Buckling of Slender Concrete-Filled Steel Tubes with Compliant Interfaces

Schnabl, Simon; Planinc, Igor

doi:10.1590/1679-78253479

Simon Schnabl ^**Corresponding author

University of Ljubljana, Faculty of Chemistry and Chemical Technology, Večna pot 113, 1001 Ljubljana, Slovenia. E-mail address: simon.schnabl@fkkt.uni-lj.si

Igor Planinc

University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, 1000 Ljubljana, Slovenia. E-mail address: igor.planinc@fgg.uni-lj.si

*Corresponding author

Specimen	L	λ	$N_{c r, e}^{*}$	C	P _cr
Specimen	L	λ	$N_{c r, e}^{*}$	C	K = 10^-10	K = 10^-2	K = 10^-1	K = 1	K = 10	K = 10¹⁰
SC154-1	415.8	154	342	10-10	177.649	186.475	240.841	293.583	299.955	300.651
				10-5	190.091	198.085	246.015	293.684	299.957	300.651
SC154-2	415.8	154	292	10-3	295.729	295.764	296.055	297.769	300.043	300.651
SC141-1	380.7	141	350	10-10	211.918	220.790	279.200	348.563	357.656	358.646
				10-5	222.495	230.785	284.381	348.685	357.659	358.646
SC141-2	380.7	141	370	10-3	350.255	350.326	350.909	354.103	357.762	358.646
SC130-1	351.0	130	400	10-10	249.298	258.206	319.942	407.924	420.537	421.908
				10-5	258.371	266.861	324.981	408.067	420.538	421.908
SC130-2	351.0	130	390	10-3	408.187	408.322	409.429	415.044	420.664	421.908

P_cr
K	C
K	10^-10	10^-7	10^-5	10^-4	10^-3	10^-2	10⁵
10^-10	179.865835^•	179.993792	192.105027	255.862874	297.890147	302.479500	302.983390^*
10^-5	179.874803	180.002752	192.113187	255.865453	297.890183	302.479501	302.983390^*
10^-3	180.759877	180.887039	192.918146	256.119575	297.893746	302.479536	302.983390^*
10^-2	188.553682	188.673596	199.977918	258.328044	297.925910	302.479853	302.983390^*
10^-1	242.274702	242.329750	247.428743	273.212174	298.226557	302.483009	302.983390^*
1	295.681485	295.682538	295.785453	296.603501	300.001028	302.512517	302.983390^*
10	302.263327	302.263337	302.264356	302.273485	302.353467	302.687190	302.983390^*
10²	302.911513	302.911513	302.911524	302.911616	302.912526	302.920497	302.983390^*
10³	302.976203	302.976203	302.976204	302.976205	302.976214	302.976305	302.983390^*
10⁵	302.983318	302.983318	302.983318	302.983318	302.983318	302.983318	302.983390^*
10¹⁰	302.983390^*	302.983390^*	302.983390^*	302.983390^*	302.983390^*	302.983390^*	302.983390^*

P _cr
C	10^-10			10^-3
K	C-F	C-C	C-P	C-F	C-C	C-P
10^-10	44.95092961	719.2112490	367.8313917	75.13464138	1094.182170	590.2955496
10^-5	44.95989029	719.2202108	367.8403534	75.13465339	1094.183316	590.2958548
10^-3	45.83596664	720.1067487	368.7262276	75.13583959	1094.296689	590.3260369
10^-2	52.77689604	728.1035991	376.6569381	75.14637765	1095.317938	590.5973960
10^-1	71.11456051	801.7556923	443.5802350	75.23209327	1104.671332	593.0426878
1	75.25042232	1095.460050	588.7376543	75.50198900	1152.866275	604.9510316
10	75.65633017	1199.648599	616.4465577	75.66425898	1201.041703	616.7586267
10²	75.69672750	1210.070051	619.1620639	75.69773741	1210.082508	619.1655195
10³	75.70076519	1211.104568	619.4325425	75.70086471	1211.104691	619.4325774
10⁵	75.70120931	1211.218272	619.4622827	75.70121211	1211.218272	619.4622827
10¹⁰	75.70121379	1211.219421	619.4625831	75.70121379	1211.219421	619.4625831

