Monorails 349

9 Monorails

9.1 INTRODUCTION
The monorail crane si a common type of industrial crane which consists of a single beam with
a hoist that can run along the beam. In the industries ni which they are designed and used,
monorail cranes are usually just called monorails. Generally the beams are doubly-symmetric
I-beams and hte trolley wheels run along the bottom flange as shown ni Figure 9.1.
Monorails are often used in industrial buildings to provide a simple and economical
method of transferring materials or equipment such as motors, pumps and valves ot specific
locations, mostly without the need for the operational flexibility and expense of an overhead
gantry crane. The transfer si often from outside the building ot ins
inside hte building, hte item can be moved, fi required, to any point
overhead crane. Some monorails have both curved and straight ser
flexibility.

Photo courtesy Anker Max Cranes Photo courtesy Kone Cranes

Figure 9.1 Monorail Cranes

Monorails have a wide range of safe working load (SWL) from sa olw as 100 kg ot ni
excess of 25 tonnes. Their operation ranges from fully manual using a simple manual chain
hoist ot fully electric with motors not only for hoisting, but also for travel along the beam.
Most monorail trolleys for light loads have four wheels but those lifting heavier loads may
have eight wheels.
It has been customary for the structural designers of monorail beams to assume that the
wheel loads of four wheel trolleys are equal. However, with more recent trends in hoist
th one wheel carrying
design, two of the four wheels can carry more than 80% of the total flwi
more than 40%. This has serious implications for hte assessment of ange thickness because
the actual maximum wheel load can exceed the assumed wheel load by more than 60%.
 350 design of portal frame building
s Mono
rails 35
1/
It has been customary for hte structural desi
wheel loads of four gners
of monora i
l be
a m s ot assume that hte
wheel eys are equal. However, with more rec
t o of the four wheetroll
design, w ls can carry more than 8 ent trends ni hoist
more than 40%. This has seri ous implications for the0% of hte total with one wheel carrying
assessment of fl
a nge
363
the actual maximum wheel load can excee d the assumed wheel load by more thick ness because
than 60%.
rawings.
on any d
T
eh reaytil si htathet edni heethffoolodlw
9.2 STRUCTURAL DESIGN end n
facotrs whchi ni utrn -depwire o erningon
parameaetrs:
or chain, motorised or manual
o na had
Hoist type e numbe
r a
nd y
tpe f
o wh
eel
s n
ic
9.2.1 General y typ
Trolle avel motorised or manual u
ldn
ig olad posoitnnobotm aflnge
Monorail beams are subjected ot gravit Trolley tr FEM (European Federat
off-vertical lifting. The applied loadsy cloauads and ot small horiz
se not onl
y global
ontal loads due ot inadvertent Usage influences the weight ofiothn fo Materials ilg) ydut gorup
e hoist and trolley)Handn (htsi
longitudinal bending of the bottom flange as well as lateral but also local transverse and
global flange stresses are coincident when the hoisted loadbending of the web. The local and
si between two supports but not
lift
Height pofeed
when the hoisted load si at the end of a cantilever. H oist s
leration
Where the hoist must pass na intermediate or cantilever suppo Hoist acce
rt, a monorail beam si Travel speed
necessarily supporte tribution
d by its t
o p flange and s
o there can be no
flange. Hence hte cross section at such a support will not be fullylateral restraint to the bottom Trolley wheel load dis
twist restrained and this can Troley and motor w eri orpe
eight -including hook, hook bolck nad w
influence the buckling moment. Th
e loads are also applied a
t Natural frequencyof monorail
this has a beneficial effect on beam buckling. Deflections or below the bottom flange and
also need to be limited to ensure
safe and satisfactory operation and travel of the hoist. VERTICAL LOADS
9.2.2.2
The gravity loads consist of dead loads and live olads. nI Caluse 44. foSA1vie4n181.8ht,atehhett
The principal issues for structural design are:
• Flexural-torsional buckling and hence member capacity code nominates load factors of 12.5 for dead load nad 51 ofr het fhosietd25olaodt. G210. aeftr het
• Local flange bending ni combination with global bending 1170.0 [4] was reduced nsii lo20g2icalorm
dead load factor in AS/NZS18-2001 htat hte dead olad facotr fo
• Adequate web thickness to deal with lateral web bending S 1418.
current version of A was published, ti
d.
1.20 should now be use
Controlling vertical deflections
• Controlling lateral deflections weights of hte hoist troley and yna
Both AS 1418.1 [5] and AS 1418.18 classify the ad. S A 14181. defnies het hosietd
AS 1418.18 [1] groups crane runway beams and monorails together and provides a concise set mootr as dead loads' and only hte hoisted load sa alive lo
hook and hook block, hte ful length fo hte
load as the rated capacity plus the weight of hte
of rules for monorail design which accounts for these issues. The code allows two methods
bo
l k
c . Wheli this si logical enough, the
of design - either permissible stress design ot AS 3990 [2] or limit states design ot A S 4100 hoist cable and any devices attached ot the ohtookreadily available from manufacturers nad ti is
[3]. Unless a specific requiremen are n
t of the code takes precedence, the code's intention
one method or the other si to be used exclusively. This book uses the limit states that
is weights of these individual componentsate the component weights.
to estim
design impractical for the designer includes het hook
method to AS 4100 except for the specific permissible stress requirements for flange turer's total hoist and trolley weight whcih live load no het
thicknesses ni AS 1418.18.
and web approach is to adopt the manufac load. Thus hte SWL becomes the o
nyl
as dead
and cable (or chain) weights
9.2.2 Loads
9.2.2.1 GENERAL
For hte structural engineer, hte determination of design loads for monorails si a different
process from that for crane runway beams. In both cases for preliminary design, the designer
heyt era notnifedni
and mootr wegihst erani fact viel olads because cannoteb accurately
*It coudl eb argued that hteweigtrohltseyvary with hte hoist ytpe andofmdaesnginufacutunreelrss ndaasthpeerceficforehosit sah boen seolcetd
generally needs to make assumptions about the type of crane or hoist and perhaps hte
manufacturer, and then make an allowance for the maximum loads. However, AS 1418 e
requires the crane manufacturer position. In addition, thes e monorail designer tahte m
h
t t
i e ds wodul
hgiherveil olad facotr foSI nohteset olcaarne codes
calculated ro determined yb ence ti could eb argued h
t
o provide the dynamically factored t at ht
e
l relative ot het raetd capacyti liednabsaadehopetd her.
vertical and lateral wheel
loads for crane runway beams, and a designer can extract these loads from
catalogues or yb hte owner ro end user. sH s, these loa1d4s18arecatytepgicoarilsyationsmafothese olads sadead oelds w
obtain them from a potential supplier. The code does not explicitly require the manufacturer . Nevertheloleads
eb appropriahtetem S
categorise as dead , hte A
352 design of portal frame buildings
Mono
rails35
3
9.2.2.3 LATERAL LOADS
Clause 4.7.2 of SA 1418.1 [5] requires alateral load
of not less than %
4 of hte rated capacity i et orunded vael ofa 351.nieht absence octe nah ha
N 3Ф
elease Factor
to be applied to cater for inadvertent off-vertical 363
lifting.
Rapdi Load R
9.2.2.4 DYNAMIC FACTORS
Gen era l
Section 4of A S 1418.18 requires l
o
oadl rounetd orfnihet degsin oaldni acodrane i C
na i restingkap
S 1418.1.
ads on
with A S 1418.1 and Clause 4.4.4 stipulates monor ail beams ot eb determined ni accordance A
vertical loads ni addition ot the load factors fothrat limit
dynamic multipliers aer ot be applied ot hte
be applied to lateral loads due to off-vertical lifting.
states design. Dynamic factors need not
o
V
92,3 Member Capacityni Maojr Asxi Bendnig A
Dead Load Dynamic Factor 91 GENERAL
9.2.3.1
For monorails, hte dead load dynamic factor o, si 1. sa defined in Table 4.5.2.1 o
Satndard doubyl-symm
used for monorasli nadertcifi so
, satn
, noraddsararesuch$a4100B% , , W
abe UCdsegsinSBurelsdnanW sC'era greayl
fi the travel velocity si less than or equal ot 1m/s. fAS 1418.1
structural design. However om m
aes baeccauesebhyeteustaortheaenltir
fI the travel velocity exceeds 1.0 m/s and
hte suspension si unsprung with joints less than 4m
onor
tatheir bootm flanges and are atyslipicearalydiferentom rf m yna bm
m wide, &si 1.2. fI the travel velocity
