1 Introduction
2 Existing Design Codes and Recommendations
2.1 Generic Formula
Design criteria | Factor for bar stresses at the joint faces
\(\varvec{\alpha}_{\varvec{s}} = 1 +\varvec{\kappa}\)
| Basic bond strength \(\varvec{u}_{\varvec{b}}\), MPa (psi) | Factor for column axial stress on bond
\(\varvec{\alpha}_{\varvec{p}}\)
|
---|---|---|---|
AIJ (2010) |
\(1 + \frac{{\varvec{A}_{{\varvec{s},\varvec{bot}}} }}{{\varvec{A}_{\varvec{s}} }}\)
|
\(0.7\varvec{f}_{\varvec{c}}^{{\varvec{'}\frac{2}{3}}}\)
\(\left( {3.7\varvec{f}_{\varvec{c}}^{{\varvec{'}\frac{2}{3}}} } \right)\)
|
\(1 + \frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }}\)
|
Eurocode 8 (CEN 2004) |
\(1 + 0.75\frac{{\varvec{A}_{{\varvec{s},\varvec{bot}}} }}{{\varvec{A}_{\varvec{s}} }}\)
|
\(0.56\varvec{f}_{\varvec{c}}^{{\varvec{'}}^{{\frac{2}{3}}}}\)
\(\left( {2.9\varvec{f}_{\varvec{c}}^{{\varvec{'}}^{{\frac{2}{3}}}} } \right)\)
|
\(1 + 0.8\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }}\)
|
NZS 3101 (2006) |
\(1 + 1.55 - \frac{{\varvec{A}_{\varvec{s}} }}{{\varvec{A}_{{\varvec{s},\varvec{top}}} }} \le 1.8\)
|
\(\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 1.5\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} }\)
\((\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 18\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} } )\)
|
\(0.95 + 0.5\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }} \le 1.25\)
|
Brooke and Ingham (2013) |
\(1 + \frac{0.7}{{\varvec{\alpha}_{\varvec{o}} }}\frac{{\varvec{A}_{{\varvec{s},\varvec{top}}} }}{{\varvec{A}_{\varvec{s}} }} \le 1 + \frac{1}{{\varvec{\alpha}_{\varvec{o}} }}\)
|
\(\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 1.25\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} }\)
\((\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 15\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} } )\)
|
\(0.9 + 2.0\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }} \le 1.20\)
|
Li and Leong (2015) |
\(1 + \frac{0.6}{{\varvec{\alpha}_{\varvec{o}} }} + \frac{0.8}{{\varvec{\alpha}_{\varvec{o}} }}\left( {1 - \frac{{\varvec{A}_{\varvec{s}} }}{{\varvec{A}_{{\varvec{s},\varvec{top}}} }}} \right)\)
|
\(\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 1.25\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} }\)
\((\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 15\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} } )\)
|
\(0.95 + 0.5\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }} \le 1.10\)
|
2.2 Comparison of Existing Equations for Minimum Column Depth
