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i.CKIf01iESDG-BMEHT
The' writer wishes to show his appreciation to
Mr<, -Ro JU Hoffman^ Engineer of Bridges and Dams of. the
Arizona Highway Department,, who suggested the particu­
lar bridge and made the drawings and list of bids for
the structure available to the writer.
The writer also wishes to. state that he was fortu­
nate in having one such as Assistant Professor Go Ho :
Handforth for the thesis advisor« Professor Handforth
showed eonfidehee. and gave;-invaluable advice in the
preparation of this,thesis» vY
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OF COEEBHIS;
Ghapter
• V „■ : ACKNCMIiEDGEMEHa? ..... .
X02\f
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AUJMINUM
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ii
o © © -o © © © © © © © © © © © © & © © © © © © © © © © © ©
0==..o=ae.0OD e
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,
.IL■
ovo••«.«»..=..=.
II.
STRITGTTJRAL ALUMISGM VS. STEEL ..... ...... .
l5
III.
BRIDGE DESIGN ...... ....... ...... ...... ....
26
, IV. ’ RESULTS Aim-CONCLUSIONS .... ......... ... =.
JO
-ARPEHDIX A - SPECIFICATIONS ...
.. ?5
BIBLIOGRAPHT ...... *.©. .....................
93
M S I -0Z:TimiiS
■lumber
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Page
lo Tensile Properties of Aluminum Alloy
, :v
l4S-T6 at Elevated Temperatures r;<,e:v.„
.« 23
,
:; ;TI.oMoment Table'for E20^$iB^I^. Truck Train « . . i|3
III*
Section Talues for Cross Seoiions of Girder
1T0:
Itemized Quantities of Aluminum and Steel
6ii\ -
.To 68 ,
LIST OP FIGUHSS
Humber •
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Stre^s^strain Cure for Aluminum Alloy II4.5 -T6 , o, 19
;2«
Influence Lines for Pier lot o»s» 0 0 o> =0 oo> ooot» lj.2
3V ' Influence Lines for piers 2 and 3° °c° 0 0 vo»»* oo 47
4
d
Coefficrents of Unit Loads o »ooco @o oo©o««o©oo©© 49
£«■ Allowable Compressive Stresses for Axially ,
yz .'Loaded Columns © ©©©©©©©©©©©©©©©©©©©©©©.©©.*©©©©©>9-S
■.
6 0
Allowable Compressive Stresses in -Beams and .
‘ Girder Flanges © ©©©©©©©©©©© ©©©©©©•©©©©©©©©©©©© 90
7©
Allowable Shear Stresses on Web©'©©©©©©©»© ©©©©© 91
■ 8 ©:vAllowable Longitudinal Compressive Stresses for , \.
Webs of Girders © ©©©©©©©©©©©©6 .©©©©©©,©©©©©©©©© 91
9©
Chart for Determining Effective Width for
", Gut standing Legs -of Angles © ©©©«© ©©©©©©©6 ©©©© 92
; ■10©
Spacing and' .Moment of Inertia of Vertical .
:•St iffne rs on Webs of Girders ©tl©©©©©©.©:#©©©©©© 92
11.
Drawing of Designed Bridge --
°in rear pocket©
lifROBnCTlOH
lihen one studies the mechanical properties of the
."aluminiun alloys and not.es the comparatively high values of
the strengths and also the lightness of the alloyss one
vwon&erSgwhyV with all these favorable properties, are not
.
::aluminum .alloys used: more extensively in structures of the
larger sizes=
Such a question arose in the writer’s mind,
so he decided to carry through an investigation of. the de­
sign of a: strueture and compare the design and cost of the.
■.structure using, either an aluminum alloy or structural
..■eteelo v
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■& bridge was chosen.for the comparative examination
■since the writer8s interests, are mainly along this line
'and for the reason ‘that more-material-is available concerning the use of structural aluminum as a bridge building
.material -than for. any other types of large structures,
-.As to the .type of .bridge-g:-;-a highway plate :girder .
i'
y-hrldge was -chosen 'because this type is .predominantly built
in Sri zona for the Highway Department and such a-bridge
,
y
had been built within the last' few years = - The.plate -gird~
er. is favored in the- construction..of -highway bridges beyi
.cause •it Is so rugged and.compact that it will effectively
.resist and check shock and vibration! in addition the
2
following reasons may be presented for using a plate girder
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instead of a truss bridge g ..
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It has fewer critical points where overstress may
he likely to exist because of poor and faulty "design orv '
workmanship o /
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{ 2o .iihe. smaller number of sections are' easily and
quickly obtainedo
' 3o
: .:
The cost per pound for •erection is decidedly less
. sihce the girder can be .assembled almost entirely in the
shop and ahipped as a nnlt ready for- erection*
lj.o It is less liable to Injury by accidents.
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The cost of maintenance is less» due to the ab-
sehce of small parts ahd details to"work loose under traf=
fic o
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The ordinary limit of length for plate girders is
about 100 feet2 but this limit has often been exceeded by - /
Wenty^five to thirty percent for simple spans and by much
•more for swing spans.
Usually it is the difficulty in
shipping very long plate girders from the shop' to the
'■
bridge site that determines the higher limits of such a ■
The bridge chosen for comparison, is referred to as
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the Aqua Fria Bridge- which was" designed., and let to bid by ■
the Arizona Highway Departmento
.1 o: Economics of Bridgeworkj
It is located on the
Jo
A . L » Waddelo •
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PhoenlX”Preseo11 Highway at the crossing of the hew River
and the Aqua Pria River, approximately sixteen miles north
and seventeen miles west of phoenix*
. The design, of the al'uminum bridge Is 'limited to the
metal structureo
It should be noted that the use of
existing piers affected the design and. cost of the pro­
pose d aluminum bridge» ;..;t
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' Alizmin'um was' discovered a little over one hxmdred ■::■
years ago and for the.next forty years or so it was just
another element«, intricately produced, and not .much more
than a. chemi.cai .curiosityo
In 1886 an electrolytic proc-
ess was discovered to produce'metallic aluminum on, a commercial.basis« The spectacular development of the alumimito industry since then may .he- ascribed to the. metal's
.
