DESIGN OF SLENDER COLUMNS

Transcription

1 Slovak Chamber of Civil Engineers DESIGN OF SLENDER COLUMNS Prof. Dipl. - Ing. Dr. Vladimír BENKO, PhD. Slovak University of Technology in Bratislava ECEC European Council of Engineer s Chambers CPD-Lectures at 16th of September, 2015 Belgrade/SRB Bratislava /SVK 1

2 Failure of the Concrete Slender Columns by Stability loss Experimental and numerical analysis 2

3 Why slender concrete columns? 3

4 Influence of slenderness on deformation and resistance of columns a) short column N Ed e 0 N Ed b) e 0 e 2 N Ed N Rd(a) M 0Ed = M Rd c) slender column N Rd(b) M 2 e 0 e 2 NEd N Rd(c) e 0 N cr cross-section failure e 2 e 2 e 2 stability loss critical cross section M Ed 4

5 EN betónových konštrukcií 5 Structural analysis 5.1 General 5.2 Geometric imperfections 5.3 Idealization of structure 5.4 Linear elastic analysis 5.5 Linear analysis with limited redistribution 5.6 Plastic analysis 5.7 Non-linear analysis 5.8 Analysis of second order effects with axial load 5.9 Lateral instability of slender beams 5.10 Prestressed members and structures 5

6 EN betónových konštrukcií 5.7 Non-linear analysis 5.8 Analysis of second order effects with axial load Definitions General Simplified criteria for second order effects Slenderness Criterion for isolated members Slenderness and effective length of isolated members Global second order effects in buildings Creep Methods of analysis General method Method based on nominal stiffness Method based on nominal curvature... 6

7 5.7 Non-linear analysis (4)P The use of material characteristics which represent the stiffness in a realistic way but take account of the uncertainties of failure shall be used when using non-linear analysis... (5) For slender structures, in which second order effects cannot be ignored, the design method given in may be used. 7

8 5.8 Analysis of second order effects with axial load General method (3) Stress-strain relationships for concrete and steel given in 3.1.5, Expression (3.14) and (Figure 3.8) may be used. With stress-strain diagrams based on design values... 8

9 Method of partial coefficients according to Eurocodes EN 1990 E d R d g F E k R g k M g F g M E d R d partial factor for actions, also accounting for model uncertainties and dimensional variationsneistoty partial factor for a material property, also accounting for model uncertainties and dimensional variations design value of the effect of actions design value of the resistance 9

10 design charecteristic mean N [kn] Section λ= y z g F E k R g k M mean characteristic design 1000 g M 500 N cr N Rd(c) 0 41,8 62,7 68,9 MATERIAL PROPERTY M [knm] M [knm] 10

11 Applied research - Faculty of Civil Engineering, STRABAG 7 columns series S1 (normal concrete C45/55) 6 columns series S2 (HPC C70/85) 6 columns series S3 (HPC C100/115) 11

12 150 e 1 =40 l = 3840 Planned strain for stability loss section 240 x 150 mm 4 φ 14 L=3840 mm λ=89 e 1 =40 N e 1 =? mm e 2 =? 240 z z y os vnesenia sily N 12

13 e 0 - scheduled eccentricity N [kn] 250x150 C45/ e25 mm e30 mm 400 e40 mm 200 Stredný ID Návrhový ID M [knm] 13

14 z y C45/55-11/2013 C70/85-11/2013 C100/115-12/2014 C200 -??/201? 14

15 l = e 1 =40 Planned strain for stability loss 240 section 240 x 150 mm 4 φ 14 L=3840 mm λ=89 e 1 =40 mm -800 N (kn) y M-N diagram C45/55 os vnesenia sily z e 1 =40 N ATENA -600 STAB2NL NÁVRHOVÝ ID e 2 =? -400 NbR = 351 NbR = N M (knm) 15

16 Predicting the failure of the columns by loss of stability -400 N (kn) M-N diagram (S1) 41% NÁVRHOVÝ ID STREDNÝ ID e1=40mm KISAC CUHAK KENDICKY BOHUNICKY MORAVCIK, KOTES BELES FRANA STRAUSS S1-2 S1-3 S1-4 S1-5 S M (knm) 40 16

17 Predicting the failure of the columns by loss of stability Spoločnosť Riešiteľ Softvér N [kn u y [mm] M [kn.m] STU Bratislava Kišac M. Aténa 357,8 20,9 21,8 STU Bratislava Čuhák M. Metóda A 344,4 35,5 26,0 STU Bratislava Kendický P. Stab2NL 336,8 26,4 22,4 Leptón s.r.o. Bohunický B. Metóda C 342,0 44,0 28,0 ZU Žilina Moravčík M. Atena 396,6 38,7 31,2 Nemetschek-Scia Beleš I. Scia 325,5 49,4 29,1 Dlubal - CZ Fráňa J. Dlubal 363,0 30,3 25,5 BOKU Wien - A Strauss A. Atena 323,0 18,9 19,0 23% 161% 17