3 Simplification of Design Equation for the Minimum Joint Depth
4 Database Investigation
4.1 Assessment of Anchorage Performance of Beam Bars in the Joint
First author | Specimen | Failure mode | Test parameters | Performance evaluationc | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\varvec{f}_{\varvec{c}}^{\varvec{'}}\)
MPa |
\(\varvec{f}_{{\varvec{ya}}}\)
MPa |
\(\varvec{h}_{\varvec{c}}\)
mm |
\(\frac{{\varvec{h}_{\varvec{c}} }}{{\varvec{d}_{\varvec{b}} }}\)
|
\(\frac{{A_{s,bot} }}{{A_{s,top} }}\)
|
\(\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }}\)
|
\(\frac{{\varvec{V}_{{\varvec{jh} \cdot \varvec{m}}} }}{{\varvec{V}_{\varvec{n}} }}\)
a
|
\(\varvec{A}_{{\varvec{sh},\varvec{ratio}}}\)
b
|
\(\frac{{\varvec{Q}_{\varvec{r}} }}{{\varvec{Q}_{\varvec{m}} }}\)
|
\(\frac{{\varvec{K}_{\varvec{o}} }}{{\varvec{K}_{\varvec{i}} }}\)
|
\(\frac{{\varvec{E}_{\varvec{D}} }}{{\varvec{E}_{{\varvec{PP}}} }}\)
| Rating | |||
Teraoka (1994) | HNO. 9 | BJ | 93 | 599 | 400 | 18.0 | 1.00 | 0.20 | 0.98 | 1.03 | 0.87 | 0.11 | 0.35 | o |
Nakachi (1995) | NO. 1 | BJa | 45 | 493 | 400 | 20.9 | 1.00 | 0.20 | 0.70 | 2.33 | 0.69 | 0.02 | 0.21 | x |
NO. 2 | BJ | 48 | 493 | 400 | 20.9 | 1.00 | 0.20 | 1.02 | 2.18 | 0.69 | 0.02 | 0.23 | x | |
NO. 3 | BJa | 31 | 493 | 400 | 20.9 | 1.00 | 0.20 | 0.80 | 3.36 | 0.63 | 0.00 | 0.17 | x | |
NO. 4 | BJ | 32 | 493 | 400 | 20.9 | 1.00 | 0.20 | 1.13 | 3.21 | 0.62 | 0.03 | 0.25 | x | |
NO. 5 | BJa | 60 | 493 | 400 | 20.9 | 1.00 | 0.20 | 0.94 | 1.72 | 0.54 | 0.01 | 0.29 | x | |
NO. 6 | BJ | 65 | 493 | 400 | 20.9 | 1.00 | 0.19 | 1.18 | 1.61 | 0.67 | 0.05 | 0.30 | x | |
Hosoya (2003) | NO. 1 | BJa | 47 | 535 | 450 | 23.6 | 0.83 | 0.19 | 0.75 | 0.61 | 0.62 | 0.02 | 0.23 | x |
Maruta (2004) | CC-3 | BJ | 185 | 543 | 400 | 18.0 | 1.00 | 0.07 | 0.98 | 0.29 | 0.62 | 0.14 | 0.35 | x |
Hori (2004) | B1 | BJ | 89 | 542 | 400 | 20.9 | 0.75 | 0.27 | 0.88 | 0.33 | 0.79 | 0.13 | 0.35 | o |
Brooke (2006) | 1B | B | 31 | 552 | 800 | 32.0 | 1.00 | 0 | 0.77 | 2.01 | 0.92 | 0.18 | 0.40 | o |
2B | B | 41 | 552 | 800 | 32.0 | 1.00 | 0 | 0.70 | 1.29 | 0.67 | 0.17 | 0.51 | x | |
3B | BJa | 45 | 537 | 675 | 27.0 | 1.00 | 0 | 0.75 | 1.13 | 0.80 | 0.18 | 0.42 | o | |
4B | BJa | 43 | 537 | 675 | 27.0 | 1.00 | 0 | 0.74 | 1.19 | 0.81 | 0.12 | 0.36 | o | |
Umemura (2006) | PJN | BJ | 76 | 554 | 500 | 22.5 | 1.00 | 0.15 | 0.94 | 0.87 | 0.83 | 0.11 | 0.35 | o |
Kimoto (2006) | I6C | BJa | 71 | 518 | 400 | 20.9 | 1.00 | 0.20 | 0.87 | 0.39 | 0.76 | 0.09 | 0.28 | o |
I6P | BJa | 71 | 518 | 400 | 20.9 | 1.00 | 0.20 | 0.87 | 0.39 | 0.80 | 0.11 | 0.29 | o | |