* diversity of':properties.s: .which has made possible a great ',
many; variety of applications 0 - :.p. I '
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.'. The principal aluminum ore is bauxite, a hydrated
:- aluminum bxlde appro ximatlhg the fo
.
AI2O321120“ .Al™ -
though aluminum is the most widely distributed of the .
metals9 it is never found free In:nature because it is■so
. re active». Hp until World War il.Arkansas led I n .the pro ^ .
duetioh of -bauxite in the' United States s accounting for ' .
over ninety“Six percent of the total preduction=
' ■ m
the production of aluminum several processes are
■’ Involved 1 .The commercial'aluminum ore P bauxite, is found ,
in beds or lenticular masses0 When the ore is near the
"surface it is mined by.the open=pit method; when deep in
the ground it is bhtained thro'G.gh shafts and tunnels« The:
■ore is‘crushed and dried at fhe mine as .a' preliminary Step
in the purification processo
The next phase isfto reduce
it to pure aluminum oxide*
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• ' . The- mest commonly used: procedure to purify the ore is
to disperse it in a _solutiph of Sodium hydroxide*
this pure aluminum hydrate is precipitated^
From
The'■'insoluble
impurities9 mostly ferric oxide, are removed by filtering.
This hydrate■is then.calcined .to remove the chemically
combined water and leave, pure
ready for electrolysiso
The aluminum is then ,
. •■
- . ■ :Eiectrolytic•furnaces used in the production of metal­
lic aluminum consist of an iron box lined with carbon
■ -
blocks which serve as a cathode:o The anodes are a set of
carbon plates, which, .are ‘lowered from the celling by means
of a block and tackle' or some, other device mhose-operation' ;
can be controlled*
After an arc has been struck, some
■■-:_:
cryolite: is thrown' into the furnace*. :This is an aluminum
mineral (fluoride of sodium and 'aluminum), mined 'chiefly, in
Greenland*:- ■The cryolite melts -(1000° CV) to a .clear con.due ting'llqulh, in which the purified;anhydrous 'aluminum
,
:oxide is- easily .dissolvedo
.
The flow of current through the
ceil liberate s. enough heat; to .keep the-cryolite fused 0 The;'
aluminum that is produced:is ^deposited .at the:bottom .of'■the
furnace and is tapped out from the. cell and cast into bars •
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The .pig metal is then ^emeTted to remove dross, elec=
:troljte» etc os and" is poured into molds of various shapes :
asVa.,preliminary step to workingo
The .metal is then shaped
hy trolling it into sheetss harsy or standard sections3 by
..
drawing:it into wire, or by forging, .casting, and extrudingo
" • ; ‘Commercial aluminum sheets must have, -ah aluminum con. tent of not less than ninety=>nine percento .
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: Very pure .aluminum- is made also by an 'electrolytic re=
fining process in- which a copper^aluminimi alloy serves as ;: *
.
. the anode, beneath the moiten salts containing fluorides of
•aluminum, ■sodium, and bs.rium<>
The cathode is a layer of '
1pure- aluminum which is so light; that;it floats- on top Of; '
■the bath of molten salts „ fure *aluminum has such;a silvery
: luster that it has generally replaced silver in astronomic
cal mirrors =
"
Since the development of the process to produce alumi­
num on a cbmmerclal'hasis.,- it has become one of the impor^
tant engineering' materialsThis rapid progress of its ap”
plication is due largely to its many favorable properties,
particularly 'its light weight,combined with a relatively
high strength of. its alloys„ .The physical and-chemical•
properties of aluminum are- .enumerated as -follows t
Physicals
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SpecificSr-avity»-.•Commercially pure aluminum. ■ -
■•;--=-i I, Jhcpd Aluminum" .and''Its Alloys, 19111o
. •=; ;1;;.;
weighs :Q; O98'pounds per etibie inch:or about 169 pounds per
cubic footo 'fhis corresponds to a- specific gravity of :
2o71«
; p; . 2o : Electrical Conductivity0--Aluminum that is practi-cally pure has -a volume conductivity in excess of sixty-
>
four percent of the International Annealed Copper standard,,
but because of its. low specific gravity,, the mass, conduc­
tivity is more/than 212 percent o Commercial aluminum con­
ductors are of such purity that;.the conductivity is not
less than sixty^ohe percent,
'
(Values of conductivity of
wrought and cast alloys may be found in Tables 9 and 10 of
Alcoa,- Aluminum and'its Alloys, 1944°)
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”3o- Thermal and ■Expansion Conductivity 0--Aluminum has ..
a thermal conductivity of 0o52 in Cog0so ..units {calories//:./
per seeondi per square; centimeter,/per centimeter of thickness, per degree centigrade)„
The coefficient of thermal
-
expansion' is a/ little more than' twice that of steelj its :/'./
value being about Do009012 per degree Fahrenheit=
4o .Modulus of Elasticity :/(B}®«==■The modulus of el as-
■
tieity,which/Is the ratio of stress to strain within the /
elastic limit varies, for"different alloys of aluminum,
from 19 million to 19q6'million pounds per square incho.' /; .
For practical purposes, aluminum may b e ■taken/ as having/an
S value ofl0o3 raillion'pounds per square inch.
: ho
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Poissonss Hatib o"-This value is -taken as 0*33 •>
/ 60 : Brine 11 Hardness MuraberB==The Brlnell Hardness v
8
#-umber:var ies wi &
the alloys of aluminum $ these values,
range from 23 to
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Further •physical properties'will’later'.be •presented
for a' specific alloy .designated ooimierGialiy by Alcoa as
.
