mode in tension and shear, for each anchor element. The % utilization for that element must then be calculated in order to determine which element controls the design for that failure mode. These calculations are performed internally by PROFIS Anchor Channel software. The PROFIS Anchor Channel report will only show calculation results for the controlling anchor element.

Hilti Anchor Channel Tutorial Design Example #2 / 29 Shear Strength Design Calculations for Anchor Channel Systems

The applied shear load of 2000 lb for this example acts perpendicular to the channel longitudinal axis; therefore, shear nominal strength values for this example will have a “y” subscript.

shear load acts perpendicular to the channel longitudinal axis

shear load acts in the direction of the channel longitudinal axis

fill channel with HIT HY 100 adhesive

or use serrated T-bolts

COMMENTS Consideration must be given to the direction of the applied shear load with respect to the channel longitudinal axis. ESR-3520 assumes three load directions (x, y and z) to define the directions in which tension (z-direction) and shear (x or y-directions) loads can act. Shear load acting in the direction of the channel longitudinal axis acts in the x-direction (Vua,x). Nominal shear strength parameters for this load direction will be given an “x” subscript (Vsl,x, Vcb,x etc.). ESR-3520 Section 2.0 USES notes that the channel must be filled with HIT-HY 100 adhesive when shear load acts in the direction of the channel longitudinal axis. This provision will be revised to permit use of serrated T-bolts as an alternate to filling the channel with HY 100 once testing per AC232 is complete. Shear load acting perpendicular to the channel longitudinal axis acts in the y-direction (Vua,y). Nominal shear strength parameters for this load direction will be given a “y” subscript (Vsl,y, Vcb,y etc.).

Hilti Anchor Channel Tutorial Design Example #2 / 29 Nominal concrete breakout strength in shear for anchor element #1 Vcb,y,1 = Vb,1 ψs,V,1 ψco,V,1 ψc,V,1 ψh,V,1 ESR-3520 Equation (30) Calculate the basic concrete breakout strength in shear (Vb,1). Vb,1 = λ αch,V f’c ca1

4/3 ESR-3520 Equation (31)

λ = 1.0 (normal weight concrete) αch,V = 10.5 (reference ESR-3520 Table 8-6) f’c = 3500 psi ca1 = 4.5 in (reference page 1) Vb,1 = (1.0) (10.5) (3500)0.5 (4.5)4/3 → Vb,1 = 4615 lb Calculate the modification factor for anchor influence (ψs,V,1). ψs,V,1 = ESR-3520 Equation (32) si = spacing between each anchor element = 5.91 in sxx,1 = distance of each influencing anchor element from anchor element #1 s2,1 = distance from anchor element #2 to anchor element #1 = 5.91 in s3,1 = distance from anchor element #3 to anchor element #1 = 11.82 in scr,V = critical anchor spacing for shear loading ca1 = 4.50 in (reference page 1) bch = 1.71 in (reference ESR-3520 Table 8-1) scr,V = 4ca1 + 2bch → scr,V = 21.42 in ESR-3520 Equation (33) Va

ua,1 = shear load on anchor element #1 (Sa1,total) = 543 lb (see p. 2) Va


ua,3 = shear load on anchor element #3 (Sa3,total) = 543 lb (see p. 2) influence of anchor element #2 on anchor element #1: = 1.04 influence of anchor element #3 on anchor element #1: = 0.30 ψs,V,1 = → ψs,V,1 = 0.427

COMMENTS The parameter αch,V is a factor that is used to account for the influence of the channel size on the concrete breakout capacity in shear. The value 10.5 is a constant. The parameter ca1 corresponds to the perpendicular distance from the anchor channel longitudinal axis to the concrete edge, in the direction of the applied shear load. The value calculated for concrete breakout strength in tension (Vcb) is based on the location of the anchor element being considered. The parameter ψs,V is a modification factor that is calculated to account for the influence of anchor elements located within the distance scr,V from the anchor element being considered. Reference ESR-3520 Equation (32) for more information on how to calculate ψs,V. The parameter scr,V corresponds to the maximum distance that is assumed with respect to the influence of an anchor element on the anchor element being considered. Any anchor elements that are within scr,V from the anchor element being considered are assumed to have an influence on that anchor element. Reference ESR-3520 Equation (33) for more information on how to calculate scr,V.