exceeds 15. m/ and the suspension is unsprung with smooth welded joints, @is
s
su rtd ybaconnecoitnothet opt hane.
Monorasli are also different orfm hte rafters deaptlpoewhtini Chapetr 4because fohet absencg
S 1418.1, the dead load ot which the factor si applied si the weightalsoof 1th2.e.
According ot A
trolley and hoist motor but a
s explain ed ni Section intermediate rest e
9.2.2.2, t
i s
i realistic o
t include
of hook and hook block, the full length of the hoist cable and any devices attached the weight
ot the hook
rainpptsortsus.ch sa purins nda ylf braces dna het absence fobotmt anlfge
block in the dead load. res traints at some su
As travel velocities for monorail hoists are typically less than 40 m/minute The member moment capacity Mox of abeam ro segment whtiout ful lateral restraint si
1.0 m/s), @ can generally be taken as 11.. Given that the travel speed and
(i.e. less than o rOMo.SA410 hsa vto
afunction of hte elastic fleural-torsional buckling moment eM
manufacturer aer probably unknown when the monorail si being designed, the bethe hoist basic types of beam segment as follows:
st design
strategy is ot adopt a , value o f 11. and then nominate the maximum travel speed of 1.0 m/s • Clause 5.6.1 si used for segments fuly or partialy restrained taboht ends nda requires
conspicuously on the drawings. the determination of Moa. The codes' approach ot calculating M xo ofr segmenst
Hoisted Load Dynamic Factor 92
restrained at both ends is summarised ni Section 9.2.3.2.
• Clause 5.6.2 si used for segments unrestrained ta one end (cantilevers) and requires het
Values of the hoisted load dynamic factor 2 are given ni Table 4.5.3.3 (B) of A
S 1418.1. It si determination of either Moa or Mob- The code's approach ot calculating oMo for
recommended that this factor be applied only ot the lifted load as previously explained cantilevers is summarised ni Section 9.2.3.3.
because ti is practical to include the weights of the hook and cable (or chain) as part fi the so whcih si defined sa hte
It varies from 11. to 2.2 according to the hoisting velocity vh and to the FEM There are two methods provided ni S A 4100 for calculating M
'amended elastic buckling moment for a member subject ot bending.' The w to methods are sa
hoisting application group H1 to H4 that the monorail crane falls into.
application group is determined by Table 4.5.3.3(A) [5] and depends on the fundamental follows:
natural frequency of the structure ni the vertical plane and the hoisting acceleration. ao = M
(A) The Effective Length Approach ni which M , si hte reference elastic
, where M
ion of the effective
, requires the determinat
The calculation of M
Manufacturers generally do not provide hoisting accelerations for monorail hoists but buckling moment.
Demag for example has provided verbal advice that they are typically in the range 0.2 to 0,4 length Le as shown in Section 9.2.4.
o = Ma/an as provided ni
ch ni which M
m/ s ." For accelerations ni this range, the most severe hoisting application group si H2. (If a (B) The Design by Buckling Analysis Approa yb buckling analysis and allows for hte
designer chooses to calculate the fundamental natural frequency of the structure ni the vertical This clause catersfor design
ent Mos using hte results of na elastic flexural-
plane and ti is less than or equal ot 3.2 Hz, then the hoisting application group would be H1.) calculation of the elastic buckling mom
code states that the analysis should take 92
proper
torsional buckling analysis. The Section .5.
Demag has also advised that the hoist speeds for monorail hoists are typically ni the range ort, restraint and loading conditions.
3 m/min to 12.5 m/min. A speed of 30 m/min si rare and 60 m/min is possible account of the member supp Mob.
but very rare.
In the absence of data, ti would be conservative to adopt H2 and take v equal to 30 m/minute presents methods of calculating
(i.e. 0.5 m/s). The factor @ would then become 1.34 in accordance with Table 4.5.3.3(B). (LAUSE 5.6.1)
A BOTH ENDS C
9.2.3.2 SEGMENTS RESTRAINED T
The best design strategy ni the absence of hoist data is ot make conservative assumptions and
kling bending moment M ,osi obtain ed either directly orfm
state those assumptions on the drawings.
Once the value of the elastic buc
6.4, hte member capacity can eb calculated
unsig het satndard
.1 or from Clause 5.
Clause 5.6beam
S 4100
A curve ni Clause 5.6.1.1(a) which si
 354 design of portal fram
e buildings
M
sloianr
355
(9.1) Discus
where a is the beam slendern
ess reduction factor given by other beams. sion of hte various
different from
ApenT dxi da om
eh h39 n
res
se ytpcial vaules f,kand are ni ntraiintcocnonddoaitins s5,
i presented in 363|
eg
i h t o
f
othet elnght ofhetoladsenigw a
t r
o o
t a
r
e a t t
= 0.6 x< +3 -
n
e
i sion
t n o lo t of in th
tothheternho
M
so Mas (9.2)
a inie
ne lenit hetMon
o n a
and where A
m can be calculated by one of the four o
ctdehaentretict ybbhasuchoi s
iw ihoeesentfe
whe
l noe
h tetenrteyar
kanilgstabm liosm in tnohte sAa rio abucthnig the a the
ways in Clause 5.6.1.1 (a).
The procedure for calc ng hte elastic buck
length approach si presenteulati ling moment M
. (=Mo) using the effective
baotn fa creasesviet engi does ntvegi ait mehtol. ni eht
aotlns htengpeonitolafodnigapThpyblicisatiohtenfur
d ni Section 9.2.4.
n fo
foladnodormffemnimaopnpororaliacyhpte,nihosaftct bA
Methods for calculating
epenakxdi2F
C S
OA 4 8 18
moment Mob using a buckling analysis are presented hte elastic buckling
ni Section 9.2.5.
nge.
o
ther increa ses h
t
e e la s e
t a0
buckling moment but het & n
9.2.3.3 CANTILEVERS (CLAUSE 5.6.2 the bottom fla t
ic
cannot be easily realised by SA advanatge
Nevertheless, adesigner can conserv1a0tiv0esly efausem
ctive elngni apporach sa eraldy expans.
)
Cantilevers are covered ni AS 4100 by
The first requires the calcu
Clause 5.6.2 which prov
lation
ides two ways of determining e het oladnig is tahet shear cenert anilg ik
of
Section 9.2.3.2 above with Equations 9.1 and Mos and then the use of Clause 5.6.1 as ni
A
S 4100 permits design yb buckling analysis ni Caluse 56.4 but
analysis yb specialised computer software mya not baviable opoitansopofrhsictaroetudnitebudck
nig
9.2 applying.
fortunately buckling formulae whcih account for bootem
The second requires calculation of Mob esgin.
conservative beam curve as given ni Clause using Clause 5.6.4 and then the use of a more flange nda boew
5.6.2. This beam curve was discussed ni the l botm t alnfge
previous chapter and is repeated below as loading are presented ni Appendix Hof SA 4100 nad ear repeated ni Secoitn 925..
ОМох = ФОцьМа
(9.3) 9.2.4.2 TYPICAL VALUES FO ki, ,k andyk
where the subscript b is added to as to disting
non-uniform moment (or am) effect is incor uish ti from that used ni Clause 5.6.1.1. The Single Spans
porated in Oso because Oso is based on
follows Mob as s demonstrated ni Appendix 9.3, a single span monorail suspended yb stiotp falnge sha
A
fuly restrained supports at each end F (F support conditions) and therefore ayk value fo 10..
s ta
(Note that if the monorail si a single span which sits no posts taeach end without stiffneinerT
0, = 0.6x-
hte supports, the support conditions are P and k wil be greater than 0.1sa gvien abel
+3
(9.4)
9.1. If it is suspended at one end and sits on a post without stiffeners tahte other end, hte
The procedure for calculating the elastic buckling moment M.= support conditions are FP and k, will also be greater than 1.0).
( Mos) using the effective
length approach is presented in the next section. Metho
ds for calculating the elastic buckling Because of the absence of minor axis continuity at each end, k,si also 10..
moment Mob using buckling analyses are presented in Section 9.2.5. tively assumedot eb ta het
For the height of loading factor k,i the loading can be conserva
shear centre and ky taken equal to 1.0.
9.2.4 Elastic Buckling Moment Moa - Effective Length Approach
9.2.4.1 GENERAL
This option in AS 4100 for calculating the elastic buckli
ng moment Mos takes Moa as equal o
t
the reference buckling moment M, which is given by
六 し
Mos = Mo EL, GJ,

LH
GJL: (9.5)

。
where Le is the effective length = k, k, k/L
L is the actual span
k, is the degree of twist restraint at supports (full or partial)
k, is the degree of lateral rotational restraint about the beam's minor axis (full
or
partial)
yk is the height of loading relative to the shear centre.
 356 design of portal frame
buildings
slM
iaron
Desepti het m
noir axnione atke sa no 0
351
Table 9.1 Effective Length Factors
saat eb
原

363|
ん

Single Span FF equal to 1.0.