18 EXPERIMENT - C45/55 C100/115 (BRATISLAVA 2014) l=88 18

19 Production of the columns (ZIPP Bratislava spol. Ltd.) 7 columns series S1 (normal concrete C45/55) 19

20 Production of the columns (ZIPP Bratislava spol. Ltd.) processing of concrete with immersion vibrators production of samples (cylinders, cubes, prisms) 20

21 Experimental verification (laboratory Bratislava 2014) laboratory conditions l= 89 21

22 Experimental results of the columns: series S1 (C45/55) compression strain εc= 1,55 in case of loss of the stability (λ=89) -350 N (kn) M-N diagram C45/55 N (kn) ε-n diagram C45/ ID design ID characteristic ID mean S1-1 S1-2 S1-3 S1-4 S1-5 S1-6 S1-1 S1-2 S1-3 S1-4 S1-5 S M (knm) ε ( ) -2 1,55 22

23 Results of tested columns: series S1 (C45/55) -350 N (kn) Diagram e2 - N S1-1 - S1-3 S1-4 - S1-6 e =40mm 0 e =40mm 0 S1-1 S1-2 S S stred stĺpa stred stĺpa S1-5 S e 2 (mm) 23

24 Column N [kn u y [mm] M [kn.m] S ,4 57,6 31,7 S ,4 42,7 26,8 S ,6 38,3 26,0 S ,2 58,4 26,7 S ,0 59,4 29,4 S ,4 55,0 29,6 23% 52% 24

25 Evaluation of the failure predictions at what normal force occurs the failure of the column by the loss of stability? 1. STRAUSS (ATÉNA) 4,8 %, 2. BELEŠ (SCIA) 5,5 %, 3. KENDICKÝ (STAB2NL) 8,7 %. what will be the deformation in the critical cross section of the column by the loss of stability? 1. BELEŠ (SCIA) 5,6 %, 2. BOHUNICKÝ (own software) 18,6 %. 3. MORAVČÍK - KOTEŠ (ATÉNA) 34,8 %, 25

26 Overall evaluation of the failure predictions 1. BELEŠ 2. BOHUNICKÝ 3. MORAVČÍK - KOTEŠ 26

27 Failure by Stability loss -400 N (kn) M-N diagram C45/ S1-1 S1-2 S1-3 S1-4 S1-5 S1-6 NÁVRHOVÝ ID Charakter. ID Stredný ID e1=40mm M (knm) 27

28 Overall Reliability of the Cross Section N (kn) M-N diagram C45/ N Rk =850,6 g M =1, N Rd =635,9 g F =1,4 g G =1, N Ek =453,6 e1=40mm -200 NÁVRHOVÝ ID Charakter. ID Stredný ID M (knm) 28

29 Overall Reliability of the Cross Section N (kn) M-N diagram C45/ N Rm =982,5-800 g Mm =1, N Ed =635,9 g F =1,4 g Gm =2, N Ek =453,6 e1=40mm -200 NÁVRHOVÝ ID Charakter. ID Stredný ID M (knm) 29

30 Overall Reliability of the Column according to 5.7 (4) N (kn) M-N diagram C45/ e1=40mm NÁVRHOVÝ ID CHARAKTER. ID -600 Stredný ID S N Rbm =332,6 g F =1, N Ek =237, g B g g Gm F 2,17 1,4 1,55 M (knm) 30

31 Overall Reliability of the Column according to (3) M-N diagram C45/55 N (kn) e1=40mm NÁVRHOVÝ ID -800 CHARAKTER. ID Stredný ID S N s fcd -400 N Rbm =332,6 g F =1,2-200 N Rbd =269,1 g F =1,4 g G =1,68 N Ek =192, M (knm) 31

32 5 Nationale Erläuterungen zu ÖNORM EN Zu Abschnitt 5.8.6(3) Wird die Stabilitätslast (rechnerisches Versagen durch Stabilitätsverlust) mit den mittleren Baustoffkennwerten berechnet, so muß sie mindestens das 1,3 fache der maßgebenden Bemessungslast erreichen. Die Aufnahme der Schnittgrößen unter der maßgebenden Bemessungslast ist mit den Bemessungswerten der Baustofffestigkeiten nachzuweisen. 32

33 Concrete slender columns 33

34 Slovak Chamber of Civil Engineers DESIGN OF SLENDER COLUMNS Prof. Dr. - Ing. Vladimír BENKO, PhD. Slovak University of Technology in Bratislava Thank you for your attention! 34