Designing a Cold-Formed Steel Beam Using AS4600:2018 and 2005 - Webinar

Designing a Cold-Formed Steel
Beam Using AS4600-2018 & 2005
Understanding the design process using the Direct
Strength Method
Brooks H. Smith, CPEng, PE, MIEAust, NER, RPEQ
brooks.smith@clearcalcs.com

Outline
• Introduction
• How CFS is Unique
• Changes Since AS4600-2005
• Designing a CFS Beam
• Flexural Capacity
• Shear Capacity
• Bearing Capacity
• Load Interactions
• Deflection
• Example Beam Calculations
• Conclusion & Questions
214 February 2019 ClearCalcs.com | FEA Structural Design in the Cloud

Introduction – About the Presenter
• Chartered Professional Engineer
• MCivE, MIEAust, NER, RPEQ, P.E. (USA)
• Currently the lead engineering developer for ClearCalcs
• Recently released CFS beam and column/stud calculators
• 8 years of previous experience in:
• Structural engineering R&D consulting, specialising in cold-formed steel
• Research fellowship in system behaviour of thin-walled steel
• Forensic structural engineering, specialising in reinforced and PT concrete
3
Brooks H. Smith

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Intro Video Hyperlink

Introduction – Today’s Goals
• To be able to design a cold-formed steel beam to AS4600-2018
• Cee or Zed sections bent about strong axis
• Negligible holes in the cross-section
• Direct Strength Method (Clause 7)
• Detailing will only be broadly addressed
• We’ll distribute this slide deck and video after the webinar
• Please ask quick questions as I go – best to answer while on the topic
• Please ask using the “Q&A” feature, NOT the chat/messaging feature
• I’ll save involved questions until the end
• Note: Everything today is based on the standards
• We are not on the AS4600 committee, are not communicating any special
knowledge

Outline
• Introduction
• Shear Capacity
• Deflection

How CFS is Unique
• Buckling is a major issue
• Most sections will buckle before yielding
• Bearing / web crippling can easily control
• Buckling of the web for either bottom supports or top point loads
• Design may require finite element/strip analysis
• But this only needs to be done once, and can be avoided
• Highly-customizable shapes
• So design methodology can be used
for any cross-section

Buckling in Cold-Formed Steel
• Hot-rolled steel classifies sections as compact, non-compact, or
slender – and requires extra equations for “slender”
• In cold-formed steel, “slender” checks always need to be done
• Local, distortional, or global buckling modes
• Global encompasses both lateral and lateral-torsional buckling
• Stiffeners function to mitigate buckling

Bearing / Web Crippling
• If the web isn’t directly restrained either at supports or under point
loads, web crippling must be checked
• In hot-rolled steel, checks are simple and rarely control
• But in CFS, they may commonly control and are highly-dependent upon the
precise cross-section and arrangement of forces
https://doi.org/10.1016/j.tws.2012.01.003

Finite Element / Strip Analysis
• The Direct Strength Method, which is a preferred method in AS4600-
2018, requires a rational analysis that usually takes the form of the
Finite Strip Method
• Generally only needs to be done once for a section, and alternate
methods do exist
https://dx.doi.org/10.1016/j.tws.2014.01.005
https://doi.org/10.1016/j.tws.2013.09.004

Highly-Customizable Shapes
• Standard sections available, but custom sections also economical
• Lysaght®, Stratco®, FrameCAD®, et al have standard sections
https://commons.wikimedia.org/wiki/File:Zg-prof.jpg

Outline
• Introduction
• Shear Capacity
• Deflection

Updates Since AS4600-2005
• Old member capacity calculations (Cl 3.3 & 3.4), based on the
Effective Width Method, moved to Appendix D
• Direct Strength Method (Cl 7.2) is now most complete in main body
• And expands prequalification, more properly includes G500 and G550
• Inelastic reserve capacity is now included in DSM buckling
• Inelastic reserve was previously only including in section capacity
• Shear calcs have been added to DSM section (Clause 7)
• Adopting the AISI S100 equations
• Significant revisions to screw, bolt, and PAF connection calculations
• Outside the scope of this webinar

