SN009 - Effective lengths and destabilizing load parameters for beams and cantilevers.pdf

NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

 NCCI: Effective Effective lengths and destabilizing load parameters parameters for beams beams and cantilevers - common cases SN009a-EN-EU

NCCI: Effective lengths and destabilizing load parameters for beams beams and cantil evers evers - comm on cases This NCCI presents values for the effective length parameter k and the destabilizing  parameter D for beams and cantilevers cantilevers with or without intermediate lateral restraints, restraints, for use with NCCI document SN002.

Contents

   t   n   e   m   e   e   r   g    A   e   c   n   e   c    i    L    l   e   e    t    S   s   s   e   c   c    A   e    h    t    f   o   s   n   o    i    t    i    d   n   o   c    d   n   a   s   m   r   e    t   e    h    t   o    t    t   c   e    j    b   u   s   s    i    t   n   e   m   u   c   o    d   s    i    h    t    f   o   e   s    U  .    d   e   v   r   e   s   e   r    3  s    1   t    0   h    2   i   g  ,   r    0   l    l    3  a   y    a   t    h    M   g  ,   i   y  r   a  y    d  p   o   s   r   c   u  s    h   i    l    T   a   n   i   r   o   t   e    d  a   e    t   m   a  s    i   e   r   h    C    T

1.

General

2

2.

Destabilizing load condition

2

3.

Simple beams without intermediate restraint

2

4.

Simple beams with intermediate lateral restraint

3

5.

Cantilevers without intermediate restraints

4

6.

Cantilevers with intermediate lateral restraints

4

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NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

 NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases SN009a-EN-EU

1.

General

The general expression for non-dimensional slenderness, W    y . f    y 

 λ LT

=

 λ LT

=

M  cr  1

C 1

λ  LT is

given by:

which, as shown in SN002, may also be expressed as:

UVD   λ z  β w

Where D  λ z    t   n   e   m   e   e   r   g    A   e   c   n   e   c    i    L    l   e   e    t    S   s   s   e   c   c    A   e    h    t    f   o   s   n   o    i    t    i    d   n   o   c    d   n   a   s   m   r   e    t   e    h    t   o    t    t   c   e    j    b   u   s   s    i    t   n   e   m   u   c   o    d   s    i    h    t    f   o   e   s    U  .    d   e   v   r   e   s   e   r    3  s    1   t    0   h    2   i   g  ,   r    0   l    l    3  a   y    a   t    h    M   g  ,   i   y  r   a  y    d  p   o   s   r   c   u  s    h   i    l    T   a   n   i   r   o   t   e    d  a   e    t   m   a  s    i   e   r   h    C    T

is a parameter to allow for the effect of destabilising loads =

λ z  λ 1

and λ z

 L

kL =

iz

 in which

for a beam is the distance between points of restraint to the compression flange for a cantilever is the length of the cantilever

k 

is the effective length parameter dependant on the restraint conditions at the supports

and

expressions for the other parameters are given in SN002.

2.

Destabil izing load condition

The destabilizing load condition should be taken into account where a load is applied to the top flange of a beam or cantilever, and both the load and the flange are free to deflect laterally and relative to the shear centre of the cross section (i.e. rotational movements).

3.

Simple beams without int ermediate restraint

The effective length parameter, k for lateral-torsional buckling of a simple beam with restraints at the ends only, may be obtained from Table 4.1. If the restraint conditions at each end differ, the mean value of k should be taken. For the destabilizing load condition, the destabilizing parameter D should be taken as 1,2 otherwise D should be taken as 1,0.

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NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

 NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases SN009a-EN-EU

The conditions of restraint against rotation on plan of flanges at member supports should be assessed taking into account the stiffness of the connections as well as the stiffness of the supporting members or other construction supplying restraint at the supports.

4.

