Hilti Anchor Channel Tutorial Design Example #1 Page 1 / 21 · Hilti Anchor Channel Tutorial Design...

Hilti Anchor Channel Tutorial Design Example #1 / 21 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 6.0 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

Hilti Anchor Channel Tutorial Design Example #1 / 21 Determine the tension and shear loads acting on the T-bolts. compatibility equations: → = assume L = “unity” AT-bolts = (2)(tensile stress area of T-bolt) = (2)(157 mm2)/(25.4 in)(25.4 in) = 0.487 in2

ET-bolts = (modulus of elasticity for T-bolt) = 29,000,000 psi Econcrete = (modulus of elasticity for concrete) = 30,000 MPa = 4,351,200 psi FT-bolts = = (3.244)(σc)

COMMMENTS Assume the fixture is rigid. Calculate the tension and shear forces acting on each T-bolt. The application is statically indeterminate. Use compatibility equations and statics equations to solve for the location of the neutral axis (x). Once x is known, the tension force on each T-bolt can be calculated. Using the compatibility equations, define the tension force acting on both T-bolts (FT-bolts) in terms of the concrete compressive stress under the base plate (σc). Reference the PROFIS Anchor Design Guide section Base Plate Calculations for more information.

fixture

σc

FT-bolts

1500 lb

2.5” - x

x

2.5”

not to scale

9.5” - x

7.0”

P L A E

(FT-bolts) (L) (AT-bolts) (ET-bolts)

(σc) (L) (Econcrete)

(AT-bolts) (ET-bolts) (σc) (Econcrete)

Hilti Anchor Channel Tutorial Design Example #1 / 21 sum forces and moments: ΣF + 1500 lb - FT-bolts + (0.5)(σc)(x)(8 in) = 0 FT-bolts = 1500 + (4x)(σc) from compatibility equations: FT-bolts = (3.244)(σc) ∴ (3.244)(σc) = 1500 + (4x)(σc) → σc = ΣM + (FT-bolts)(2.5 – x) + (0.5)(σc)(x)(8 in)(0.67 x) – (1500 lb)(9.5 – x) = 0 (3.244)(σc)( 2.5 – x) + (2.667σc)(x2) – (1500)( 9.5 – x) = 0

COMMMENTS Using the statics equations, define the concrete compressive stress under the base plate (σc) in terms of x. Solve for the location of the neutral axis (x) via trial and error. Once x is known, the values for σc and FT-bolts can be calculated. Once FT-bolts is known, the tension force on each T-bolt can be determined.

try x = 0.611 in: solve for the tension force acting on each T-bolt: σc = → σc = 1875 psi FT-bolts = (3.244)(1875 psi) → FT-bolts = 6083 lb there are two T-bolts → the tension on each bolt = FT-bolts/2 ∴ the tension force on each T-bolt = 6083 lb/2 ≈ 3042 lb/bolt solve for the shear force acting on each T-bolt: the shear force on each T-bolt = 2000 lb/2 = 1000 lb/bolt Determine the flexural moment (Mu,flex) acting on the anchor channel. COMMENTS

Mu,flex is a bending moment. Assume Mu,flex occurs at the “point of load application” → Mu,flex occurs at the location of the T-bolt. Assume the channel is a simply supported beam.

1500 3.244 - (4x)

(3.244)(1500)(2.5 – x) 3.244 - (4x) + (2.667)(1500)(x2)

3.244 - (4x) = 0 - (1500)(9.5 – x)

(4866)(2.5 - x) + (4000)(x2) = (14,250 - 1500x)(3.244 - 4x)

(4866)(1.889) + (4000)(0.373) = (14,250 - 916.5)(3.244 - 2.444)

10,684 ≈ 10,667 ( ∆ = 17 → OK)

1500 3.244 - (4)(0.611)

3.416 in

5.91 in

3042 lb

F1 F2

3.416 in

1284 lb Mu,flex

COMMENTS The applied shear force is distributed equally on each T-bolt.

⊗

ΣF: 3042 lb – F1 – F2 = 0 F1 = 3042 lb - F2 ΣM: (3042 lb)(3.416 in) – (F2)(5.91 in) = 0 F2 = 1758 lb → F1 = 1284 lb ΣM: (1284 lb)(3.416 in) – Mu,flex = 0 Mu,flex = 4386 in-lb

Hilti Anchor Channel Tutorial Design Example #1 / 21 Determine the tension forces acting on each anchor element. The T-bolt #1 tension force (3042 lb) will have an influence on each anchor element as shown below. The tension forces on anchor elements #1, #2 and #3 resulting from this influence will be defined as Ta1,1, Ta2,1 and Ta3,1 respectively. The influence factor I#x,1 corresponds to the influence on anchor element #x from T-bolt #1. The parameter “s” corresponds to the spacing between each anchor element. The parameter l in corresponds to the influence length for T-bolt #1. =in 4.93 ( Iy )0.05 s where Iy is given in ESR-3520, Table 8-1 = (4.93) (0.1392 in4)0.05 (5.91 in)0.5 ESR-3520 Equation (3) = 10.86 in =in 10.86 in =in 10.86 in

COMMENTS The highest loaded anchor element in tension does not always control the anchor channel design in tension. The highest utilization, defined by the parameter (Ta,total / φNn) controls the design. Therefore, the tension design strengths must be calculated for each anchor element and checked against the total factored tension load acting on that element. The most unfavorably loaded anchor element (highest utilization) controls the design in tension. The tension forces acting on each anchor element can be determined assuming a triangular force distribution. The triangular force distribution assumes the tension force acting on each T-bolt (3042 lb) has an influence on each of the anchor elements within a given distance (l in) from the T-bolt. The resulting tension force on each anchor element (Tax,1) from the tension force acting on T-bolt #1 will be proportionate by the factor (I#x,1) to the distance of the anchor element with respect to the distance l in. Note that the influence length (l in) does not necessarily coincide with the channel length.