DSM Preference & More Prequalification
• All Effective Width Method calculations are in Clause 2 or have been
moved to Appendix D
• Previously, only a distortional buckling calculation in Appx D; now all buckling
• DSM is now valid for more members, especially G500 and G550

Inelastic Reserve in Buckling
• Inelastic reserve equations now available for all types of buckling
• New sections in clauses:
• Eqn 7.2.2.2(5)
• Eqn 7.2.2.3(5-6)
• Eqn 7.2.2.4(5-6)

Shear Calculations In DSM
• New shear calculation, added to Clause 7
• But, fun fact: it’s mathematically (almost exactly) identical to the old
equations – just expressed differently!
• Example:
Original equation
DSM equation
where
!"
#$(#&'")
= 0.905 and, assuming . = ./, then
01
234
51
" =
61
7
84
, therefore
9.:9;<=>61
7
84
= ?@A

Outline
• Introduction
• Shear Capacity
• Deflection

Designing a Cold-Formed Steel Beam
• Calculate your demands by AS1170
• Limit states which must be checked:
• Positive moment flexural capacity (midspans)
• Negative moment flexural capacity (supports)
• Shear capacity
• Bearing capacity
• Load interaction limits
• Deflection

Geometric Derivatives
• First, make sure you have some of the basic geometric properties:
• !" = effective section modulus about the strong axis
• !# = gross section modulus about the strong axis
• $% = second moment of area about the strong axis
• $& = second moment of area about the weak axis
• '( = gross cross-sectional area
• )* = distance from centroid to shear center along x-axis
• +%, +& = radii of gyration about centroidal principal axes
• +*- = polar radius of gyration about the shear center = +%
/
+ +&
/
+ )*
/
• 1 = St Venant’s torsion constant
• $2 = Torsional warping constant

Flexural Capacity – Section Capacity
• Based on yielding, or including inelastic reserve capacity
• If several conditions are met, then inelastic reserve may also be included:
1. No global or distortional buckling occurs (we’ll calculate this later)
2. !" does not include effects of cold-forming (usually the case)
3.
#$
%$
≤
'.''
⁄*+ ,
, where -. is the depth of the compressed portion of the web
4. /∗ ≤ 0.603.!", where 3. is the web area
5. Webs are within 30° of the vertical
• Inelastic reserve capacity 45 is the minimum of:
• 1.259:!" , or
• Moment causing a strain of ;<+*+
, , where =" is defined for each elements within the cross-
section in Cl 3.3.2.3(i-iii)
• For 45 , >? = 0.95 when flanges are stiffened, >? = 0.90 otherwise

Direct Strength Method Req’ts (Cl 7.1.2)
• DSM is applicable to most sections you may encounter
• But should still check this:

Flexural Cap. – Global Buckling (Cl 7.2.2.2)
• !" is taken as the minimum of !"#, !"%, !"&
• Yield moment is based upon first yield
• !"# is final global buckling capacity, !' is critical global buckling
• Determined analytically, but equations vary by section
• May alternatively be determined via Finite Strip Analysis or Effective Width Method

Flexural Cap. – Global Buckling (Cl D2.1)
• Main global buckling parameter !" depends upon section:
• Cee or Zed sections:
where !#, !%, !& are moments at quarter points
where '(), '(* are effective unbraced lengths
+,
-")
-"*
BUT, for Z-sections, .) must be based upon the inclined principal axis

Flexural Cap. – Global Buckling (Cl D2.1)
• Alternative equation exists for !" for Zed sections
• Useful if you lack information about the principal axis properties
• #$% is the second moment of area about the centroidal axis (parallel to web)
• & is the unbraced length