Simple beams wit h intermediate lateral restraint

The effective length parameter, k, for lateral torsional buckling of a simple beam with intermediate restraints should be taken as 1,0. For the destabilizing load condition, the destabilizing parameter D should be taken as 1,2 otherwise D should be taken as 1.0. For the segment between a support and the adjacent intermediate lateral restraint, account should be taken of the restraint conditions at the support. The effective length parameter k should be taken as the mean of the value given above and the value given by Table 4.1 for the restraint conditions at the support.

   t   n   e   m   e   e   r   g    A   e   c   n   e   c    i    L    l   e   e    t    S   s   s   e   c   c    A   e    h    t    f   o   s   n   o    i    t    i    d   n   o   c    d   n   a   s   m   r   e    t   e    h    t   o    t    t   c   e    j    b   u   s   s    i    t   n   e   m   u   c   o    d   s    i    h    t    f   o   e   s    U  .    d   e   v   r   e   s   e   r    3  s    1   t    0   h    2   i   g  ,   r    0   l    l    3  a   y    a   t    h    M   g  ,   i   y  r   a  y    d  p   o   s   r   c   u  s    h   i    l    T   a   n   i   r   o   t   e    d  a   e    t   m   a  s    i   e   r   h    C    T

Table 4.1

 Effective length parameter, k Conditions of restraint at supports

K

Compression flange laterally restrained.

Both flanges fully restrained against rotation on plan.

0,7

Nominal torsional restraint against rotation about longitudinal axis.

Compression flange fully restrained against rotation on plan.

0,75

Both flanges partially restrained against rotation on plan.

0,8

Compression flange partially restrained against rotation on plan.

0,85

Both flanges free to rotate on plan.

1,0

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NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

 NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases SN009a-EN-EU

5.

Cantilevers without intermediate restraints

The effective length parameter k for lateral-torsional buckling of a cantilever with moment continuity, lateral and torsional restraint at the support (the common case) and with no intermediate lateral restraint may be obtained from Table 6.1. For all other support conditions k and D should be obtained from Annex A and L should be taken as the length of the cantilever. For the destabilizing load condition, k and D should be obtained from Annex A and L should be taken as the length of the cantilever, unless the top flange also has intermediate restraints. If a bending moment is applied at its tip the effective length parameter k from Table 6.1 or Annex A should be increased by 30% or by 0.3, whichever is the greater.

6.    t   n   e   m   e   e   r   g    A   e   c   n   e   c    i    L    l   e   e    t    S   s   s   e   c   c    A   e    h    t    f   o   s   n   o    i    t    i    d   n   o   c    d   n   a   s   m   r   e    t   e    h    t   o    t    t   c   e    j    b   u   s   s    i    t   n   e   m   u   c   o    d   s    i    h    t    f   o   e   s    U  .    d   e   v   r   e   s   e   r    3  s    1   t    0   h    2   i   g  ,   r    0   l    l    3  a   y    a   t    h    M   g  ,   i   y  r   a  y    d  p   o   s   r   c   u  s    h   i    l    T   a   n   i   r   o   t   e    d  a   e    t   m   a  s    i   e   r   h    C    T

Cantilevers with intermediate lateral restraints

Provided that the end restraint conditions correspond with Table 6.1 and the load is not destabilising, the effective length parameter k for lateral torsional buckling of a cantilever with intermediate restraints to its compression flange should be taken as 1.0, and L should be taken as the length of the relevant segment between adjacent lateral restraints.

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NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

 NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases SN009a-EN-EU

Table 6.1

   t   n   e   m   e   e   r   g    A   e   c   n   e   c    i    L    l   e   e    t    S   s   s   e   c   c    A   e    h    t    f   o   s   n   o    i    t    i    d   n   o   c    d   n   a   s   m   r   e    t   e    h    t   o    t    t   c   e    j    b   u   s   s    i    t   n   e   m   u   c   o    d   s    i    h    t    f   o   e   s    U  .    d   e   v   r   e   s   e   r    3  s    1   t    0   h    2   i   g  ,   r    0   l    l    3  a   y    a   t    h    M   g  ,   i   y  r   a  y    d  p   o   s   r   c   u  s    h   i    l    T   a   n   i   r   o   t   e    d  a   e    t   m   a  s    i   e   r   h    C    T

 Effective length parameter k and destabilizing parameter D for a cantilever without intermediate restraint, with effective restraint at the support.

Restraint to cantilever tips

k

D

1) Free

1,0

2,5

2) Lateral restraint to top flange

0,9

2,8

3) Torsional restraint

0,8

1,9

4) Internal and torsional restraint

0,7

1,7

Examples of restraints to cantilever suppo rts, all providi ng effective moment continuity and lateral and torsional restraint Cantilevered beam continuous over supporting beam, with lateral and torsional restraint.