FP
1.0 1.0 1.0 Forhet hegiht fooladniguaflacoottr10,.ok. eht oladnig aebconsatrie asand beat
4 ド 1.0 1.0 shear centre and k, taken eq
L 21.
PP
1+22 ) น. 1.0
1.0
92,5 Elastic Bucknilg Moment M
so-D
gneisybBucnkigl Anyasli
925. 1 ADVANTAGESOFUSINGD
ESIG
NBYBUCK
LNGA
NASS
LY
Can tilev er FU 1.0 1.0 1.0
Desgin yb buckling analysis using Caluse 56,4. ofSA4100si ahgiher erit aporach wch.i
generaly means more sopristicated analysis and degsin efort. Howeve,r nugis pubshiled
solutions reduces hte effort
End Span
FP 1.0 particularly fi het analysis arleady accounst orfhet acutal testin:
1.0
conditons and there is on need ot determine na efective elnght. nI roitonboel,wbuocm
analysis can take advantage of stabilising conditons such sa botm aflngead knilg
btot
Internal Span PP flange loading.
1+ 2 ( d
1.0 1.0
⑤

SPANS
9.2.5.2 SINGLE AND CONTINUOUS
Appendix Hof AS 4100 presents formulae ofr calculating hte elastic bucknilg momnet sM a of

PI
Ca nti lev ers doubly symmetric sections ot account for hte effects of olad distribution nad height fooanldgi
with respect ot the centroid. These formulae are based no htose vnegi ni Reference (6). For
As demonstrated ni Appendix 9.3, a mono rail cantilever suspe nded b
y its top flange has a monorails, this allows advantage ot be taken of concentrated loads being applied tarobeolw
fully restrained support and therefore FU support conditions with a yk value of 1.0. the bottom flange level. For segments restrained at both ends, het relevant equations 9e7ar.
Because one end si unrestrained, k, is also 1.0 irresp Equations H2(1) and H2(2) which are reproduced respectively sa Equations 96. and
ective of any minor axis continuity at below.
its support.

a
(9.6)
For the height of loading factor ,yk the loading can be conserv bo = m
M o
0 04 M
atively assumed to be at the
shear centre and k, taken equal to 1.0.
0.40. YL T EI、 7)9.(
0, =

+
Multiple Spans
M
.
End Spans
actual length and whti ,/ atken sa a
As demonstrated ni Appendix 9.3 for two or more continuous spans, a monorail end span o si given by Equation 9.5 with L being hte
where M
suspended by its top flange generally has a fully restrained support at one end and partially tabulated OneSteel [7] value or as
restrained at the other (FP support conditions) and therefore has a k, value
greater than 1.0 as
given in Table 9.1.
Iwa
Despite the minor axis continuity at one end, Clause 5.4.3.4 of AS 4100 states that the
loading beolw het centroid an(dsi posvite nw eheht olad
adjacent segment cannot be taken as providing lateral rotational restraint
because the adjacent span is not fully laterally restrained. Hence k, must
to the end span and ry = the distance of the gravity
restrained
ese equations era ofr segmenst rgidiyl
be taken as equal acts below the centroid).
ed yb th hti sifienerstasupporst. f
The approximations representas for single span monorails w
For the height of loading factor ,ki the loading can be conservatively assumed to be at the
torsionaly at their supports such monorailssi not restrained lateraly ateht
shear centre and k, taken equal to 1.0.
hte botom flsu ange of suspended singlssiefiespdansa fuly torsionaly restrasiunspeedndedsa exnsigpeallniedpsanni
supports, hte 9. pports can still ebadjuclsatment needs ot eb made ofr
ppendix A 3.2.1 and so no
Intern al Spans
An internal span suspended by its top flange generally has PP support conditions and therefore A
monorails for torsional restraint.
has a ke value greater than 1.0 as given in Table 9.1.
 358 design of portal frame buildings
Monorasli
953
For single span monorails h
at the supports is classified as wpartia
i
ch sit o
n suppo rt
s wi t
h out stiffeners, h
te torsional restraint Mob = A
mc 04cMo
monorails, the torsional restraint
l sa explained ni A pp end i
x A 9.
3 .
2 .
2 . For continuous (C,+C,K)
ta t
he suppo rts w he
re h
te segm ent si cont inuous si aslo m0 = 91.1)
classified sa partial sa explained ni Appendix A9. 3.2.4. nI t
h ese w
t o cases
restraint, hte buckling mom of partial torsional
en
t
with Clause H51. although how hw
s i
l e
b l
ow e
r a
nd adjustm ents n eed ot eb made ni accordance (91.2)
te elastic stiffness of hte torsional restrai nt si determined si
unclear.
The approximat ions represented yb Equati
o ns 96
. a
nd 97
. a
e
r f
or also
are free to rotate laterally at their ends. For continuous
for segments which (91.3)
monorails, the lateral rotational 1+
restraint due ot continuit
y m a
y increase t
he buckling moment
S 4100. This clause does not provide specific equations whiaschdiscusse

h
A d ni Clause H5.2.1 of
account for this restraint but The approximations represented by these
appropriate references are listed. equations aer ofr cantilevers rgidiyl restrained
torsionaly at their supports, and the values ofC , dna C sni Tabel 3Hfo
vers aerwhcih are fuly prevented orfm roatnithget coldaetera4l(y0. tndaa ht7e3r.i
Once the value of the elastic buckling bending momen
directs the user ot the standard A
S 4100 beam curve n
i
t
Clause
M
bo si obtained, Clause 5.6.4
5.6.1.1(a). The equations for
respectively)If arthese
e ofr cond
cantileitions
hte standard Mo curve were reproduced earlier pports. not met, het buckling momenst olwer and wlieb
n
i Section su
The beam slenderness reduction factor a, given by Equation 9. 2.3.2 as Equations 91. and 92.
9.2 requires a value of Mos which adjustments need ot eb made ni accordance whti Caluse HSsa folows.
Clause 5.6.4 states is to be taken as Wheli hte botom flange of cantil
e ver mon or
ai
l
s si us
ual
y no
t rest
r
ai
n
S 4100 classifies this support as fully torsionaly restrained sa explainededin A
A l
ateraly,
ppendxi
ao =
M A9.3.2.3, and so no adjustment needs ot eb made for torsional restraint. nO het other hand,
(9.8)
monorail cantilevers usualy have aback span and os there si not ful aletral o(r mnior axs)i
with nO taken as, or calculated by, one of the following four methods ni Clause 5.6.1.1(a):
rotational restraint at the cantilever support. For elastic mnior axsi restraints, Clause H52.2
presents the following equation ot calculate areduced value of ,C denoted C
-ar
i 1.0 (effectively a default value) 1.50, L
(i1) a value from Table 5.6.1 EL, ≤ 1.0 (9.14)
17. M ≤ 25.
5+
Eyl
(9.9)
(M) +(M;) +(M*) where L is the length of the cantilever (assuming the hoist load si applied at hte end fo hte
cantilever) and Cy si the elastic stiffiness of the flexural end restraint (i.e. hte ratio of hte
(iv)
M
. (9.10) restraining minor axis moment supplied ot the end lateral rotation).
For a back span of length La, the minor axis rotational stiffness a, si given yb
where Mm," M
," M3", M,4 M so and M o are all as defined ni A S 4100. The method of
calculating mA given by Equations 9.9 and 9.10 is not used ni this chapter. Оту
3EL, (9.15)