Flexural Cap. – Inelastic Reserve (Cl 7.2.2.2.2)
• Allows small amounts of localized yielding that doesn’t affect stability
• Optional provision; certain connections or member types may forbid it
• Only allowed if !" > 2.78!(
• !) is the member plastic moment, equal to *+,(
• Generally not given in manufacturers’ information, but may be
calculated by setting compression area equal to tension area

Flexural Capacity – Finite Strip
• Local and distortional buckling critical buckling capacities (!"# and
!"$) most easily determined via Finite Strip Method:
• CUFSM (free), from Johns Hopkins University, or
• THIN-WALL (paid), from the University of Sydney
• Critical capacities generally do not depend upon length
• As long as the beam is longer than about 500-800 mm

Flexural Capacity – Finite Strip 2

Flexural Cap. – Local Buckling (Cl 7.2.2.3)
• Local buckling involves the corners of the cross-section staying still,
while the flat portions bend
• Calculations account for local buckling’s interaction with global buckling
• Usually occurs with a half-wavelength of about 100-250 mm
!"

• Inelastic reserve capacity also possible in local buckling, provided that
!" ≤ 0.776 and ()* > (,
• Calculation depends upon if first yield is in tension or compression:
• First yield in compression (or if theoretically simultaneous with tension):
• First yield in tension:
where -,. = 3 and (,1 based upon yield in compression fiber ((, is conservative)
Flexural Cap. – Local Buckling IR (Cl 7.2.2.3)

Flexural Cap. – Distort’l Buckling (Cl 7.2.2.4)
• Distortional buckling involves movement of the corners of the cross-
section, but where not all corners move together
• Does not assume an interaction with global buckling
• Usually occurs with a half-wavelength of about 400-800 mm
!"

Flexural Cap. – Dist. Buckling IR (Cl 7.2.2.4)
• Distortional buckling may also include inelastic reserve, provided that
!" ≤ 0.673
• Again, calculation depends upon the nature of first yield:
• First yield in compression:
• First yield in tension:
where )*+ = 3 and -*. is based on yield in compression fiber (conservatively -*)

Flexural Capacity – Overall (Cl 7.2.2)
• Overall flexural member capacity is minimum of local, distortional,
and global buckling capacities
• !" = 0.90 for all types of buckling (Table 1.6.3)
!"'" = 0.90 ∗ min('"-, '"/, '"0)

• Based upon !" = area of flat portion of web (i.e. without corner radii)
• #$% is comparable to &'(, &'*, &', but calculated analytically
• For unreinforced webs, +, = 5.34
• For reinforced webs having transverse stiffeners (2 = length of shear panel):
Shear Cap. – Shear Buckling (Cl D3)
https://dx.doi.org/10.1016/j.engstruct.2012.07.029

Shear Cap. – Without Stiffeners (Cl 7.2.3.2)
• Based upon shear yield and buckling slenderness:
• Overall result: !"#$ = 0.90 ∗ #"

Shear Cap. – With Stiffeners (Cl 7.2.3.3)
• Assuming minimum shear web stiffeners, with spacing not exceeding
twice the web depth
• These equations are essentially identical to flexural local buckling!
• Overall result: !"#$ = 0.90 ∗ #"

Bearing Capacity – Overview (Cl 3.3.6)
• All based upon just one equation:
• Accounts for effects of web angle (!), corner radius ("#), bearing length ($%),
and web height slenderness (&')
• The key is in all those () coefficients
• Different tables for Cee, Zed, built-up I-sections, hats, and steel decks
• Note that equation and tables are per web, so box sections, nested Zees, etc
would multiply *% by 2
• +, is not constant and also looked up in the tables!

