CHAPTER 4 Behaviour and strength of shear connectors in steel-concrete-steel
4.4 Strength of J-hook connectors subjected to combined shear and tension loads
4.4.7 Strength of J-hook connectors subjected to combined tension and shear loads
In PCI 6th Edition and ACI 318, the strength of connectors subjected to combination of axial tension and shear loads is shown in Fig. 4.46. The formulae describing the strength of the connectors under combined shear and tension is specified as follows
5/3 5/3
1
n n
N V
N V
(4.18a)
1.2
n n
N V
N V
(4.18b)
Where, Vn=shear capacity of J-hook connectors embedded in ULCC and governed by Eqns. 4.6a&b as specified in section 4.2; NJ =tension capacity of J-hook connectors embedded in ULCC as specified in section 4.3 by design approaches A~E including Eqns.
4.9~4.13; =reduction factor specified in PCI.
The strength of the J-hook connectors subjected to tension and shear loads by the FE models are compared with the predictions by Eqns. 4.17 and 18 in Figs. 4. 45 and 4.46.
From the comparisons, it can be easily observed that the Eqns. 4.17 and 18 all give reliable and satisfactory predictions. Therefore, the Eqns. 4.18 specified in PCI and Eqn.4.17 will be used to check the strength of the J-hook connectors under tension-shear interactions.
In summary, a step by step procedure on applying these formulas is as follows:
1) Determine the longitudinal shear strength of J-hook connectors Vu by Eqn. 4.6;
2) Determine the tensile strength of J-hook connectors Nn as specified in section 4.3 using design Eqns. 4.9~4.13; 3) Substituting the calculated N and V into Eqn. 4.18 or 4.17 to check the capacity of the connector.
‐ 167 - Table 4.10a Details of push-out test specimens
Specimen t d
mm c
h mm
hs
mm
mm B u
MPa
fck
MPa Ec
GPa w kg/m3 c
h d Sohel
(2008)
NWC-10 6 9.9 40 49.9 300 405 48.3 32.5 2400 4.04 LWC-10 6 9.9 40 49.9 300 405 28.5 12.7 1450 4.04 LWFC-10 6 9.9 40 49.9 300 405 28.1 12.6 1460 4.04
NWC-16 6 15.5 40 55.5 300 450 65 30.0 2400 2.58
LWC1-16 6 15.5 40 55.5 300 450 26.4 11.7 1440 2.58
LWC2-16 6 15.5 40 55.5 300 450 30.2 17 1700 2.58
LWC2-12 6 11.5 40 51.5 300 450 30.2 17 1700 3.48
Dai (2008)
HPF-10 6 10.0 40 50.0 200 610 28 12.3 1460 4.00
HPP-10 6 10.0 40 50.0 200 610 24 11.7 1440 4.00
HPF-8 6 7.9 40 47.9 200 610 28 12.3 1460 5.07
HPP-8 6 7.9 40 47.9 200 610 24 11.7 1440 5.07
By author
ULCC1-12 4 11.8 50 61.8 250 464 60 16.5 1490 4.23 ULCC2-12 6 11.8 50 61.8 250 464 60 16.5 1440 4.23 ULCC3-12 8 11.8 50 61.8 250 464 60 16.5 1440 4.23 ULCC4-12 12 11.8 50 61.8 250 464 60 16.5 1440 4.23 ULCC5-12 6 11.8 75 86.8 250 464 60 16.5 1440 6.35 ULCC6-12 6 11.8 100 111.8 250 464 60 16.5 1440 8.47 ULCC7-12 6 15.5 75 90.5 250 405 57 16.5 1440 4.84 ULCC8-12 6 19.5 75 94.5 250 403 57 16.5 1440 3.85 ULCC9-12 6 15.5 75 90.5 200 405 57 16.5 1440 4.84 ULCC10-12 6 19.5 75 94.5 200 403 57.8 16.5 1440 3.85
LWC1-12 6 11.8 50 61.8 250 464 25 11.5 1345 4.23
NWC1 6 11.8 50 61.8 250 464 45 37 2355 4.23
NWC2 6 12.0 50 62.0 250 464 70 39 2365 4.17