I1P | BJ | 105 | 518 | 400 | 20.9 | 1.00 | 0.20 | 0.97 | 0.33 | 0.81 | 0.15 | 0.35 | o | |
Yagenji (2009) | JU-S | BJa | 55 | 541 | 400 | 20.9 | 0.67 | 0.10 | 0.91 | 0.55 | 0.63 | 0.03 | 0.26 | x |
Li (2015) | NS1 | B | 60 | 510 | 450 | 37.5 | 1.00 | 0 | 1.06 | 0.83 | 0.90 | 0.33 | 0.43 | o |
NS2 | B | 61 | 508 | 450 | 28.1 | 0.50 | 0 | 0.65 | 0.58 | 0.92 | 0.13 | 0.24 | o | |
NS3 | B | 61 | 508 | 450 | 28.1 | 1.00 | 0 | 0.76 | 0.82 | 0.95 | 0.29 | 0.42 | o | |
NS4 | B | 60 | 513 | 450 | 22.5 | 0.64 | 0 | 0.53 | 0.64 | 0.87 | 0.09 | 0.28 | o | |
AS1 | B | 61 | 510 | 450 | 37.5 | 1.00 | 0.30 | 1.02 | 0.82 | 0.87 | 0.13 | 0.44 | o | |
AS2 | B | 61 | 508 | 450 | 28.1 | 0.50 | 0.30 | 0.55 | 0.58 | 0.64 | 0.00 | 0.09 | x | |
AS3 | B | 61 | 508 | 450 | 28.1 | 1.00 | 0.30 | 0.73 | 0.82 | 0.78 | 0.13 | 0.42 | o | |
AS4 | B | 62 | 513 | 450 | 22.5 | 0.64 | 0.30 | 0.53 | 0.62 | 0.69 | 0.04 | 0.37 | x | |
Alaee (2017) | IN80 | B | 80 | 564 | 450 | 28.1 | 0.50 | 0 | 0.45 | 0.99 | 0.79 | 0.09 | 0.29 | o |
IN100 | B | 100 | 564 | 450 | 28.1 | 0.50 | 0 | 0.40 | 1.01 | 0.83 | 0.21 | 0.36 | o |
First author | Specimen | Failure mode | Test parameters | Performance evaluationc | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\varvec{f}_{\varvec{c}}^{\varvec{'}}\)
MPa |
\(\varvec{f}_{{\varvec{ya}}}\)
MPa |
\(\varvec{h}_{\varvec{c}}\)
mm |
\(\frac{{\varvec{h}_{\varvec{c}} }}{{\varvec{d}_{\varvec{b}} }}\)
|
\(\frac{{A_{s,bot} }}{{A_{s,top} }}\)
|
\(\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }}\)
|
\(\frac{{\varvec{V}_{{\varvec{jh} \cdot \varvec{m}}} }}{{\varvec{V}_{\varvec{n}} }}\)
a
|
\(\varvec{A}_{{\varvec{sh},\varvec{ratio}}}\)
b
|
\(\frac{{\varvec{Q}_{\varvec{r}} }}{{\varvec{Q}_{\varvec{m}} }}\)
|
\(\frac{{\varvec{K}_{\varvec{o}} }}{{\varvec{K}_{\varvec{i}} }}\)
|
\(\frac{{\varvec{E}_{\varvec{D}} }}{{\varvec{E}_{{\varvec{PP}}} }}\)
| Rating | |||
Oka (1992) | J-1 | BJ | 81 | 638 | 300 | 23.6 | 0.78 | 0.11 | 1.15 | 0.26 | 0.70 | 0.12 | 0.28 | x |
Teraoka (2004) | HJ-5 | BJ | 54 | 645 | 400 | 20.9 | 1.00 | 0.18 | 0.92 | 0.66 | 0.76 | 0.07 | 0.25 | o |
HJ-8 | BJ | 93 | 599 | 400 | 18.0 | 1.00 | 0.20 | 0.97 | 0.27 | 0.91 | 0.10 | 0.33 | o | |
HJ-12 | BJ | 89 | 604 | 400 | 18.0 | 1.00 | 0.17 | 1.55 | 0.58 | 0.71 | 0.10 | 0.35 | x | |
Abe (2006) | MJIS | BJ | 86 | 626 | 475 | 21.4 | 1.00 | 0.15 | 0.98 | 0.55 | 0.80 | 0.11 | 0.36 | o |
Hori (2006) | B15-4 | B | 152 | 616 | 380 | 19.9 | 0.67 | 0.33 | 0.74 | 0.70 | 0.96 | 0.22 | 0.40 | o |
B15-5 | B | 146 | 616 | 380 | 19.9 | 0.67 | 03 | 0.75 | 0.73 | 0.93 | 0.22 | 0.36 | o | |
