hancock's notes

8/18/2019 Hancock's Notes

1/104

Design

of

Cold -Formed

Australian

steel

institute

SteelStructures

Seminar

Presenter:

Professor Greg

Hancock,

Emeritus Professor,

and

Professorial Research

Fellow,

University

of Sydney.

www.steel.org.au

Acftvv)

l\)

67


2/104

DESIGN

OF

COLD-FORMED

STEEL

STRUCTURES

Introduction to

Cold-Formed Steel

Design

Emeritus

Professor

Gregory

Hancock

2


3/104

rut

uNivfRsmrof

W?

SYDNEY

Cold-Formed

Steel

Structures

Lecture

1

Introduction

to Cold-Formed

Steel Design

Emeritus

Professor

Gregory Hancock

AM FTSE

I

ywl

niHwuBinif

Wsgl

SYDNEY

Cold-Formed

Steel Design

Standards

Australian/New

Zealand

Standard

AS/NZS 4600:2005

North

American

Specification

-

2012

Developed

by the AISI

Eurocode 3

Part

1.3


4/104

1

TMf iisivntsrrv or

KW

SYDNEY

North

American

Specification

North

American

Specification

for the

Design of Cold-Formed

Steel Structural

Members

2012

Edition

Cold-Formed Steel Structures

AS/NZS

4600

:

2005

HEtsrvmsmrof

SYDNEY

Austrafcm/New

Zealand Standard'

Cold-formed

steel

structures

Design

of

Cold-Formed

Steel

Structures

(to

AS.NZS

4600:2005)


5/104

TM

LMVEHHTY Of

r-5

SYDNEY

Eurocode

3

Part 1 .3

Bimn

STAN

OA*

D

Eurocode

3

—

Design

of

steel

structures

—

Part

1-3:

General

rule*

—

Supplementary

rule*

for cold-formed

member* and

nheetln#

a ihw>h»«hi ' -< i

>

Bmnh

Slirdyffc

esj

cvpimcv

Australian/

New

Zealand

Standard

AS/NZS

4600:2005

Similar to the

North American Specification

Increased

range

of

steels

G450

-

G550

to

Australian

Standard AS 1397

steels

less

than

1

.0

mm thick can be

used fo r

structural members, i.e.

wall

studs

and

truss chords

in

steel

framed houses

>0.90fy and

0.90fu

used

in

G550

design


6/104

( Pwl

ni t

LMvutsmoF

WsW

SYDNEY

AS

1397-2011

Coating Classes

Zinc

(Z)

Zinc/Iron

Alloy

(ZF)*

Zinc/Aluminium (ZA)*

Australian Standard*

Continuous

hot-dip

metallic coated steal

sheet and strip—

Coatings

of

zinc and

zinc

alloyed

with

aluminium and

magnesium

Zinc/Aluminium/Magnesium

(ZM)*

Aluminium/Zinc (AZ)

Aluminium/Zinc/Magnesium

(AM)

New

in AS

1397

-2011

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

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ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

Roll-Forming

Machine

YDNEY


7/104

r*fcl

niriMMKsnroF

WiW

SYDNEY

Common

Section Profiles

and

Applications of Cold-Formed

Steel

Section

1

.2

Punching and marking

in

C-Section

YDNEY


8/104

3a

THF

t

M\

fKSI

TY

or

SYDNEY

(3)

Roof and Wall

Systems

of

Industrial,

Rural

and

Commercial

Buildings

Section

1.2(a)

ÿ

ÿ

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

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ÿ

ÿ

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ÿ

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a

ÿ

ÿ

ÿ

ÿ

Roof and

Walls

in

1

wvmsmroF

SYDNEY


9/104

31*7*1

THU MMWTVOF

SHW

SYDNEY

2D

Frame

with Purlins

N'5

\

QtoVTVe.

Purlin

and

Cleat

YDNEY


10/104

n

ÿ

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

10

(b)

Typical sheeting

profiles

for screwed

connections

me

imvmutyof

SYDNEY

Innovative

SupaZed™ Section

Simple

Complex

Z

(Zed)

sections

Simple Complex

C

(Channel) sections

(a)

Typical

Sections

(c)

Typical

sheeting

profiles

for

concealed fasteners

Fig.

1.1 Roof

and

Wall

Section

Profiles

THEUMVtRSfTYOP

SYDNEY

Concealed Fixed Kliplok™

Sheeting

Kliplok™

Concealed Fasteners


11/104


12/104

mf LMvatsrnror

few SYDNEY

AS

4084-2012

New

Features in 2012

Limit States

Design to

AS/NZS

4600

Loading

(action)

combinations for

racks

Geometric

non-linear

analysis

(GNA)

Extended

range

of

test methods

Australian

Standard*

Stool

storage

racking

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

n

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

SYDNEY


13/104

SYDNEY

(c)

Structural

members

for plane

and space

trusses

Section

1.2(c)

Tubular

(a)

Tubular

truss

top

chord

Tubular

-web

member

_

Tubular

bottom

chord

Bolted

or welded connections

(b)

Channel

section

truss

Channel

_

section

~

top

chord

Channel

or

~

tubular

web

member

-Channel

section

bottom

chord

Fig.

1.8

PlaneTruss Frames


14/104

DIE

UMVEKSTTYOF

WW

SYDNEY

(e)

Domestic

wall

framing

and

(f) Floor

bearers

and

joists

Sections

1.2(e)

and

(f)

rui i

Mvnsrnrop

SYDNEY

Wall and

floor

systems

N

%

Lippedor

unlipped

channel

stud

I

oggin

9ÿ%

%

Mechanical

or

welded

connection

k

Bottom plate

(a)

ÿMill

framing

Particle board

A

sheeting

r

Hat

section

i

i

joists

vj

|

I

Deep

hatsection

bearers I

or

UB bearers

Ajl

(b)

Floor

system

Fig.

1.10 Domestic Construction

14


15/104

Tltf UNIVERSITY

OF

SYDNEY

Braced Wall

Panel

15

SYDNEY


16/104

G550

Sheet

Steels

YDNEY

Deformed

elongated

grains

Structure

composed

entirely

ol

new grains

ew

grains

growing

New

grains

forming

/

/

Remnants

of

deformed

grains

Cold

reduced

to

thickness.

G550

less

than

1.0

mm thick

Stress

relief annealed.

Higher

fy

&

fu

and lower

ductility

-

Anisot

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

rm

university

of

SYDNEY

Two-storey

steel

house

composed

of

G550 Steel

16

ÿ


17/104

Typical

Stress-Strain

Curves

YDNEY

High

strength

steel

G550

Conventionalsteel

G300

Strain-hardening

range

th f

ixivritsrTVOF

SYDNEY

Roof

trusses

in Indonesia

composed

of

G550 Steel


18/104

Shopping complex

roof

composed

of

G550

Steel

SYDNEY

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

niluKivfftsmroF

Steel Framing Design

Guide

YDNEY

Aligns with AS/NZS

1170 and

AS/NZS

4600

Guidance

on roof systems,

wall

systems,

floor

systems,

bracing

systems, connectors

testing,

durability,

fabrication

and construction practice

Screw

capacities tabulated


19/104

rnEi

vujtvnrof

WsW SYDNEY

(g) Steel

decking for

composite construction

Section 1

.2(g)

r»1

nil

l

MVEKSI7YOF

W:

W

SYDNEY

Composite

decking

*

-

-S

Concrete

Reinforcing

mesh

Decking profile

Studs in

decking

Fig.

1.12 Deck

Profiles

for

Composite

Slabs

19

Concrete

Concrete

Interlockingtrough

sections

Ribbed decking Interm ittent

indentations

in

profile

(Embossments)


20/104

R»1

t>«

LMvtitsrrror

WW

SYDNEY

Portal

frames,

steel sheds

and

garages

Aligns with

AS/NZS

1170

and

AS/NZS

4600

Guidance

on shed

basics,

loads

(actions),

analysis,

design (especially effective

lengths),

and connections

Detailed

information

on

wind

actions

AUSTRALIAN

STEEL

INSTITUTE

STEEL SHED

GHOUP

Design

Guide

Portal

Frames

Steel

Sheds

and

Garages

111

Thlf Guide

applies

to steelframed

and

predominantlysteelclad

fhedt

and

garages

manufacturedfrom materialscertifiedor

tested

for

compliance with

Australian

Standards

June

2009

pWll

mi

LMvmsm

or

bW

SYDNEY

Special

considerations

in cold-

formed steel

design

Thinner

sections

High

strength steels

Cold-forming

processes

Connections

Section 1

.4

20


21/104

n«

uwvtKsnYOP

SsW

SYDNEY

Local

buckling

and

post-local

buckling of

ihin

elements

21

(a)

Stiffened

compression

Fig.