Discontinuous cantilever, at same level as continuous supporting beam

Cantilever supported from flange of column

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NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

 NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases SN009a-EN-EU

 Annex A: Effective length parameter k and destabilising D for cantilevers without intermediate  restraint, for a range of restraints at the support. Restraint condition s  At supp or t a) Continuous, with lateral restraint to top flange

k

D

At ti p 1) Free

3,0

2,5

2) Lateral restraint to top flange

2,7

2,8

3) Torsional restraint

2,4

1,9

4) Lateral and torsional restraint

2,1

1,7

1) Free

2,0

2,5

2) Lateral restraint to top flange

1,8

2,8

 

1,9

3) Torsional restraint

1,6

1,7

4) Lateral and torsional restraint

1,4

1) Free

1,0

2,5

2) Lateral restraint to top flange

0,9

2,8

3) Torsional restraint

0,8

1,9

4) Lateral and torsional restraint

0,7

1,7

1) Free

0,8

1,75

2) Lateral restraint to top flange

0,7

2,0

3) Torsional restraint

0,6

1,0

4) Lateral and torsional restraint

0,5

1,0

L

b) Continuous, with partial torsional restraint

   t   n   e   m   e   e   r   g    A   e   c   n   e   c    i    L    l   e   e    t    S   s   s   e   c   c    A   e    h    t    f   o   s   n   o    i    t    i    d   n   o   c    d   n   a   s   m   r   e    t   e    h    t   o    t    t   c   e    j    b   u   s   s    i    t   n   e   m   u   c   o    d   s    i    h    t    f   o   e   s    U  .    d   e   v   r   e   s   e   r    3  s    1   t    0   h    2   i   g  ,   r    0   l    l    3  a   y    a   t    h    M   g  ,   i   y  r   a  y    d  p   o   s   r   c   u  s    h   i    l    T   a   n   i   r   o   t   e    d  a   e    t   m   a  s    i   e   r   h    C    T

L

c) Continuous, with lateral and torsional restraint

L

d) Restrained laterally, torsionally and against rotation on plan

L

Tip restraint condition s 1) Free (not braced on plan)

2) Lateral restraint to top flange

3) Torsional restraint

4) Lateral and torsional restraint

(braced on plan in at least one bay)

(not braced on plan)

(braced on plan in at least one bay)

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NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

 NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases SN009a-EN-EU

Quality Record RESOURCE TITLE

NCCI: Effective lengths and destabilizing load parameters for beams and cantilevers - common cases

Reference(s) ORIGINAL DOCUMENT Name

Compan y

Date

Created b y

James Way

The Steel Construction Institute

22/4/05

Technical cont ent checked by

Charles King

The Steel Construction Institute

11/5/05

1. UK

G W Owens

SCI

7/7/05

2. France

 A Bureau

CTICM

17/8/05

3. Sweden

 A Olsson

SBI

8/8/05

4. Germany

C Muller

RWTH

10/8/05

5. Spain

J Chica

Labein

12/8/05

G W Owens

SCI

25/4/06

Editorial content checked by Technical content endorsed by the following STEEL Partners:    t   n   e   m   e   e   r   g    A   e   c   n   e   c    i    L    l   e   e    t    S   s   s   e   c   c    A   e    h    t    f   o   s   n   o    i    t    i    d   n   o   c    d   n   a   s   m   r   e    t   e    h    t   o    t    t   c   e    j    b   u   s   s    i    t   n   e   m   u   c   o    d   s    i    h    t    f   o   e   s    U  .    d   e   v   r   e   s   e   r    3  s    1   t    0   h    2   i   g  ,   r    0   l    l    3  a   y    a   t    h    M   g  ,   i   y  r   a  y    d  p   o   s   r   c   u  s    h   i    l    T   a   n   i   r   o   t   e    d  a   e    t   m   a  s    i   e   r   h    C    T

Resource approved by Technical Coordinator TRANSLATED DOCUMENT This Translation made and checked by: Translated resource approved by:

Corrig endum 26/02/08 Reference to SN002 corrected

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