si 1.5

scr,V

Vaua,i

Vaua,1 1 +

1

Σ n+1 i=2

1 -

anchor element #1 anchor element #2

scr,V scr,V


5.91 in 1.5

21.42 in

916 lbi 543 lb

1 -

11.82 in 1.5

21.42 in

543 lbi 543 lb

1 -

1 + (1.04 + 0.30)

1

Hilti Anchor Channel Tutorial Design Example #2 / 29 Calculate the modification factor for corner influence (ψco,V,1). ψco,V,1 = ESR-3520 Equation (35) ca2(+x) = 5.91 in + 5.91 in + 0.984 in + 5.0 in = 17.8 in (reference page 1) ca2(-x) = ∞ → = 1.0 ESR-3520 Equation (34) ccr,V = (2)(ca1) + (bch) → ccr,V = (0.5)(scr,V) ESR-3520 Equation (36) ca1 = 4.5 in (reference page 1) bch = 1.71 in ESR-3520 Table 8-1 ccr,V = (2)(4.5 in) + 1.71 in 10.71 in ca2(+x) > ccr,V → ψco,V,1 = 1.0 ESR-3520 Equation (34) Calculate the modification factor for cracked/uncracked concrete (ψc,V,1). Cracked concrete conditions with no supplementary reinforcement → ψc,V,1 = 1.0. Note: if cracked concrete conditions are assumed, and supplementary edge reinforcement as defined in ESR-3520 Section 4.1.3.3.3 is used, ψc,V,1 can be increased to either ψc,V,1 = 1.2 or ψc,V,1 = 1.4. If uncracked concrete conditions are assumed, ψc,V,1 = 1.4. Calculate the modification factor for member thickness (ψh,V,1). ψh,V,1 = if h < hcr,V ESR-3520 Equation (37) h = concrete thickness = 8.0 in (reference page 1) hcr,V = 2ca1 + 2hch ESR-3520 Equation (38) ca1 = 4.5 in (reference page 1) hch = channel height = 1.40 in ESR-3520 Table 8-1 hcr,V = 2(4.5 in) + 2(1.40 in) = 11.80 in 8.0 in < 11.80 in → h < hcr,V → calculate ψh,V,1 ψh,V,1 = = 0.823

COMMENTS The parameters ca1 and ca2 correspond to the distance from the center of the anchor element being considered to a fixed edge. ca1 is measured perpendicular to the anchor channel longitudinal axis, and is considered when calculating the basic concrete breakout strength in shear (Vb) and the modification factor for member thickness (ψh,V). ca2 is measured parallel to the anchor channel longitudinal axis, and is considered when calculating the modification factor for corner influence (ψco,V). When concrete breakout in shear (Vcb,y) is being calculated for anchor element #1. It is important to note that values for ca1 and ca2 must be considered with respect to the relevant edge distances from anchor element #1. The parameter ccr,V corresponds to the maximum distance that is assumed with respect to the value for ca2. Any ca2 value less than ccr,V must be considered when calculating ψco,V. If more than one ca2 value is less than ccr,V, ψco,V will be calculated for each ca2 value, and the product of these ψco,V values will be used to calculate the nominal concrete breakout strength in shear (Vcb,y). Concrete is typically assumed to be cracked under normal service load conditions. If cracked concrete conditions are assumed, an increase in Vcb,y is permitted via the modification factor ψc,V if supplementary edge reinforcement is used. If uncracked concrete conditions are assumed, an increase in Vcb,y is likewise permitted via the modification factor ψc,V . Reference ESR-3520 Section 4.1.3.3.3 for more information.

ca1

ca2(+x)

anchor

element

#1

ca2 0.5

ccr,V

h 0.5

hcr,V

8.0 in 0.5

11.80 in

anchor

element

#2

anchor

element

#3

ca2,x- 0.5

ccr,V

ca2(-x)