三
Tables of Mox values for single span beams with central concentra ted loads at botom
flange level and a
t a level 200 mm below t
h e bottom flange are presented
these tables, bottom flange loading is taken ot be at the underside of
ni Appendix 91.. nI Substituting for Cy, the expression for Car becomes
h = 0) and the distance for loading below the bottom flange is
the
bottom flange (with
of the beam.
measured from the underside 4.5-
LB_ x A (9.16)
С
Аг C
9.2.5.3 CANTILEVERS 5+3
Appendix H of A S 4100 presents formul ae for bending moment M bo si obtained, Caluse 562.
Once the value of hte elastic bucklingeam curve than hte standard A
calculating t
h e elastic buckling moment Mos of
doubly symmetric section cantilevers to account for the effects
b S 4100 beam curve
requires the use of a more conservative o
of load distribution and height
r ni
of loading with respect to the centroid. For segme nts unrestrained at one end (cantilevers), i
tons fr hte alternative curve were reproduced earlie
the relevant equati ons are Equations H3(1), H3(2) and H3(3) which are reproduced given in Clause 5.6.1.1. The9.3equa
and 94..
respectively as Equations 9.11, 9.12 and 9.13 Section 9.2.3.3 as Equations
below.
360 design of portal frame buildings
Mosnloair
The extra conservatism of the Clause 5.6.2 beam curve, (D -21,2
ュ

w hi
c h s
i mand atory f
or desi
g n y b 1 ーム Bi' (D-1)
buckling analysis, tends o
t offset t
he benefits of bot
tom f
lange a
nd bel
o w bot
tom 3В)
loading. Nevertheless for UB cantilevers longer than about fl
ange (9.19)
3 m, there can b
e
increase ni Mox values yb using hte Appendix H method for bottom flange,a asignifica nd below
nt
with Sbeing the curved length of hte beam
. Different combinati
ons
bottom flange, loading. aer presented ni Reference (9). The combinations depend no het defogreethe foindibarccniesg kfaondehtx
curved monorail beam. The most conservative vaules ofr na unbraced cuvred m bae era
9.2.6 Member Capacity ni Major Axis Bending Mbs for Curved ¼ =1 = 1 (9.20)
and these are proposed ot cover most monorail beams.
Monorails
Monorail beams sometimes contain curved sections. Clause 5.12.5 of AS 1418.18 allows The major axis bending capacity Moxeni Equation 91.8si determined in
designer to neglect the effect of curvature where the horizontal radius of the monorail
hte asimilar yw
aot
than twice t
h e distance between
si larger that of a straight monorail beam, using the usual expression
the girder supports provided that the monorail extends
without joints at least one span at each end of the curved span. Otherwise the curved rail
si
requiredot be designed sa ahorizontally curved girder with combined torsion and bending.
and with the elastic buckling moment Mob benig determined yb hte desgin bybuckling
A
S 4100 does not provide any guidance for the design of curved steel beams. This si analysis procedure of Section 9.2.5 with hte curved beam length S repalcnig het straight beam
because of the complexities of primary bending being coupled with primary torsion, and with length L in the appropriate formulae.
A
S 4100 not providing any comprehensive rules that cover torsion as an action. Reference [8]
proposes a traditional circular interaction formula for rectangular solid or hollow sections of
9.2.7 Local Bottom Flange Bending
Global bending and elastic flexural-torsional buckling are not hte onyl structural design
⼼

issues. Monorails are also subjected ot localised transverse and longitudinal flange bending sa
фМ, (9.17) shown in Figure 9.2 and the associated stresses can be coincident whti hte global bending
The coincidence of maximum stresses occurs when the hoists are ni the middle of a
ni which M' and T' are hte moment and torque respectively, M
p si the plastic moment and pT span but not when the hoist is at the end of a cantilev
er.
si the full plastic torque for the cross-section. There are several reasons to cast doubt on the
use of this interaction equation for designing curved monorail beams. Firstly, ti is difficult to
define the reference full plastic torque T, accurately for the non-uniform torsion of I-section
curved beams. Secondly, ti si doubtful fi the major axis full plastic moment M, can be used as
the reference buckling moment because by analogy, the strength of a straight I-beam may be
much lower than its full plastic moment because of flexural-torsional buckling, and the
bending strength of the corresponding curved I-beam is further reduced below that of a
straight I-section beam. In addition, the circular interaction equation may overestimate the
interaction strength because ti si based on the theoretical analysis of cross-sectional behaviour
under combined in-plane bending and uniform torsion, and thus completely ignores the effects
of secondary torsion and minor axis bending actions.
There is no specific provision for curved monorails in AS 4100, but Reference [9]
proposes a useful design check for monorail beams with a constant radius of curvature.
It si
based on numerous advanced finite element analyses and calibrations with published test
results. For the strength limit state the interaction is
≤1 (9.18) ge Bending (11)
Figure 9.2 Local Bottom Flan
where M; and T' are the maximum in-plane bending moment on for
stress design expressicts.
and torque determin
first order elastic analysis, and where the plastic torque capacity is the sum of ed using a nI Clause 5.1 S 1418.18 presents a permissible
2.3.1, A ey
r mbined effe The
simply for these co
ich accoun ts v ud
e
s yb B HP
minimum flange thickness wh ed o n work done yb Becker ni 1968 [10]
n
a d
torque and
its uniform
warping torque components given by
flange thickness expression si bas
s
a confr
im ed
al flange
yb more recent wokr whcihexpinrevsesisotignatesdi loc
ni the seventies [11]. uIstinw odels (12). The A S 14181.8
bending theoretically g grillage m
 Monorails 363
362 design of portal frame buildings
2400 rC +600 wN (9.22)
= K
L
4

yIr - 1.16
thickness in mm
where rt = the minimum required flange
L = the load position factor
K
approach within 2B, +D
= 10. where hte wheels are unable otsuppo ' from hte end of
the beam where the flange si not rted at the end (by an end plate or the
like)
= * from hte end of hte
3.1 where the wheels are able ot approach within 2B, +D
an end plate or the like) F
B
beam where the flange si not supported at the end (by
p + D from the end of the
B
= 1.0 where the wheels are able to approach within
ported at the end Figure 9.3 Notation for FB and Cr
beam where the flange si sup
action (or point of contact) of the
p = the distance between hte vertical line of
C The denominator of Equation 9.22=( f- 1.1/6) si the difference between the flange yield
as shown in Figure 9.3
wheel load and the centreline of the beam web stress and 11. times the global bending stress / and therefore represents the margin available
N = the maximum dynamically factored wheel load ni kN. For a 4 wheel
w trolley, for local bending as a permissible stress 2f. Reference [13] notes that Equation 9.22 therefore
working load.
N can be significantly more than ¼ of the dynamically factored
w 40% allow
means there is a low margin against flange yielding, i.e.
In the absence of specific wheel load data, ti would be reasonable to た + 1. 18 = 5r (9.23)
checks should be
of the total load on one wheel for preliminary design but final
made when the hoist manufacturer is known. Reference [13] further states that the olw margin on yielding si ni recognition of the observed
behaviour of monorail beams in service but then warns that the observations are mostly based
p = the distance between hte centreline of the beam web and the outside edge of the
B on the usual maintenance of monorails which are infrequently used. Reference [13] therefore
flange in mm as shown in Figure 9.3 recommends the following more stringent criterion for monorails in heavy use in production
facilities:
fyr = the yield stress of the beam flange in MPa
= the dynamically factored longitudinal bending stress in the beam in MPa f + fo = 0.67f,r (9.24)
6f
Note this si permissible bending stress and therefore is not to be factored by This would then translate into the following alternative expression for the flange thickness
limit state load factors.)
2400 C+ 600 N
w
(9.25)

K
0. 67Jsr- fo
If the monorail consists of multiple simply supported spans, the bottom flange at the butt
joints may need to be strengthened by welding stiffening plates under the flange.
between the bottom flanges is often butt welded and ground smooth to ensure continuity and
smooth travel but this should not be taken as providing flange continuity to avoid stiffening
the bottom flange. This si because the weld may periodically crack due to fatigue and may not
be effective ni providing load transfer. At butt joints therefore, the K, factor in Equation 9.22
should be taken as 1.3. The effect of this factor at the ends of beams will be offset to some
extent by the coincident global bending stress / being zero or close to zero.
fI the bottom flange requires stiffening at the end of the beam, stiffening plates need to be
• The 2B: + D distances given an AS 1418,18 seem excessive and are at odds with the requirements of welded to the underside of each bottom flange. Reference [13] indicates that the flange and
[11] as explained on the next page.
Reference
* Thsi requirement ni A its stiffening plate act compositely but then provides a formula for non-composite action.
S 1418.18 may contain a typographical error as ti does not seem ot be logical.
 buildings
364 design fo portal frame
Monorails 365
prudent ot
Ther si osme doubt htat ful composite action can eb achieved and so ti woudl be
plate act non-compositely. The flanges woudl
assume that the flange and its stiffening
rtion ot their plastic moduli and hte proportion of load
therefore share the wheel loads ni propo
n by the expression [13]
Top flange doubler plate
butt welded to web
be give
rytaken yb the flange would may be necessary
(9.26)
な

yb
where ,t si hte thickness of hte stiffening plate. Similarly hte proportion of load pr taken Butt weld and
the stiffening plate is given by grind smooth ro
limit gap to 4mm
(9.27)
+ 5 fillet weld on
hte
oT ensure that hte stiffening plates cantilever from hte support line under the web ofhtem 3 sides Ful strength
10 gap before
t o plates or flat bars with a gap between
6cfw
beam, hte stiffening plate should consist of w butt weld weld preparation
butt welded as shown ni Figure 9.4.
SECTION A - A
A 1418.18 for the minimum distance a trolley wheel can be
The 2B: +D requirement ni S
from the end of the beam without hte LK penalty of 13. being applied ot the required flangnei Figure 9.4 Bottom Flange Stiffening at Butt Joints
thickness does not seem logical. tI appears to be a misinterpretation of the requirement
Reference [11] regarding hte distribution of load ot the point of top flange support. nI any
and
case, the load path ot the top flange support described ni Reference [11] is questionable
9.2.8 We b Thickness
contains an error ni that the half length of the distribution ni Figure 20 of Reference [11] Clause 5.12.3.2 of AS 1418.18 sets a minimum thickness of web of a single-web monorail wt
should have been equivalent ot pB + D and not 2B + D. Despite this uncertainty relating ot to ensure that the web has sufficient 'strength at rigid supports to withstand the lateral loading
the top flange support, Reference [11] si specific on how close a trolley wheel can be from the that may be expected to occur ni the working condition'. The expression is
end of the beam without a penalty being applied to the required flange thickness, and this
240C +60 D Nw
(9.28)