14S-t6„
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Chemical; . ..
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Corrosion0=^-All of the aluminum alloys are classi­
fied as materials resistant to.cdrrosiono
These alloys are
generally used without any protection except where they are
in'contact -with other metals.
The protection, usually bitu?
.minous paint9'.is necessary,, to’'prevent galvanic:action,; ,’
' .Besides the inherent physical and chemical, properties
of aluminum, its affinity for heat treatment' and alloying
furthers its position of importance as an engineeringmaterial.
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The yield: strength of commercially .pure alumi™ :
num fully annealed is about p 9 000 pounds per square inch,- •'....
but by.means of alloying and heat treatment the yield :
strength can be increased to >8,000 pounds per square inch
- or. more, Compared to the pure aluminum the variation in
weight of the alloys is about four percent, while the in-crease in:yield strehgth; is well over 1, 000 percent, The
metals used for alloying aluminum are silicon, 'copper, mag­
nesium, mangahese, and chromium with contents of the
alloying elements varying from Oijr to no0'percent.
Some
9
of the alroninurii alloys contain as much as 12 percent of
' silicon o
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The different methods of manufacturing aluminum alloy
shapes are much the same as used, in the steel Industry in
that they., vary with 'the product and alloys. The one method
of manufacture applicable only to the aluminum product is
the process of extrusions
Orossrseetions$ lengths9 and
weights of aluminum alloy products may he found in any of
the hand-books printed by the Aluminum Company of America
or Reynolds Aluminum! .
Extruded shapes are' produced by forcing the /metal
.'
throu#i an orifice having the desired cross-section and then
straightened by stretching0: limitations to this prooess de­
pend upon the weight per foot of length and the total weight
of the piece extrudedo
Shapes that can be circumscribed by
a fifteen inch circle can generally be extruded«
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By using a specially designed section rather than one
. made up of one or several of the standard shapeSp better
economy of metal and fabrication can be effected,,
The
proper design of an extruded section places the effective . •"
area "of the cross=sectlon so that it is used more effi­
ciently and facilitates joining by riveting or welding=
Two methodsg cold working and heat treatments are
used to alter the properties of aluminum alloys = Cold
. working has the same general effect upon the- alloys of
10
aliHQliitM as. upon the steel .alloys0 It Increases the
stretigth and hardness and reduces the ductility*
The ef­
fect of the heat treatsent given an aluminum alloy is quite
different from the effect of heat treatment on the iron-,
carbon :alloys| hdwever,, the ob jective of this treatment is
the same— that is$ to distribute the harder metal evenly
and so prevent,:Slipping along the plane of weakness of the
softer metal, ,•
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The solution heat treatment for wrought alloys of
aluminum is a carefully controlled process» The tempera­
tures of heating vary from 910° P, to:1,000° P, depending
upon the alloy and quenching.
As in all cases of heat
treatment, the::time of heating depends on the size of the
load in the furnace and on the thickness of the material,The sudden change of temperature caused by quenching may
result in some distortion of the material but this distor­
tion is corrected by the follow-up process of rolling or
stretching.
Careful consideration must be given when con­
templating ‘heat solution treatment to a pre-formed materi­
al,
The solution heat treatment is followed by an aging -
or precipitating heat curing at room temperature for some
alloys, and at temperatures, ranging from 315° F» to 365° P,
for others.
The aging treatment does not produce severe
distortion or deformation-to the member.
Most Of the alirv
minum alloys can be heat treated, but not all,
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worked wrought alloys, and casto
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The wrought alloys whose properties are controlled by
heat treatment -are des'lghated by numbers , denoting the :
chemical composition^ followed by the letter 8, and then by
the letter Os W»; or To
The letter Q designates the soft,
.slowly cooled, condltioh, if means the alloy has gone through
the heat treatmentp and T represents the final condition of
heat treatment and agingo
The .ultimate tensile strength of
the:"S" alloys.under the "T
coridition can be increased ,
through'subsequent heat treatment combined. With cold
workingo
Another number is added'to designate the specif­
ic heat treatmento
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The cold worked wrought alloy is labelled, with a num- -
her and the'letter S followed by either b or Ho
The letter
0 indicates 'a fully annealed condition and H,the fully
hardened condition o The strained .hardened condition after
heat treatment is represented by BT» :
:
Each cast alloy of aluminum is designated by a number
followed by the symbol T and another number that specifies
: the .heat treatment i n v o l v e d g - ■ ..
••b -l
• . Since the alloys of aluminum are generally less resis­
tant to corrosion than is pure aluminum, they may .be given
a thin coat.of pure aluminum, so better resisting
12
cprrosiono
The aluminum coated product is cormnercially
known as Aldad*
. ■;
,v,.In- forming and... fabrication of aluminum alloys the. same
methods- are used, as for other metals» Of course s there are
certain differences lu the'.specifications for working alU" .
minim, alloys but these can be met with little change of
equipment and training of personnel,
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Any"of.the.aluminum companles can furnish 11tenature
treating the various processes of fabrication that will.be
coveredIn a general way b^ this.paper.
'
'Sheetsp platess and shapes' of aluminum alloys can be
sheared on any of the equipment used for steels provided
that the thickness of the aluminum is not morel than one?
halfIncho
Material exceeding one -half inch in thickness
..should' be sawed,.
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\ The; sawing operation can be used for straight or
curved cuts<, For best results in sawing1high blade speeds ;
are recommended! for band saws a speed of '5,000, feet per
minute should be used and a speed of 105000 feet per minute
gives good results with circular saws0 Consideration must
be given to the set and rake of the teeth in order to, ob­
tain a.cut free from jagged edges0 .