Takamori (2007) | HNO. 18 | BJ | 147 | 646 | 700 | 24.5 | 1.00 | 0.10 | 0.96 | 0.62 | 0.96 | 0.14 | 0.31 | o |
HNO. 19 | BJ | 165 | 657 | 700 | 24.5 | 1.00 | 0.10 | 1.04 | 0.57 | 0.93 | 0.19 | 0.34 | o | |
HNO. 20 | BJ | 140 | 640 | 700 | 24.5 | 1.00 | 0.10 | 1.10 | 0.68 | 0.93 | 0.18 | 0.35 | o | |
Hwang (2014) | C2-600 | BJa | 32 | 710 | 550 | 24.8 | 0.60 | 0 | 0.89 | 1.70 | 0.71 | 0.03 | 0.15 | x |
C3-600 | BJa | 32 | 710 | 450 | 20.3 | 0.60 | 0 | 1.09 | 1.46 | 0.73 | 0.11 | 0.19 | x | |
C4-600 | BJa | 30 | 635 | 550 | 21.7 | 0.50 | 0 | 0.79 | 1.81 | 0.73 | 0.06 | 0.17 | x |
First author | Specimen | Failure mode | Test parameters | Performance evaluationc | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\varvec{f}_{\varvec{c}}^{\varvec{'}}\)
MPa |
\(\varvec{f}_{{\varvec{ya}}}\)
MPa |
\(\varvec{h}_{\varvec{c}}\)
mm |
\(\frac{{\varvec{h}_{\varvec{c}} }}{{\varvec{d}_{\varvec{b}} }}\)
|
\(\frac{{A_{s,bot} }}{{A_{s,top} }}\)
|
\(\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }}\)
|
\(\frac{{\varvec{V}_{{\varvec{jh} \cdot \varvec{m}}} }}{{\varvec{V}_{\varvec{n}} }}\)
a
|
\(\varvec{A}_{{\varvec{sh},\varvec{ratio}}}\)
b
|
\(\frac{{\varvec{Q}_{\varvec{r}} }}{{\varvec{Q}_{\varvec{m}} }}\)
|
\(\frac{{\varvec{K}_{\varvec{o}} }}{{\varvec{K}_{\varvec{i}} }}\)
|
\(\frac{{\varvec{E}_{\varvec{D}} }}{{\varvec{E}_{{\varvec{PP}}} }}\)
| Rating | |||
Noguchi (1992) | OKJ-1 | BJ | 70 | 718 | 300 | 23.6 | 0.78 | 0.12 | 1.21 | 0.47 | 0.59 | 0.12 | 0.31 | x |
OKJ-4 | BJ | 70 | 718 | 300 | 23.6 | 0.78 | 0.12 | 1.22 | 0.95 | 0.73 | 0.13 | 0.33 | x | |
Watanabe (2005) | NO. 2 | B | 107 | 724 | 400 | 20.9 | 1.00 | 0.15 | 1.15 | 1.01 | 0.93 | 0.20 | 0.33 | o |
NO. 3 | BJ | 107 | 724 | 400 | 20.9 | 1.00 | 0.15 | 1.48 | 1.01 | 0.85 | 0.17 | 0.39 | o | |
NO. 4 | BJ | 157 | 724 | 400 | 20.9 | 1.00 | 0.15 | 1.28 | 0.69 | 0.91 | 0.20 | 0.38 | o | |
NO. 5 | B | 107 | 748 | 400 | 18.0 | 1.00 | 0.15 | 1.18 | 1.01 | 0.86 | 0.14 | 0.37 | o | |
Hori (2006) | B15-1 | BJ | 189 | 690 | 380 | 19.9 | 0.67 | 0.23 | 0.66 | 0.21 | 0.56 | 0.08 | 0.55 | x |
B15-3 | BJ | 186 | 690 | 340 | 17.8 | 1.00 | 0.23 | 0.74 | 0.19 | 0.65 | 0.09 | 0.48 | x | |
Kuo (2011) | X100 | BJ | 120 | 744 | 600 | 23.6 | 0.50 | 0.03 | 0.86 | 0.97 | 0.94 | 0.18 | 0.20 | o |
Lee (2016) | CG1 | BJ | 81 | 738 | 600 | 23.6 | 0.67 | 0.05 | 0.86 | 0.65 | 0.82 | 0.16 | 0.21 | o |
CG3 | BJ | 85 | 738 | 600 | 23.6 | 0.67 | 0.05 | 0.86 | 0.62 | 0.90 | 0.18 | 0.20 | o | |
CG4 | BJ | 83 | 738 | 600 | 23.6 | 0.67 | 0.05 | 0.91 | 0.64 | 0.91 | 0.21 | 0.20 | o | |