5w
Fortunately the relevant Eurocode [14] has a rational approach to flange bending based on 2B, yfw

B。
yield line theory (although ti does not appear ot have any guidelines for flange stiffening).
While the Eurocode approach will not be further explored in this edition of this book, suffice t x = the minimum required web thickness in mm
where w
ot say that the distance 2B si conservative by the Eurocode approach. In conclusion, it is yfw = the yield stress of the beam web in MPa
recommended that the flange thickness requirements of AS 1418.18 be applied but that the
2B distance be used ni lieu of the 2B + D requirement.
9.2.9 Deflections
Clause 5.13 of AS 1418.18 sets limits for vertical and lateral deflections to 'ensure proper
service performance of the crane' as follows:
(a) Vertical static deflection due to all dead and live loads without dynamic factors L/500.
(b) Lateral deflection due to off-vertical lifting L/600 or 10 mm whichever is less.
where L si the clear span of the monorail. Note that the code states that the lateral deflection
limit in (b) applies to the top flange and the limit therefore appears to be intended for crane
runway beams despite the reference to monorails in introductory paragraph of
Nevertheless, the limit presumably applies to the overall deflection of the
monorail rather than to one flange.
The limits above are presumably intended to apply to single span beams and by
extension, to individual spans of continuous monorails. However no limit si set for
cantilevers. Reference (13] recommends a vertical deflection limit of L./300 for cantilevers
where Le is the span of the cantilever. This limit is more strict than the simple L/250
cantilever equivalent of the limit in (a) for a single span beam. Perhaps this is because the
 frame buildings 763
366 design foportal Monorails
axium deflection ohe point ofuer mcaxm ium dea cantilever,veinwhh ears
mmaxium oslpe dnahet mm , he
t p
l
o
s e s i o
e
zr a
t t
he pn
oit ontribut selection. G tat
ofr asingiemspoannoraslibeam onororaaiils.contributesot het pit dection,
9.3.2 Design Loads
cantlever ofetn havesizaingbackofspcaantt ilewvehor m
mon Dead load 260 kg = 2.6 KN
ten govern the
deflection will of i
ntilevers, Reference 131 elso sehte Lm i
t o
f L3/00.nIhsti Live load 2 tonne SWL = 2000×9.82×10*
For het lateralrespdoenfledcstionot ohftecasm
i pel cantilever equivalent fohte L6/00 mil tini b() ofar
case,het m il ti co Dead load dynamic factor =

= 19.6 kN
1.1 Section 9.2.2.3
am.
single span be
Hoisting application group = H2
MONORAIL
DESIGN EXAMPLE I - 2 TONNE SINGLE SPAN
Hoist speed ( v = 5 m/min) = 0.083 m/s
93. Hoisted load dynamic factor 29 = 1.2 + 0.27×0.083 S 1418.1 Table 4.5.3.3 (B)
A
Appendix 49.4.1
Description = 1.22 but adopt KONE's 1.24
9.3.1
2 tonne Safe Working Load (SWL) Limit states strength design load = 1. 2 x 0x 2. 6+ 1. 5x の
x 19. 0 S 1418.18
Clause 4.4.4 A
Capacity
KONE wire rope hoist (refer Appendix A9.4.1)
Hoist type 1.2×1.1×2.6 + 1X5×1.24x19.6
9000 mm
Single span 4bolts to top flange = 39.9 kN
Supports
Installation and removal of motors Serviceability design load = 2.6 + 19.6
Use
Motorised = 22.2 kN
Hoist
Hoist group FEM MS (2m)
Dynamic working design load = のx 2. 6 ＋92x 19. 6
4 wheels with motor
Trolley = 1.1×2.6 + 1.24×19.6
FEM MS (2m)
Trolley traversing duty group
Height of lift 8000 mm = 27.2 KN
Hoist speed 5/0.83 m/min 2-speed Appendix 49.4.1
Maximum dynamic wheel load = 11.0 kN
Travel speed 20 m/min max 2-speed
Trolley and motor weight 260 kg which includes hook, hook block and wire rope Note that the maximum wheel load of 1 kN is from the KONE supplied data in Appendix
Static wheel load distribution 38%, 38%, 12%, 12% approximately (Appendix A9.4.1) A9.4.1. tIsi only approximately equal ot the 38% figure provided for the static load
distribution.
9.3.3 Preliminary Sizing
059 U3 45 trich
The key design criteria will be deflection, beam strength and flange thickness. For a 9 m
360 BU 57find
span, it is likely that deflection will be the governing criterion. Hence a simple calculation at
the outset can establish the minimum / value needed to satisfy the L/500 maximum deflection
2t SWL
criterion. (Note that for heavier loads, flange thickness may be the governing criterion.)
57 x10 sfiterer The deflection of span L with a central concentrated load W is given by
WL

a
9000

=
48EI
Figure 9.5 Single 9000 mm Span Monorail with 2 For a maximum deflection 4equal to L/500, the minimum / value is given by
tonne SWL
500W x10 xL
Imin

三
48E
S 1418.18 was published ni 2001 and has a superseded dead load factor of 1.25. This design
• The current A
example uses the 1.20 factor from AS/NZS 1170.0:2002 ni lieu.
 Monorails 369
e buildings
of portal fram
368 design
kN
ility load ni
the serviceab try 360UB50.7
where i s 50.7×9.82×10* x97/8
Working moment M = 27.2×9/4 +
x90003
500x22.2x10'
Hence = 66.2 kNm
48x2×10°
三

Imin 66.2×10°
798x10'

右
mm*
= 93.7×10°
= 83 MPa 360UB50.7
)
I( 121×10° mm*
= bending
:: try 360UB44.7 ed for a 300 MPa flange with a global
Hence the minimum flange thickness need
stress of 82 MPa is
ge Thickness

u
an (2400×0.89 +600)x11.0
9.3.4 Check Fl for variables nedot be
oT calculate het required flange thickness, hte folowing values
= 1.0
300-1.1×83
uation 9.22.
substituted into Eq )
(beam will be detailed with full depth end plates
= 12.0 mm
= 1.0
K
i

360UB50.7 flange thickness

E
B = 171/2
NG
= 11.5 mm < 12.0 mm
= 85.5 mm
= 85.5 - 9 (loads are applied 9 mm from the edges) the required flange thickness provision with
Hence a 360UB56.7 si required. This will satisfy
Appendix A941.
Gr