Hilti Anchor Channel Tutorial Design Example #2 / 29 Nominal concrete breakout strength in shear for anchor element #1 Vcb,y,1 = Vb,1 ψs,V,1 ψco,V,1 ψc,V,1 ψh,V,1 ESR-3520 Equation (30)

Vb,1 = 4615 lb (reference page 15) ψs,V,1 = 0.427 (reference page 15) ψco,V,1 = 1.0 (reference page 16) ψc,V,1 = 1.0 (reference page 16) ψh,V,1 = 0.823 (reference page 16) Vcb,y,1 = (4615 lb) (0.427) (1.0) (1.0) (0.823) → Vcb,y,1 = 1621 lb

COMMENTS The calculated value for Vcb,y,1 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φVcb,y,1). Design strengths for this example are summarized in the table on page 23 titled Summary for Concrete Breakout in Shear. The calculated φVcb,y,1 value for anchor element #1 will be checked against the factored load acting on anchor element #1 (Sa1,total) to obtain the % utilization (Sa1,total / φVcb,y,1). The anchor element with the highest % utilization will control the design with respect to concrete breakout failure in shear.







COMMENTS The value calculated for concrete breakout strength in shear (Vcb) is based on the location of the anchor element being considered. The basic concrete breakout strength in shear (Vb) is not dependent on the anchor element being considered, but it is dependent on the concrete geometry via the parameter ca1. However, the calculated value for Vb will be the same for each anchor element if the ca1 value is the same for each element. The parameter ψs,V will be dependent on the anchor element being considered and the concrete geometry. Reference ESR-3520 Equation (32) for more information on how to calculate ψs,V. The parameter scr,V corresponds to the maximum distance that is assumed with respect to the influence of an anchor element on the anchor element being considered. Any anchor elements that are within scr,V from the anchor element being considered are assumed to have an influence on that anchor element. The calculated value for scr,V will be the same for each anchor element if the ca1 value is the same for each element; however, the number of anchor elements within the distance scr,V from the anchor element being considered may not always be the same. Reference ESR-3520 Equation (33) for more information on how to calculate scr,V.

si 1.5

scr,V

Vaua,i

Vaua,2 1 +

1

Σ n+1 i=2

1 -


scr,V scr,V


5.91 in 1.5

21.42 in

543 lbi 916 lb

1 -

5.91 in 1.5

21.42 in

543 lbi 916 lb

1 -

1 + (0.365 + 0.365)

1

Hilti Anchor Channel Tutorial Design Example #2 / 29 Calculate the modification factor for corner influence (ψco,V,2). ψco,V,2 = ESR-3520 Equation (35) ca2(+x) = 5.91 in + 0.984 in + 5.0 in = 11.89 in (reference page 1) ca2(-x) = ∞ → = 1.0 ESR-3520 Equation (34) ccr,V = (2)(ca1) + (bch) → ccr,V = (0.5)(scr,V) ESR-3520 Equation (36) ca1 = 4.5 in (reference page 1) bch = 1.71 in ESR-3520 Table 8-1 ccr,V = (2)(4.5 in) + 1.71 in 10.71 in ca2(+x) > ccr,V → ψco,V,2 = 1.0 ESR-3520 Equation (34) Calculate the modification factor for cracked/uncracked concrete (ψc,V,2). Cracked concrete conditions with no supplementary reinforcement → ψc,V,2 = 1.0. Note: if cracked concrete conditions are assumed, and supplementary edge reinforcement as defined in ESR-3520 Section 4.1.3.3.3 is used, ψc,V,2 can be increased to either ψc,V,2 = 1.2 or ψc,V,2 = 1.4. If uncracked concrete conditions are assumed, ψc,V,2 = 1.4. Calculate the modification factor for member thickness (ψh,V,2). ψh,V,2 = if h < hcr,V ESR-3520 Equation (37) h = concrete thickness = 8.0 in (reference page 1) hcr,V = 2ca1 + 2hch ESR-3520 Equation (38) ca1 = 4.5 in (reference page 1) hch = channel height = 1.40 in ESR-3520 Table 8-1 hcr,V = 2(4.5 in) + 2(1.40 in) = 11.80 in 8.0 in < 11.80 in → h < hcr,V → calculate ψh,V,2 ψh,V,2 = = 0.823

