Bending and axial compression verification

  815 127

. 944 1274

. 812 7815

. 823 127

. 952 1274

.

b) for the bottom part of the column:

815 127

. 944 1274

. 812 7815

. 823 127

. 952 1274

. 812 7815

.

The software does not give the results of the lower section because it is not the most solicited segment.

Finite elements modeling

■ Linear element: S beam,

■ 6 nodes,

■ 1 linear element.

χ

ycoefficient corresponding to non-dimensional slenderness

λ

y

Column subjected to axial and shear force to the top

χ

y

χ

zcoefficient corresponding to non-dimensional slenderness

λ

z

Column subjected to axial and shear force to the top

χ

z

Internal factor,

k

_yy

Column subjected to axial and shear force to the top

k

yy

Internal factor,

k

_yz

Column subjected to axial and shear force to the top

k

yz

Internal factor,

k

_zy

Column subjected to axial and shear force to the top

k

zy

Internal factor,

k

_zz

Column subjected to axial and shear force to the top

k

zz

Bending and axial compression verification term depending of the compression effort over the Y axis: SNy Bending and axial compression verification term depending of the compression effort

over the Y axis

SNy

Bending and axial compression verification term depending of the Y bending moment over the Y axis: SMyy Bending and axial compression verification term depending of the Y bending moment

over the Y axis

SMyy

Bending and axial compression verification term depending of the Z bending moment over the Y axis: SMyz Bending and axial compression verification term depending of the Z bending moment

over the Y axis

SMyz

Bending and axial compression verification term depending of the compression effort over the Z axis: SNz Bending and axial compression verification term depending of the compression effort

over the Z axis

SNz

Bending and axial compression verification term depending of the Y bending moment over the Z axis: SMzy Bending and axial compression verification term depending of the Y bending moment

over the Z axis

SMzy

Bending and axial compression verification term depending of the Z bending moment over the Z axis: SMzz Bending and axial compression verification term depending of the Z bending moment

over the Z axis

SMzz

12.29.2.1 Reference results

Result name Result description Reference value

χ

y

χ

_ycoefficient corresponding to non-dimensional slenderness

λ

y ¹

χ

z

χ

_zcoefficient corresponding to non-dimensional slenderness

λ

z ^0.81

k

yy Internal factor,

k

_yy ^0.95

k

yz Internal factor,

k

_yz 0.82

k

zy Internal factor,

k

_zy ^0.94

k

zy Internal factor,

k

_zy 0.82

SNy Bending and axial compression verification term depending of the

compression effort over the Y axis 0.15

SMyy Bending and axial compression verification term depending of the Y

bending moment over the Y axis 1.72

SMyz Bending and axial compression verification term depending of the Z

bending moment over the Y axis 1.58

SNz Bending and axial compression verification term depending of the compression effort over the z axis

0.19 SMzy Bending and axial compression verification term depending of the Y

bending moment over the Z axis 1.71

SMzz Bending and axial compression verification term depending of the Z

bending moment over the Z axis 1.56

12.29.3Calculated results

Result name Result description Value Error

Xy Coefficient corresponding to non-dimensional slenderness 1 adim 0.0000 % Xz Coefficient corresponding to non-dimensional slenderness 0.811841

adim 0.2273 %

Kyy Internal factor, kyy 0.950358

adim 0.0377 %

Kyz Internal factor, kyz 0.823048

adim 0.3717 %

Kzy Internal factor, kzy 0.941635

adim 0.1739 %

Kzz Internal factor, kzz 0.815493

adim -0.5496 %

SNy Bending and axial compression verification term

depending of the compression effort over the Y axis 0.152455

adim 1.6367 %

SMyy Bending and axial compression verification term

depending of the Y bending moment over the Y axis 1.72357

adim 0.2076 %

SMyz Bending and axial compression verification term

depending of the Z bending moment over the Y axis 1.57508

adim -0.3114 %

SNz Bending and axial compression verification term

depending of the compression effort over the z axis 0.187789

adim -1.1637 %

SMzy Bending and axial compression verification term

depending of the Y bending moment over the Z axis 1.70775

adim -0.1316 %

SMzy Bending and axial compression verification term

depending of the Z bending moment over the Z axis 1.70775

adim -0.1316 %

12.30 EC3 / NF EN 1993-1-1/NA - France: Verifying an user defined I section class 3 column fixed on the bottom (evaluated by SOCOTEC France - ref. Test 26)

Test ID: 5714 Test status: Passed

12.30.1Description

The test verifies a user defined cross section column.