Lee (2014) | A24 | BJ | 116 | 725 | 600 | 23.6 | 0.75 | 0.04 | 0.94 | 0.86 | 0.78 | 0.13 | 0.25 | o |
B24 | BJ | 104 | 725 | 600 | 23.6 | 1.00 | 0.04 | 1.11 | 0.95 | 0.81 | 0.13 | 0.25 | o | |
Alaee (2017) | IH80 | B | 80 | 712 | 450 | 28.1 | 0.50 | 0 | 0.62 | 0.97 | 0.96 | 0.20 | 0.25 | o |
IH80A | B | 80 | 712 | 450 | 28.1 | 0.50 | 0.30 | 0.62 | 0.97 | 0.86 | 0.36 | 0.46 | o | |
IH100 | B | 100 | 712 | 450 | 28.1 | 0.50 | 0 | 0.54 | 1.01 | 0.95 | 0.22 | 0.28 | o | |
IH60 | BJa | 60 | 707 | 450 | 23.7 | 1.00 | 0 | 0.60 | 1.29 | 0.80 | 0.04 | 0.22 | x | |
IH60A | BJa | 60 | 707 | 450 | 23.7 | 1.00 | 0.30 | 0.56 | 1.29 | 0.77 | 0.04 | 0.18 | x |
4.2 Joints with Grade 490 or 500 MPa Beam Bars
4.3 Joints with Grade 590 or 600 MPa Beam Bars
4.4 Joints with Grade 690 MPa Beam Bars
4.5 Overall Observation
5 Summary and Recommendations
-
Relatively pinched hysteresis behavior can be observed in the beam-column joints with bond deterioration along the beam bars passing through the joint. Such damage in the joint core is unlikely to be easily repairable and therefore should be avoided in a design basis earthquake event.
-
The ACI 318 (2014) requirement of a minimum joint depth of 20 \(d_{b}\) is based on test data with Grade 420 reinforcement and may be too short for bar \(f_{y}\) exceeding 420 MPa. ACI 352R-02 (ACI-ASCE Committee 352 2002) recommends a simple multiplier of \(f_{y} /420\) on the 20 \(d_{b}\) criterion without accounting for the various concrete strength, which is very conservative for high-strength concrete and unconservative for low-strength concrete, according to the presented database investigation.
-
Based on the evaluation of the assembled test data, this study recommends that the joint depth, or the column dimension in parallel to the beam bars extending through the joint should not be less than the larger of 20 \(d_{b}\) and \(\alpha_{o} f_{y} d_{b} /\left( {4\sqrt {f_{c}^{'} } } \right)\). Cruciform beam-column joints with column dimension meeting this criterion can demonstrate acceptable hysteresis performance up to a limiting drift ratio of 3.5% at least.
-
The proposed design equation is empirical and should be used with limitations of \(f_{y}\) not exceeding 690 MPa and \(f_{c}^{'}\) not exceeding 100 MPa.
-
The simplified design equation is proposed for typical interior beam-column joints with column axial load exceeding 0.15 \(A_{g} f_{c}^{'}\). If the seismic forces lead to significant variation of the column axial load, the detailed design equations including the effects of column axial load and other parameters should be used.