COMMENTS The parameters ca1 and ca2 correspond to the distance from the center of the anchor element being considered to a fixed edge. ca1 is measured perpendicular to the anchor channel longitudinal axis, and is considered when calculating the basic concrete breakout strength in shear (Vb) and the modification factor for member thickness (ψh,V). ca2 is measured parallel to the anchor channel longitudinal axis, and is considered when calculating the modification factor for corner influence (ψco,V). When concrete breakout in shear (Vcb,y,2) is being calculated for anchor element #2. It is important to note that values for ca1 and ca2 must be considered with respect to the relevant edge distances from anchor element #2. The parameter ccr,V corresponds to the maximum distance that is assumed with respect to the value for ca2. Any ca2 value less than ccr,V must be considered when calculating ψco,V. If more than one ca2 value is less than ccr,V, ψco,V will be calculated for each ca2 value, and the product of these ψco,V values will be used to calculate the nominal concrete breakout strength in shear (Vcb,y). Concrete is typically assumed to be cracked under normal service load conditions. If cracked concrete conditions are assumed, an increase in Vcb,y is permitted via the modification factor ψc,V if supplementary edge reinforcement is used. If uncracked concrete conditions are assumed, an increase in Vcb,y is likewise permitted via the modification factor ψc,V . Reference ESR-3520 Section 4.1.3.3.3 for more information.

ca1

ca2(+x)

anchor

element

#1

ca2 0.5

ccr,V

h 0.5

hcr,V

8.0 in 0.5

11.80 in

anchor

element

#2

anchor

element

#3

ca2(-x) 0.5

ccr,V

ca2(-x)



COMMENTS The calculated value for Vcb,y,2 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φVcb,y,2). Design strengths for this example are summarized in the table on page 23 titled Summary for Concrete Breakout in Shear. The calculated φVcb,y,2 value for anchor element #2 will be checked against the factored load acting on anchor element #2 (Sa2,total) to obtain the % utilization (Sa2,total / φVcb,y,2). The anchor element with the highest % utilization will control the design with respect to concrete breakout failure in shear.







COMMENTS The value calculated for concrete breakout strength in shear (Vcb) is based on the location of the anchor element being considered. The basic concrete breakout strength in shear (Vb) is not dependent on the anchor element being considered, but it is dependent on the concrete geometry via the parameter ca1. However, the calculated value for Vb will be the same for each anchor element if the ca1 value is the same for each element. The parameter ψs,V will be dependent on the anchor element being considered and the concrete geometry. Reference ESR-3520 Equation (32) for more information on how to calculate ψs,V. The parameter scr,V corresponds to the maximum distance that is assumed with respect to the influence of an anchor element on the anchor element being considered. Any anchor elements that are within scr,V from the anchor element being considered are assumed to have an influence on that anchor element. The calculated value for scr,V will be the same for each anchor element if the ca1 value is the same for each element; however, the number of anchor elements within the distance scr,V from the anchor element being considered may not always be the same. Reference ESR-3520 Equation (33) for more information on how to calculate scr,V.

si 1.5

scr,V

Vaua,i

Vaua,3 1 +

1

Σ n+1 i=2

1 -


scr,V scr,V

si si

anchor element #2

11.82 in 1.5

21.42 in

543 lbi 543 lb

1 -

5.91 in 1.5

21.42 in

916 lbi 543 lb

1 -

1 + (0.30 +1.04)