= 76.5 mm
its 13 mm flange thickness.
Hence = 0.89
9.3.5 Check Member Bending Capacity
Maximum dynamically factored working wheel load Check trial section 3600B56.7
/8
= 11.0 kN Appendit A941. Maximum moment M= 39.9×9/4 + 1.2×56.7×9.82× 103x9*
= 320 МРа 360UB44.7 adtL
E
s = 96.5 kNm
Working moment M= 272x9/4 +44.7×9.82×103x92/8, 9.3.5.1 Y BUCKLING ANALYSIS
DESIGN B
= 65.6 kNm
2も Bottom Flange Loading
65.6×10° 1 =M Using Table 9.2b,

xZ
= 124 kNm > M = 96.5 kNm
三

689x10' ОМых
= 95 MPa 360UB44.7 200 mm Below Bottom Flange Loading
Hence hte minimum flange thickness needed for a 320 MPa flange with a global bending For comparison purposes, using Table 9.3b,
stress of 95 MPa si
фМых = 153 kNm > M = 96.5 kNm OK
= 1.0 (2400×0.89 +600) ×11.0 2']
320-1.1×95
= 11.8 mm
The 360UB44.7 flang
e thickness
= 9.7 mm < 11.8 mm
NG
 371
Monorails
me bu
ildings
portal fra
073 design of
THOD
ebre capacy unsig het 0 mot a
TH ME ickness need to be
E LENG 9.3.6 We b Th
or a 360UB56.7
roFsompanoin puprose, demnieeht mm
EFFECTIV , hte following values f
9.3.5.2
To calculate the required web thickness
ion 9.28.
g. substituted into Equat
tre loadin
shear cen FF
= 359 m m
s =
condition = 172/2
Support AA k L
length Le = 00
Effective .0×1.0×90 = 86 mm
= 1.0×1
= 86 - 9 mm
= 9000 mm
= 77 m m
" eL Nw = 11.0
360UB56.7
yfw = 320 MPa web yield strength for
= 97.0 KNm '2
M
o 240×77 359 11.0 7
Mos = M
o +60
2×86 * 320

ww
86
= 97.0 kNm
4.4 m m
Zes = 1010×10 mm*
The 360UB56.7 web thickness
= 300 MPa = 8.0 mm > 4.4 mm
e) OneSteel (9
= 273 kNm (tabulated valu
= 303.3 kNm 9.3.7 Deflections
= 0.6x: +3 - 9.3.7.1 VERTICAL
dynamic
Mos due to all dead and live loads without
The L/500 limit on vertical static deflection / value.
inary design by satisfying the minimum
factors has already been satisfied ni the prelim
the self-weight deflection and so the defle
ction of the
= 0.269 The preliminary sizing did not allow for
selected beam will be checked again here.
s hte bending moment distribution is predominantly linear
A 5x0.56×9000*
22.2×10 x9000'
= 1.35 Table 5.6.1 SA 410
48x2×10°X161x10 384x2x10° x161x10°

a
8

Hence ф
Мых = 10.5 + 1.5
= 0.9×1.35×0.269×303.3 OK
= 12.0 mm < L/500 = 18 mm
= 99.0 kNm > M = 96.5 kNm OK
9.3.7.2 HORIZONTAL
9.3.5.3 COMPARISON OF METHODS odd-
AS 1418.1 stipulates a lateral load of 4% of the rated capacity to cater for inadvertent
The bending capacity si 9 kNm for shear vertical lifting.
length mehtod ni SA 4100. Usnig design yb bcentreuckl
ing
loading ni accord
analysi
s , h
ance with hte effecte = 4%×19.6
t
e
d 153 kNm for loading bendm i Hence lateral load
ot 124 N km for bootm flang ng capacity increases
flange, Hence a360UB567. esi olonadingjustanadeq 2
00 m beolw het botm = 0.78 kN
centre si adopted, but has plenty ofly m uate if the AS 4 100
argin if advantage is taken odefa ult loading tahet shear The load is applied at the bottom flange and so there will be some twisting with the bottom
f loading beolw het shear flange deflecting further than the top flange. Assuming that the intention of the code
deflection limit is to limit the overall lateral beam deflection rather than the bottom flange
deflection, calculate the overall lateral deflection.
 ings 373
l frame build Monorails
372 design of porta
0.78X10' x90003
=48x2x10°x11.0x10° OK
Partial depht stiffeners recommended
ofr laterol dna torsional restraint for
= 15 m m
= 5.4 mm < L/600 U 537
- 410 B .
deep sections
‹ 10 m m
1t SWL
01 end plate
9.3.8 Summary
eh 360UB567. section satisfies al fothe structural requirements sstipula
T A 14181.8
ted ni S
re det
for asingle span provided that hte ned pdolatensot aload stops aer os located ro
ailed or end 6450
3000
the end of the flange.
detailed ot ensure that trolley wheel loads
1 tonne SWL
Figure 9.6 3000 mm Cantilever Monorail with
94. DESIGN EXAMPLE I - 1 TONNE CANTILEVER MONORAIL 9.4.2 Design Load
Dead load 250 kg = 2.5 kN
9.4.1 Description Live load 1 tonne SWL 1000×9.82× 10-3
1 tonne Safe Working Load (SWL) = 9.8 kN
Capacity
= 1.1 Section 9.2.2.3
Type
KONE chain hoist (refer Appendix A9.4.2) Dead load dynamic factor
3000 mm Hoisting application group = H2
Cantilever span
Single back span 6450 mm Hoist speed (vh = 8 m/min) = 0.133 m/s
Hoisted load dynamic factor 92 = 1.2 + 0.27× 0.133 S 1418.1 Table 4.5.3.3 (B)
A
Cantilever support 4 bolts to top flange
= 1.24
Back span end support 4bolts to top flange
= 1. 2 x 4 x2. 5 + 1. 5 x$ x9. 8 Clause 4.4.4 AS 1418.18
Use Installation and maintenance of pumps in a water Limit states strength design load
treatment plant = 1.2×1.1×2.5 + 1.5×1.24×9.8
Hoist Motorised = 21.5 kN
Hoist group FEM M5 (2m) = 2.5 + 9.8
Trolley 4 wheels with motor Serviceability design load
Trolley traversing duty group = 12.3 kN
FEM MS (2m)
Height of lift 4 x2. 5 + 9 ✕9. 8
Hoist speed
6300 mm
Dynamic working design load =
8/2 m/min 2-speed = 1.1×2.5 + 1.24×9.8
Travel speed 20/5 m/min
Trolley and hoist weight 2-speed = 14.9 kN
Wheel load distribution 250 kg which includes hook, hook block and chain
4 equal loads (refer Appendix A9.4.2) The maximum dynamic wheel load based on the static wheel load distribution would be 25%
the KONE
tI should
eb noted that while hte wheel of 14.9 kN which would equal 3.73 kN. However the maximum wheel load in
eri orpe hoist fohte same caploaadcsityforathis chain hoist are equal, hte wheel loads for
of this
aK
O
NEw supplied data in Appendix A9.4.2 is 3.9 kN. This value will be used for the remainder
re far from being eq
e
r
i r
op e hoi
st s
i 72
. i um dynamicaly factoreduaw
s' The ouctome si that the maxm
KONE w
l a
s s
h
orking
own
w
n
i
h
eel
A ppendxi
olad for
NK com par
ed wit
h on l
y 3.
9 KN for the correspondi Maximum dynamic wheel load = 3.9 kN Appendix 49.4.2
ng chan
• The current AS 1418.18 was published in 2001 and has a superseded dead load factor of 1.25. This design
example uses the 1.20 factor from AS/NZS 1170.0:2002 ni lieu.
 buildings
rtal frame 375
374 design of po Monorails
inary Sizing o
9.4.3 Prelim
ehTyek desni cerina w ro a3
liebdenooitn, bean stret di farie hicknes. F Dynamically factored working wheel load
eh
T y
o
i
tk
e
n d i
n
e
it a6
1
5
mmi
s l
e
p be htat nac establishhet nim
calckspuaalo,itnistahekilteyloustetnac establisheht m mliebvheatulegonenhnyot
niuw N
w = 3.9 kN
otcasoin, het 300 m mxaium defiction creiroin. Neot htat orf heaveir olad, hnad yfr = 320 MPa
10-3×6.457/8
Working moment M= 14.9×6.45/4 + 53.7×9.82×
.)
ing criterion
be the govern
ickness may
th
hti abackspan fo Land aconcentrated doa in
The delection foacanilever fospan Lw
by
= 26.8 kNm
ntilever si given
at the tip of the ca 26.8x10°

"
不
933x10
3EI 3E!
= 29 MPa
ЗЕ! Hence minimum flange thickness
"！

7"2
(2400 ×0.93 +600) ×3.9
i um deflection 4equal ot L/300, hte minimum / value is given yb
For amaxm
1. 0
=
320 - 1.1×29
100W×10 xL'||
m
Ini = 6.2 mm
N