'Aluminum alloy rivets may be driven either hot or
colds
with squbese-type riyeters or pneumatic .hammers,
The pneumatic hammers and back-up tools used to drive the
almnlnmn rivets should he- heavier ■than 'those used for;steel
rivets of the same 'size« For hot driving-, the 'rivets
: V
'should be heated in a -iuiiia.ee having accurate temperature v:
,control» Rivets must be transferred from thefurnace and
’driven as soon as possible: since) quenching is obtained by
.contact ';wlth the cold metal rand- toolso 'Riveting the -heat'r
treated aluminum, al1oys produces no more distortion in the
structure than that found in the riveting operation for
f The drilling}, punching},, and reaming of aluminum, al­
loys 'is much the,same as for structural steel= The only
differences are that for'almnihxrri^;the: material has to be,/marked differently and drilling and /reaming operations
.'■'■■-/■:
are fas ter fo r the aluminum alloys. -As in all cutting op­
erations of metal}, the best results are obtained when the
tools are sharp and a liberalamount1of lubricant.is used,
aluminum alloys could not be
welded satisfactorilys now certain alloys can be welded by
oxy=-acetylene torch}, electric arc-:and resistance welding
methods o Weldihg tends to decrease -the strength of tem­
pered material because of the annealing effects but in
/
Some: cases good resuits can be obtained by heat treating.
the alloy after-gelding, :/■ " ;
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Cutting aluminum alloys with a torch is hot advisable
since the high heat, damages the’metal and/ the cut is
di :;
;a
exceedingly .ragged 'because the aluminum seems -to melt in­
stead of bufninga
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It is an evident fact that limitations of steel de­
signs have been caused by the weight of steel and that a
.light metal is needed for long bridge spans!
The answer
to the. problems in steel seems to be at hand with the ad­
vent of structural aluminum.» '
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Thspb.aliminvm: has come.of age as a' structural materi• ai is evidenced by.the construetioh of several bridges 'and;
crane booms with aluminum = The two outstanding bridges ,
that have been built of an aluminum alloy are located in
-England and in Ganada<,
The.aluminum bascule bridge a t ..;
Sunderland^ England^ is recognized as the•first movable
type bridge to be built of this metalo
A sixty percent
weight saving over ah equivalent steel structure was. ob­
tained by using .aluminumo ' -The Canadian bridge at irridaV
Quebec^ is a 290-foot arch in which it was calculated to
save 200 tons in weight over a comparable steel design.
In the United States one of the more important projects
,using aluminum was., the 'reconstruction of a railroad
bridge,over the Grasse River, near Massena, Hew York , log: Engineering News Record, pec. l6y -19ii-u0 ■
! ;'2o;:;: Roads and Bridges, August, 1949°
.
3=
Civil Engineering) Beco s 191^»
.
.
in which--two of the steel deck girders were replaced with
aluminum0 This span is 100 feet long and 10 feet deep 'and
weighs 539 000. pounds = In comparison^, ad jacent steel spansP
with eq.ual lengths' and.depths df 9 feet, weigh" 128,000
■
: pounds o - The .complete aluminum., span., with both girders and
brae ihg as a unit 9-was:•shipped:to the.
.bridge'site and ;, . . .
placed with a locomotive- crane within, a few hours. The
steel spans were shipped in parts to the site and then as­
sembled with field rivetSg requiring:two days per span0
Another bridge that has made Use of aluminum.is the Smith"'
field Street Bridge of Pittsburgh^
;
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lip to now, most of the structural design in aluminum
hasTbeen with the .alloy ll[-S-T6o The .typieal mechanical properties of thls alloy-as compared with structural.steel are s
'
Aluminum
" (11{S?T6)
Ultimate tensile .strength, p.oSoi0
'
;
Steel'
.
70,000
.. 60,000
Tensile, yield strength, p-oSolo ,/
(06 2%' offset for aluminum)
(Biastic limit for steel}
.
; :. 53$ 000
;33,000
Shearing Strength, p^Soio
..
Ill's000
1|.5,000
Hodulus of elasticity, po'Spio •
(In tension and compressionj ..
10,600,000
.
29,000,000
1 6. . A
Modulus of elasticity, poSoia
";(In, shear) - h,,A -A 3 ,, ;
: 3-
ii,000,000
v . . / A 3:"
12,000,000
:.rA-'\A.;;A I.;
O033
0o33..a 3
.PoisSon8s ratio
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Ooefflclent of expansion per
degree': B
;
Wei^it, Ibo per cubic.in,
^A
;A
""
■A
■0q000012
OolOl
"r
■ . '3
0, OOOOO6I4.5
0o288
.
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Modulus of El asticity. -The lower modulus, of elastic­
ity of aluminum (10p600$, 000 p0sc1». for 1^8=T6 as compared
to 29$0G0v?000 posoio for steel) has to be considered in de'temining the type and depth ;of a structure as well as, for
compression members o pffbtand one would say that although
aluminum is, about one-third as heavy as steel, three times
as much cross sectional area 'would be needed in aluminum
as for steel to limit the deflection of equal s p a n s -there­
fore 9 there is no actual saving in welghto
Fortunately the
moment of inertia does not vary directly as the area:hub as
square of the depth along with the square of the distance
in transferring the axes = Admittedly the depth of the' .'sec­
tion must be Increased In comparison with steel which .
-brings /about an increase in the usually;accepted depth -.' :
ratios of various span types so as to reduce deflection
and also for economical reasons.
Because:of the low .modulus of elasticitys working
stresses for columns, web. plates 5, and other members Subject to buckling have to be checked0 This implies that
either the Width-thickness and.h/r ratios for aluminum,"
alloys must be'less than comparable values for steely, or
else lower working stresses must be used.