1.16

Compression Elements

(c)

Edge

stiffener

b)

Unstiffened

compression

element

lement

(d)

Intermediate stiffener

(e)

Effective

widthfor

a stiffened element

(f) Effective

widthfor

an unstiffened element

Multiple

stiffened segment

b

_

Intermediat&J

stiffener

nu

t

NIVmiflY

OF

SYDNEY


22/104

SYDNEY

Effective

Width Method

Actual Effective

ÿ

Effective

Actual

(a)

Stiffened element

(b)

Unstiffened

element

Fig.

4.3 Effective Stress

Distributions

Winter Effective

Width

Formula

Design

of

CoTd-Formcd

Steel Structures

(to

AS/NZS

46002005)

Section 4.3

where

k

= plate buckling coefficient

(depends

on boundary

conditions)

Uca-t

SYDNEY

Effective

Section in

Bending

Fig.

4.13

Bending

stress

with effective widths

ÿ

ÿ

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

a

ÿ

ÿ

ÿ

22


23/104

yWl

Till

CMWKSITY OF

WS

SYDNEY

Distortional

buckling

(a) Compression

(b)

Flexure

Fig. 1.18 Distortional

BucklingModes

DM

ÿ

23


24/104

*5*75

I

in*

im \

i

Rsrrr or

SYDNEY

Flange

buckling

model

Shear centre of

flange

and

lip

Lentroid

Flange-web

of flange

junction

and

lip

a;

I'i.niijc

M 2EI

IT

T~

M

-II'

1

o T

[b)

Symmetric

Web

Bending

(c)

Asymmetric

Restrained

Web

Bending

Fig.

5.9

Flange

Distortions

BucklingModel

D«sign of Cold-Formed

Steel Structures

I

(10

AS-NZS

4600:2005)

Section

5.3

The

flange

may

be

restrained

by

the

web

Flexural-torsional

(lateral)

buckling

YDMY

Lateral

Buckling

Mode

Lateral

Buckling

Mode

(a)

Iand

T-sections

bentabout

x-axis

Lateral

Buckling

Mode

Lateral

Buckling

Mode

(b)

Ha t

and

InvertedHat

Sections

bent about y-axis

Fig.

5.1

Lateral Buckling

Modes and

Axes

24


25/104

rwn

the

t

xivmsmf

or

WW

SYDNEY

Elastic buckling moment

The elastic buckling

moment

(/W0)

of

a

simply

supported I-beam,

monosymmetric I-beam or

T-

beam

bent about

the x-axis

perpendicular

to

the

web

where

Bridging

minimises

flexural-torsional

buckling

l \ .i

,

ÿMi

I

ÿ

U

1

JM

as

ÿ

i

®

yi:

25

Section

5.2


26/104

TMEUMNEHSmrOf

SH

SYDNEY

Propensity

for

twisting

Eccentricity

from

shear

centre

(e)

Load

(P)

Centroid

Shear

centre

Torsional

deformation

lexural

deformation

f

of shear

centre

/

/

Torque

=

P e

(a)

Eccentrically

loaded

channel

beam

26

SYDNEY

Bridging

minimises

twisting


27/104

nn

i

MvetsnVor

SYDNEY

Bridging/ Bracing

Systems

/

Sheeting

£

it

r

§

Bridging members

x

(a)

Bridging

or

bracing

members

Stiff

support

ÿ

Bridging

may

be omitted

/

Sheeting

Sheeting

fb)

Alternating

members

Cleats

at

supports

E

y5

-3

Stiff

perimeter

member

ft?

(c)

Diaphragm

connected

to

perimeter

support

Sheeting connected at

ridge

Sheeting

Bridging

may

be

omitted

(d)

Opposing

and

balancing

purlins

and

sheeting

27

no

LMVUtsrrror

SYDNEY

Buckled

web

Concentrated

force

Fig.

6.6

Web Crippling

of an

Open Section


28/104

the

university

of

SYDNEY

ÿ

I/vvvac-M

_

Web

crippling

under

bearing

Flanges restrained

Flanges

not

restrained

HSS|

nif UNIVERSITY

or

WsW

SYDNEY

Web

crippling empirical

equation

(i) Back lo back

(ii) Single

web (iii)

Single

web

channel

beam

(stiffened

or partially

(unstiffened

stiffenedflange)

flange)

(a)

Restraint

against

web rotation

Bearings

FreeJ

endl-

-tÿ1~

HH

ÿBearing

fb) Bearinglength

and

position

Dusjfln

of

Cold-Formed

Steel

Suocturos

(to

A&'NZS

46002005)

Section

6.6

New

in AS/NZS

4600:2005

The

design

equation

is:

Rb

=

7777777777777777777777777777777

73ÿ77/

Bearing surface

(c)

Section

geometry

CtwJv

sin

0

Fig.

6.7

Factors affecting We b

Bearing

Capacity

ÿ

ÿ

ÿ

ÿ

ÿ

n

n

n

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

28


29/104

fW

j

THE

t'MVERSTTY OF

WsW

SYDNEY

Corrosion

Protection

Zinc

(Z,

ZF),

Aluminium-Zinc (ZA,

AZ)or

Aluminium/Zinc/ Magnesium

(ZM,

AM) coating

protects the steel no matter how

thin

Coated and

painted

steel

can be passed

through roll forming machines

without

damage

29

OLD

TASL&

SYDNEY

Coating classes for

corrosion

conditions

Coating

Class

Application

ZlOO A

very thin, smooth and ductile coating for

higher

finishes

in

internal,

protected environments, eg

for refrigerators

and

dryers

(in

conjunction

with paints).

Z200

A light

coating for internal

protected

environments such as

ducting

and

washing

machines

Z275,

Z350 General

purpose

coatings.

Z450,

AZ150

Recommended

coatings

for

typical

exterior

protection,

eg

roofing and

accessories,

and

cladding.

Z600,

AZ200

Heavy duty

coatings designed

for

culverts

and bo x

gutters.


30/104

ruELsivfusmroF

WsW

SYDNEY

Connections

in thin

sheet

steels

Bolted

connections

Screwed

connections

Welded

connections

Riveted

connections

Power

actuated fasteners

(PAFs)

Bolted

connections

in

shear

YDN

1

(a) Single

bolt

(rf = 1)

CP CP

dr

O

l.5df 3df

(b)

Three bolts in

lineof

force

(rf

= t)

(c)

Two

bolts across

line of force

(r

f

=

1

)

fd)

Double

shear

(with

washers)

'e)

Single

shear

(with

washers)

ÿ

)kJ

QjsLb

Tojÿt

30


31/104

TUHlNÿ

N

tj

I

(a )

Thicknesses

el

.

Pi

(b )

Nominal screw

diameter

(df

)

e]>

3df,

pi

>3df

N

e2>1.5df,p2>3df

(c)

Minimum

edge

distances and

pitches

Fig.

9.15

Screws

in

Shear

_

|

n»

iMvmsrrror

r-5

SYDNEY

Bearing / Tilting

Failure

Vl

ÿ

v

:WSki'

ÿm

v

x

31


32/104

*PW|

THE UNIVERSITY

OF

r.-jrj

SYDNEY

Welded

connections

Arc

spot

weld

(puddle

weld)

Arc

seam

welds

(e)

Flare-bevel weld

Fig.

9.1

Fusion

Weld Types

sydney

Failure

modes in

transverse

fillet welds

r

£.

