Simplified Design Equation of Minimum Interior Joint Depth for Special Moment Frames with High-Strength Reinforcement

Lee, Hung-Jen; Chen, Hsi-Ching; Tsai, Tsung-Chieh

doi:10.1186/s40069-018-0303-2

International Journal of Concrete Structures and Materials

Table 1 Comparison of existing design equations for the minimum joint depth.

From: Simplified Design Equation of Minimum Interior Joint Depth for Special Moment Frames with High-Strength Reinforcement

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)	\(1 + \frac{0.6}{{\varvec{\alpha}_{\varvec{o}} }} + \frac{0.8}{{\varvec{\alpha}_{\varvec{o}} }}\left( {1 - \frac{{\varvec{A}_{\varvec{s}} }}{{\varvec{A}_{{\varvec{s},\varvec{top}}} }}} \right)\)	\(\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 1.25\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} }\) \((\varvec{\alpha}_{\varvec{f}}\varvec{\alpha}_{\varvec{t}} 15\sqrt {\varvec{f}_{\varvec{c}}^{\varvec{'}} } )\)	\(0.95 + 0.5\frac{\varvec{P}}{{\varvec{A}_{\varvec{g}} \varvec{f}_{\varvec{c}}^{\varvec{'}} }} \le 1.10\)

With limitation of \(\varvec{A}_{{\varvec{s},\varvec{top}}} \ge \varvec{A}_{{\varvec{s},\varvec{bot}}}\), where \(\varvec{A}_{{\varvec{s},\varvec{bot}}}\) = area of bottom beam bars; \(\varvec{A}_{{\varvec{s},\varvec{top}}}\) = area of top beam bars; \(\varvec{A}_{\varvec{s}}\) = area of the bar group \(\varvec{A}_{{\varvec{s},\varvec{top}}} \varvec{ }\) or \(\varvec{A}_{{\varvec{s},\varvec{bot}}}\) containing the bar for which development length is being calculated; \(\varvec{\alpha}_{\varvec{o}}\) = bar overstrength factor; \(\varvec{\alpha}_{\varvec{f}}\) = 1.0 for a beam bar passing through a joint subjected to unidirectional loading, and \(\varvec{\alpha}_{\varvec{f}}\) = 0.85 for bi-directional loading; Bar location factor \(\varvec{\alpha}_{\varvec{t}}\) = 0.85 for a top beam bar where more than 300 mm of fresh concrete is cast below the bar, \(\varvec{\alpha}_{\varvec{t}} = 1.0\) for all other cases. \(\varvec{P}\) = axial compression force on column; \(\varvec{A}_{\varvec{g}}\) = gross area of column; \(\varvec{f}_{\varvec{c}}^{\varvec{'}}\) = concrete compressive strength.

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