The column
curve,(Fig0; 5s p, 90 5 was developed by the Committee on
Design In Light Weight Structural Alloys"of the .iSOE
Structural -Division for the alloy
The curve- is
.
based on the tangent mbdul'u.s. foyiMla and Tor ^
under 72
with a eut-off point at 22,000 pos0i0 For higher values of
L/r than 725 the unit stress and -for the partial restraint
curve is reduced by the -formula:
.
- ^/a - 7lia006?QQQ
'
'
/ V
; ; ,'
:.
.
The limitation of h/r suggests the use oT box sections,
and the continuity of girders.? so as to proyide end res^
. traint to compression membersj, as well as for stringers and
floor beamso
/'
,
; .
■■
The :low modulus of elasticity tends to relieve the:
.
shock of. impact and decreases the secondary Stresses
•• caused by' the misalignment of the members» :•
Stress Concentra.tion===The stress-strain curve- (Figo
: 1, Po 19 )• of a heat treated aluminum alloy shows;that there
■ is a high ratio of yield strength to ultimate strength.
This limits the distribution of excessive local stress| ;; thereforej, it is necessary to avoid stress concentrations'caused by reentrant cornerseccentric loadingp inaccurate
. fabrication and erection strains. •
In the Smithfield Street Bridge at Pittsburgh,
some
"-valuable .lessons; in the use of aluminum were learned.
This structure made the first extensive use- of structural •
.It. Engineering tfews Reeordg Nov. 23s Dec. 23j, 1933.
19
F/&./
5 t f £5s -
Strain
F D g /7 1 .L /M /N U M / ) l l d V
/4 5 -T 6
0
i o
-[
5 6
*t
©
k 'j
ppee
52 4
/4 K/P5
Smess
70 F F S
AL IS £ LONGAT/ON
C /S STFAIN
Q,Z% OFF-5FT -53 KPS
UNIV OF
a
FIZONA
T e s t/n o
Lap
# 2 A? /#? -
(0
/zy
ZO
z.j#
3 0
4 0
5 0
6ZJT
./e
6 0 .
A L
20
aliAmintim in. 'br'idges.o
Some of the railway ,ties came to hear
only on the 'extreme toe of the flange angles of the track
stringerso
This caused.excessive local stressing of the
angle legs as cars passed overV Cracks developed at the
vertex of the angles in a few places which required repa.lrs
and better alignment of the ties.
Of course, this mishap
cannot be entirely blamed on the properties of aluminum;
•some of the fault must be assigned -to careless design and
poor inspection^
'•.
1
Post Comparlsono°-The compafative cost between struc­
tural aluminum and steel per -pound; may,be roughly compared
2.' '
''
•‘
:as follows (194-9 prices)^
■. v.^
'
■
.
Silicon
steel
Base price
'
3^
Silicon extra
• -
Freight
lo5
/
Carbon.
steel
3ij-/
2/
16
5°5
1
Fabrication
Erection
Aluminum
llsB”T6
2
:
lo5
., :
. \
Idpt
Pound price ratio.
0o277
■
65^f
16/
loO
0o214.6
The weight-ratio of the aluminum alloy and Steel is
about 0»352;vthus the relative cost of'liiB-16 aluminum
2» Do -Bi Steinmans Engineering Bews Records, Sept. ls
19490
.
y :v
‘ '.
.. ;
per square inch of .eross section is i>27 as compared, to
silicon steel and loij.3 as compared to carbon steel0 If
,the working tensile stresses are '2j^9000,'22,000'. and 18S000
PoSolo *s for silicon steel<, aluminums and carbon, steel,
respectively, the relative cost of the aluminum for equal
tensile strength becomes 1*39 compared with silicon steel
and 1 oI? compared with carbon steelo
1
With the present increase of aluminum production and
structural use,, it is believed that the ratios will come
to unity In the near future«
..
- • v;
Shape s and PI ates0*>-Unt il a few years ago the sizes
available in plates and shapes were somewhat limited be> cause of the equipment, used; in shaping and. the limited de­
mand for structural aluminum» As the demand for struc­
tural aiuminum has Increased the equipment has improved
and soon the Aluminum Company of -.America (ALCOA) will have
•a press in operation capable pf exerting a force of
13,200 tonsc,
.
Alcoa will be able to quadruple the weight
of its■-,extrusions from 600 to 2,300 pounds per .piece 0
fhe use of extruded section is a factor With which .
steel will have to centend.
The extruded section gives
the engineer a chance to design one piece chords or
columns and other special shapes for better distribution
and economical use of materials
reduce fabrication costo
The extruded shape will
Standard structural shapes
.
which are,listed in alminum handbooks, as being available
■
should be used because the price per pound for such shapes
is less than that for special extruded sections p. The use
of special extrusions may be justified when the quantity '
is large enough to outweigh the extra cost or where a
weight savings must be accomplishedo
Temperature *— The: coefficient of thermal expansion for
the alloy lii.S-T6 is about twice that ,of steel = This does
not mean that the temperature stress in an aluminum member
will also be. twice that occurring in a similar steel mem­
ber; that is not true because the lower modulus of elas­
ticity compensates for the greater coefficient Of expansiono
- ■'
i',
'
.g
Structural aluminum should not be used where it will
be exposed to high temperatures» Some one has said that
aluminum "likes to-be coldo"
Table I gives the tensile
properties of the alloy llpS-TS at elevated temperatures 0;
The Alcoa Structural Handbook gives these properties for
other alloys of alumihum0. These values are based on the •
lowest strengths during 10,OQO hours of heating at testing
temperatureo
The resistance .to corrosion is usually re­
duced by exposure to elevated temperatureSo
!
Fabricationo--Generally, less power is required and
lighter tools can be -used in fabricating structural alumi­
num than; with steel = This does not appreciably .reduce the
:
TABLE T
TENSILE: ERCffiEBTIES ■OP"AMlltil:AELOT 14S=T6s IT EBEVMED TEMPERATURES (ALCOA)
Tempo
° F o
Tensile
: Yield strength poSoi, ■
s t r e n g t h - .