Geometry

-

Inclinationfailure

5k

Weld

shear,

§§ ÿ

weld

teanng

If

& plate

teanng

Failure

modes

(a)

Single

lap joint (TNO

tests)

4

Sheet

w

tear

Geometry

and

failure mode

(b)

Double

lap joint (Cornell

tests)

32


33/104

§

sydney

Failure

modes in fillet welds

HAZ Failure

3.0

mrr

I-4.-I

(a)

Single

thickness of sheet

(c)

Minimum

edge

distance

(arc

spot welds)

(b)

Double thickncss

of

sheet

(d) Geometry

andminimum

edge

distance

(arc

seam

welds)

VmÿsID

W £)

33

Weld throat

failure


34/104

IMIfNIVfKmrOF

rjrj

SYDNEY

Failure

modes in arc spot

welds

(a)

Inclination failure

Buckled

plate

(b) Tearing and

bearing

at weld

contour

Buckled

plate

(c) Edge

failure

(d)

Net

section

failure

(e)

Weld

shear

failure

SYDNEY

Flare welds

w1

ii

(a)

Flare-bevel

weld

Jl

-OTfe'K

-

t

w

is the lesser

of

0.707twi

and

0.707tW2

filled flush

to

surface or

(5/1

6)R filled flush to

surface

ÿX

(b)

Flare V-weld

Fig. 9.5

Flare

Weld Cross-Sections

34


35/104

Power

Actuated

Fasteners

(PAFs)

YDNEY

JL>8

Figure

2 PAF

Geometric

Variables

Used

in

the

Strength

Prediction

Model

New

Clause E5 of

NAS

2012

Includes

tension

(pull

out) and

shear

|ywl

rMUMvmurvof

WsW

SYDNEY

Second Order Elastic

Analysis

Appendix

2

of NAS

2012

Members shall satisfy the

provisions

of

Section

C5

(Section

3.5 in

AS/NZS

4600)

with

the

nominal

column

strengths

determined using

Kx

and

Ky = 1.0

(i.e. effective

length leb

in

AS/NZS 4600

equal

to

the actual length),

and ax

and

ay

=

1

.0

and Cmx

and

Cmy

=

1

.0 .

Flexural and

axial

stiffness shall be

reduced using

E*

in p lace

of E

E*

=

0.8 Tb E

where Tb

depends on the rat io of the load to the yield load

and

is

basically

1.0

for

elastic problems and reduces above

0.5

Py

35


36/104

|

>*741

fMf

UNIVERSITY

OF

WsW

SYDNEY

Conclusions

High

strength cold-formed sections can

be

designed

safely

to AS/NZS 4600:2005

Cold-formed

sections offer

many

advantages over

hot

rolled

sections

including

high

strength,

light weight and ease

of

fabrication

Cold

-formed

sections

allow

for

innovative

building

products

to

be

developed

ÿ

Gothic

j

j

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

36


37/104

DESIGN OF COLD-FORMED

STEEL STRUCTURES

Direct

Strength

Method

of

Design

of

Cold-Formed

Beams/Purlins

Emeritus

Professor

Gregory

Hancock

37


38/104

THttMvtusrrrop

3ST

SYDNEY

Cold-Formed

Steel

Structures

Lecture 2

Direct Strength

Method of Design of Cold-

Formed Beams/Purlins

Emeritus

Professor

Gregory

Hancock

AM FTSE

r

Oitf? Wirt}

&c7

1

v(r

ÿ

SYDNEY

Direct

Strength Method

(DSM)

First proposed

by

Schafer

and Pekoz

in

1998

Included

in

the

2004

Supplement

to the North American

Specification

as

Appendix

1

and

now in

NAS

2007

Included

in AS/NZS 4600:2005

as

Section 7

Developed

for

columns

and

beams

Not developed explicitly

for

beam-columns

Not developed explicitly and

calibrated

for

shear

38


39/104

M l

the

uxivmsmr


40/104

IP

sydney

Finite

strip

subdivision

of edge-stiffened

plate

Cubic

polynomial

transversely

Flexural

displacements

of

plate

Membrane

displacement

of

edge

stiffener

Linear

Sine curves

(b)

Membrane

an d

flexural

buckling

displacements

G ea

sydney

Signature curve

of

buckling

stress

versus

half-wavelength

For Beams

Each

buckling moment

is

calculated

from

the

buckling

stress by

multiplying by

the

gross section

modulus

(Zf)

Local

Mode

(M0,)

Distortional Mode

(Mod)

Flexural-Torsional Mode

(M0)

\


41/104

I

yW

I

mr

MNFRurvor

SW

SYDNEY

DSM

Flexural-Torsional

Buckling

Moment

Capacity (Mbe)

For

For

M0

<

0.56

My

Mbe

=

M0

Eq.

7.2.2.2(1)

2.78M

>M0

>0.56M

ÿ

10

(

10

Mv

I 9

36M.

Eq.

7.2.2.2(2)

For

\

S3

Eq

7-2

Z2(3)

where

M0

=

Elastic FT

buckling

moment

m0

>

2.imy

Mbe

=

My

Mv

=

Yield

moment

of

Gross

Section

ÿ

ÿ

ÿ

Q

a

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

41

Q

Flexural-torsional,

distortional

and

local

buckles

M

i

vwiumror

SYDNEY

Local

Buckle

Simulated

Wind

Uplift

Testing

Distortional

Buckle


42/104

THEUMVEKSTYOF

SYDNEY

DSM Local

Buckling Moment

Capacity (Mbi)

m

Eq. 7.2.2.3(1)

Eq.

7.2.2.3(2)

where

M0i

=

Elastic

local

buckling

moment

Mbe

=

Flexural-torsional

buckling

moment capacity

Eq.

7.2.2.3(3)

/\/

=mmm

DSM

Distortional

Buckling

Moment

SYDNEY

Capacity

(Mbd)

Eq. 7.2.2.4(1)

Eq. 7.2.2.4(2)

where

M0d

=

Elastic distortional

buckling

moment

Mv

=

Yield

moment

Ad

Eq.

7.2.2.4(3)

42


43/104

f

1

nif

i

sivfrmtv

oj°

WiSl

SYDNEY

Direct

Strength

Method fo r

beams

°

Distortional tests

x

Local

tests

cvtf

Winter

Local curve

.....

istortional

curve

'°t0

Mo%

S°

o

i qs

(

12. 1

)

to

(12.3)

and

(12.7)

to

(12.9)

Eqs

1

12.

10)

to

1

12

12)/ÿÿ

and

(

12.16)

to

(

12 .

18)

Strength

versus

Slenderness

M,

is the

yield

moment

ÿ

or

VM7u

JVJX)

VpaCÿA

-

q,vq

efctfo

LxA&yit*

(jp

sydney

Direct

Strength Design

Moment

The Direct Strength Design

Moment

is

the

least of:

ÿpMbe

i

cpMbl

and

(pMbd

where

(p

is

the

Capacity

Reduction Factor

equal

to 0.9

43


44/104

tails

%1J

UMIT* *0 *

fM-Ql-AUIIKO

COMTMOIO*

Mnuu

Till

isi\msin

of

SYDNEY

Prequalified

compression members

4 *n

0-W

For

prequalified compression

members, use

cp

=0.85

For non-prequalified

compression

members,

use

cp

=0.80

NAS 2012

has

an

extended range

of

prequalified

members

including

return lips

rPwl

THE LMVIKSITYOF

Ws57

SYDNEY

Prequalified members

subject to

bending

ÿ

For

prequalified

members,

subject

to

bending, use

cp

=0.90

For non-prequalified

members

subject

to

bending, use

cp

=0.80

NAS 2012 has an

extended

jflHHjBi

range

of

prequalified

members

including

return

lips

44


45/104

| 1 ni t

t

sivi

emr of

rif

SYDNEY

10.5.2 Simply

Supported C-Section

Beam

Example

Problem

Determine

the nominal member moment

capacity

of

the

C-section beam

in

Example

5.8.1 using

the

Direct

Strength Method.

The section geometry

is shown

in

Fig.

4.12 and

the beam geometry

in Fig.

5.22.

The section dimensions

are given

in

Example 4.6.3

and the beam

dimensions

in Fig. 5.22.

Fig. 4.12

D

=

200mm

B

=

75 mm

t

=

1.5 mm

dL

=

16.5 mm

fy

=

45 0

MP a

Fig.

5.22

®

SYDNEY

From

Example

5.8.1

C. Design Load on

Braced Purlin

C1.

Clause 3.3.3.2.1

Members

subject

to

lateral

buckling-

Open

section members

(a ) singly-symmetric

sections.