The cross section has an “I symmetric” shape with: 408mm height; 190mm width; 9.4mm center thickness; 14.6mm flange thickness; 0mm fillet radius and 0mm rounding radius.

The column is subjected to 1000kN axial compression force and a 200kNm bending moment after the Y axis. All the efforts are applied on the top of the column.

The calculations are made according to Eurocode 3 French Annex.

12.30.2Background

An I40.8*0.94+19*1.46 shaped column subjected to compression and bending, made from S275 steel. The column has a 40.8x9.4mm web and 190x14.6mm flanges. The column is fixed at it’s base The column is subjected to an axial compression load -1000000 N, a 200000Nm bending moment after the Y axis and a 5000N lateral force after the Y axis.

This test was evaluated by the French control office SOCOTEC.

12.30.2.1 Model description

■ Reference: Guide d’evaluation Advance Design, EN 1993-1-1: 2005;

■ Analysis type: static linear (plane problem);

■ Element type: linear.

The following load case and load combination are used:

■ Exploitation loadings (category A): Fz=-1000000N N; My=200000Nm

Units

Metric System

Geometrical properties

■ Column length: L=2000mm

■ Cross section area:

A = 9108 mm . 72

²

■ Overall breadth:

b 190 = mm

■ Flange thickness:

t

_f

= 14 . 6 mm

■ Root radius:

r 0 = mm

■ Web thickness:

t

_w

= 9 . 4 mm

■ Depth of the web:

h

_w

= 408 mm

■ Elastic modulus after the Y axis,

W

_el,y

= 1261435 mm . 06

³

■ Plastic modulus after the Y axis,

W

_y

= 1428491 mm . 78

³

■ Elastic modulus after the Z axis,

W

_el,z

= 175962 mm . 65

³

■ Plastic modulus after the Z axis,

W

_pl,z

= 271897 . 69

■ Flexion inertia moment around the Y axis: Iy=257332751mm⁴

■ Flexion inertia moment around the Z axis: Iz=16716452.10mm⁴

■ Torsional moment of inertia: It=492581.13mm⁴

■ Working inertial moment: Iw=645759981974.33mm⁶

Materials properties

S275 steel material is used. The following characteristics are used:

■ Yield strength fy = 275 MPa,

■ Longitudinal elastic modulus: E = 210000 MPa.

■ Shear modulus of rigidity: G=80800MPa Boundary conditions

Loading

The column is subjected to the following loadings:

■ External: Point load From X=0.00m and z=2.00m: FZ =-1000000N; Mx=200000Nm and Fy=5000N

12.30.2.2 Cross section Class

According to Advance Design calculations:

Cross-class classification is made according to Table 5.2

- for beam web:

The web dimensions are 378.8x9.4mm.

1 20 . 0 275 1

0091 . 0 1.000 2

1

2 − =− >−

⋅ ×

=

⋅ −

⋅

=

y Ed

f A

ψ

N

5

therefore the beam web is considered to be Class 3.

- for beam flange:

therefore the haunch is considered to be Class1

In conclusion, the section is considered to be Class 3.

12.30.2.3 Buckling verification

a) over the strong axis of the section, y-y:

- the imperfection factor α will be selected according to Tables 6.1 and 6.2:

34 . 0 α =

Coefficient corresponding to non-dimensional slenderness after Y-Y axis:

χ

ycoefficient corresponding to non-dimensional slenderness

λ

y will be determined from the relevant buckling curve according to:

1 1

2 2

≤

− Φ +

= Φ

y y y

y

λ

χ

(6.49)

λ

ythe non-dimensional slenderness corresponding to Class 4 cross-sections:

y cr

y

y

N

f A

,

= * λ

Cross section area:

A = 9108 mm . 72

²

( mm ) ^{N kN}

b) over the weak axis of the section, z-z:

- the imperfection factor α will be selected according to Tables 6.1 and 6.2:

1 1

λ

zthe non-dimensional slenderness corresponding to Class 1, 2 and 3 cross-sections:

z

Flexion inertia moment around the Z axis: Iz=16716452.10mm⁴ Cross section area:

A = 9108 mm . 72

²

In document AD Validation Guide Vol II 2017 R2 En (Page 112-127)