Ltbhandouts 5

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Lateral Torsional Buckling

SCI Education

15th May 2020

Lateral Torsional Buckling

Why free webinars?  Strange times  But perhaps you would consider joining the SCI…..

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Lateral Torsional Buckling

SCI Education

15th May 2020

LTB  A reminder of the structural mechanics • The buckling curves

 A reminder of the codified verification process  Use of software for Mcr  Some unorthodox situations

Lateral torsional buckling

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Lateral Torsional Buckling

SCI Education

15th May 2020

Lateral torsional buckling

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Lateral Torsional Buckling

SCI Education

15th May 2020

Web stiffeners – and LTB  No stiffener lateral



Web stiffeners – and LTB  No stiffeners lateral

 With stiffeners (no change)



AISC: “transverse stiffeners are simply along for the ride”

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Lateral Torsional Buckling

SCI Education

15th May 2020

Bending resistance  Cross section: Mc,Rd =  LTB: 𝑀

,

𝜒

𝛾 𝛾 1.0 and 𝜒 1.0  So LTB resistance is always less than cross sectional resistance

Buckling curves Cross sectional resistance

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Lateral Torsional Buckling

SCI Education

15th May 2020

Buckling curves Plateau (no LTB: short lengths)

LTB methods overview Three methods in BS EN 1993-1-1:  Buckling curves, 6.3.2.2 & 3 • General case • Rolled sections & “Equivalent welded sections” • Simplified assessment methods, 6.3.2.4 • General method, 6.3.4

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Lateral Torsional Buckling

SCI Education

15th May 2020

Mcr Elastic Critical Bending Moment  Required for the calculation of the nondimensional slenderness 𝜆̅

For rolled sections:  6.3.2.3

  = 0.75 for rolled sections  𝜆̅ , = 0.4

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confirmed in UK NA

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Lateral Torsional Buckling

SCI Education

15th May 2020

Calculate LT  User-defined function in Excel  Look-up tables in P362

Calculate LT?  User-defined function in Excel  Look-up tables in P362  Figure in P362

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Lateral Torsional Buckling

SCI Education

15th May 2020

UK NA

Selection of curves  For the special case only:  Curves to be selected from Table 6.5 • But Table 6.5 is modified in the UK NA

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Lateral Torsional Buckling

SCI Education

15th May 2020

UK NA

For the special case only: More resistance (optional)  Modification of LT:

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Lateral Torsional Buckling

SCI Education

15th May 2020

More resistance  kc from Table 6.6 (or the UK NA)

Precisely the same for the standard cases

How to calculate Mcr?  Spreadsheet • Download the data tables • Use “vlookup” to return section properties

M cr  C1

©TheSteelConstructionInstitute

π 2 EI z L2

I w L2GI T  I z π 2 EI z

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Lateral Torsional Buckling

SCI Education

15th May 2020

C1 some classic shapes

C1 for linear BMD

𝜓

smaller moment larger moment

respect the sign!

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Lateral Torsional Buckling

SCI Education

15th May 2020

C1 for linear BMD  C1 = 1.77 – 0.88 + 0.11  2 𝜓

May be negative if moments reverse – respect the sign!

 (from New Steel Construction, Nov/Dec 2013)

C1 for varying BMD

 From New Steel Construction, Dec 2013

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Lateral Torsional Buckling

SCI Education

15th May 2020

C1 (if you ever need it)

How to calculate Mcr?  Use software • LTBeam from CTICM • Mcr tool from steelconstruction.info

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14

Lateral Torsional Buckling

SCI Education

15th May 2020

LTBeam

Note the uniform BMD (not UDL)

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Lateral Torsional Buckling

SCI Education

15th May 2020

Mcr = 111 kNm

Central point load

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Lateral Torsional Buckling

SCI Education

15th May 2020

Mcr = 151.4 kNm

C1

𝐶

.

1.36

 “near enough!”

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Lateral Torsional Buckling

SCI Education

15th May 2020

Mb = 128 kNm

Blue Book

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Lateral Torsional Buckling

SCI Education

15th May 2020

Some observations  C1 = 1 is the most conservative, and always safe  The Blue Book uses the special case and uses the benefit of the f factor • The benefit of f increases as C1 increases

Some classic questions  What is the effective length?  The Eurocode leaves that to the designer, describing “the buckling length”  BS 5950 had good advice in Table 13

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Lateral Torsional Buckling

SCI Education

15th May 2020

Some classic questions  What are the end conditions?  So-called “fork supports”

Some classic questions  What about cantilevers?  The Eurocode leaves that to the designer, describing “the buckling length”  BS 5950 had good advice in Table 14  But why not use LTBeam?