anchor element 1

anchor element 2

anchor element 3

Ta1,1 Ta2,1 Ta3,1

T-bolt #1

T-bolt #2

3042 lb

I1,1 I2,1

I3,1

s = 5.91 in

s = 5.91 in 3.41 in 2.50 in 7.45 in 2.45 in

anchor channel

I1,1 7.45 in

1.0 10.86 in

= → I1,1 = 0.686

I2,1 8.36 in

1.0 10.86 in

=

→ I2,1 = 0.770

I3,1 2.45 in

1.0 10.86 in

→ I3,1 = 0.226

1.0 I1,1 + I2,1 + I3,1

→ k1 = k1 = 0.595

Ta1,1 = (k1) (I1,1) (3042 lb)

→ Ta1,1 = 1242 lb

Ta2,1 = (k1) (I2,1) (3042 lb)

→ Ta2,1 = 1394 lb

Ta3,1 = (k1) (I3,1) (3042 lb)

→ Ta3,1 = 409 lb

Check: Ta1,1 + Ta2,1 + Ta3,1 = 3042 lb 3045 lb ≈ 3042 lb → OK

=

Reference ESR-3520 Section 4.1.2.2 for more information about tension load calculation parameters

ESR-3520 Equation (2)




Even when a T-bolt is located directly over one anchor element, the T-bolt load is still distributed to all other anchor elements within the distance lin from the T-bolt.

Hilti Anchor Channel Tutorial Design Example #1 / 21 Determine the tension forces acting on each anchor element. The T-bolt #2 tension force (3042 lb) will have an influence on each anchor element as shown below. The tension forces on anchor elements #1, #2 and #3 resulting from this influence will be defined as Ta1,2, Ta2,2 and Ta3,2 respectively. The influence factor I#x,2 corresponds to the influence on anchor element #x from T-bolt #2. The parameter “s” corresponds to the spacing between each anchor element. The parameter l in corresponds to the influence length for T-bolt #2. =in 4.93 ( Iy )0.05 s where Iy is given in ESR-3520, Table 8-1 = (4.93) (0.1392 in4)0.05 (5.91 in)0.5 ESR-3520 Equation (3) = 10.86 in =in 10.86 in =in 10.86 in

COMMENTS The highest loaded anchor element in tension does not always control the anchor channel design in tension. The highest utilization, defined by the parameter (Ta,total / φNn) controls the design. Therefore, the tension design strengths must be calculated for each anchor element and checked against the total factored tension load acting on that element. The most unfavorably loaded anchor element (highest utilization) controls the design in tension. The tension forces acting on each anchor element can be determined assuming a triangular force distribution. The triangular force distribution assumes the tension force acting on each T-bolt (3042 lb) has an influence on each of the anchor elements within a given distance (l in) from the T-bolt. The resulting tension force on each anchor element (Tax,2) from the tension force acting on T-bolt #2 will be proportionate by the factor (I#x,2) to the distance of the anchor element with respect to the distance l in. Note that the influence length (l in) does not necessarily coincide with the channel length.

anchor element 1

anchor element 2

anchor element 3

Ta1,2 Ta2,2 Ta3,2

T-bolt #1

T-bolt #2

3042 lb

I3,2 I2,2

I1,2

s = 5.91 in

s = 5.91 in 3.41 in 2.50 in 7.45 in 2.45 in

anchor channel

I1,2 2.45 in

1.0 10.86 in

=

→ I1,2 = 0.226

I2,2 8.36 in

1.0 10.86 in

=

→ I2,1 = 0.770

I3,2 7.45 in

1.0 10.86 in

→ I3,1 = 0.686

1.0 I1,1 + I2,1 + I3,1

→ k2 = k2 = 0.595

Ta1,2 = (k2) (I1,2) (3042 lb)

→ Ta1,2 = 409 lb

Ta2,2 = (k2) (I2,1) (3042 lb)

→ Ta2,2 = 1394 lb

Ta3,2 = (k2) (I3,1) (3042 lb)

→ Ta3,2 = 1242 lb Check:

Ta1,2 + Ta2,2 + Ta3,2 = 3042 lb 3045 lb ≈ 3042 lb → OK

Reference ESR-3520 Section 4.1.2.2 for more information about tension load calculation parameters

=





Hilti Anchor Channel Tutorial Design Example #1 / 21 from page 4: from page 5: total force on anchor element: Ta1,1 = 1242 lb Ta1,2 = 409 lb Ta1,total = 1242 lb + 409 lb = 1651 lb Ta2,1 = 1394 lb Ta2,2 = 1394 lb Ta2,total = 1394 lb + 1394 lb = 2788 lb Ta3,1 = 409 lb Ta3,2 = 1242 lb Ta3,total = 409 lb + 1242 lb = 1651 lb check: Ta1,total + Ta2,total + Ta3,total = 6083 lb (reference page 3) 1651 lb + 2788 lb + 1651 lb = 6090 lb ≈ 6083 lb → OK Anchor element #2 has the highest tension force acting on it, and the highest utilization (Ta2,total / φNn) for the concrete geometry, T-bolt loading and T-bolt configuration. Check the calculated tension design strengths (φNn) for anchor element #2 against Ta2,total. The tension design is satisfied if φNn > Ta2,total for each design strength. The anchor channel can also fail in tension by bending. The design strength φMs,flex must therefore be checked against the flexural moment (Mu,flex) acting on the anchor channel. Reference page 3 for the calculations to determine Mu,flex. The tension design with respect to channel bending is satisfied if φMs,flex > Mu,flex.