Uplift on

tension

flange

q

_

Lateral

+

torsional

brace

when included

/ez=

/e

y=

3500

mm

/ez=

/ey=

3500 mm

L =

7000

mm

M3

=

7wL2/128

BMP

r

.

M5

=

X

m4

m5

Mmax

M6

=

(a) Loading

and

bending

moment distribution

Fig 5.22

Elastic

Buckling Moment

\m o

CbAroXyjj

oyJ

oz

(Eq. 3.3.3.2(8))

C„

=

12-5

(MmaJ

2.5(MmJ+3(M3)+4(M4)-

(Eq.

3.3.3.2(9))

-3(M5)I

a

45


46/104

THFiMvttsmror

I

ÿsydney

From Example 5.8.1

Buckling

Stresses

and Buckling

Moment of Full Section

=

113.86MPa

(Eq. 3.3.3.2(11))

,

_

GJ

Ar

2

+

ATo\

V

7T2EI.

103.36MPa

(Eq.

3.3.3.2(12))

Cb

=

1.299 (Eq. 3.3.3.2(9))

(Eq.

3.3.3.2(8))

Yield Moment of

Full

Section

M0=

7.612 kNm

M= 15.269

kN m

(Eq.

3.3.3.2(7))

inn

Signature

Curve for

C-Section

10

Co/yCT

Frrfji

\

\

r i

Distortional

\

\

mode

A

Local

\ mode

\

\

J


47/104

ÿRB

IT»f LMVfitsmroF

WB

SYDNEY

A.

Compute the

Elastic

Local

and Distortional

Buckling Stresses

and Moments

using

the Finite Strip

Method

fol

=

303.9 MPa at

120 mm

half-wavelength

fod

=

256.2

MPa at

600

mm half-wavelength

Zxf

=

3.393

*104

mm3 (Ex. 5.8.1)

Mol=

Zxffol

=

10.311

kNm

M0C)

=

Zxf

fod

=

8.693

kNm

r-9&]

r»«

iMvuaiiYor

W?

SYDNEY

B

Compute

the Inelastic Lateral

Buckling

Moment Capacity

(Mbe)

Since

Mbe

=

M0

=7.612

kNm

C Compute the Local

Buckling Moment Capacity

(Mbl)

Since

QjUQ ,

use

Eq.

7.2.2.3(2)

ÿ

n

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

[

|

O

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

47


48/104

£*5*1

I

HI

l

MVEKSITYOF

S-W

SYDNEY

D

Compute

the Distortional

Buckling

Moment

Capacity

(

Mbd

)

Since

—

l~

N\l>

N i

I

*Wll

T>if

t

Mvursn

t

of

WSW

SYDNEY

E.

Nominal

Member Flexural

Moment

Capacity

(Mb)

Mh

is

the

least

of

Mbe,

Mbl

and

M,

Mb

= 7.139

kNm

This

can

be

compared

with

6.665

kNm

in

Example

5.8.1

using the

effective width method.

48


49/104

[•ÿwl

rmcNivnsmroF

P ig

SYDNEY

Summary

The

Direct

Strength

Method

(DSM)

uses

the same

equations

for

the

flexural-torsional

buckling moment

and

yield

moment

of

the

full

section

as the

Effective Width

Method

(EWM)

The DSM

computes

the elastic

local

buckling

moment and

elastic distortional

moment of

the

full section

from

the

signature

curve

and

there

is no need

to compute

effective

widths.

The

DSM

Moment

Capacity is

simply

taken from

the

least

of

the

Inelastic Lateral

Buckling Moment

Capacity

(Mbe)

Local

Buckling

Moment

Capacity

(Mbl)

Distortional

Buckling

Moment

Capacity

(Mbd)

wÿm

ÿ

Sydney

I

Signature curves

for

C-Section

and

Supacee

Maximum

Stress

in

Section

at

Buckling

(MPa)

Buckle

Half-Wavelenuth

(mm)

49


50/104

ug

sydney

Failure

Modes

of

SupaCee

Section

Members

M

Test Series

4

ÿ

/£L~i

*'ÿ 1

With

straps

(local

buckling) Without

straps (distortional

buckling)

M9n|

ntflMVIKSfTYOF

WsW

SYDNEY

New

developments in DSM

2012 Edition of the North

American

Specification

has

3 significant

extensions

to

the

DSM.

These are:

Inclusion of holes

in

both

flexural

and

compression

members

Inclusion

of inelastic

reserve

capacity beyond

My for

stocky

sections

in

bending

DSM

design

for

shear,

and

combined bending

&

shear

50


51/104

Distortional

buckling

in compression

with

holes

YDNEY

Yielding at net

section

DSM curve (no

holes)

Transition

to

P

NAS 2012

rules

courtesy of AISI

Distortional

buckling with holes

°d2'' y

Based on research

at

Johns Hopkins

University

(Moen

and

Schafer)

Elastic

buckling

Ad2

Assumptions

for this

plot

°ynet-0'°0Py

0.5

1

1.5

2

distortional

slendernessA

Inelastic reserve

capacity

of

beams

\n

inelastic

bending

reserve

considered:sections

1.2.2.2.2

and

1.2.2.3.2

Elastic

Buckling

inelastic

bendinpX

V.

reserve

ignored:

sections

1.2.2.2.1

and 1.2.2.3.1

post-buckling

DSM Local

Buckling

Strength

DSM Distortional

Buckling

Strength

2 3

_

slendcrncss

=

*-Hÿ)

I

ÿ2i-(l-0.24—

)

V—

as

M,

J

I

My

t03\,

,05

51

NAS

2012

rules courtesy

of

AISI (Shifferaw

an d

Schafer

JHU)


52/104

DSM

design

fo r shear

Research

by

Pham

and Hancock

at

the University

of Sydney

Approved

fo r

the 2012 Edition of

the

NAS as

Ballot

326C

Considers the

case of

the whole section

in pure

shear

Based on a

signature

curve for pure

shear

recently

developed at the

University of Sydney

MPnl

THECMVUrSITYOF

SYDNEY

niHMvmsmroF

SYDNEY

Shear flow distributions

in

a

lipped

channel

80 mm


53/104

SYDNEY

Buckling

modes

from

spline

finite

strip

method

The

intermediate

stiffeners

can

enhance the

shear

buckling

stresses

Plain

C

and Supacee with Aspect

Ratio 1:1

The

flanges

and lips can

have a

significant

influence

on improving

the

shear buckling

capacity of

thin-walled

channel

sections

Plain C

and Supacee

with Aspect Ratio 2:1

Shear

design

curves in

DSM format

YDM-Y

AlSI-Shear Curve

Elastic

Buckling

Curve

Tension

FieldAction

Curve

----

SM

ProposalC urve for

Shear

/

_

\04

/

\

V

v

r

cr

V

V

\

y

/

V

y

y

includes TFA

V=V,

53

excludes TFA

Vcr is the

shear

buckling load

of

the

whole

section


54/104

54

TMF

IMMHSin

w

SYDNEY

Shear

Tests compared with

DSM

Shear Proposals

1.2

-n

+

l

-V

v

a

ÿ

ÿV.'kx\.

4

X*0

AlSI-Shear

Curve-without

TFA

ÿ

-°

ÿ

Elastic Buckling Curve-Vcr

ÿ

c

n.

:/

X

—

Tension

Field

Action

(TFA)

Curve

*

ÿ

DSM Proposed

Curve for

Shear-with

TFA

A

C 15015

ÿ

C 1

50

1

9

\

*

I

5024

A

C20015 \.

m a

—

»-

—

_

O

C20019

N .

O

C20024

X

SC15012

ÿ

X

SC

15015

+

SCI

5024

ÿ

X

SC20012

ÿ

X

SC20015

+

SC20024

a

UMR-Shear Tests

ÿ

ÿ

ÿ

UMR-Excluded

Shear

Tests

i i i

i

ÿ

I i

0 0.2 0.4 0.6

0.8 1.2

1.. 1.6

1.:

2

2.2

2.4

2.6

2.)