1

Hilti Anchor Channel Tutorial Design Example #2 / 29 Calculate the modification factor for corner influence (ψco,V,3). ψco,V,3 = ESR-3520 Equation (35) ca2(+x) = 5.00 in + 0.984 in = 5.984 in (reference page 1) ca2(-x) = ∞ → = 1.0 ESR-3520 Equation (34) ccr,V = (2)(ca1) + (bch) → ccr,V = (0.5)(scr,V) ESR-3520 Equation (36) ca1 = 4.5 in (reference page 1) bch = 1.71 in ESR-3520 Table 8-1 ccr,V = (2)(4.5 in) + 1.71 in 10.71 in ψco,V,3 = = 0.748 Calculate the modification factor for cracked/uncracked concrete (ψc,V,3). Cracked concrete conditions with no supplementary reinforcement → ψc,V,3 = 1.0 Note: if cracked concrete conditions are assumed, and supplementary edge reinforcement as defined in ESR-3520 Section 4.1.3.3.3 is used, ψc,V,3 can be increased to either ψc,V,3 = 1.2 or ψc,V,3 = 1.4. If uncracked concrete conditions are assumed, ψc,V,3 = 1.4. Calculate the modification factor for member thickness (ψh,V,3). ψh,V,3 = if h < hcr,V ESR-3520 Equation (37) h = concrete thickness = 8.0 in (reference page 1) hcr,V = 2ca1 + 2hch ESR-3520 Equation (38) ca1 = 4.5 in (reference page 1) hch = channel height = 1.40 in ESR-3520 Table 8-1 hcr,V = 2(4.5 in) + 2(1.40 in) = 11.80 in 8.0 in < 11.80 in → h < hcr,V → calculate ψh,V,3 ψh,V,3 = = 0.823

COMMENTS The parameters ca1 and ca2 correspond to the distance from the center of the anchor element being considered to a fixed edge. ca1 is measured perpendicular to the anchor channel longitudinal axis, and is considered when calculating the basic concrete breakout strength in shear (Vb) and the modification factor for member thickness (ψh,V). ca2 is measured parallel to the anchor channel longitudinal axis, and is considered when calculating the modification factor for corner influence (ψco,v). When concrete breakout in shear (Vcb,y,3) is being calculated for anchor element #3. It is important to note that values for ca1 and ca2 must be considered with respect to the relevant edge distances from anchor element #3. The parameter ccr,V corresponds to the maximum distance that is assumed with respect to the value for ca2. Any ca2 value less than ccr,V must be considered when calculating ψco,V. If more than one ca2 value is less than ccr,V, ψco,V will be calculated for each ca2 value, and the product of these ψco,V values will be used to calculate the nominal concrete breakout strength in shear (Vcb,y). Concrete is typically assumed to be cracked under normal service load conditions. If cracked concrete conditions are assumed, an increase in Vcb,y is permitted via the modification factor ψc,V if supplementary edge reinforcement is used. If uncracked concrete conditions are assumed, an increase in Vcb,y is likewise permitted via the modification factor ψc,V . Reference ESR-3520 Section 4.1.3.3.3 for more information.

ca1

ca2(+x)

anchor

element

#1

ca2 0.5

ccr,V

h 0.5

hcr,V

8.0 in 0.5

11.80 in

anchor

element

#2

anchor

element

#3

5.984 in 0.5

10.71 in

ca2(-x) 0.5

ccr,V

ca2(-x)



COMMENTS The calculated value for Vcb,y,3 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φVcb,y,3). Design strengths for this example are summarized in the table on this page titled Summary for Concrete Breakout in Shear. The calculated φVcb,y,3 value for anchor element #3 will be checked against the factored load acting on anchor element #3 (Sa3,total) to obtain the % utilization (Sa3,total / φVcb,y,3). The anchor element with the highest % utilization will control the design with respect to concrete breakout failure in shear.

Summary for Concrete Breakout in Shear Anchor Element

Nominal Strength Vcb (lb)

Design Strength φVcb (lb)

Factored Load

Saxx,total (lb)

% Utilization Saxx,total / φVcb

COMMENTS

φ-factors for concrete breakout in shear are given in ESR-3520 Table 8-6. The concrete breakout calculations (φVcb ) were influenced by the anchor location and the concrete geometry via the modification factors ψs,V and ψco,V