( O f f
■-po.Soio
m -
70,000 '• ■
212
: 62,000
300
39,000
W
Wo
’A ' .
A
%
-
60,000
■ : - : A/13-
56,000;; A
: . 18:
-'v :
32,000
; 17,000 ;
9,500
.
:
8,000
■ 5,500
600 :.
700
''
! 5,000
Elongo in 2"
s e t s 0 o 2 % )
; 3 ,5003 3 ::
20
:w
60
■
:A
- 65
-
76
cost of power used: 02? the time of motion because most fab­
ricators. are equipped with machinery and tools necessary :
for.working with steel; .The hot field riveting should be
minimized so as tov take advantage of the higher effleiency
,(in shear strength and cost), of the cold-driven shop rivets
whose operation Costs less than the hot-driven steel rivets
However p.'/the cold-driving equipment is more expensive due
to itd bigger-'sizel and higher pressure-o:- . .
■
■Eire ting aluminura in the shop is slow/ but the machin­
ing and; reaming can be done faster in aluminum than wi th.
steel; besides, the lighter weight can be moved by hand
without waiting for a traheo
The low modulus ;:of
elasticity
and high, yield strength
affect structural:alumihum adyersely in that ml stakes of • ■
fabrioatidh are more-costly for aluminum than for steel;
■
it is more; difficult to straighten curved, or buckled plates
offaluminuroo : ;. ;
v f;
fi t \
f
Due to. its relatively .low weightj larger shopassembled sections of aluminum can be transported and han­
dled in the- fieldo
■
:;V;
.v
•
'
p
:p.
Corrosion Res 1sfaneeo--Most-of the aluminum alloys are
■considered as being,resi stant-'to copros ion,unde roatmo s-oxpheric 'conditions o ''.This .resistance is reduced when one of
the .alloying metals is copper, and also with the degree and
nature of the thermal treatment = Under severe conditions '
of oo3?ro8i:o%the alrniiAim may be,, painteel-In much the '....
same method as pSed'With steeio/vThe only differences are
in the supface preparation and priming coat0 The most ef­
fective ppote.ction is provided -by appiying. surface layers >
of:pure, .nluminum ^or -of-;a :corro slon-re sis tant aluminum al.lqy„
The; initial fine film of oxide formed on the surface
:of aluminum prevents further corrosion.
providing additional metal thickness
The necessity of
to take
care of‘cor- .V
rosion is much;less important: for, aluminum than for steel* .
'Dr* Do Bo 8teinman, in' an article of the Engineering News
Records,: Sdpto 1$, 19491 recommends the minimum' thickness
:
of metal, for bridges of structural aluminum to be $/X6 in',
for main members and'l/lj. in. for all other parts except
„
"fillers. ■;This limitation will prevent the use. of material.;
t h a t
i s
t o o
t h i n
A l l o y s
C o n t a c t
o f
w i t h
■ c h e m i c a l
m e t a l s
o r
m e t a l s /
s u c h
a v o i d e d
b y
m a t e r i a i s
g a l v a n i c
a s
; s t e e l s
w i t h "
s h o u l d
a c c i d e n t a l
m u s t .
t h a t
d a m a g e
u s i n g
c o n t a c t
r e s i s t
a l u m i n u m '
s e r i e s |
r e p l a c e m e n t ^
A l s o
t o
w i l l
a c t
b e
i o n .
;c o p p e r j ,
o r ;
c b n e r e t e s .
b e
g u a r d e d
a r e - a b o v e
c a u l k i n g
n o t
b e .
d a m a g e .
i t
f r o m
i n
c a u s e d
t h e
t o
D i r e c t
t h e
c o m i n g
i n
e l e c t r o -
a l u m i n u m
c o n t a c t
w i t h
l e a d ,
o r
n i c k e l i
f i l l e r s
o f
p u r e a l u m i n u m .
w e t
a l l o w e d .
w o o d
o r
o t h e r
L
.
s h o u l d
' :
.
b y
t h e s e
a b s o r b e n t
■
■
b e
' .
26
--
;
-
:
;;
.
':
C H A P T E R
1 1 1 .
'.f
.
b r i d g e p e s i g e ;j'
'
' -
-
'
. V-'
^ , -; : \ - • ;
The design of the alujninum girders -is somewhat re- : ; ;
strie ted in that existing piers were to be useds thus . {...■■>.
leaving'no eholee of span:lengths that would tend to re-:%
duce the importance of live loads as .compared to dead
ioadl -.
.■;’
■
:
=:/V;-;-: , 1' ■'' ;
,
", - p.'G-f
■. .. The entire steel bridge spans about ^00 feet and the
roadway!-s"clear ■width is 3^1- feef = The design was, governed
by the American Association 'of f tate '/Highway"Officials > . .
specifications of 'l9i^>. ^helng revised, to.19h7s and the
.loading class is H20raSi6=l9hii for three laneSo
The struc­
tural' steel was limited to a wprking- stress of Ips000
"PoSfio
'■
-. , -
' '■ ■"
'■' This invesfIgation idill carry through only the design
of the metal structure using the aluminum alloy designated
by the code number li|S-T6 (see fluminum specifications)» .
;: Due toiits location the bridge is classified as' hA
.
and .the truck loading 1 s B20-316 „ For a. three lane bridge .