Failure

mode

of SupaCee

section

V

Test

Series

SYDNEY


55/104

ÿ

ÿ

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

n

n

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

THE

UNIVERSITY OF

SYDNEY

Buckling

modes

in

pure shear

Local buckling

Distortional

buckling

WsW

SYDNEY

Signature

curve

for plain

lipped

channel

in pure

shear

Maximum Shear

Stress

in

Section

at

Buckling

(MPa)

iiiiim

annum

Buckle Half-Wavelength

(mm)


56/104

TUf

tMVEHyTYOF

WsW

SYDNEY

DSM for

shear

-

Conclusions

Extensions

of the

Direct

Strength Method

(DSM)

of

design

of

cold-formed

sections

for

shear have

been

proposed

The

proposals are based on the shear buckling load Vcr

of the whole section

in

line

with

DSM

philosophy

A signature curve for

pure shear

has

been

developed to

allow easy calculation of Vcr for

use

in

the

DSM

Local

and distortional buckling modes in

pure

shear

have

been

identified using the SAFSM

The proposals

have

been

approved

as

a ballot

(CS 326C)

of

the

American

Iron

and

Steel Institute

Specification

Committee

(Sp

Sydney

DSM

fo r Shear

with

Stiffeners

Research currently underway at

the University

of Sydney

.

--->

—

i

56


57/104

ÿ

ÿ

(\aA

0ÿ

o

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

SYDNEY


58/104

THE

UNIVERSITY

OF

ÿ

SYDNEY

DSM

design

for

purlins

Vacuum

test rig

with

continuous

lapped

purlins

under wind

uplift

Vacuum

test

rig

YDNEY

Simulated

upwards loading

Simulated

downwards

loading

58


59/104

7

metre

simple

span

One row

of

bridging

nirc-NivfitHTYor

SYDNEY

Vacuum rig test

programs

Table 1. Purlin-Sheeting

Test

Programs

Performed

at the University

of Sydney

Series

Loading

Spans* Bridging

t

Sheeting

Type

Rafter

Fixing

SI

Uplift

3-span lapped

0,1.2

Screw

fastened

Cleats

S2

Uplift 2-span lapped

0,1,2

Screw fastened Cleats

S3 Uplift

Simply supported

0,1,2 Screw fastened Cleats

S4 Downwards 3-span lapped 0,1

Screw

fastened Cleats

S5

Uplift

Simply

supported

0, 1,2

Concealed fixed Cleats

S6

Uplift 3-span lapped

1

Concealed fixed Cleats

S7

Uplift Simply

supported

0,1,2

Screw fastened

Cleats

S8 Uplift

Simply supported

3-span lapped

1,2

Screw fastened Cleats

*

3x7.0 m

spans

with

900

mm laps between

bolt

centres for

3-span

lapped

configuration

2x10.5

m

spans

with 1500

mm

laps

between

bolt

centres

for

2-span lapped

configuration

1x7.0

m

span

for

simply

supported

configuration.

t

0:

Zero

rows

of

bridging

in each span

1

: One row

of

bridging in each span

2:

Single

and

double

spans:

Tw o rows of

bridging

in

each

span

Triple spans:

Tw o rows

of

bridging

in the

end

spans,

one row in

the central span

59

SYDNEY


60/104

sydney

Flexural-torsional

buckling

model

for

M0

FELB (Finite

Element

Sheeting

screw fastened

to

top

flange

Lap

Lap

\

i~i

Lateral

Buckling)

d5

—

UP*

-

Lateral andtorsional

brace

End

span Interior

span

j

(a)

Element

Subdivision

ÿ

FELB

approach

models

full

length

lapped

purlin

inward

/

-

outward

|

\

|

N.

Lateral

fciHffi

\

N

\/

outward

of

centroid

Outward

loading

Lateral

of

centroid

ÿÿÿ ÿyÿInward

loading

(c)

Buckling

modes

Fig. 5.6

BMD

and

Buckling

Modes

for

Half

Purlin

ÿ

Till

UNIVERSITY

i

sydney

Flexural-torsional

buckling

model

for

Mo

Cb

approach

uses

BMD

between

brace

points

=

Elastic

buckling moment

m3

Mi

Mm*

MS

(a) Positive

moment

(or

negative)

alone

12.5M,,,

1

mm

2.5Mmax

+

3M3

+

4M4

+

3M5

m3

m4n

_pfc

Ms

(b)

Positiveand

negative

moments

60


61/104

IM

UMVBOmrOF

SYDNEY

ydney

Design programs PURLIN 4600

and SUPAPURLIN

Deform

Stress

Strength

Service

f

*?

ÿ

O

ÿ

Inwards

C

Outwards

Al

Equal

to

Span 1

Bridging

Span

Rows Locations

1

|7iJ

I

50

1

50

2

| 33

1

B |

33

3

|7jJ

1

50

1

50

*

pfij

I

50

1

50

r-ji

rii

Ffjl

r±i

rd l

Fzjl

Fd

rn

50

)

50

1

|

_

|

|

I-

50|

50;'

I-

P ~

SupaPurlin

1

J)

Analysis

and

Design

of

Supa

Purlins

Al

Copyright

© 2003

-

University

of

SydneT

SERVICEABILITY

DESIGN

Maximum

Deflection

The

maximum deflectionis

5

=

-53.92 n

Located at 4000 mmfrom left

support

This

represents a span/deflection

ratio

I

Combined

bending

and

shear

Interaction

relationships

61


62/10462

Experimental

rig for

V

and

MV

tests

niE

lSIVFRMTVOF

SYDNEY

Loading

Rain

bphencal

Head

U

wo C

hannel

Section Members

LVDT 7

LoadTransfer

Plate

rlali Round

BU ]

LVD

8

A|_ÿ

ip-.

LVUTs

1,4

LVDT*

3.6

200-

V

Series

200-

V

Series

400-

»ÿ

Series

1 400-1- Senes

50

Shear

Diagram

m

:

1

Moment

Diagram

Interaction

with

Ms]

\

Vv

based

on DSM

p

AC15015

ÿ

C15019

C

15024

A

C20015

ÿ

C20019

o

C20024

X

SC15012

X

SC15015

+

SCI5024

X

SC20012

X

SC20015

S SC20024


63/104

riir

iwvEBTTTor

SYDNEY

I

Comparisons

with tests

Cb

approach

[&o

7.0

6.0

5.0

4.0

+

3.0

2.0

1.0

0.0

O

Test Load/

EWMLoad

Test Load/

DSM

Load (Proposal

2)

A

Test Load/EWMLoad

-

Downwards

A

Test Load/E6M

Load

(Proposal

2)

-

Downwards

1

2

O

o

a

O

i

i

o

o

A

8

l

1/0

1/1

1/2

2/04)

2/1-1

2/2-2

3/0-0-0

3 /1 -1 -1 3 /2 -1 -2

Span

I

Bridging

Configuration

THE

UNIVERSITY OF

SYDNEY

I

Comparisons with

tests

FELB

approach

12.5

12.0

1.5

1

0.0'

s

8

O Test

Lead/

EWMLoad

Test Load/ ESMLoad

(Proposal

2)

A

Test Load/

EWMLoad

-

LbwrAords

A

Test Load/

ESMLoad

(Proposal

2)

-

Dcrv\rr»\ards

1

o

o

D

O

a

i

»

ÿ

8

9

I

A

A

o

8

1/0

1/1

1/2

2/0-0

2/1-1

2/2-2

3/0-0-0

3/1-1-1

3/2-1-2

Span

I

Bridging

Configuration

ÿ

a

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

D

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ


64/10464

Sheeting shear

and flexural

stiffnesses

YDNEY

Line

of

support

(b) Sheeting

shear

stiffness

(k )

Line

of

support

(a)

Plan of sheeting

(c) Sheeting flexural

stiffness

(kÿ)

Effect

of torsional restraint of

sheeting

(krs)

Yinn

Sheeting

Torsion

Stage

Vertical

Bending

Stage

(a)

Deflection

Flange

element

Spring

stiffness

K

Conventional

bending theory

with I

computed

for

twisted section

Torsion Stage

(b)

Models

Vertical

Bending Stage


65/104

0p[VJ\

_

NCTVTdD

65

M l

mi

i

siviksiTY

or

SYDNEY

Conclusions

The

DSM and

EWM

methods

have

been

compared

with

a range of vacuum

rig tests on purlin

sheeting

systems

with single,

double and

triple spans.

Both methods

produced safe designs with

the

DSM

slightly less conservative

than the

EWM

in

general.

An

extension

of the

DSM to shear and

combined

bending

and shear has been

proposed

with the

section moment

capacity

Ms

based on

Msi

The

proposals

produce

safe

designs.