1

Vcb,y,1 = 1621

φ = 0.7 φVcb,y,1 = 1135

Sa1,total = 543

48%

2

Vcb,y,2 = 2195

φ = 0.7 φVcb,y,2 = 1537

Sa2,total = 916

60%

3

Vcb,y,3 = 1213

φ = 0.7 φVcb,y,3 = 849

Sa3,total = 543

64% CONTROLS

Anchor element #3 has the highest % utilization with respect to concrete breakout failure in shear. It was necessary to calculate the design concrete breakout strength (φVcb) relative to anchor elements #1, #2 and #3; and then determine the % utilization (Saxx,total / φVcb) based on the factored load acting on that element. Once the % utilization for all three anchor elements was calculated, a comparison could be made to determine which anchor element had the highest % utilization. Anchor element #3 had the highest % utilization (64%), thereby controlling the design with respect to concrete breakout failure in shear. ICC-ES AC232 provisions for anchor channel systems require the design strengths (φNN and φVN) for tension and shear respectively to be calculated for each possible failure mode in tension and shear, for each anchor element. The % utilization for that element must then be calculated in order to determine which element controls the design for that failure mode. These calculations are performed internally by PROFIS Anchor Channel software. The PROFIS Anchor Channel report will only show calculation results for the controlling anchor element.

Hilti Anchor Channel Tutorial Design Example #2 / 29 Nominal concrete pryout strength in shear for Anchor Element #1. Vcp,y,1 = kcp Ncb,1 ESR-3520 Equation (41) kcp = 2.0 ESR-3520 Table 8-6

Ncb,1 = Nb,1 ψs,N,1 ψed,N,1 ψco,N,1 ψc,N,1 ψcp,N,1 ESR-3520 Equation (6)

Nb,1 = 19,407 lb (reference page 7) ψs,N,1 = See calculations below. Reference ESR-3520 Section 4.1.3.3.4. ψed,N,1 = 0.668 (reference page 7) ψco,N,1 = 1.0 (reference page 7) ψc,N,1 = 1.0 (reference page 7) ψcp,N,1 = 1.0 (reference page 7) Calculate the modified factor for anchor influence (ψs,N,1). ψs,N,1 = ESR-3520 Equation (10) modified per Sec. 4.1.3.3.4 si = spacing between each anchor element = 5.91 in sxx,1 = distance of each influencing anchor element from anchor element #1 s2,1 = distance from anchor element #2 to anchor element #1 = 5.91 in s3,1 = distance from anchor element #3 to anchor element #1 = 11.82 in scr,N = critical anchor spacing for tension loading (hef = 5.83 in) scr,N = (2) 2.8 - → scr,N = 20.20 in ESR-3520 Equation (11) Va



ua,3 = shear load on anchor element #3 (Sa3,total) = 543 lb (see p. 2) influence of anchor element #2 on anchor element #1: = 1.00 influence of anchor element #3 on anchor element #1: = 0.267 ψs,N,1 = → ψs,N,1 = 0.441

COMMENTS The ICC-ES Acceptance Criteria AC232 includes amendments to the ACI 318 anchoring to concrete provisions. These amendments are given in Section 3.1 Strength Design – Amendments to ACI 318. Part D.6.3.2 (ACI 318-11) and Section 17.5.3.2 (ACI 318-14) of these amendments requires the factor ψs,N to be modified when calculating concrete pryout strength in shear. All of the parameters used to calculate ψs,N in tension are used except the parameter (Na

ua,i / Naua,1). The

shear loads acting on the anchor elements are substituted for the tension loads such that (Va

ua,i / Vaua,1) is used instead of

(Naua,i / Na

ua,1). These provisions for calculating concrete pryout strength are also given in ESR-3520 Section 4.1.3.3.4.

si 1.5

scr,N

Vaua,i

Vaua,1 1 +

1

n+1 i=2

1 -

5.91 in 1.5

20.20 in

916 lbi 543 lb

1 -

11.82 in 1.5

20.20 in

543 lbi 543 lb

1 -

1 + (1.00 + 0.267)

1

anchor element #2

scr,N scr,N


1.3 hef 7.1 (hef)

anchor element #1

Σ



Nb,1 = 19,407 lb (reference page 7) ψs,N,1 = 0.441. (reference page 24) ψed,N,1 = 0.668 (reference page 7) ψco,N,1 = 1.0 (reference page 7) ψc,N,1 = 1.0 (reference page 7) ψcp,N,1 = 1.0 (reference page 7) Ncb,1 = (19,407 lb) (0.441) (0.668) (1.0) (1.0) (1.0) = 5717 lb Vcp,y,1 = (2) (5717 lb) = 11,434 lb

COMMENTS The calculated value for Vcp,y,1 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φVcp,y,1). Design strengths for this example are summarized in the table on page 29 titled Summary for Concrete Pryout in Shear. The calculated φVcp,y,1 value for anchor element #1 will be checked against the factored load acting on anchor element #1 (Sa1,total) to obtain the % utilization (Sa1,total / φVcp,y,1). The anchor element with the highest % utilization will control the design with respect to concrete pryout failure in shear.



