DESIGN OF SLENDER COLUMNS · 2015. 11. 17. · EN 1992-1-1 | CPD-Lectures on Eurocodes September 16th, 2015 | vladimí[email protected] 1 Slovak Chamber of Civil Engineers ECEC –Europea

1EN 1992-1-1 | CPD-Lectures on Eurocodes September 16th, 2015 | vladimí[email protected]

Slovak Chamber of Civil Engineers

ECEC – European Council of Engineer‘s ChambersCPD-Lectures at 16th of September, 2015Belgrade/SRB – Bratislava /SVK

Prof. Dipl. - Ing. Dr. Vladimír BENKO, PhD.

Slovak University of Technology in Bratislava

DESIGN OF SLENDER COLUMNS


Failure of the Concrete Slender Columns by Stability loss

Experimental and numerical analysis


Why slender concrete columns?


Influence of slenderness on deformation and resistance of columnse0 NEda) short column

M0Ed= MRd

e0

NRd(a)

NEde0 e2

c) slender column

NEd

MEd

Ncr

e2

NRd(c)

M2

e2

NRd(b)

e2e0NEd

b)

critical cross sectionstabilityloss

cross-sectionfailure

e2


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

EN 1992-1-1 betónových konštrukcií




5.8.1 Definitions

5.8.2 General

5.8.3 Simplified criteria for second order effects

5.8.3.1 Slenderness Criterion for isolated members

5.8.3.2 Slenderness and effective length of isolated members

5.8.3.3 Global second order effects in buildings

5.8.4 Creep

5.8.5 Methods of analysis

5.8.6 General method

5.8.7 Method based on nominal stiffness

5.8.8 Method based on nominal curvature...

EN 1992-1-1 betónových konštrukcií


(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 5.8.6 may be used.


(3) Stress-strain relationships for concrete and steel

given in 3.1.5, Expression (3.14) and 3.2.3 (Figure

3.8) may be used. With stress-strain diagrams

based on design values ...


5.8.6 General method


Method of partial coefficients according to Eurocodes

d dE R

gF partial factor for actions, also accounting for model uncertainties and dimensional variationsneistoty

Ed design value of the effect of actions

Rd design value of the resistance

gM partial factor for a material property, also accounting formodel uncertainties and dimensional variations

gg

kk

FM

RE

• EN 1990


Section λ=0

MATERIAL PROPERTY

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60

N[k

N]

M [kNm]

z

y

characteristicch

are

cte

risti

c

62,741,8

desig

n

design

68,9

mean

me

an

gM

kF k

M

REg

g

M [kNm]

N [

kN

]

Ncr

NRd(c)


Applied research - Faculty of Civil Engineering

• 7 columns series S1 (normal concrete C45/55)

• 6 columns series S2 (HPC C70/85)

• 6 columns series S3 (HPC C100/115)

, STRABAG


Planned strain for stability loss

• section 240 x 150 mm

• 4 φ 14

• L=3840 mm

• λ=89

• e1= ? mm

l´=

3840

e1=40

N

N

e2=?e

1=

40

os vnesenia silyy

z

150

240

y

z


e0 - scheduled eccentricity

0

200

400

600

800

1000

0 10 20 30 40

N [kN]

M [kNm]

250x150 C45/55

e25 mm

e30 mm

e40 mm

Stredný ID

Návrhový ID


y

z

C45/55 - 11/2013

C70/85 - 11/2013

C100/115 - 12/2014

C200 - ??/201?


Planned strain for stability loss

• section 240 x 150 mm

• 4 φ 14

• L=3840 mm

• λ=89

• e1=40 mm

l´=

3840

e1=40

N

N

e2=?

e1=

40

os vnesenia silyy

z

150

240

y

z

-800

-600

-400

-200

0

0 10 20 30

N (kN)

M (kNm)

M-N diagram C45/55

ATENA

STAB2NL

NÁVRHOVÝ ID

NbR = 351NbR = 337


-400

-300

-200

-100

0

0 10 20 30 40

N (kN)

M (kNm)

M-N diagram (S1)

NÁVRHOVÝ ID

STREDNÝ ID

e1=40mm

KISAC

CUHAK

KENDICKY

BOHUNICKY

MORAVCIK, KOTES

BELES

FRANA

STRAUSS

S1-2

S1-3

S1-4

S1-5

S1-6

41%

Predicting the failure of the columns by loss of stability


Spoločnosť Riešiteľ Softvér N [kN| uy [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%

Predicting the failure of the columns by loss of stability


EXPERIMENT - C45/55 C100/115 (BRATISLAVA 2014)

l=88


Production of the columns (ZIPP Bratislava spol. Ltd.)