COMMENTS The total tension force acting on each anchor element (Tax,total) will be the sum of the T-bolt forces (Tax,1 + Tax,2) acting on that element. As a check, the sum of the total tension forces acting on all of the anchor elements should equal the sum of the tension forces acting on all of the T-bolts. The highest loaded anchor element in tension does not always control the anchor channel design in tension. The highest utilization, defined by the parameter (Ta,total / φNn) or (Mu,flex / φMs,flex) controls the design in tension. For this example, the concrete geometry, T-bolt loading and T-bolt configuration result in anchor element #2 having the highest utilization. Tension design strengths (φNn) will be calculated for anchor element #2 and checked against the total factored load acting on anchor element #2 (2788 lb). The flexural bending strength (φMs,flex ) will likewise be checked against the the factored bending moment 4386 in-lb.

Hilti Anchor Channel Tutorial Design Example #1 / 21 Determine the shear forces acting on each anchor element. The T-bolt #1 shear force (1000 lb) will have an influence on each anchor element as shown below. The shear forces on anchor elements #1, #2 and #3 resulting from this influence will be defined as Sa1,1, Sa2,1 and Sa3,1 respectively. The influence factor I#x,1 corresponds to the influence on anchor element #x from T-bolt #1. The parameter “s” corresponds to the spacing between each anchor element. The parameter l in corresponds to the influence length for T-bolt #1. =in 4.93 ( Iy )0.05 s where Iy is given in ESR-3520, Table 8-1 = (4.93) (0.1392 in4)0.05 (5.91 in)0.5 ESR-3520 Equation (3) = 10.86 in =in 10.86 in =in 10.86 in

COMMENTS The highest loaded anchor element in shear does not always control the anchor channel design in shear. The highest utilization, defined by the parameter (Sa,total / φVn) controls the design. Therefore, the shear design strengths must be calculated for each anchor element and checked against the total factored shear load acting on that element. The most unfavorably loaded anchor element (highest utilization) controls the design in shear. The anchor channel is not rigid; therefore, the shear forces acting on each anchor element can be determined assuming a triangular force distribution. The triangular force distribution assumes the shear force acting on each T-bolt (1000 lb) has an influence on each of the anchor elements within a given distance (l in) from the T-bolt. The resulting shear force on each anchor element (Sax,1) from the shear force acting on T-bolt #1 will be proportionate by the factor (I#x,1) to the distance of the anchor element with respect to the distance l in. Note that the influence length (l in) does not necessarily coincide with the channel length.

anchor element 1

anchor element 2

anchor element 3

Sa1,1 Sa2,1

Sa3,1

T-bolt #1

T-bolt #2

1000 lb

I1,1 I2,1

s = 5.91 in

s = 5.91 in 3.41 in 2.50 in 7.45 in 2.45 in

anchor channel

I1,1 7.45 in

1.0 10.86 in

= → I1,1 = 0.686 I2,1

8.36 in

1.0 10.86 in

=

→ I2,1 = 0.770

I3,1 2.45 in

1.0 10.86 in

→ I3,1 = 0.226

1.0 I1,1 + I2,1 + I3,1

→ k1 = k1 = 0.595

Sa1,1 = (k1) (I1,1) (1000 lb)

→ Sa1,1 = 408 lb Sa2,1 = (k1) (I2,1) (1000 lb)

→ Sa2,1 = 458 lb

Sa3,1 = (k1) (I3,1) (1000 lb)

→ Sa3,1 = 135 lb Check:

Sa1,1 + Sa2,1 + Sa3,1 = 1000 lb 1001 lb ≈ 1000 lb → OK

Reference ESR-3520 Section 4.1.2.3. The parameters shown for tension load calculations are also relevant for shear load calculations when the shear load acts perpendicular to the channel longitudinal axis.

=


ESR-3520 Equation (1) ESR-3520 Equation (1) ESR-3520 Equation (1)

I3,1

Hilti Anchor Channel Tutorial Design Example #1 / 21 Determine the shear forces acting on each anchor element. The T-bolt #2 shear force (1000 lb) will have an influence on each anchor element as shown below. The shear forces on anchor elements #1, #2 and #3 resulting from this influence will be defined as Sa1,2, Sa2,2 and Sa3,2 respectively. The influence factor I#x,2 corresponds to the influence on anchor element #x from T-bolt #2. The parameter “s” corresponds to the spacing between each anchor element. The parameter l in corresponds to the influence length for T-bolt #2. =in 4.93 ( Iy )0.05 s where Iy is given in ESR-3520, Table 8-1 = (4.93) (0.1392 in4)0.05 (5.91 in)0.5 ESR-3520 Equation (3) = 10.86 in =in 10.86 in =in 10.86 in

COMMENTS The highest loaded anchor element in shear does not always control the anchor channel design in shear. The highest utilization, defined by the parameter (Sa,total / φVn) controls the design. Therefore, the shear design strengths must be calculated for each anchor element and checked against the total factored shear load acting on that element. The most unfavorably loaded anchor element (highest utilization) controls the design in shear. The anchor channel is not rigid; therefore, the shear forces acting on each anchor element will be determined assuming a triangular force distribution. The triangular force distribution assumes the shear force acting on each T-bolt (1000 lb) has an influence on each of the anchor elements within a given distance (l in) from the T-bolt. The resulting shear force on each anchor element (Sax,2) from the shear force acting on T-bolt #2 will be proportionate by the factor (I#x,2) to the distance of the anchor element with respect to the distance l in. Note that the influence length (l in) does not necessarily coincide with the channel length.