Nb,2 = 19,407 lb (reference page 10) ψs,N,2 = See calculations below. Reference ESR-3520 Section 4.1.3.3.4. ψed,N,2 = 0.668 (reference page 10) ψco,N,2 = 1.0 (reference page 10) ψc,N,2 = 1.0 (reference page 10) ψcp,N,2 = 1.0 (reference page 10) Calculate the modified factor for anchor influence (ψs,N,2). ψs,N,2 = ESR-3520 Equation (10) modified per Sec. 4.1.3.3.4 si = spacing between each anchor element = 5.91 in sxx,1 = distance of each influencing anchor element from anchor element #2 s1,2 = distance from anchor element #1 to anchor element #2 = 5.91 in s3,2 = distance from anchor element #3 to anchor element #2 = 5.91 in scr,N = critical anchor spacing for tension loading (hef = 5.83 in) scr,N = (2) 2.8 - → scr,N = 20.20 in ESR-3520 Equation (11) Va

ua,1 = tension load on anchor element #1 (Sa1,total) = 543 lb (see p. 2) Va


ua,3 = tension load on anchor element #3 (Sa3,total) = 543 lb (see p. 2) influence of anchor element #1 on anchor element #2: = 0.353 influence of anchor element #3 on anchor element #2: = 0.353 ψs,N,2 = → ψs,N,2 = 0.586

si 1.5

scr,N

Vaua,i

Vaua,2 1 +

1

Σ n+1 i=2

1 -

5.91 in 1.5

20.20 in

543 lbi 916 lb

1 -

5.91 in 1.5

20.20 in

543 lbi 916 lb

1 -

1 + (0.353 + 0.353)

1

anchor element #2

scr,N scr,N si si

anchor element #3

1.3 hef 7.1 (hef)

anchor element #1


ua,i / Naua,2). The shear loads

acting on the anchor elements are substituted for the tension loads such that (Va

ua,i / Vaua,2) is

used instead of (Naua,i / Na




Nb,2 = 19,407 lb (reference page 10) ψs,N,2 = 0.586. (reference page 26) ψed,N,2 = 0.668 (reference page 10) ψco,N,2 = 1.0 (reference page 10) ψc,N,2 = 1.0 (reference page 10) ψcp,N,2 = 1.0 (reference page 10) Ncb,2 = (19,407 lb) (0.0.586) (0.668) (1.0) (1.0) (1.0) = 7597 lb Vcp,y,2 = (2) (7597 lb) = 15,194 lb

COMMENTS The calculated value for Vcp,y,2 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φVcp,y,2). Design strengths for this example are summarized in the table on page 29 titled Summary for Concrete Pryout in Shear. The calculated φVcp,y,2 value for anchor element #2 will be checked against the factored load acting on anchor element #2 (Sa2,total) to obtain the % utilization (Sa2,total / φVcp,y,2). The anchor element with the highest % utilization will control the design with respect to concrete pryout failure in shear.



Nb,3 = 19,407 lb (reference page 13) ψs,N,3 = See calculations below. Reference ESR-3520 Section 4.1.3.3.4. ψed,N,3 = 0.668 (reference page 13) ψco,N,3 = 0.77 (reference page 13) ψc,N,3 = 1.0 (reference page 13) ψcp,N,3 = 1.0 (reference page 13) Calculate the modification factor for anchor influence (ψs,N,3). ψs,N,3 = ESR-3520 Equation (10) si = spacing between each anchor element = 5.91 in sxx,1 = distance of each influencing anchor element from anchor element #3 s1,3 = distance from anchor element #1 to anchor element #3 = 11.82 in s2,3 = distance from anchor element #2 to anchor element #3 = 5.91 in scr,N = critical anchor spacing for tension loading (hef = 5.83 in) scr,N = (2) 2.8 - → scr,N = 20.20 in ESR-3520 Equation (11) Va