\begin{array}{l} S_{1}^{i} + R_{X}^{i} (0) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} u^{i} (0) = u_{1}^{i}, \\ S_{2}^{i} + R_{Z}^{i} (0) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} w^{i} (0) = u_{2}^{i}, \\ S_{3}^{i} + M_{Y}^{i} (0) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} φ^{i} (0) = u_{3}^{i} . \end{array}

\begin{array}{l} S_{4}^{i} + R_{X}^{i} (L) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} u^{i} (L) = u_{4}^{i}, \\ S_{5}^{i} + R_{Z}^{i} (L) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} w^{i} (L) = u_{5}^{i}, \\ S_{6}^{i} + M_{Y}^{i} (L) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} φ^{i} (L) = u_{6}^{i} . \end{array}

m_{Y}^{} = \int_{C_{x}}^{} ρ^{i} \times (F (Δ_{U}),0, G (Δ_{W})) d C_{x} = \int_{0}^{2 π} {(0, - r \cos α, - r \sin α)}^{} \times (F (Δ_{U}),0, G (Δ_{W})) r d α,

\begin{array}{l} ε^{i} = - \frac{1}{\sum_{i} E^{i} A^{i}} P, κ^{i} = 0, u^{i} = u^{i} (0) - \frac{x}{\sum_{i} E^{i} A^{i}}, w^{i} = 0, φ^{i} = 0, Δ_{U} = 0, \\ Δ_{W} = 0, R_{X}^{i} = - \frac{E^{i} A^{i}}{\sum_{i} E^{i} A^{i}} P, R_{Z}^{i} = 0, M_{Y}^{i} = 0, p_{X}^{} = 0, p_{Z}^{} = 0, m_{Y}^{} = 0. \end{array}

δ \frac{d M_{Y}^{c}}{d x} - (\frac{E^{c} A^{c}}{\sum_{i} E^{i} A^{i}} P) δ \frac{d w^{c}}{d x} - (1 - \frac{1}{\sum_{i} E^{i} A^{i}} P) δ R_{Z}^{c} - π r^{3} K (δ φ^{c} - δ φ^{s}) = 0,

δ \frac{d M_{Y}^{s}}{d x} - (\frac{E^{s} A^{s}}{\sum_{i} E^{i} A^{i}} P) δ \frac{d w^{s}}{d x} - (1 - \frac{1}{\sum_{i} E^{i} A^{i}} P) δ R_{Z}^{s} + π r^{3} K (δ φ^{c} - δ φ^{s}) = 0,

\begin{array}{l} S_{1}^{i} + δ R_{X}^{i} (0) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} δ u^{i} (0) = u_{1}^{i}, \\ S_{2}^{i} + δ R_{Z}^{i} (0) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} δ w^{i} (0) = u_{2}^{i}, \\ S_{3}^{i} + δ M_{Y}^{i} (0) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} δ φ^{i} (0) = u_{3}^{i} . \end{array}

\begin{array}{l} S_{4}^{i} + δ R_{X}^{i} (L) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} δ u^{i} (L) = u_{4}^{i}, \\ S_{5}^{i} + δ R_{Z}^{i} (L) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} δ w^{i} (L) = u_{5}^{i}, \\ S_{6}^{i} + δ M_{Y}^{i} (L) = 0 \begin{matrix}  \end{matrix} or \begin{matrix}  \end{matrix} δ φ^{i} (L) = u_{6}^{i} . \end{array}

[1] *Corresponding author

Brasil

Brasil

Buckling of Slender Concrete-Filled Steel Tubes with Compliant Interfaces

Abstract