I1,2 2.45 in

1.0 10.86 in

→ I1,2 = 0.226

= I3,2 7.45 in

1.0 10.86 in

→ I3,2 = 0.686

1.0 I1,2 + I2,2 + I3,2

→ k2 = k2 = 0.595

Sa1,2 = (k2) (I1,2) (1000 lb)

→ Sa1,2 = 135 lb

Sa2,2 = (k2) (I2,2) (1000 lb)

→ Sa2,2 = 458 lb

Sa3,2 = (k2) (I3,2) (1000 lb)

→ Sa3,2 = 408 lb

Check: Sa1,2 + Sa2,2 + Sa3,2 = 1000 lb 1001 lb ≈ 1000 lb → OK

=

Reference ESR-3520 Section 4.1.2.3. The parameters shown for tension load calculations are also relevant for shear load calculations when the shear load acts perpendicular to the channel longitudinal axis.

anchor element 1

anchor element 2

anchor element 3

Sa1,2 Sa2,2

Sa3,2

T-bolt #1

T-bolt #2

1000 lb

I2,2

s = 5.91 in

s = 5.91 in

3.41 in 2.50 in 7.45 in 2.45 in

anchor channel

I3,2 I1,2

I2,2 8.36 in

1.0 10.86 in

→ I1,2 = 0.77

=





Hilti Anchor Channel Tutorial Design Example #1 / 21 from page 7: from page 8: total force on anchor element: Sa1,1 = 408 lb Sa1,2 = 135 lb Sa1,total = 408 lb + 135 lb = 543 lb Sa2,1 = 458 lb Sa2,2 = 458 lb Sa2,total = 458 lb + 458 lb = 916 lb Sa3,1 = 135 lb Sa3,2 = 408 lb Sa3,total = 135 lb + 408 lb = 543 lb Check: Sa1,total + Sa2,total + Sa3,total = 2000 lb (reference page 3) 543 lb + 916 lb + 543 lb = 2002 lb ≈ 2000 lb → OK Anchor element #2 has the highest shear force acting on it → check calculated shear design strengths against Sa2,total. The shear design is satisfied if φVn > Sa2,total for each design strength.

COMMENTS The total shear force acting on an anchor element (Sax,total) will be the sum the forces (Sax,1 + Sax,2) acting on that element. As a check, the sum of total shear forces acting on the anchor elements should equal the sum of the shear forces acting on the T-bolts. The highest loaded anchor element in shear does not always control the anchor channel design in shear. The highest utilization, defined by the parameter (Sa,total / φVn) controls the design. For this example, the concrete geometry, T-bolt loading and T-bolt configuration result in anchor element #2 having the highest utilization. Shear design strengths will be calculated for anchor element #2, and checked against the total factored load acting on anchor element #2 (916 lb).

Tension

Failure Mode Nominal Strength

(Nn)

Design Strength

(φNn)

Factored Load (Nua)

Design Check

φNn > Nua

COMMENTS AC232 strength design tension provisions require calculation of nominal strengths corresponding to possible failure modes in tension. Each nominal tension strength (Nn) is multiplied by a strength reduction factor (φ-factor) to obtain a design tension strength (φNn). Tension design strengths for steel failure modes are checked against the tension load (Nua) acting on the anchor element or T-bolt. Tension design strengths for concrete failure modes are checked against the tension load (Nua) acting on the anchor element. The tension design strength φMn, corresponding to the design bending strength of the anchor channel, is checked against the factored flexural moment (Mu,flex) acting on the anchor channel.

steel failure: channel lips

Nn = Nsl φNn = φNsl Nua = TT-bolt φNsl > TT-bolt

steel failure: anchor element

Nn = Nsa φNn = φNsa Nua = Ta2,total φNsa > Ta2,total

steel failure: anchor/channel connection

Nn = Nsc

φNn = φNsc

Nua = Ta2,total

φNsc > Ta2,total

steel failure: channel bending

Nn = Ms,flex φNn = φMs,flex Nua = Mu,flex φMs,flex > Mu,flex

steel failure: T-bolt

Nn = Nss φNn = φNss Nua = TT-bolt φNss > TT-bolt

concrete failure: breakout

Nn = Ncb φNn = φNcb Nua = Ta2,total φNcb > Ta2,total

concrete failure: pullout

Nn = Npn φNn = φNpn Nua = Ta2,total φNpn > Ta2,total

concrete failure: side-face blowout

Nn = Nsb

φNn = φNsb

Nua = Ta2,total

φNsb > Ta2,total

Tension Strength Design Calculations for Anchor Channel Systems

Hilti Anchor Channel Tutorial Design Example #1 / 21 Nominal steel strengths in tension. nominal strength corresponding to local failure of channel lips → Nsl Reference ESR-3520 Table 8-1 and Table 8-3. Check: schb = clear distance between T-bolts T-bolts are spaced at 5 in o.c. Each bolt has a diameter = 16 mm. ∴ schb = 5 in – (16 mm)(1 in/25.4 mm) = 4.37 in HAC-60F channel width (bch) = 1.71 in → 2(bch) = 3.42 in If schb is < 2(bch), calculate the reduction factor and multiply Nsl by this factor. 4.37 in > 3.42 in → no reduction required. Nsl for an HAC-60F channel = 11,240 lb nominal strength corresponding to the anchor element → Nsa Reference ESR-3520 Table 8-3. Nsa for the anchor element of an HAC-60F channel = 11,240 lb nominal strength corresponding to anchor/channel connection → Nsc Reference ESR-3520 Table 8-3. Nsc for an HAC-60F anchor element/channel connection = 11,240 lb nominal strength corresponding to channel bending → Ms,flex Reference ESR-3520 Table 8-3. Ms,flex for an HAC-60F channel = 19,355 in-lb nominal strength corresponding to the T-bolt → Nss Reference ESR-3520 Table 8-7. Nss for an M16 diameter HBC-C 8.8 F T-bolt = 28,235 lb

COMMENTS Nominal tension steel strengths for anchor channel parameters are given in ESR-3520 Table 8-3. ESR-3520 Section 4.1.3.2.2 requires a check to made to determine if the clear distance between two T-bolts (schb) is > the parameter 2(bch), where bch corresponds to the channel width. Values for bch are given in Table 8-1 of ESR-3520. If schb is < 2(bch), the value for Nsl given in ESR-3520 Table 8-3 must be reduced by the parameter calculated using Equation (5) in ESR-3520. Nominal tension steel strengths for T-bolts are given in ESR-3520 Table 8-7.