66/104

DESIGN OF COLD-FORMED

STEEL STRUCTURES

Connections

:

.

Emeritus

Professor

Gregory

Hancock

66


67/104

n«n

n«l

MVFRVTY

OP

WjW

SYDNEY

Cold-Formed

Steel

Structures

Lecture 3

Connections

Emeritus

Professor

Gregory

Hancock

AM

FTSE

Connections

in

thin

sheet steels

Bolted

connections

Screwed

connections

Welded

connections

Power

actuated fasteners

(PAFs)

67


68/104

nil

i

v\ Km;yi>«-

.,

.

.

sydney

Bolted

Connection

in

Shear

Geometry

(a) Single

bolt

(ff

-=

1)

0

0df

I.Sdf

3df

lb)

Three bolts

in line

of

force

(rr

y

)

—

'

[c)

Two

bolts

across

line

of force (rf

=

1

[d)

Double shear

(with washers)

(e) Single

shear

(with

washers)

Failure

Modes

in

Bolted

Connections

in

Shear

SYO\l

Y

(a)

Tearout failure of sheet

(Type

I)

Buckled

plate

(b) Bearing failure of sheet material

(Type

II)

(c)

Tension failure of

net section (Type

III)

(d) Shear

failure

of

bolt

(Type

IV)

68


69/104

Tlif

LMVftSmrOF

SsW

SYDNEY

Tearout

and

bearing failures

Failure Type

ÿ

I

o

II

I

and

II

a

n

and

II I

Tearout

Failure

of Sheet

(Type

I

(c )

Net

Section Tension Failure

ii

Sydney

Failure

Modes

in G550 Steel

Bolted

Connections

0.42

(.550

CPU

ranv.

(a)

End

tearout

failure (b)

Bearing

Failure


70/104

ime

university

or

Snw

SYDNEY

Tearout and

bearing failures

1 1

_

fu/fy>

1.08

T

1

*

/>

s-

a 7

:

/

ÿ

Failure

Type

SNs\

fbu

e

o

I

fu

dh

a

11

/

i i i

i

Iand

II

i i

Tearout Failure of Sheet

(Tvpe

Bearina

Failure of

Sheet

(Tvoe

II

0

1 2 3

4

5 6

7

e/dh

_

(b) Single

shear

connectionsfwithoutVashers

SYDNEY

Eurocode

Bearing coefficient

C

—

AS/NZS

4600

:

2005,

NAS

d/t

22 : C

=

1

.8

AS/NZS 4600:

1996 AISI

£c

50

CSA-S136

d/t

15: C

=

2.0

15

d/t

20

25

Fig.

9.

1

3

Bearing Coefficient C

for

Bolted Conections

30

70

The modification

factors

depends

on

the

type of

bearing and

is

specified

in

Table

5.3.4.2(A)

of AS/NZS 4600


71/104

Sp

SYDNEY

Modification factor a for

bearing

Table

5.3.4.2(A)

Single

shear

and outside sheets

of

double

shear

With

washers under both bolt head

and nut

1.00

Same

as above

without washers

or with only

one washer

0.75

Inside

sheets

of

double

shear with

or

without

washers

1

.33

(jg)

IN \i V. .

,

'

I

I

wSYDNEY

Modification

factor a fo r bearing

New

in

NAS 2012

Table

E3.3.1-2

Single

shear

and outside sheets of double

shear

With

short slotted

holes

parallel

to

the

applied

load

and without

washers

under both bolt

head

and

nut,

or

with

only

one

washer

0.70

Single shear and

outside

sheets

of double shear

with

short

slotted holes

perpendicular

to

the

applied

load and

without washers under

both bolt

head

and

nut, or with only

one

washer

0.50

Inside

sheets of

double

shear

using

short slotted

holes

perpendicular

to

the applied load

with

or

without

washers

0.90

71


72/104

Net

section failures

YDNEY

(1

-

rf

+

2.5rf(df/sf))

f

o

One

Bolts

<

a

Tw o

*•

ÿ

Three

Multiple

bolts

case

df/Sf

(b)

Single

shear

without washers

Net section failures

YDNEY

0.1

+

3.0

(1

-0.9rf

+

3rf

(df/sf)

f

o

One

Bolts

<

a

Tw o

ÿ

Three

Multiple

bolts

case

df/sf

(a)

Single

shear

with

washers

ÿ

ÿ

a

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ


73/104


74/104

die

i

MVMsmrof

WjW

SYDNEY

A.

Plate Strength

for Net Plate

Clause

5.3.

1

df

= 12 mm

Clause

3.

2

dh

=

diameter of standard hole

=

df

+

2.0

=

14 mm

An

=

(b-dh)t

=

{80 -

14)2.5= 165

mm2

Nt

is the lesser

of

Nt=\fy

=

(80

x2.5)

x

300

=

60000

N

=

60.0

kN

Nt=

0.

85

kt

An

fu

=

0

.85

x

1.0

x

165

x

34 0

=

47685

N

=

47.69

kN

<

60.0

kN

(Eq.

3.2.2(1))

(Eq. 3.2.2(2))

vn

ITHCCMVUSITYOF

SW

SYDNEY

Hence

Nd

=

(p

Nt

=

0.90

x

47.69

=

42.92 kN

Clause

5.3.3

Where washers

are provided under both

the bolt head

and the nut for multiple bolts

in

the

line

parallel

to

the

force.

Nf

=

fuAn

(Eq. 5.3.3(3))

Nf

=

340

x

165 = 56.1

kN

Now

0=0.55

fo r

single shear connections

in

Clause

5.3.3(a)

Vw

= 0.55 *56.1

=30.85

kN


75/104

p£*yT|

niECMYMsmrof

WW

SYDNEY

B.

Number of Bolts

Required

Strength

Grade

4.6,

hence

fuf

-

400

MPa

Clause 5.3.5. 1

Vfv

=

0.62fufAo

= 0.62

x

400

x

113.1

=

28048

N

=

28.05

kN

Hence

ÿ

=

0.80 for Clause

5.3.5.1

Vtv

=

0.80

x

28.05

=

22.44

kN

3(/>

Vlv

=

67.32

kN

>

30.85

kN

If

the

shear

plane

contains the bolt

thread,

then

the

minor

diameter area

of

the

bolt

should

b e u se d fo r th is

calculation. In

this

case

30V/v

=

43.3 kN

>

30.H5

kN

(Eq. 5.3.5.1(2))

ru n

wvtptsfiYor

riW

SYDNEY

C. Check

Bearing Capacity

Clause 5.3.4.2

Vb

a

C

fu

dft

(Eq. 5.3.4.2)

Table

5.3.4.2(A)

(Modification Factor

d)

Single

shear

with washers

under

both

bolt head

and nut

Table 5.3.4.2(B)

(Bearing

Factor

C)

Hence

a

=1.0

MS9M

m

Vb

= 3.00

fudft

=

3.00 x340

x

12

x

2.5

=

30600

N

= 30.6

kN

ÿ

=

0.60 as given

in

Clause 5.3.4.2

Vb=

78.36

kN

3Vb

= 55.08 kN

>

30.85

kN

75


76/104

nafel

IMF UMVERSTY

Of

jSJ

SYDNI \

D.

Tearout

Clause

5.3.2

Use

e =

25 mm

Vf

=

te

fu

( Eq. 5.3.2(2))

=

2.5

*25 *340 = 21250

N

= 2125

kN

Now

$

= 0.70

for

Clause 5.3.2

since

fu/fy

=

1.13

>

1.08

Vf

= 0.70

x

21.25

= 14.88

kN

3Vf

= 44.63

kN

>

30.85

kN

Also

the distance

from

the

centre

of

a

standard hole

to

the

end

of the

plate

must be

greater

than or equal to

1.5df

=18

mm

<

25 mm

an d

distance

between centre

of

bolt

holes

must

be

greater

than

or equal to

3df

=

36 mm

>

e +

6 mm = 31 mm.

Hence

bolt

hole

spacing

is governed by

the

3df

requirement and not

tearout.

W

I ] nu

lmvimirror

WsW

SYDNEY

I

I

Sf

0

C

I

i>d4°

1.5df|

3df

(b)

Three

bolts

in

line of

force

(r

f

=

ÿ-)

Final solution is three

M12

Grade

4.6 bolts in line

spaced

36

mm

between the centres of

the bolt

holes and

25

mm

from the

end

of the

plate

to

the centre of the last bolt hole .