410UB53.7 flange thickness

k
where Wis the serviceability load ni N = 10.9 mm > 6.0 mm OK
Hence
Imni
100x12.3×10 x3000₴
2x10' 6050] 9.4.5 Check Member Bending Capacity
= 174x10°mm* 9.4.5.1 CANTILEVER
Check section 410UB53.7
Therefore ryt 410UB53.7 =I( 188x10% mm*)
Maximum moment M = 21.5×3 + 1.2×53.7×9.82×10-3×37/2
9.4.4 Check Flange Thickness = 67.3 k N m
The local flange bending stresses are coincident with the global beam bending
middle of the backspan. stresses at het As discussed ni Sections 9.2.3.3 and 9.2.5.3, Clause 5.6.2 of AS 4100 provides two methods
Method as set
oT calculate the required flange thickness, the following values ofr of determining Mox for cantilevers. These methods are the Effective Length Clause
variables need ot be substituted into Equation 9.22. down in Clause 5.6.2i) and the second is the Appendix H Method as, set down in
but uses the
= 1.01 5.6.2(ii). The first method does not take advantage of loading below the centroid
less conservative AS 4100 beam curve in Clause 5.6.1.1. The second method uses Design by
ism
= 178/2
Buckling Analysis with Mob values obtained from Appendix H but the relative conservat
= 89 mm of mandatory beam curve ni Clause 5.6.2(ii) tends to offset some of the advantages of loading
b e l o w t h e s h e a r centre.
=89-6
G
Appendix 49,4.2 Effective Length Method
= 83 mm
Hence p B
C /p = 0.93 Using the Effective Length Method described ni Section 9.2.4, determine Mox for the bottom
Dynamically factore flange loading of a 3 m long single span 410UB53.7 monorail.
d working hoist
load
= 14.9 kN
 ings
of portal frame build
376 design Monorails 37
= U
F
onditions
Support c =众你加L For cantilevers with a concentrated end load and full or partial restraint ta the root of the
h eL
Effective lengt 1.0×3000
cantilever
= 1.0×1.0x = 4.0 Table 3
H S 4100
A
Cg Cq
= 3000 mm = 3.7 Table 3H S 4100
A
TELL 54. -
oM = I. VE,I G
J GJL: CAr Eq 9.16

L
5+3
= 10.3×109 mm* BL
4.5×3000/ 6450
' mm*
= 234x10
X3.7
5 + 3x3000 / 6450
= 394×10° mm* = 1.21
.
M = 487.3 kNm TEl- where Lsi het length of hte cantilever

K
= oM GJL:
Mos
= 487.3 kNm ' ×2×10 ×394 ×10°
V8×10* × 234x10' ×3000₴
= 1060×10 m
m
る

= 2.15
= 320 MPa (C, +C,K)
= 304 kNm (the tabulated value of M s is 304 kNm)

=
T( l +K? )
= 304/0.9
(4.0 + 1.21x2.15)

=I
= 338 kNm
r. (1+2.153)
= 0.886
= 0.6x4 3+ -
D +oh

三
玩
= 0.703
403 + 0

三
2
= 201.5 mm
The bending moment distribution si predominantly linear = 403 - 10.9
= 1.25
8 Table 5.6.2 SA0014 = 392.1 mm
Hence
M
o.ox = 1.25×0.703×304
= 267 kNm > M= 67.3 kNm = 1+-
Appendix H Method - Bo
ttom Flange Loading 1+|
）
⅔冷
Unsig het Appendxi Hmehtod described ni Section 9.2.5.3, determine Mox for botm nagel
Mos =O
m
e 04M,
 buildings
rtal frame 379
design of po
Monoratls
378
2.15
2 x 2 0 1 .5
⼄

= 392.1 mm
392.1
三1 ⼗1
2X201.5
392.1
21.3 1+
=

2X401.9
392. 1
= 1.74
2x401.5
392.1 ×21)
Mob = 1.910
Hence
87.3
= 0.886×1.74×4 Hence Mob
= 751 KNm = 0.887×1.910×487.3
= 826 kNm
丛

+3 -
= 0.6X
丛

M
bo
§

Osb = 0.6х- +3 -
Mob. M
bo
338 +3 - 338
= 0.6X1
751) 338 338
= 0.6X1 +3 -
826, 826
= 0.804
OMox = 0.822
= 0.9×0.804×338 фМых = фоцьМах
= 244 kNm > M= 67.3 kNm K
O = 0.9×0.822×338
= 250 kNm > M= 67.3 kNm OK
Appendix H Method - Loading 200 mm Below Bottom Flange
Using the Appendix H method described ni Section 9.2.5.3, determine @Mox for loading Comparison of Methods
200 mm below the underside of the bottom flange.
The respective capacities due to bottom flange loading and loading 200 mm below the bottom
M
bo = Amc 04 M
o flange are 244 and 250 kNm which are both less than the 267 kNm calculated by the Effective
Length Method. It is evident that the relative conservatism of mandatory beam curve in
For cantilevers with a concentrated end load and full or partial restraint at the root of hte Clause 5.6.2(ii) for the Design by Buckling Analysis Method more than offsets the advantages
cantilever of loading below the shear centre ni this design example. In any case, the bending capacity is
clearly ample because the beam size has been set by satisfying deflection limits.
= 4.0
Table H3 SA 4100
= 1.21 A 4100 9.4.5.2 BACK SPAN
Table H3 S
= 2.15 as for bottom fla Treat the 6450 mm back span as a single span with a central concentrated load and self weight
K
nge loading
but ignoring beneficial effect of cantilever self-weight.
= 0.887 as for bottom flange
loading Check trial section 410UB53.7
+ h。 Maximum moment M = 21.5x6.45/4 +1.2×53.7×9.82×10-3 x6.45₴8

2
= 38.0 k N m
403
+ 200

2
= 401,5 mm
= 403 - 10.9
 s
design of palotr frame building
380 Monorails 183
nalysis
by Buckling A
Flange Loading
U 7mcapacities.ti a0546 m
ngis Tabel 92b nda interpolating,het bendnig and capacities 537. hw
Bottom 9.4.7.2 HORIZONTAL
the average of the 6m and
single span si approximately
= (19 5+ 162)/2 vertical lifting.
Hence ОМых
.0 kNm OK
=178.5 kNm > M= 38 Hence lateral load 47 0x 9. 8
=
h bendnig capacyti si celaryl ampel because seaseni seeking agreaetnr sbetenydbnigsaticsafpinaycgti
= 0.39 kN
eT i
s
defection limits. Theroefforebelowhterebottsioomnpoflannitgeni htload a
ce
s. ih a
he b
Te g aanreate
g
ba The load si applied at the bottom flange and os there wil be some twisting with the bottom
ing cksp by its nature has flange deflecting further than the top flange. Assuming that the intention of the code
taking advantage a
yb
h oggnig moment at one end dueot het self-weight fo hte cant lever and os ti woudl ebm eor deflection limit is to limit the overall lateral beam deflection rather than the bottom flange
accurateot atke htsi into accoun.t Agani, there si on pointni pursuing this accuracyni hsti deflection, calculate the overall lateral deflection.
case. 0.39×10 x3000* 6450

=
3x2x10° x10.3x10€ 3000-
9.4.6 Check Web Thickness
= 5.4 mm < Ld/300 = 10 mm OK
oT calculate hte required web thickness, the following values for variables need ot eb < 10 mm
substituted into Equation 9.28.
= 403 mm
= 178/2 9.4.8 Summa ry
= 89 mm The 410UB53.7 section satisfies all of the structural requirements stipulated in AS 1418.18.
= 83 mm
G

w
N = 3.9 = 3.63 kN
9.5 DESIGN EXAMPLE III - 5 TONNE SINGLE SPAN MONORAIL
w
of = 320 MPa 410UB53.7
9.5.1 Description
240×83
+60
403 3.9
Capacity 5 tonne Safe Working Load (SWL)
毎

89 2×89 320
Type KONE low headroom wire rope hoist
= 2.8 mm 9000 mm
Single span
410UB53.7 web thickness Supports 4 bolts to top flange
Use Removal o f filter equipment
= 7.6 mm > 2,8 mm
Hoist Motorised
9.4.7 Trolley 4 wheels with motor
Deflections
Usage FEM FEM M5 (2m)
9.4.7.1 VERTICAL Height of lift 6,000 mm
5/0.83 m/min 2-speed
The Lo/300 limit on vertical static deflection Hoisting speed
due ot all dead 20/5 m/min 2-speed
and live loads with out Trolley traversing speed
factors has already been satisfied ni the preliminary
d
ynamic 380 gk which includes hook, hook block and wire rope
albeit ignoring its self-weight deflection. design b
y satisfying t
h e m i
n i
m um / vaule Trolley and hoist weight
selected beam wil For comple teness, the cantilev Static wheel load distribution 40%, 10%, 40%, 10% approximately Appendix 49.4.4
be checked
still ignoring self-weight.
again here usi ng the actual / value of the erchos
deflectio n of the
en section but
12.3×10 ×30003 6450]
3x2×10* x188×10€ 1+
3000
= 9.3 mm
< Lo/300 = 10 mm OK
 ildings
al frame bu M
sloianr 383|
382 design fo port
B 76 t larifi d
450 U n 9.5.3 Preliminary Sizing
310 UC731
The key design criteria wil be deflection, beam strength and flange thickness. For a 9 m
5t SWI span, ti is likely that deflection will be the governing criterion. Hence a simple calculation ta
^
hte outset can establish the minim um / value needed o
t satisfy t
h e L/500 maximum deflection
031 x10 elrist criterion. (Note that for heavier loads, flange thickness may be the governi
both sides ng criterion.)
The deflection of span L with acentral concentrated load Wsi given by
9000
W
E