schb 2(bch) (0.5) 1 +

Hilti Anchor Channel Tutorial Design Example #1 / 21 Nominal concrete breakout strength in tension. Ncb = Nb ψs,N ψed,N ψco,N ψc,N ψcp,N ESR-3520 Equation (6) Calculate the basic concrete breakout strength in tension (Nb). Nb = 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 = (24) (1.0) (0.971) (3500)0.5 (5.83)1.5 → Nb = 19,407 lb Calculate the modification factor for anchor influence (ψs,N). ψs,N = ESR-3520 Equation (10) si = distance of each influencing anchor element from anchor element #2 = spacing between anchor element #1 or #3 and 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) Na

ua,i = tension load on anchor element #1 (Ta1,total) or #3 (Ta3,total) Reference page 6. Ta1,total = Ta3,total = 1651 lb Na

ua,1 = tension load on anchor element #2 (Ta2,total) Reference page 6. Ta2,total = 2788 lb influence of anchor element #1 on anchor element #2: = 0.352 influence of anchor element #3 on anchor element #2: = 0.352 ψs,N = → ψs,N = 0.587

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 parameter ψs,N is a modification factor that is used to account for the influence of adjacent anchor elements on the anchor element being considered (see comments on page 4, 5 and 6). The value calculated for concrete breakout strength in tension (Ncb) is based on the location of the anchor element being considered. For this example, anchor element #2 has the highest utilization in tension. Therefore, for this example, ψs,N is calculated to account for the influence of anchor element #1 and anchor element #3 on anchor element #2. This influence takes into consideration the loading on each anchor element as well as the distance (spacing) of these elements from anchor element #2. Reference ESR-3520 Equations (10) and (11) for more information on how to calculate ψs,N. The parameter scr,N corresponds to the maximum distance that needs to be considered with respect to the influence of any adjacent anchor elements on the anchor element being considered. Any adjacent anchor elements that are within scr,N from the anchor element being considered are considered to have an influence on that anchor element. The value for si corresponds the distance of the influencing anchor element from the anchor element being considered.

hef 0.15

7.1

si 1.5

scr,N

Naua,i

Naua,1 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 #1 anchor element #2

scr,N scr,N si si

anchor element #3

1.3 hef 7.1 (hef)

Hilti Anchor Channel Tutorial Design Example #1 / 21 Calculate the modification factor for edge influence (ψed,N). ψed,N = 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 = = 0.668 Calculate the modification factor for corner influence (ψco,N). ψco,N = ESR-3520 Equation (16) where ca2 = 5.91 in + 0.984 in + 6.0 in = 12.894 in (reference page 1) ccr,N = (0.5)(scr,N) = (0.5)(20.20 in) = 10.10 in (reference page 11) ca2 > ccr,N → ψco,N = 1.0 ESR-3520 Equation (15) Calculate the modification factor for cracked/uncracked concrete (ψc,N). Cracked concrete conditions → ψc,N = 1.0. Note: if uncracked concrete conditions are assumed, ψc,N = 1.25. Calculate the modification factor for splitting (ψcp,N). Cracked concrete conditions → ψcp,N = 1.0. ESR-3520 Equation (17) Note: if uncracked concrete conditions are assumed: ψcp,N = 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 concrete breakout in tension (Ncb) for this example is 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,N corresponds to the maximum edge distance that needs to be considered 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

#2

#1 #3

ca1 0.5

ccr,N

4.5 in 0.5

10.10 in

ca2 0.5

ccr,N

ca,min ccr,N

cac cac

:

Hilti Anchor Channel Tutorial Design Example #1 / 21 Nominal concrete breakout strength in tension. Ncb = Nb ψs,N ψed,N ψco,N ψc,N ψcp,N ESR-3520 Equation (6)

Nb = 19,407 lb (reference page 11) ψs,N = 0.587 (reference page 11) ψed,N = 0.668 (reference page 12) ψco,N = 1.0 (reference page 12) ψc,N = 1.0 (reference page 12) ψcp,N = 1.0 (reference page 12) Ncb = (19,407 lb) (0.587) (0.668) (1.0) (1.0) (1.0) → Ncb = 7610 lb Nominal pullout strength in tension. Npn = ψc,P Np (reference ACI 318-11 Eq. (D-13) and ACI 318-14 Eq. (17.4.3.1) Np = 8 Abrg f’c (reference ACI 318-11 Eq. (D-14) and ACI 318-14 Eq. (17.4.3.4) Abrg for an HAC-60F anchor channel = 0.40 in2 (reference ESR-3520 Table 8-1) f’c for this example = 3500 psi cracked concrete conditions assumed → ψc,P = 1.0 (reference ACI 318-11 D.5.3.6 and ACI 318-14 17.4.3.6) Np = (8) (0.40 in2) (3500 psi) = 11,200 lb ∴ Npn = (1.0) (11,200 lb) = 11,200 lb Nominal side-face blowout strength in tension. Nsb = N0

sb ψs,Nb ψg,Nb ψco,Nb ψh,Nb ψc,Nb ESR-3520 Equation (19) Reference ESR-3520 Section 4.1.3.2.5. Check to see if hef > 2ca1. hef = 5.83 in (reference page 1) ca1 = 4.5 in (reference page 1) 2ca1 = 9.0 in → hef < 2ca1 → no side-face blowout calculation is necessary