Design

load capacity

is

30.85

kN

which

is controlled by

the plate strength design capacity

and

not

the bolt

capacity

in shear

or plate bearing

capacity.

n

ÿ

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

.ÿ

ÿ

ÿ

n

ÿ

ÿ

ÿ

76


77/104

TIIE UNIVERSITY

0T

SsW

SYDNEY

Block

shear

rupture

ffs*

-A/

\

V-

Ch-.z-o-

q~ÿAgvÿ

p

_

I

L_

S*

(a)

Small

shear

force and

large

tension

force

6Z?

«9

U

fuAnt£0.60fuAnv

0.60ÿ,,ÿ fjAj,

s*

(b)

Large

shear force

and

smalltension

force

Fig.

9.20 Block

Shear Rupture

Screw

connections in

shear

(b)

Nominal

screw

diameter

(df

)

n\n

MB*

(a )

Thicknesses

el

Pi

(c)

Minimum

edge

distances and

pitches

Fig. 9.15 Screws

in Shear

ej>

3df,

pi>3df

N

e2>1.5df,p2>3df

77


78/104

SYDNEY

Bearing

Failure

of

Screwed

Connections

mi

t

vunsmroF

SYDNEY

Tilting Failure of Screwed

Connections

042/042

C.550

ÿ

n

ÿ

Q

ÿ

n

n

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

78


79/104

79

to

-u

TMELMVOHmrOF

SYDNEY

Design for Shear

When

t2

<

t1

use

the smallest

of

CSA-S136

d/tÿlO

dA

<

15

:

C

= 30t/d

d/tÿl5:

C

=

2.0

AS/NZS 4 60 0 1 99 6A1S1

C-2.7

AS/NZS 4600

:

2005

d/t£6:

C-2.7

6

<

dA

<

13

: C

=

3.3

-

O.lt/d

d/t£:

C

-

2.0

When

t2>

2.5

t1

use

the

smaller of

Fig. 9.17

Bearing

Coefficient C

for

Screwed Connections

When

2.5t1

>

t2

>t1

, use linear

interpolation

h

'

'

1

i

Design

for

Tension

dW |

7/x_t

],

tensile strength

f

.

\ 1

\7/

t2

,

tensile

strength

f

ÿ

-U-N

(a) Valley

(pan)

fixed

TT

n

t[

,

tensile strength

f

ul

t2

, tensile

strength f

ÿ

(b)

Crest

fixed

Fig. 9.18 Screws in

Tension


80/104

n« tMvmsmfor

teSf

SYDNEY

Design

for

Tension

Pull-Out

Failure

Pull-Over

Failure (pan

fastened)

Eq.

5.4.3.2(2)

Eq. 5.4.3.2(2)

where

dw

is

the

larger

of the

screw

head

diameter

and

the washer

diameter but

not

greater than 12.5 mm

Pull-Over

Failure (crest

fastened)

c = 0.54 (corrugated sheeting)

0.89

(wide

pan

trapezoidal

sheeting)

0.79 (narrow pan trapezoidal sheeting

80

Combined

tension and

shear

in

screwed

connections

NAS 2012 has new

rules

for:

Combined shear and

pullover (E4.5.1

)

Combined shear and

pullout

(E4.5.2)

Combined shear and tension

in screws

(E4.5.3)

SYDNEY


81/104

1 TwruMMBrsiTroF

SsW

SYDNEY

Welded connections

(a)

Buttweld

,

I.;'

'

spot

weld

(puddle

weld)

seam

welds

(e)

Hare-bevel weld

Fig.9 .1 FusionWeld

Types

_ _ _ _ _

Fai

we

I

Geometry

Inclination failure

Weld

shear

weld

tearing

&

plate

tearing

Failure

modes

(a) Singlelap

ioint

(TNO

tests)

Geometry

and

failure mode

(b)

Double

lap

joint

(Cornell tests)

81


82/104

Failure

modes

in

longitudinal

fillet

welds

2N -

ÿ

2N

I

A

Geometry

Transvi

plate

tearing

mrnr

Weld

shear

and tearing

at

weld

contour

Failure

modes

(a)

Single

lap joint

(TNO

tests)

lll I

4N-

ÿ4N

1

12>

tj

Sheet

tear

ÿ

K

Geometry

and

failure mode

(b) Double

lap joint (Cornell

tests)

Fig. 9.4

Fillet

Welds

subject to

Longitudinal Loading

SYDNEY

Failure

modes

HAZ

Failure

Weld throat

failure

n

ÿ

ÿ

Q

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

o

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

a

ÿ

ÿ

82


83/10483

SYDNEY

(b)

Longitudinal(Fig.

9.4b)

(a) Transverse

(Fig.

9.2b)

100

Theoretical Ultimate Load

=

4V

Theoretical Ultimate Load

=

2VW

STg

6T-

WHt

Arc spot

and

arc seam

welds

ÿ

jt

U-d.—

|

(a) Single

thickness

of sheet

®Tnin

®mm

J_

-o

o

(c)

Minimum

edge

distance

(arc

spot welds)

(b)

Double thickncss

of

sheet

-min

(d)

Geometry

and

minimum

edge

distance

(arc

seam

welds)

Fig.

9.6

Arc Spot

and

Arc

Seam

Weld Geometry


84/104

ÿ

I

THE

UNIVERSITY OF

&j)

SYDNEY

Failure

modes

in

arc spot

welds

(a)

Inclination failure

Buckled

plate

(b)

Tearing

and

bearing

at

weld contour

Buckled

plate

(c) Edge

failure

(d)

Net section failure

(e) Weld

shear

failure

Flare

welds

YDNEY

t

w

is the lesser of

0.707twi

and 0.707tW2

filled flush to surface or

(5/1

6)R

filled flush to surface

0.833

tlw

fu

(a)

Flare-bevel

weld

(b)

Flare V-weld

Fig.

9.5

Flare

Weld

Cross Sections

i

84


85/104

88

Sydney

9.8.1 Welded

Connection

Design

Example

Problem

The

80

mm

wide 2.5

mm

thick

G300 sheet is

to

be

welded

to

the

5

mm

plate

shown

in F ig .

9.21

using either:

(a )

Longitudinal fillet

welds,

or

(b )

Combined

longitudinal

and transverse

fillet

welds,

determine

the

size

of each weld to

fully

develop the

design

capacity

of

the plate

I

*W>|

Tut i

sivmsnvoF

few

SYDNEY

A.

Plate Strength

for

Full

Plate

For

a G300

steel,

fy

=

300

MPa

and

fu

=

340

MPa

Clause

3.2

Use lesser

of

Nt

=

Ag

f=(bt)

fy

= (80

x

2.5)

x

300

=

60000 N

=

60.0

kN

(Eq.

3.2.2(1))

N,

=

0.85ktAnfu

=

0.85kt

(bt)

fu

=

0.85

x

1.0

x

(80

x2. 5)

x

340

=

578000

N

=

57.8

kN

(Eq. 3.2.2(2))

Hence the

design

capacity

o f the

connection

(

Nd

) is given

by

Nd=t,

N,

=

0.90

x57.8

=

52.02 kN

85


86/104

n» UMXtKMlYC*'

ÿ

SYDNEY

B.

Longitudinal Fillet Weld

Design

Clause

5.2.3.2(b)

Assuming

El

Vw

=

0.75

t

lwfu

(Eq.

5.2.3.2(3))

Now

j>

Vw<

Nd

where

25

2 2

m

t

2.5

niEusivf

(tsirv

of

WW

SYDNEY

C. Combined

Longitudinal

and

Transverse

Fillet Weld Design

Firstly,

locate

transverse

fillet weld across

full

width of

end

of

plate

as shown

in Fig. 9.21(b).

Clause

5.2.3.3

W

J

transverse

=

t b

f

u

=

2.5

*

80

*

340

=

68.0

kN

Now

< >

$

(

VJ

transverse


87/104

THUMVtKSin

OF

ÿ

SYDNEY

Try

(lw)i=15

mm,

hence

Hence for a

longitudinal

fillet weld each side,

2

\/ =

2

x

7.