ua,3 = tension load on anchor element #3 (Sa3,total) = 543 lb (see p. 2) influence of anchor element #1 on anchor element #3: = 0.267 influence of anchor element #2 on anchor element #3: = 1.00 ψs,N,3 = → ψs,N,3 = 0.441

si 1.5

scr,N

Vaua,i

Vaua,3

1

Σ n+1 i=2

1 -

11.82 in 1.5

20.20 in

543 lb 543 lb

1 -

5.91 in 1.5

20.2 in

916 lb 543 lb

1 -

1 + (0.267 + 1.00)

1

anchor element #2

scr,N scr,N

si si

anchor element #3

1.3 hef 7.1 (hef)

anchor element #1


ua,i / Naua,3). The shear loads

acting on the anchor elements are substituted for the tension loads such that (Va

ua,i / Vaua,3) is

used instead of (Naua,i / Na


1 +



Nb,3 = 19,407 lb (reference page 28) ψs,N,3 = 0.441 (reference page 28) ψed,N,3 = 0.668 (reference page 28) ψco,N,3 = 0.77 (reference page 28) ψc,N,3 = 1.0 (reference page 28) ψcp,N,3 = 1.0 (reference page 28) Ncb,3 = (19,407 lb) (0.441) (0.668) (0.77) (1.0) (1.0) = 4402 lb Vcp,y,3 = (2) (4402 lb) = 8804 lb

Summary for Concrete Pryout in Shear Anchor Element

Nominal Strength Vcp (lb)

Design Strength φVcp (lb)

Factored Load

Saxx,total (lb)

% Utilization Saxx,total / φVcp

COMMENTS

φ-factors for concrete pryout in shear are given in ESR-3520 Table 8-6. The concrete pryout calculations (φVcp ) were influenced by the anchor location and the concrete geometry via the modified ψs,N factor.

1

Vcp,y,1 = 11,434

φ = 0.7 φVcp,y,1 = 8004

Sa1,total = 543

7%

2

Vcp,y,2 = 15,194

φ = 0.7 φVcp,y,2 = 10,636

Sa2,total = 916

8.6%

3

Vcp,y,3 = 8804

φ = 0.7 φVcp,y,3 = 6163

Sa3,total = 543

8.8% CONTROLS

Anchor element #3 has the highest % utilization with respect to concrete pryout failure in shear. It was necessary to calculate the design concrete pryout strength (φVcp) relative to anchor elements #1, #2 and #3; and then determine the % utilization (Saxx,total / φVcp) based on the factored load acting on that element. Once the % utilization for all three anchor elements was calculated, a comparison could be made to determine which anchor element had the highest % utilization. Anchor element #3 had the highest % utilization (8.8%), thereby controlling the design with respect to concrete pryout failure in shear. ICC-ES AC232 provisions for anchor channel systems require the design strengths (φNN and φVN) for tension and shear respectively to be calculated for each possible failure mode in tension and shear, for each anchor element. The % utilization for that element must then be calculated in order to determine which element controls the design for that failure mode. These calculations are performed internally by PROFIS Anchor Channel software. The PROFIS Anchor Channel report will only show calculation results for the controlling anchor element.

COMMENTS The calculated value for Vcp,y,3 will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φVcp,y,3). Design strengths for this example are summarized in the table below titled Summary for Concrete Pryout in Shear. The calculated φVcp,y,3 value for anchor element #3 will be checked against the factored load acting on anchor element #3 (Sa3,total) to obtain the % utilization (Sa3,total / φVcp,y,3). The anchor element with the highest % utilization will control the design with respect to concrete pryout failure in shear.

Note that the % utilizations for anchor element #2 (8.6%) and anchor element #3 (8.8%) are approximately the same (9%). PROFIS Anchor Channel calculations permit a distinction to be made regarding the controlling anchor element, even when the different in % utilization is only 0.2%.

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