• 7 columns series S1 (normal concrete C45/55)


• processing of concrete with immersion vibrators

• production of samples (cylinders, cubes, prisms)

Production of the columns (ZIPP Bratislava spol. Ltd.)


l= 89

Experimental verification (laboratory Bratislava 2014)

• laboratory conditions


Experimental results of the columns: series S1 (C45/55)

• compression strain εc= 1,55‰ in case of loss of the stability (λ=89)

-350

-250

-150

-50

0 10 20 30

N (kN)

M (kNm)

M-N diagram C45/55

ID design

ID characteristic

ID mean

S1-1

S1-2

S1-3

S1-4

S1-5

S1-6

-350

-250

-150

-50

-2-10

N (kN)

ε (‰)

ε-N diagram C45/55

S1-1

S1-2

S1-3

S1-4

S1-5

S1-6

1,55‰


Results of tested columns: series S1 (C45/55)

-350

-300

-250

-200

-150

-100

-50

0

0 20 40 60 80 100

N (kN)

e2 (mm)

Diagram e2 - N

S1-1

S1-2

S1-3

S1-4

S1-5

S1-6

e =40mm0

stred stĺpa

S1-1 - S1-3 S1-4 - S1-6

e =40mm0

stred stĺpa


Column N [kN| uy [mm] M [kN.m]

S1-1 324,4 57,6 31,7

S1-2 323,4 42,7 26,8

S1-3 332,6 38,3 26,0

S1-4 271,2 58,4 26,7

S1-5 296,0 59,4 29,4

S1-6 311,4 55,0 29,6

23% 52%


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 %,


Overall evaluation of the failure predictions

1. BELEŠ

2. BOHUNICKÝ

3. MORAVČÍK - KOTEŠ


-400

-300

-200

-100

0

0 10 20 30 40

N (kN)

M (kNm)

M-N diagram C45/55

S1-1

S1-2

S1-3

S1-4

S1-5

S1-6

NÁVRHOVÝ ID

Charakter. ID

Stredný ID

e1=40mm

Failure by Stability loss


-1200

-1000

-800

-600

-400

-200

0

0 10 20 30 40

N (kN)

M (kNm)

M-N diagram C45/55

e1=40mm

NÁVRHOVÝ ID

Charakter. ID

Stredný ID

NRd=635,9

NRk=850,6

NEk=453,6

gM=1,34

gF=1,4

gG=1,88

Overall Reliability of the Cross Section


-1200

-1000

-800

-600

-400

-200

0

0 10 20 30 40

N (kN)

M (kNm)

M-N diagram C45/55

e1=40mm

NÁVRHOVÝ ID

Charakter. ID

Stredný ID

NEd=635,9

NEk=453,6

gMm=1,55

gF=1,4

gGm=2,17

NRm=982,5

Overall Reliability of the Cross Section


-1000

-800

-600

-400

-200

0

0 10 20 30 40

N (kN)

M (kNm)

M-N diagram C45/55

e1=40mm

NÁVRHOVÝ ID

CHARAKTER. ID

Stredný ID

S1-3

NRbm=332,6

NEk=237,5

gF=1,4

55,14,1

17,2

F

Gm

Bg

gg

Overall Reliability of the Column according to 5.7 (4)


-1000

-800

-600

-400

-200

0

0 10 20 30 40

N (kN)

M (kNm)

M-N diagram C45/55

e1=40mm

NÁVRHOVÝ ID

CHARAKTER. ID

Stredný ID

S1-3

N s fcd

NRbm=332,6

gF=1,4

gF=1,2

gG=1,68

NEk=192,2

NRbd=269,1

Overall Reliability of the Column according to 5.8.6 (3)


Zu Abschnitt 5.8.6(3)

Wird die Stabilitätslast (rechnerisches Versagen durchStabilitätsverlust) 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.

5 Nationale Erläuterungen zu ÖNORM EN 1992-1-1


Concrete slender columns


Slovak Chamber of Civil Engineers

Thank you for your attention !

Prof. Dr. - Ing. Vladimír BENKO, PhD.

Slovak University of Technology in Bratislava

DESIGN OF SLENDER COLUMNS

Documents

DESIGN OF SLENDER COLUMNS · 2015. 11. 17. · EN 1992-1-1 | CPD-Lectures on Eurocodes September 16th, 2015 | vladimí[email protected] 1 Slovak Chamber of Civil Engineers ECEC –Europea