sx004a-en-eu-example- pinned column using non slender h-section or rhs

8/10/2019 SX004a-En-EU-Example- Pinned Column Using Non Slender H-section or RHS

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Document Ref: SX004a-EN-EU Sheet 1 of 4

CALCULATION SHEET

Title Example: Pinned column using non slender H-section or

RHS

Eurocode Ref EN 1993-1-1

Made by Matthias Oppe Date June 2005

Checked by Christian Mller Date June 2005

Example: Pinned column using non slender H-section or RHS

Within this worked example on a pinned column H-section or RHS in a

simple structure the column buckling resistance for various rolled cross-

sections (H-sections or RHS), different steel grades and member lengths

should be calculated.

Ed

8,

0

N

Ed

[m]

8,

0

N

0,1cr. =L

L 7,0cr. =

L

L

SN008

Partial factors

M0= 1,0

M1= 1,0

EN 1993-1-16.1(1)


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August18,

2010

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CALCULATION SHEET


RHS




Basic dataDesign a column of a multi-storey building in consideration of the followingdata.

Axial load : NEd= 2000 kN

Column length : 8,00 m

Buckling length : y-y axis: 00,800,80,1 = m

z-z axis: 60,500,87,0 = m

Steel grade : S235

Section classification: Class 1

HE 300 B Steel grade S235

Depth h= 300 mm

Width b= 300 mm

Web thickness tw= 11 mm

Flange thickness tf= 19 mm

Fillet r= 27 mm

z

z

y y

tf

tw

b

h

Euronorm

53-62

Section area A= 149 cm2

Second moment of area /yy Iy= 25170 cm4

Second moment of area /zz Iz= 8560 cm4

Yield strength

Steel grade S235

The maximum thickness is 19,0 mm < 40 mm, so :fy= 235 N/mm2

Note: The National Annex may impose either the values offyfrom theTable 3.1 or the values from the product standard.

EN 1993-1-1Table 3.1


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2010



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CALCULATION SHEET


RHS




Design buckling resistance of a compression memberTo determine the design column buckling resistanceNb,Rd, the reduction factor

for the relevant buckling curve must be defined. This factor is determined

by calculation of the non-dimensional slenderness based on the elasticcritical force for the relevant buckling mode and the cross sectional resistanceto normal forces.

Elastic critical forceNcr

The critical buckling force is calculated as follows :

28151800

25170210002

2

2

ycr,

y2

ycr, ,

L

EIN === kN

45657560

8560210002

2

2zcr,

z2

zcr, ,L

EIN =

=

= kN

Eis the Youngs modulus : E = 210000 N/mm2

Lcris the buckling length in the buckling plane considered: Lcr,y= 8,00 m

Lcr,z= 5,60 m

Non-dimensional slenderness

The non-dimensional slenderness is given by :

655028151

523149

ycr,

yy ,

,

,

N

A f =

==

787045657

523149

zcr,

yz ,

,

,

N

A f =

==

For slenderness 2,0 or for 04,0cr

Ed N

Nthe buckling effects may be

ignored and only cross sectional checks apply.

EN 1993-1-1 6.3.1.2(1)

EN 1993-1-1 6.3.1.2(4)


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2010



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CALCULATION SHEET


RHS




Reduction factorFor axial compression in members the value of depending on the non-

dimensional slenderness should be determined from the relevant bucklingcurve according to:

1,0but

-

1

22

+

=

where : ( )

++=

20,2-10,5

is an imperfection factor.

EN 1993-1-1 6.3.1.2(1)

For h/b= 300/300 = 1,00 < 1,2 and tf = 19,0 < 100 mm

- buckling about axis y-y:

Buckling curve b, imperfection factor = 0,34

( )[ ] 0,7920,6550,2-0,6550,3410,5 2y =++=

0,808

0,655-0,7920,792

1

22y =

+

=

- buckling about axis z-z:

Buckling curve c, imperfection factor = 0,49

( )[ ] 0,9530,7870,2-0,7870,4910,5 2z =++=

0,6710,787-0,9530,953

1

22z =

+=

= min (y;z) = min (0,808; 0,671)

= 0,671 < 1,0

(when > 1 then = 1)

Design buckling resistance of a compression member

5,23490,1

5,23149671,0

M1

y

Rdb, =

=

=

fA

N kN

Then we check:

0,185,05,2349

2000

Rdb,

Ed


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SX004a-EN-EU.doc

Quality Record

RESOURCE TITLE Example: Pinned column using non slender H-section or RHS

Reference(s)

ORIGINAL DOCUMENT

Name Company Date

Created by Matthias Oppe RWTH 16/06/05

Technical content checked by Christian Mller RWTH 16/06/05

Editorial content checked by D C Iles SCI 15/07/05

Technical content endorsed by the

following STEEL Partners:

1. UK G W Owens SCI 30/06/05

2. France A Bureau CTICM 30/06/05

3. Sweden A Olsson SBI 30/06/05

4. Germany C Mller RWTH 30/06/05

5. Spain J Chica Labein 30/06/05

Resource approved by TechnicalCoordinator

G W Owens SCI 07/06/06

TRANSLATED DOCUMENT

This Translation made and checked by:

Translated resource approved by:


CreatedonWednesday,

August18,

2010




sx004a-en-eu-example- pinned column using non slender h-section or rhs

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