, t h e
m i n i m u m
a n o t h e r
h d d i n g
c l e a r
f o o t
2 o S
f
e
w i d t h ,
o f
w i d t h
e
f o r :
t
o f
t h e
i s : ; a d d e d
s i d e
w a l k s
r o a d w a y
t o
i s
7.33
a c c o m m o d a t e
g i v e s
a
t o t a l
f e e t . ,
- t h e
w i d t h
b u t
g i r d e r s 0
o f
39 feet „ ,The girders are set; symmetrically about the cen- "
•
ter line of the roadway and 10 feet apart (see drawing of
the bridge in the pocket on the back cover)„ This arrange­
ment allows a reinforced concrete slab thickness of 7
inches for the -roadway -and: four supporting girders <, If
three .girders were to be used, a greater depth of concrete
would, be, needed :for .thepavement and also deeper.-girders, •
which would,bring"Up the question as to whether or not,a ,■
box girder would be more, economical than a plate .girder<> ,
Tbls point is.brbUght up just to show another possible design.
:;V- '
1
i
;
y
The lengths of span are pre-de.temined since the
existing piers are to be used with a slight modification
of their.shoulders to maintain a 1123 percent grade 0 , The
spans .are as follows, 8I4J * 92*,. 9broy'i, 92s, and 8k *, from
their 'Centers of bearing.
■•' '
Qohsideration must he given to expansion joints.
They may be located at the ends of the .bridge or in the .
;first and last spans o . These joints will be placed in the
first and last spans because this location reduces the
consequent computations considerably and the site of the
bridgeyls such’that erection, may start at any place so
desired* this also’follows -the steel design,, --’ ,
1
; -
Now that a general idea is held In mind of the eon- ;
ditions involved,, a start may be made on the .computations
28
of/shear an^
T "
/
In order to obtain the 'shears and moments subjected to
the girdbr it is necessary'to start with the. determination ■
of.the dead loads to be. carried by the girders 0. This does
/.not 'inclnde the wei#it of the girdero ; The cross sectionof the bridge .shows .the- pavement’■as a continuous beam over .
four supports ten feet apart and having >an overhang of fifty^four ihoS at each end 0 ,The reactions at the ;supports .
would then. -be:caused by the uniform load carried by the
■
;g i r d e r S o
' '/'
- V ,
':
f
:
,’ . '
j : : Due to .the -eontInuity of the slab it is necessary to ’
determine the moments over the; supports»: To obtain these
moments the Theorem of Three Moments may be used but the 'writer prefers the. method ,presented.;by Hardy Gross under.
.,
;the:.f amiliar 'name ;of .:;M-moment distfibutiono11 Since the in?
ternal spans are. equal, and the. crbss section, is uniform
■throughoutj both the relative stiffness (l/X») and the
carry-over factor for each span is equal to l/2o
’ .’The -procedure.of-moment distribution is to determine .
fixed end moments ( F o E o M i } - caused by. the load and then al­
lowing the ends to rotate unfil the moments have been
f -
balariced and- -carried over to the other ends of the spans 0
.The process of balancing and carrying-over moments is cohf
.tlnued:
until the balancing moment is equal to ten pereeht
-of the' original F o E o M a '
The.compufatlpn for obtaining the
29
,uniform load to •the girders maybe found on .page 3 9 ° . It
should be noted that the dead load 'Carried, by the girder is .
not only the•weight of the pavement -by itself but includes
the. moment reaction which is caused by the continuity of
the slab over its'supports0
. ,
^ ,
-
The next-: step -is to locate, the expansion joints in the
extreme spanso
.The location of the joint is where the
moment.equals :sero when the span is ..
loaded with the dead
load and the .live load plus impacts : Before the live load;
moments can be determined the live loads to the girders
must be found0;
";
.
;
:.t .
"■
.
; -
p-
' Under the &ASHO Standard Specifications for H i g h w a y . :
Bridges p. 199-9 > no longitudinal distribution of the -wheels is .assumed0 . The lateral distribution varies- with the. type
of floor p. number of lanes p -and the stringer spacing o
■Having a concrete floors three lanes3 and a girder spacihg
of 10 feetp the fraction of. a wheel load to an interior
girder is s/5>° 0 where “S” is the girder spacihg so
P “ 2 wheels0 ■ For the exterior girders the flooring is -
>•
assumed to act. as a simple beam; -therefore the wheel load
to an exterior girder -is 1 * 4/10 of one wheelo
A c c o r d i n g
m a y
b e
t r u c k
a p p l i e d
t r a i n p
c o n c e n t r a t e d
t o
t h e
o n e
t h e
l o a d
o f
. . ' o t h e r
o
T h e
A A S H O
t w o
is
s p e c i f i c a t i o n
w a y s 0
t o
O n e
a p p l y
l o a d i n g
a
i s
l a n e
p r o d u c i n g
t o
t h e
l i v e
l o a d
c o n s i d e r
l o a d i n g
t h e
a
"
'
w i t h
l a r g e r
.
a
-.
s t r e s s
i s
u s e d
f o r
d e s i g n
t r u c k
t r a i n ; f o r
t r u c k
a n d
s p a c e d
l o a d
a
o f
3 0
61|.0 p
m o m e n t
a p a r t .
l o a d
s t r e s s e s
. T h e
H S O - S i S - i i i i
f o l l o w e d
o u n d s
c o n c e n t r a t e d
f o r
t h e
t r a i l e r
f e e t
p u r p o s e s ,
T h e
p e r
t r u c k
p r e c e d e d
t h e
26s000
f o o t
d e f i n e
t r a i n - - l o a d i n g
e q u i v a l e n t
l i n e a r
a c r o s s
o r
a n d
s p e c i f i o a t i o n s
o n
" b y
1 5 “ t o n
u n i f o r m
a
l o a d
1 0 ~ f o o t
l a n e
e q u a l
p o u n d s
f o r
t o
. a s
&.'■.
t r u c k s ;
i s
l a n e
18s000
s h e a r
t h e
..;
a
a n d
h .
p o u n d s
s t r e s s e s *
;
..To expedite the placing:- of wheel loads to obtain maxi.mum simple beam moments a- moment table for the wheel loads
is drawn such as the one in Table 11; p, 43, -■
n Hext a portion of 'the influence- for the moment over
pier..one; is drawn (Pig, 2, p,42), This is done by distri­
buting the FoS:,Mo ls -caused by a unit load placed at inter- .
vals on the. 84-foot span* . The P,E,M, of a beam due to one
concentrated load is the simple moment under the load times
the fraction equal to the far segment of the span divided:
by the total span so that the sum of the FoEoll,fs is equal
to the simple beam moment under the load,
•. estimating the weight per foot of the girder itself
and adding this to,the already determined dead lead, the
FoEoM,8s are distributed;to obtain a moment diagram for
dead .load* . Placing the wheels of :the truck train to ob-
.