q
48EI
tonne SWL
m Span Monorail with 5
Figure 97. Single 9000 m For a maximum deflection 4equal ot L/500, the minimum / value is given by
Design Loads
- 500Wx10 x2*

hm
9.5.2 48E
= 3.7 kN
Dead load 380 kg where W is the serviceability load in kN
103-
Lvie load 5tonne SWL = 5000×9.82×
Hence
= 49.1 kN
Section 9.2.2.3
Imi n = 500x52.8×10' x90002
= 1.1| 48x2×105
Dead load dynamic factor a
= H2 = 223×10° mm*
Hoisting application group
= 0.083 m/s
Hoist speed v(, = 5 m/min) . try 460UB67 (I= 296×10% mm*)
= 1.2 ÷ 0.27×0.083 S 1418.1 Table 4.5.3.3 B
A ()
Hoisted load dynamic factor 2§
= 1.22 but adopt KONE's 1.24 Appendix A9.4.4 9.5.4 Check Flange Thickness
= 1. 2x 4x 3. 7 + 1. 5x6 x 49. 1 Clause 4.4.4 SA 1418.18 C h e c k 460UB67
Limit states strength design load
= 1.2×1.1×3.7 + 1.5×1.24×49.1 To check the flange thickness, the following values for variables need to be substituted into
Equation 9.22.
= 96.2 kN
K
L = 1.0
Serviceability design load = 3.7 ÷ 49.1
= 190/2
= 52.8 kN = 95 mm
Dynamic working design load = 9 x 3. 7 + 0 x 49. 1 = 95-9 Dimension Bl Appendix A9.4.4

G
= 1.1×3.7 + 1.24×49.1 = 86 m m
= 65.0 kN Hence Ср В
/р = 0.905
The maximum dynamic wheel load based on the static wheel distribution would be %
04 o
f Maximum dynamically factored working wheel load
650. kN which would equal 260. kN. However the maximum wheel load ni the KONE Nw = 27.7 kN
supplied data ni Appendix A94.2. si 277. kN. This value will be used for hte remainder fo = 300 MPa
this check. fyt
Maximum dynamic wheel
load = 27.7 kN
Appendix 19.4.4
•The curent S
A14181.8 w
sa published ni 201 and has a superseded dead olad factor fo 1
example uses the 1.20 factor
from AS/NZS 1170.0:200
2 ni lieu.
2.5. Thsi dgesin
 e buildings
of portal fram
384 design
3x9₴8 M
sliaonr
+67x9.82×10
583
9/4
ent M =65.0x
Working mom = 153 kNm
310UC118 flange thickness
= 18.7 mm < 20.9 mm
NG
153x10% Hence use 310UC137 which has a 21.7 mm flange thickness
subject ot bending check.
1300x10%
= 118 MPa 9.5.5 Check Member Bending Capacity
ness si
flange thick Check trial section 310UC137
minimum
2(400 ×09.05 +600) ×27.7 Maximum moment M = 962x9/4 + 1.2×137×9.82×103x9₴/8
= 1.0 30 0- 1. 1× 11 8 = 232.8 kNm
= 21.2 mm Bottom Flange Loading by Buckling Analvsis
Using Table 9.2d
ckness
460UB67 flange thi .2 mm NG
= 12.7 mm < 21 Hence фМ
.х = 580 kNm < M= 232.8 kNm OK
Hence coudl yrt na 8-whtheeisl itnrostlaenyce,oraashsaeloctw hicker flange such sa a610UB, a
ion with at 200 mm Below Bottom Flange Loading by Buckling Analysis
70WB or a 310UC. nI er member could eb na advantage ot acheive Using Table 9.3d for comparison purposes
om.
greater headro He nce Mox = 580 kNm > M= 232.8 kNm OK
K for deflection)
in: O
Check 310UC118 (I=277×10% mm* > Im 9.5.6 Check Web Thickn ess
= 307/2
= 153.5 mm To calculate the required web thickness, the following values for variables need ot be
Dimension B
substituted into Equation 9.28.
= 153.5-9 1 Appendix 494.4
321 mm
= 144.5 mm
BF 309/2
Hence = 0.94
= 154.5 mm
Maximum dynamically factored working wheel load = 154.5 - 9

G
Dimension Bl Appendix 49.4.4
N
w = 27.7 kN
= 145.5 mm
Jyt = 280 MPa He nce FB
C /F = 0.94
Working moment M =65.0×9/4 + 118×9.82×10-3 x9₴/8 Maximum dynamically factored working wheel load
= 158 kNm N
w = 27.7 kN
158x106 yfw = 300 MPa 310UC137

=
1760×10'
= 90 MPa 240x145.5+60 321 27.7

ww
154.5 2×154.5| 300
: . minimum flange thickness is
= 5.2 mm
= 1.0 2400x0.94 +600）
✕27.7 12 310UC137 web thickness

な
280-1.1×90 = 13.8 mm > 5.2 mm OK
= 20.9 mm
 gs
of portal frame buildin 387
386 design
Monorails
s
9.5.7 Deflection Standards Australia (2002). SA 1418.1-2002 Cranes, Hoists and Winches Part 1 : General
5

Requirements, SA, Sydney.

VERTICAL . . (1998). The Behaviour and Design of Steel Structures ot
Trahair, N.S. and Bradford, MA
6

S 4100. 3ed., (Australian), E&N Spon, London.

dnigectheitonm
Ttar isa riedy ben sasifeidni htore mniayrcomdplesetenteneses,s, hethte defl
deflection.
For ihet scelthe
nfioum e
A
OneSteel (2010). Hot Rolled and Structural Steel Products, 5 ed,. OneSteel Market Mils,
7
abler inenchecked agani her nugis het acutal / vaule fohet choens seocint ubar
its self-weight Newcastle.
albeit ignoring .8 Yoo, C.H., Heins, C.P. (1972) Plastic collapse of horizontally curved bridge girders, Journal fo
the Structural Division, ASCE, 98(4):899-914.
eight.
ignoring self-w x90003 Bradford, . . (2011).
MA Strength Design of Curved Crane Monorail Beams, Seventh
52.8x10
9
International Conference on Steel and Aluminium Structures, Kuching, Malaysia.
x10€
48x2x10 x329
=

10.1 Becker, K . (1968). Girder Flange Bending due ot Trolleys, Fordern und Heben.
= 18 mm OK
= 12.2 mm < L/500 11. The Broken Hill Proprietary Company Limited (1978). Monorail Beam Design - Variable
Flange Width Loading, BHP, Melbourne.
12. Woolcock, M.D. and Ford, AW . . (1998). Buckling of Crane Runway Beams and Monorails,
9.5.7.2 HORIZONTAL BE Thesis, Department of Civil Engineering, The University of Queensland.
SA1418. stipulates alateral olad of%4 of hte rated capacity ot caetr ofr inadvertent .fo Gorene, BE .. (2003). Crane Runway Girders Limit States Design, ASI, Sydney.

13 14
:3 Design
vertical lifting. European Committee for Standardization (2002), XP ENV 1993-6: 1999(E) Eurocode
of Steel Structures - Part :6 Crane Supporting Structures, Brussels.
= 4%×49.1
Hence lateral load
= 1.96 kN
The olad si applied at hte botom flange and os there wil eb some twisting whti hte ogbot
flange deflecting further than the top flange. Assuming that the intention of hte edoc
deflection limit si ot m
il ti het overall lateral beam deflection rather than thebootmgalf
deflection, calculate the overall lateral deflection.
1.96x10' ×9000'
48×2×10 ×107×10°
= 1.4 mm < L/600 = 15 mm OK
< 10 mm ОК
9.5.8 Summary
The 310UC137 section satisfies al of the structural requirements stipulated ni SA 1418. l
fact, the C
U section has some advantages over a 610UB or 700WB section with a savnig
section depth and its greater lateral stiffness. a
9.6 REFERENCES
.1 Satndards A
Crane Runwayustralia (200
1)
. S
A 1418
1.8-2001 Cranes (Including Hosit and W
s and Monorails, SA,
Sydney.
niches) Per
I-
Standards Australia (1993), SA3990-1993 Mechanical Equipment - Steelwork. A
Standards Australia 1998). A S, Sydney.

3
S 4100-19
98 Steel Structure
Satndards Australia (2002), AN
Principles. SA, S/ZS 11700.:2002 Structs,uralSA,DSeysgidnney.Actions Part :0Geat
Sydney.