NWC3 6 15.5 75 90.5 250 405 45 37 2355 4.84
NWC4 6 15.5 75 90.5 250 405 70 39 2365 4.84
‐ 168 - Table 4.10b Push-out test results and predictions
Ptest
(kN)
Failure
Mode J
Pby
author (1)/(3) PJby
EC4 (1)/(5) (1) (2) (3) (4) (5) (6) Sohel (2008)
NWC-10 31.0 SS 24.9 1.24 24.9 1.24 LWC-10 20.8 CC 16.7 1.25 17.1 1.22 LWFC-10 22.3 CC 16.5 1.35 16.9 1.32 NWC-16 68.5 SS 67.9 1.01 67.9 1.01 LWC1-16 43.9 CC 36.0 1.22 38.7 1.13 LWC2-16 46.5 CC 44.4 1.05 49.9 0.93 LWC2-12 33.1 CC 25.6 1.29 27.5 1.20 Dai (2008)
HPF-10 24.0 CC 16.7 1.44 17.0 1.41 HPP-10 21.0 CC 15.6 1.34 15.4 1.37
HPF-8 15.0 CC 10.8 1.40 10.6 1.42
HPP-8 15.0 CC 10.1 1.49 9.6 1.57
By author
ULCC1-12 46.8 CC 32.9 1.42 40.2 1.16
ULCC2-12 42.1 CC 32.9 1.28 40.2 1.05
ULCC3-12 44.2 CC 32.9 1.34 40.2 1.10
ULCC4-12 48.6 CC 32.9 1.48 40.2 1.21
ULCC5-12 51.2 SF 35.0 1.46 40.2 1.27
ULCC6-12 51.6 SF 36.6 1.41 40.2 1.28
ULCC7-12 55.1 SW 57.1 0.97 61.1 0.90
ULCC8-12 86.6 SW 87.2 0.99 96.2 0.90
ULCC9-12 60.8 SW 57.1 1.06 61.1 0.99
ULCC10-12 81.3 SW 87.5 0.93 96.2 0.84
LWC1-12 24.2 CC 22.0 1.10 21.7 1.12 NWC1 47.5 SS 40.7 1.17 40.6 1.17 NWC2 57.0 SS 42.0 1.36 42.0 1.36 NWC3 64.2 SS 61.1 1.05 61.1 1.05 NWC4 70.5 SS 61.1 1.15 61.1 1.15
Mean 1.24 1.21
COV 0.14 0.16
* CC=concrete crack failure; SF=shear failure cross the shank; SW=shear failure cross the welding.
‐ 169 - Table 4.11 Comparisons between FE predictions and test results
Specimen PTest (kN)
PFE
(kN) PFE/PTest
ULCC1-12 93.56 91.48 0.98
ULCC2-12 84.18 91.40 1.09
ULCC3-12 88.43 93.37 1.06
ULCC4-12 97.19 96.4 0.99
ULCC5-12 102.42 107.64 1.05
ULCC6-12 103.30 101.13 0.98
Mean/Stdev - - 1.02/0.05
Table 4.12 Detailed information and FE results of FE models Specimen c
h fck ts N V V
mm MPa mm kN Test
(kN)
FE (kN)
*Notation
NV1 100 60 4 0.0 46.78 45.74
* N=Tension forces;
* V=Shear forces
*The detailed information on dimensions of the specimens NV1~NV6 are corresponded with
ULCC1~ULCC6.
7.5 - 40.60
15.0 - 38.02
25.0 - 29.50
51.0 - 0.00
NV2 100 60 6 0.0 42.09 45.60
7.5 - 38.34
15.0 - 35.92
25.0 - 28.68
51.0 - 0.00
NV3 100 60 8 0.0 44.22 46.69
7.5 - 37.62
15.0 - 34.99
25.0 - 27.70
51.0 - 0.00
NV4 100 60 12 0.0 48.59 48.20
7.5 - 38.60
15.0 - 35.75
25.0 - 28.40
51.0 - 0.00
NV5 150 60 8 0.0 51.21 53.82
7.5 - 41.00
15.0 - 37.91
25.0 - 29.65
51.0 - 0.00
NV6 200 60 8 0.0 51.65 50.57
7.5 - 41.20
15.0 - 38.29
25.0 - 30.22
51.0 - 0.00
‐ 170 - Fig. 4.31 Comparisons between the push-out test results and predictions
Fig. 4.32 load-slip curves of push-out test Fig. 4.33 Load-elongation curve of pullout test
Fig. 4.34 FE Stress-strain curve for ULCC Fig. 4.35 FE Stress-strain curve of steel 0
20 40 60 80 100
0 20 40 60 80 100
Test P (kN)
Prediction PJ(kN) Prediction by EC4
Prediction by Author
0 20 40 60 80 100 120
0 2 4 6 8 10
Applied Load (kN)
Relative Slip (mm) ULCC2-12 ULCC3-12 ULCC4-12 ULCC6-12
0 5 10 15 20 25 30 35
0 2 4 6 8 10 12 14 16
Applied Load (kN)
Elongation (mm) TUA8 TUA10 TUA11 TUA12
-10 0 10 20 30 40 50 60 70