COMMENTS The calculated value for Ncb will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φNcb). Design strengths for this example will be summarized when all nominal strength calculations have been completed. φNcb will be checked against the factored load acting on anchor element #2. → φNcb > Ta2,total will be checked. Per ESR-3520 Section 4.1.3.2.4, nominal pullout strength (Npn) is calculated using ACI 318 anchoring to concrete provisions. ACI 318-11 Appendix D and ACI 318-14 Chapter 17 provisions are referenced for this example. Side-face blowout is an edge condition. If the effective embedment depth of the anchor element (hef) is “deep” with respect to the edge distance ca1, → hef > 2ca1; lateral bursting stresses at the anchor element head will “blow out” the concrete edge below the concrete surface. When calculating Nsb, ca1 is measured perpendicular to the anchor channel longitudinal axis. ca1 is considered with respect to anchor element #2 for this example.

ca1 = 4.5 in

ca2

#2

#1 #3

Hilti Anchor Channel Tutorial Design Example #1 / 21 Strength Design Calculations for Anchor Channel Systems

Shear Failure Mode

Nominal Strength

(Vn)

Design Strength

(φVn)

Factored Load (Vua)

Design Check

φVn > Vua

COMMENTS AC232 strength design shear provisions require calculation of nominal strengths corresponding to possible failure modes in shear. Each nominal shear strength (Vn) is multiplied by a strength reduction factor (φ-factor) to obtain a design shear strength (φVn). Shear design strengths for steel failure modes are checked against the shear load (Vua) acting on an anchor element or on a T-bolt. Shear design strengths for concrete failure modes are checked against the shear load (Vua) acting on an anchor element.


Vn = Vsl,y φVn = φVsl,y Vua,y = ST-bolt φVsl,y > ST-bolt


Vn = Vsa,y φVn = φVsa,y Vua,y = Sa2,total

φVsa,y > Sa2,total


Vn = Vsc,y

φVn = φVsc,y

Vua,y = Sa2,total

φVsc,y > Sa2,total


Vn = Vss φVn = φVss Vua,y = ST-bolt φVss > ST-bolt


Vn = Vcb,y φVn = φVcb,y Vua,y = Sa2,total

φVcb,y > Sa2,total

concrete failure: pryout

Vn = Vcp,y φVn = φVcp,y Vua,y = Sa2,total

φVcp,y > Sa2,total

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 as shown in the table above.

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 #1 / 21 Nominal steel strengths in shear (load acts perpendicular to the anchor channel longitudinal axis).

nominal strength corresponding to local failure of channel lips → Vsl,y Reference ESR-3520 Table 8-5. Vsl,y for an HAC-60F channel = 16,205 lb nominal strength corresponding to the anchor element → Vsa,y Reference ESR-3520 Table 8-5. Vsa,y for the anchor element of an HAC-60F channel = 16,250 lb nominal strength corresponding to anchor/channel connection → Vsc,y Reference ESR-3520 Table 8-5. Vsc,y for an HAC-60F anchor element/channel connection = 16,250 lb nominal strength corresponding to the T-bolt → Vss Reference ESR-3520 Table 8-8. Vss for an M16 diameter HBC-C 8.8 F T-bolt = 16,940 lb

COMMENTS Nominal shear steel strengths for anchor channel parameters are given in ESR-3520 Table 8-5. Nominal shear steel strengths for T-bolts are given in ESR-3520 Table 8-8.

shear load acts perpendicular to the channel longitudinal axis

Hilti Anchor Channel Tutorial Design Example #1 / 21 Nominal concrete breakout strength in shear (load acts perpendicular to the longitudinal channel axis). Vcb,y = Vb ψs,V ψco,V ψc,V ψh,V ESR-3520 Equation (30) Calculate the basic concrete breakout strength in shear (Vb). Vb = 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 = (1.0) (10.5) (3500)0.5 (4.5)4/3 → Vb = 4615 lb Calculate the modification factor for anchor influence (ψs,V). ψs,V = ESR-3520 Equation (32) si = distance of each influencing anchor element from anchor element #2 = spacing between anchor element #1 or #3 and anchor element #2 = 5.91 in scr,V = critical anchor spacing for shear loading ca1 = 4.5 in (reference page 1) bch = 1.71 in (ESR-3520 Table 8-1) scr,V = (4)(ca1) + (2)(bch) → scr,V = 21.42 in ESR-3520 Equation (33) Va

ua,i = shear load on anchor element #1 (Sa1,total) or #3 (Sa3,total) Reference page 9. Sa1,total = Sa3,total = 543 lb Va

ua,1 = shear load on anchor element #2 (Sa2,total) Reference page 9. Sa2,total = 916 lb influence of anchor element #1 on anchor element #2: = 0.365 influence of anchor element #3 on anchor element #2: = 0.365 ψs,V = → ψs,N = 0.578

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 ψs,V is a modification factor that is used to account for the influence of adjacent anchor elements on the anchor element being considered (see comments on page 7, 8 and 9). The value calculated for concrete breakout strength in shear (Vcb,y) is based on the location of the anchor element being considered. For this example, anchor element #2 has the highest utilization in shear. Therefore, for this example, ψs,V is calculated to account for the influence of anchor element #1 and anchor element #3 on anchor element #2. This influence takes into consideration the loading on each anchor element as well as the distance (spacing) of these elements from anchor element #2. Reference ESR-3520 Equations (32) and (33) for more information on how to calculate ψs,V. The parameter scr,V corresponds to the maximum distance that needs to be considered with respect to the influence of any adjacent anchor elements on the anchor element being considered. Any adjacent anchor elements that are within scr,V from the anchor element being considered are considered to have an influence on that anchor element. The value for si corresponds to the distance of the influencing anchor element from the anchor element being considered.