79

kN

=

14.38

kN

>

7122 kN

Hence use 15 mm

additional fillet

welds

each side.

*

eorv'T

w&co

ÿ

ÿ

ÿ

ÿ

k&*

1

$F7-Hlzr&

7ÿ-hj,

?rec-5i

s

„

Power Actuated Fasteners

(PAFs)

YI)\I

>

SU

K

Figure

2

PA F

Geomeiric

Variables

Used

in

the Strength

Prediction

Model

New

Clause E5

of

NAS 2012

Includes tension (pull ou t) and shear

87


88/104

Rw|

nu

usivfRsmro

W33 SYDNEY

PAF

Design Rules

in NAS

2012

E5.2.1

Tension strength -

formula given

based

on section

area

E5.2.2

Pull-out -

independent

laboratory

testing required

E5.2.3

Pull-over -

formula

given similar

to screws

E5.3.1

Shear

strength

-formula

given

based on section

area

E5.3.2

Bearing

and

tilting strength

- new formula

E5.3.3

Pull-out

strength in

shear - new

formula

I

ftys

1 THfUSIVHlSITYOF

WSSf

SYDNEY

Bolted connections

have a

greater

propensity

for

bearing

failure and

normally

require

washers

Screws can

undergo

tilting

as

well as

bearing

failure

Welds can

have

failure

in

the

Heat

Affected

Zone

(HAZ)

and

require special

rules

based on the parent

metal

strength

G450

Steel can now

be

designed

according

the AS/NZS

4600:2005

New

rules

have been

developed fo r PAFs

in

the NAS

2012

n

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

o

ÿ

ÿ

ÿ

n

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

ÿ

a

ÿ

ÿ

ÿ

a

ÿ

ÿ

I

i

ÿ

ÿ

ÿ

88


89/104

DESIGN

OF

COLD-FORMED

STEEL STRUCTURES

Design

Examples

Emeritus

Professor

Gregory

Hancock

89


90/104

,

i

nsm

i

SYDNEY

Cold-Formed

Steel

Structures

Lecture

4

Design

Examples of Lapped Z-Section

Purlin

and

Lipped

Channel

Column

in

Compression

Emeritus

Professor

Gregory Hancock

AM

FTSE

ip

Sydney

Ex

5.8.4

Continuous

Lapped

Z-Section Purlin

w

=

1

kN/m

Fig. 5.24

race

Lap

(900

mm)

(a)

Geometry

2800 4200 3500 3500 4200 2800

(all

dimensions

in

mm)

Determine

the

maximum

uplift

and downwards

design

load on

the

Z-section

purlin

3.79

kNm at

brace

point

Includes double

stiffness

in

lap

(b)

Bending

Moment

Distribution

Reverse

signs

for

uplift loading

.42 kNm

at

end

of

lap

3.76

kNm

at

end

of

lap

Use

the

Effective

Width

Method

(EWM)

and

Direct

Strength

Method

(DSM)

3.50

kN

2.75

kN

(c)

Shear

orce

Diagram 3.80 kN

at

end

of

lap

4.25

kN

3.05

kN

at

end of

lap

90


91/104

79 mm

SYDNEY

Internal

corner

radii

(r

j

)

=

5mm

y«parallel

with

we b

x«parallel

with

flanges

(a)

Cross-section

Fig. 5.23

t

=

1.5 mm

Z-Section purlin

D =

203 mm

I

dn

=

15

mm

Bt

=

74

mm

ÿi'Ns'

t

= 1.5

mm

©

(D

©f

y

i

C

W

r

=

5.75 mm

u

= 1.57r

=

9.03

mm

c

=

0.637r

=

3.66

mm

Ig

=

0.149r3

=

28.3 mm3

(b)

Line

element

model

y«g

©

©

_

j©

©

©

©

nif

univers i ty

of

WW

SYDNEY

Program

THIN-WALL

Local and distortional

buckling stresses

Distortional bucklina

Compression

in

wide flange

ad

=

222

MPa,

A

=

600 mm

Compression

in

narrow

flange

od

=

236.7

MPa,

A =

700 mm

Local

buckling

Compression in

wide flange

al

=

304.6

MPa,

A

= 120

mm

Compression

in

narrow

flange

al

=

296.2

MPa, A = 120

mm

91


92/104

HWn

nit

isrxmsrrv of

ÿ

SYDNEY

Lipped

Zed Notepad file for PURLIN

Name

Grade D E

F

L T R1 R2

(mm)

(mm)

(mm)

(mm) (mm) (mm) (mm)

Z20015S

Name

G450

Grade

203

79

74

15.0 1.5

5.0 5.0

fol b

fod

b

fol

c

fod

c

(MPa) (MPa) (MPa) (MPa)

Z20015S

G450 300.4 229.4 58.0 105.9

The local

and

distortional buckling

stresses

are

the

mean

of

the

wide

and

narrow flange

values

from

THIN-WALL

ra»l

niF

iMvutsmroF

WW

SYDNEY

Solutions from PURLIN

Effective Width Method

Lowest

load factor

=

2.183

(cf

2.165

in DCFSS Ed

4th)

Flexural-torsional buckling 2800mm from

LH

support

Section capacity 2.690

FT

buckling 2.183

Distortional

buckling 2.235

Shear capacity 4.066

Combined M&V

2.386

Bolt

shear

3.905

92


93/104

Direct

Strength

Method

Lowest load

factor =

2.235

Distortional

buckling

2800mm

from

LH

support)

This

value

is

2.2% higher than the EWM

THI

LMVUMTYOr

r-5

SYDNEY

Ex

7.6.3

Lipped

Channel

Column

Problem

Determine

the

nominal

member

axial

capacity

(A/c)

for

the

lipped channel

section

of length

2000

mm

shown

in Fig.

7.12

assuming

the

channel

is loaded

concentrically through

the

centroid

of the

effective section

and the effective

lengths

in

flexure and torsion

are based on a lateral

and torsional

restraint

in

the

plane

of

symmetry

at

mid-height.

This

is

similar

to

a

wall

stud

in

a

steel

framed

house

with

a noggin (bridging)

at

mid-height.

D =

100

mm

B

=

75

mm

t

=

1.5

mm

dL

=

16.5

mm

fy

= 30 0

MPa

Fig. 7.12

2000

mm

1000

mm

1000

mm

93


94/104

I

425*1

rut 1

mvfiwty

of

SYDNEY

Example 7.6.3

Major

and MinorAxis

Second

Moments

of

Area

(Ix, ly) and

Torsion

Constant (J)

of Full

Section

accounting

for Rounded

Corners

lx

= 7 .1 16

x705

mm4

I

=3.155 *105mm

4

J

=

304.37 mm4

Fig. 7.12

hPftl

tmf

iT.ivutsmrof

r-5

SYDNEY

Warping

Constant

and

Shear Centre

Position for

Full

Section

with Square

Corners

=

7.

632>


95/104

AS 4100- 1998

(€%

=

-0.5)

*

0.8

AISI-LRFD-

1991

AS/NZS

4600

v

1996

and

A1SI

1996

AS

1538

-

1988

(unfactored)

kr=


96/104

SYDNEY

fn

=

(o.658Ac

If

=

213.66MPa

(c) Line

element model

(d)

Effectivew idths

rÿn

Tin

ÿ

SYDNEY

For

a

section mono-symmetric

about

the

x-axis,

the critical stress

foc

is

the lesser of

the minor

axis

flexural

buckling

stress and

the flexural-

torsional

buckling

stress

(Eq.

3.3.3.2(11))

(Eq. 3.4.3(1))

foc-

lower

value =

369.95 MPa

o

96


97/104

SYDNEY

Boundary

Conditions

S.S

s.s s.s

s.s

—

Built-in

p

;

s.sr

Built-in

r~

S.S

—

.s-

1-ivc

_

Built-in

Free

1SS

V3

l' roc

F-7

V's

SSF

EH3

Loading

Uniform

Compression

Uniform

Compression

Uniform

Compression

Uniform

Compression

Pure

Bending

Bending

+

Compression

Bending

Compression

Pure

Shear

Buckling

Coefficient

(k)

0.425

0.675

5.35

9.35

Half

-

Wavelength

L

=oo

L

=

2b

L

=oo

L

=

b

L

=

Plate

length, b

=

Pla

hancock's notes

Documents