-0.002 0 0.002 0.004 0.006 0.008
Stress (MPa)
Strain
‐ 171 - (a) Effect of μ on load-slip behaviors (b) Effect of μ on load-slip behaviors (c) Effect of μ on load capacity
Fig. 4.36 Influence of friction coefficient μ
Stud Stud
P
Load Cell Surface Plate J-hook Connector Core concrete
Middle Link
(a) Illustration of simplification of push-out test specimen in FE simulation (b) ẳ symmetric FE model for push-out test Fig. 4.37 Simplified mode for push-out test specimen with J-hook connectors
0 20 40 60 80 100
0 2 4 6 8
Applied Load (kN)
Slip (mm)
ULCC1-12 Test FE u=0.5 FE u=0.4 FE u=0.3 FE u=0.2 FE u=0.1 FE u=0
0 20 40 60 80 100 120
0 1 2 3 4 5 6 7
Applied Load (kN)
Slip (mm)
ULCC5-12 Test FE u=0.5 FE u=0.4 FE u=0.3 FE u=0.2 FE u=0.1 FE u=0
90.2 102
0 20 40 60 80 100 120
0 0.1 0.2 0.3 0.4 0.5 0.6
Load Capacity (kN)
Friction Coefficient à ULCC1-12 ULCC5-12 ULCC1-12 Test ULCC5-12 Test
Symmetric surface Symmetric surface
P
‐ 172 - Fig. 4.38a Coarse mesh size Fig. 4.38b Medium mesh size Fig. 4.38c Fine mesh size
Fig. 4.38 Different mesh size used in the FE model
(a) Effect of mesh size of ULCC1-12 (b) Effect of mesh size on ULCC6-12 Fig. 4.39 Effect of mesh size on the FE prediction
0 20 40 60 80 100 120
0 1 2 3 4 5 6 7
Applied Load (kN)
Slip (mm)
ULCC1-12 Test FE-Coarse Mesh FE-Medium Mesh FE-Fine Mesh
0 25 50 75 100 125
0 2 4 6 8 10
Applied Load (kN)
Slip (mm)
ULCC6-12 Test FE Coarse Mesh FE Medium Mesh FE Fine Mesh
‐ 173 -
Fig. 4.40a Fig. 4.40b
Fig. 4.40c Fig. 4.40d
Fig. 4.40e Fig. 4.40f
Fig. 4.40 a~f FE results verified against push-out test results 0
20 40 60 80 100
0 2 4 6 8
Applied Load (kN)
Slip (mm)
ULCC1-12 Test ULCC1-12 FE
0 20 40 60 80 100
0 2 4 6
Applied Load (kN)
Slip (mm)
ULCC2-12 Test ULCC2-12 FE
0 20 40 60 80 100
0 1 2 3 4 5
Applied Load (kN)
Slip (mm)
ULCC3-12 Test ULCC3-12 FE
0 20 40 60 80 100
0 1 2 3 4 5
Applied Load (kN)
Slip (mm)
ULCC4-12 Test ULCC4-12 FE
0 20 40 60 80 100 120
0 2 4 6 8
Applied Load (kN)
Slip (mm)
ULCC5-12 Test ULCC5-12 FE
0 20 40 60 80 100 120
0 2 4 6 8 10
Applied Load (kN)
Slip (mm)
ULCC6-12 Test ULCC6-12 FE
‐ 174 - (a) ULCC5-12 Test and FE failure (b) ULCC6-12 Test and FE failure
Fig. 4.41 Comparison of failure modes between test and FE simulation
Fig. 4.42 FE load-elongations curve verified against the test ones Fig. 4.43 FE model for shear connector under shear and tension 0
5 10 15 20 25 30 35
0 5 10 15 20
Applied Load (kN)
Elongation (mm) TUA8 TUA10 TUA11 TUA12 FE model Shear fracture
Shear fracture
Shear fracture
Shear fracture
‐ 175 - Fig. 4.44 3D and 2D stress illustration in shank of J-hook
Fig. 4.45 Tension-shear interaction strength of connectors
Fig. 4.46 Ratio of tension-shear interaction 0
10 20 30 40 50 60
0 5 10 15 20 25 30
N/Nu
V/Vu Eq.4.17 NV1
NV2 NV3
NV4 NV6
NV5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.0 0.2 0.4 0.6 0.8 1.0 1.2
N/Nu V/Vu
Eqn. 4.17 NV1 NV2 NV3 NV4 NV5 NV6 1.2
u u
n n
N V
N V
5/3 5/3
1.0
u u
n n
N V
N V
Tensile strength of J-hook connectors embedded in ULCC