si 1.5

scr,V

Vaua,i

Vaua,1 1 +

1

Σ n+1 i=2

1 -

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

anchor element #1 anchor element #2

scr,V scr,V si si

anchor element #3

Hilti Anchor Channel Tutorial Design Example #1 / 21 Calculate the modification factor for corner influence (ψco,V). ψco,V = ESR-3520 Equation (35) where ca2 = 5.91 in + 0.984 in + 6.0 in = 12.894 in (reference page 1) ccr,V = (2)(ca1) + (bch) → ccr,V = (0.5)(scr,V) ESR-3520 Equation (36) ccr,V = (0.5)(scr,V) = (0.5)(21.42 in) = 10.71 in (reference page 16) ca2 > ccr,V → ψco,V = 1.0 ESR-3520 Equation (34) Calculate the modification factor for cracked/uncracked concrete (ψc,V). Cracked concrete conditions with no supplementary reinforcement → ψc,V = 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 can be increased to either ψc,V = 1.2 or ψc,V = 1.4. If uncracked concrete conditions are assumed, ψc,V = 1.4. Calculate the modification factor for member thickness (ψh,V). ψh,V = 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 ψh,V = = 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,N). Since concrete breakout in shear (Vcb,y) for this example is 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 needs to be considered 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

#2

#1 #3

ca2 0.5

ccr,V

h 0.5

hcr,V

8.0 in 0.5

11.80 in

Hilti Anchor Channel Tutorial Design Example #1 / 21 Nominal concrete breakout strength in shear. Vcb,y = Vb ψs,V ψco,V ψc,V ψh,V ESR-3520 Equation (30)

Vb = 4615 lb (reference page 16) ψs,V = 0.578 (reference page 16) ψco,V = 1.0 (reference page 17) ψc,V = 1.0 (reference page 17) ψh,V = 0.823 (reference page 17) Vcb,y = (4615 lb) (0.578) (1.0) (1.0) (0.823) → Vcb,y = 2195 lb

COMMENTS The calculated value for Vcb,y will be multiplied by a strength reduction factor (φ-factor) to give a design strength (φVcb,y). Design strengths for this example will be summarized when all nominal strength calculations have been completed. φVcb,y will be checked against the factored load acting on anchor element #2. → φVcb,y > Sa2,total will be checked.

Nominal concrete pryout strength in shear. Vcp,y = kcp Ncb ESR-3520 Equation (41) kcp = 2.0 ESR-3520 Table 8-6

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

Nb = 19,407 lb (reference page 11) ψs,N = see calculations on page 19 Reference ESR-3520 Section 4.1.3.3.4. ψed,N = 0.668 (reference page 12) ψco,N = 1.0 (reference page 12) ψc,N = 1.0 (reference page 12) ψcp,N = 1.0 (reference page 12)

Hilti Anchor Channel Tutorial Design Example #1 / 21 Calculate the modification factor for anchor influence (ψs,N) for pryout. ψs,N = ESR-3520 Equation (10) modified per Section 4.1.3.3.4 si = distance of each influencing anchor element from anchor element #2 = spacing between anchor element #1 or #3 and 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,i = shear load on anchor element #1 (Sa1,total) or #3 (Sa3,total) Reference page 9. Sa1,total = Sa3,total = 543 lb Va

ua,1 = shear load on anchor element #2 (Sa2,total) Reference page 9. Sa2,total = 916 lb influence of anchor element #1 on anchor element #2: = 0.353 influence of anchor element #3 on anchor element #2: = 0.353 ψs,N = → ψs,N = 0.586 Vcp,y = kcp Ncb ESR-3520 Equation (41) kcp = 2.0 ESR-3520 Table 8-6

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

Nb = 19,407 lb (reference page 11) ψs,N = 0.586 ψed,N = 0.668 (reference page 12) ψco,N = 1.0 (reference page 12) ψc,N = 1.0 (reference page 12) ψcp,N = 1.0 (reference page 12) Ncb = (19407 lb) (0.586) (0.668) (1.0) (1.0) (1.0) = 7597 lb Vcp,y = (2) (7597 lb) = (15,194 lb)

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

COMMENTS Generally speaking, the nominal pryout strength calculation is independent of the direction of the applied shear load (Vcp = kcp Ncb); however, the calculated design strength (φVcp) must be checked against the relevant shear load (Vua,x or Vua,y). Per ESR-3520, when calculating pryout strength, the calculated value for nominal concrete breakout strength (Ncb) will be modified from the value used in the tension concrete breakout calculation. Specifically, the modification factor for anchor influence (ψs,N) will be modified to use factored shear loads in ESR-3520 Equation (10) instead of factored tension loads. Reference ESR-3520 Section 4.1.3.3.4. The coefficient for pryout strength (kcp) is given in ESR-3520 Table 8-6.

si 1.5

scr,N

Vaua

Vaua,1

1 +

1

Σ n+1 i=2

1 -

1.3 hef 7.1 (hef)

Hilti Anchor Channel Tutorial Design Example #1 / 21 Calculate the design strengths for tension and shear. Check versus the factored tension and shear loads. Tension: reference ESR-3520 Tables 8-3 and 8-7 for steel strength φ-factors and Table 8-4 for concrete strength φ-factors. Shear: reference ESR-3520 Tables 8-5 and 8-8 for steel strength φ-factors and Table 8-6 for concrete strength φ-factors.

Tension Failure Mode

Nominal Strength

(lb)

Design Strength (lb)

Factored Load (lb)

Utilization Nua / φNn

(%)

COMMENTS AC232 strength design tension provisions require calculation of nominal strengths corresponding to possible failure modes in tension. Each nominal tension strength (Nn or Mn) is multiplied by a strength reduction factor (φ-factor) to obtain a design tension strength (φNn or φMn). Tension design strengths (φNn or φMn) are checked against tension loads or moments (Nua or Mu,flex) respectively. If φNn or φMn are greater than or equal to Nua or Mu,flex respectively, the tension design is considered to be satisfied. This is verified when the Utilization Nua / φNn (%) and Mu,flex / φMs,flex (%) are < 100 %.