Bearing Capacity – Cees (Table 3.3.6.2(B))

Bearing Capacity – Zeds (Table 3.3.6.2(C))

Load Inter’n – Flexure & Shear (Cl 7.2.3.5)
• Calculation depends upon whether shear stiffeners exist or not:
• Without shear stiffeners:
• With shear stiffeners (only necessary if ⁄"∗
$%"& > 0.5 and ⁄+∗
$,+, > 0.7):
• Notes:
• This "& is NOT what you would calculate in Cl 3.3.1.
• "& = "%/ but without global buckling consideration (assuming globally braced):
0/ = ⁄"1 "2/
• If 0/ ≤ 0.776: "%/ = "1
• If 0/ > 0.776: "%/ = 1 − 0.15
789
7:
;.<
789
7:
;.<
"1
• Additionally, if there are web stiffeners, "& = min("%/, "%B)

Load Inter’n – Flexure & Bearing (Cl 3.3.7)
• Applies for both supports (negative moment) and point loads (usually
positive moment)
• For unreinforced single webs:
• An exception exists for members spaced ≤ 250 mm with lateral bracing
• Back-to-back C-sections:
• Nested Z-sections (! = 0.9):
• Note that a number of connection and geometric restrictions apply (see Cl 3.3.7(c))

Load Inter’n – Flexure & Bearing (Cl 3.3.7)
• Be careful of definitions regarding what value should be used for !"
in the previous equations!
• The first two equations (single web sections & back-to-back C-sections):
• BUT, nested Z-sections let you use the value calculated via DSM (as in the
flexure & shear interaction):
• First two equations are AS4600-specific, last is straight form the USA’s AISI S100…

Deflection
• Important difference between effective and gross moments of inertia
• Conservatively, you may use the !"## values given by manufacturers
• A little less conservative and more accurate is the following equation:
• $ is the moment demand due to service loads being considered (up to a max of $%)
• $& = $( except that $( is recalculated replacing all instances of $% with $
• Note: ) = 203000 $-.

Beams - Wrapping It Up
• This represents the general requirements for cold-formed steel beams
• However, there are a few alternative equations, which generally give a
little more capacity, for specific types of systems:
• Beams with one flange through-fastened to deck or sheathing (Cl 3.3.3.4)
• Beams with one flange through-fastened to standing-seam roof (Cl 3.3.3.5)
• Detailing requirements for systems are largely in Clause 4
https://www.steelconstruction.info/File:L1_Fig9.png

Outline
• Introduction
• Shear Capacity
• Deflection

Example Beam #1 – Simply Supported
45
3000 mm
• Office building floor purlin
• 450 mm load width
• No transverse shear reinforcement
• Top flange unbraced at 500 mm
• Torsionally unbraced for full span
Q = 1.5 kPa
G = 0.2 kPa
14 February 2019
Showing methods and formulas
using ClearCalcs’s new cold-formed
steel calculator
ClearCalcs.com | FEA Structural Design in the Cloud
C100-15
102mm
51mm
1.5mm

Example Beam #2 – Complex Beam
46
Q = 1.5 kPa
G = 0.2 kPa
• 10 m total length
• Office building floor purlin
• No transverse shear reinforcement
• Load width of 450 mm
• Bottom flange and torsional bracing
at 1000 mm
2000 mm 5500 mm 2500 mm
14 February 2019
Ex #1 Beam @ 4000 mm
C150-19
152mm
1.9mm
64mm

Outline
• Introduction
• Shear Capacity
• Deflection

Summing It Up
• CFS engineering design is unique because of:
Buckling • Bearing • Finite Strip Analysis • Customizable Shapes
• AS4600 changes since 2005 include:
DSM Preference • G500/550 Inclusion • Inelastic Reserve • Shear
• Beam design checks include:
• Flexure: Global buckling → FSM → Local Buckling → Distortional buckling
• Shear: Shear yield → Shear buckling → With or without stiffeners
• Bearing: Plug in coefficients, !" for end/interior and 1- / 2-flange loading
• Load interaction: Flexure+Shear and Flexure+Bearing
• Deflection: Effective 2nd moment of area
• We performed examples with simply supported and complex beams

Questions?
4914 February 2019
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Appendix
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Designing a Cold-Formed Steel Beam Using AS4600:2018 and 2005 - Webinar

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