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SCI Education

Lateral Torsional Buckling

15th May 2020

But what are the conditions at the tip?

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Lateral Torsional Buckling

SCI Education

15th May 2020

Mcr = 190.9 kNm

Triangular BMD, C1= 1.77

Mb = 158 kNm

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Lateral Torsional Buckling

SCI Education

15th May 2020

LTB  Checked between restrained positions  Low values of C1 are critical

C1 = 1.35 Buckling length = L

L

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Lateral Torsional Buckling

SCI Education

15th May 2020

C1 = 1.77 Buckling length = 0.5L

* * 0.5L

0.33L

0.5L

*

*

*

* 0.33L

C1 = 1.0 Buckling length = 0.33L

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0.33L C1 = 1.77 Buckling length = 0.33L

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Lateral Torsional Buckling

SCI Education

15th May 2020

Destabilising loads Usual assumption (neutral)

Destabilising load (load moves with flange)

Neutral

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Lateral Torsional Buckling

SCI Education

15th May 2020

Destabilising

Stabilising

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Lateral Torsional Buckling

SCI Education

15th May 2020

Effect of destabilising load  356 × 127 × 33, S355  5 m long, UDL (C1 = 1.13)  Bottom flange, stabilising,  Shear centre, neutral,  Top flange, destabilising,

Mb = 77 kNm Mb = 60 kNm Mb = 46 kNm

From look-up tables  60.1 kNm – Tables assume neutral

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Lateral Torsional Buckling

SCI Education

15th May 2020

Destabilising loads  BS 5950 increased the buckling length by a factor of 1.2 (when the compression flange is restrained)  So 5 m becomes 1.2 × 5 = 6 m

From look-up tables  48.5 kNm at 1.2 × L

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Lateral Torsional Buckling

SCI Education

15th May 2020

Effect of destabilising load  356 × 127 × 33, S355  5 m long, UDL (C1 = 1.13)    

Bottom flange, stabilising, Shear centre, neutral, Top flange, destabilising, Destabilising, BS 5950, 6m

Mb = 77 kNm Mb = 60 kNm Mb = 46 kNm Mb = 48 kNm

Beams on Padstones or similar

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Lateral Torsional Buckling

SCI Education

15th May 2020

Beams on Padstones or similar  With some fixity at the ends (built in)  BS 5950 said: • Le = 1.0L + 2D when loads are not destabilising • Le = 1.2L + 2D when loads are destabilising

356 × 171 × 45, 6 m long, UDL

Mb = 109 kNm

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Lateral Torsional Buckling

SCI Education

15th May 2020

356 × 171 × 45, 6 m long, UDL  On Padstones and a destabilising load  Le = 1.2 × 6 + 2 × 0.35 = 7.9

Mb = 80 kNm

Eurocode calculation

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Lateral Torsional Buckling

SCI Education

15th May 2020

Mcr = 89.9 kNm

Mb = 85 kNm

 Approximate answer was 80 kNm

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Lateral Torsional Buckling

SCI Education

15th May 2020

Restraints to the tension flange lateral

lateral

Less minor axis buckling of flange 

Tension flange restraint

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Lateral Torsional Buckling

SCI Education

15th May 2020

Tension flange restraint

Tension flange restraint  Mb with tension flange restraints = 110 kNm  (no significant change, was 109 kNm)

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Lateral Torsional Buckling

SCI Education

15th May 2020

One compression flange restraint

One compression flange restraint

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Lateral Torsional Buckling

SCI Education

15th May 2020

One compression flange restraint  Mb with one compression flange restraint = 223 kNm  (significant change, was 109 kNm)

Really complicated?  Use LTBeamN

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Lateral Torsional Buckling

SCI Education

15th May 2020

LTBeamN  Buckled form  Ncr and Mcr

Resources  Member buckling with tension flange restraint (July 2011)  Getting the best out of LTBeam (May 2009)  Use of LTBeamN (January 2015)  LTB – additional Eurocode provisions (September 2016)  A brief history of LTB (Feb & March 2016)  Buckling resistance of uniform members in bending (July 2018)

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37

Lateral Torsional Buckling

SCI Education

15th May 2020

Conclusions  In LTB the shape of the BMD is important  C1 = 1 is the most conservative (but can be very conservative)  Beware destabilising loads  Beware beams that sit on pads (and are not built in)

Next events  Brittle Fracture 19 May (SCI Members)  Execution to EN 1090 27 May (All)

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SCI Education

Lateral Torsional Buckling

15th May 2020

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