Nsl = 11,240

φ = 0.75 φNsl = 8430

Nua = 3042

36 % OK


Nsa = 11,240

φ = 0.75 φNsa = 8430

Nua = 2788

33 % OK


Nsc =11,240

φ = 0.75 φNsc = 8430

Nua = 2788

33 % OK

steel failure: channel bending

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

φ = 0.85 φMs,flex = 16,452 (in-lb)

Mu,flex = 4386 (in-lb)

27 % OK


Nss = 28,235

φ = 0.65 φNss = 18,352

Nua = 3042

17 % OK


Ncb = 7610

φ = 0.70 φNcb = 5327

Nua = 2788

53 % OK

concrete failure: pullout

Npn = 11,200

φ = 0.70 φNpn = 7840

Nua = 2788

36 % OK

concrete failure: side-face blowout

Nsb = N/A

φ = 0.70 φNsb = N/A

Nua = 2788

N/A

Shear Failure Mode

Nominal Strength

(lb)

Design Strength

(lb)

Factored Load (lb)

Utilization Vua / φVn

(%)

COMMENTS AC232 strength design shear provisions require calculation of nominal strengths corresponding to possible failure modes in shear. Each nominal shear strength (Vn) is multiplied by a strength reduction factor (φ-factor) to obtain a design shear strength (φVn). Shear design strengths (φVn) are checked against shear loads (Vua). If φVn is greater than or equal to Vua, the shear design is considered to be satisfied. This is verified when the Utilization Vua / φVn (%) is < 100 %.


Vsl,y = 16,205

φ = 0.75 φVsl,y = 12,154

Vua,y = 1000

8 % OK


Vsa,y = 16,250

φ = 0.75 φVsa,y = 12,188

Vua,y = 916

8 % OK


Vsc,y = 16,250

φ = 0.75 φVsc,y = 12,188

Vua,y = 916

8 % OK


Vss = 16,940

φ = 0.60 φVss = 10,164

Vua = 1000

10 % OK


Vcb,y = 2195

φ = 0.70 φVcb,y = 1537

Vua,y = 916

60% OK

concrete failure: pryout

Vcp,y = 15,194

φ = 0.70 φVcp,y = 10,636

Vua,y = 916

9 % OK

Hilti Anchor Channel Tutorial

Design Example #1 / 21 Check interaction equations for combined tension and shear. Steel failure of channel bolts under combined loads: ESR-3520 Section 4.1.3.6.1. Reference page 20 for factored load and design strength values. ESR-3520 Equation (43) Steel failure of anchor channels under combined loads: ESR-3520 Section 4.1.3.6.2. Anchor and connection between anchor and channel. Reference ESR-3520 Section 4.1.3.6.2(a). Reference page 20 for factored load and design strength values. Vsa,y = Vsc,y = 16,250 lb, Nsa = Nsc = 11,240 lb: 16,250 lb > 11,240 lb → α = 1.0 max + max < 1.0 ESR-3520 Equation (44) max + max = 0.406 OK Steel failure of anchor channels under combined loads: ESR-3520 Section 4.1.3.6.2. At the point of load application. Reference ESR-3520 Section 4.1.3.6.2(b). Reference page 20 for factored load and design strength values. Vsl,y = 16,205 lb, Nsl = 11,240 lb: 16,205 lb >11,240 lb → α = 1.0 ESR-3520 Equation (45) ESR-3520 Equation (46) Concrete failure modes of anchor channels: ESR-3520 Section 4.1.3.6.3. Reference page 20 for factored load and design strength values. Na

ua/ Ncb = 53% controls for tension. Vaua/ Vcb,y = 60% controls for shear.

α = 1.5 for anchor channels without anchor reinforcement ESR-3520 Equation (47)

Nbua 2

φNss Vb

ua 2

φVss < 1.0 +

3042 lb 2

18,352 lb 1000 lb 2

10,164 lb = 0.037 OK +

Naua

φNsa Na

ua α

φNsc ;

Vaua,y

φVsa,y Va

ua,y α

φVsc,y ;

COMMENTS When both tension and shear loads act on the anchor channel system, combined interaction checks must be made for each of the following conditions: * steel failure of the channel bolt. * steel failure of the channel. * concrete failure. The interaction check for steel failure of the channel bolt requires the ratios (factored load acting on the bolt/bolt design strength) to be checked using Equation (43) in ESR-3520. The interaction check for steel failure of the channel requires the ratio (factored load acting on the anchor element/anchor element or anchor-channel connection design strength) to be checked using Equation (44) in ESR-3520. The interaction check for steel failure of the channel requires the ratio (factored load acting on the channel lip/channel lip design strength) to be checked using Equation (45) in ESR-3520. The interaction check for steel failure of the channel requires the ratio (factored moment acting on the channel/bending moment design strength) to be checked using Equation (46) in ESR-3520. The interaction check for concrete failure requires the ratio (factored load acting on the anchor element/controlling concrete failure design strength) to be checked using Equation (47) in ESR-3520. If all of the interaction checks are satisfied, the design is assumed to meet the fastening requirements.

2788 lb

8430 lb 2788 lb 1.0 8430 lb

; 916 lb

12,188 lb 916 lb 1.0

12,188 lb ;

Nbua α

φNsl Vb

ua,y α

φVsl,y < 1.0 +

3042 lb 1.0

8430 lb 1000 lb 1.0

12,154 lb = 0.443 OK +

Mu,flex α

φMs,flex Vb

ua,y α

φVsl,y < 1.0

+

4386 in-lb 1.0

16,452 in-lb 1000 lb 1.0

12,154 lb = 0.349 OK +

Naua α

φNcb Va

ua,y α

φVcb,y < 1.0 +

2788 lb 1.5

5327 lb 916 lb 1.5

1537 lb = 0.839 OK +

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