;;
tain the maximum simple hearn moment also- Identif ies the
ordinates of the influence line for the moment over pier
one, thus, giving the .negative' moment.
In this case,.as
.
31
for all of the followingp the truck train loading causes
larger moments and shears than the;-lane loadingo. ■ '• :d
. ; :Combining the moment diagrams for dead load and live :
. load- plus impact gives- .the location, where the moment is
zero, hence locating the expansioh joint =: ;ihe:
.
vpoint of
\
zero moment under the same loading is almost Identical for
both interior and exterior girders»
•
- i . The impact is given by the formula I s
s
r ,
v
W125
. ..
n;
■where .‘‘h54 is :the loaded,length and uIn has. a majcimujn value .
°f :°30-/ v :
This procedure.is repeateds placing
live load
t h e ;
S o
/
,
.as to obtain maximum simple, beam moment and 'obtaining the ;
negative moments and combining theses, for the rest of the
spans and for both interior and exterior girders» Also
the wheels are placed so as to obtain maximum moments over
' the support So
:
;
g'./
The dead load moments and live load moments on the ex­
terior girders are in the proportion of lo3hl and 0o70s
respectively^ the moments obtained for the interior
girders0
7;'
,.
i-
.
f f.:; Deflection permitted -by the AASHG is equal to the
span -divideijby 800, for beams or girders havihg simple or
continuous .spanSl
The deflection is to be'computed by
loading/-all three lanes with the loading used to determine'
maximum moment» '.Since the girders are cross="braced the
:
; ; r .
:v::;
V
:
; :32:
.girders-are assumed to deflect equally» ,The.gross moment'.
of inertia includes the concrete pavement,
; ;f o r
'.
' t h e f e q i i i r e d
m o m e n t
o f
i n e r t i a
i s
f o u n d
Gomputations .
o n
p a g e
5 3
<,
Maximum shear and reaction are found to heist pier i n
one-and the maximum moment oh:the ;920-foot spanl ^
;
hn. approximation, to the required cross 'section of the
-girde r is made hy ;app lying:the -fundamental suppo sit ions
:'I
that all--of -the. shear will he •taken "by the web and the
bending moment -fs resisted by the flanges, The flanges
'cons ist of the -angle s, cover pi ates>: if any P land one =
eighth.nf the webg
The ecohomical depth of a steel gir­
der is equal to ohe«elghth to.one-halfithe span but the
;
■
JlASHO>sets •thelllmitltpv:be not less than one=twentieth fqh '
girders o The use of aluminum brings' about different depth:
to spah ratios to:,iimit deflection and for economy»
-
:The;depth of ifhe web.plate.is taken to.be 72 inches-^ ■having in consideration the availability of the material.
The minimum thickness that is allowed for the .web is,
ithree^elghths inch, ' The area of this- web exceeds the re- ;'
quired-, area to resist the shear of 215,6 K» since the per- .
missibie unit shear is lb#000 poSol, -
...:1
.
.Approximating the; effeetiye. depth of’the girder as
being the depth of -the. web '(7'2 -inches.) the area qf the
flange, is approached by dividing the external moment by v
.,:72'.inches,--Prom; this -are a One -e igth of the web-lis mb;
.
■33
subtracted thus leaving the area of the angles and cover, ;
plates0 The angles and plates are chosen so that the area
of the'- cover plates does not exceed fifty percent of the
total flahge area o.
■V
t •
■ ■:
The 'girder is designed by the "moment of Inertia” or
"semi-exact" method. This assumes that the neutral axis
is at the axis of symmetryy. The moment of inertia (I) for
compressive fiber stress is computed for the gross cross,
section arid the 1 for tension is the I for the gross sec­
tion minus the moment' of Inertia of the rivet holes» ‘ :
The allowable tensile' stress ls: 22s00.0 pis aio and the
.allowable compressive is determined by the graph in Figure
6,
: The terms of the ■abscissa:'are^defined as fol^ n t:'
lowsiy'. ; '
it:
' L " unsupported lateral length3 in, '
:■ .'iti
■■'■■■ ;:.>h.- ;
; ;v
■ /d':vy .
Sc - section modulus of the gross section,, in„^
• ■.
T^d:^lh 7
B
, ;
;
.
:
.
1t_
=
m o m e n t
3* / L w h e r e
iib'
■
'
o f
i n e r t i a
: '-t . 3 the ;v
.. y .
b
.
', ■
b ’..
V a l u e s
d a r d
b
O f
o
f
t h e
o f
. t h e
s
d : - =
s h a p e s ,
s e c t i o n s
.s u n i
y
i r i o
d e p t h
i n .
f o r
p l a t e s
• t e r m
b t
r
t o r s i o n f a c t o r s
t o r s i o n
b u t
O
b e a m ,
f a c t o r
a r e
n o n = r e g u l a r
t h i s
^/3
o f
v a l u e
f o r
e a c h
m a y
f o r
.-.
'
t h e
t
i
".tt.'
.
■ s h a p e s
a
o r
0
/
. ■
'
f o r . - m a n y
■
_
s i a n t
:
■ f
.
f o r . ■ b u i l t - u p : r :,
.
b y
For-
a
t a k i n g
.
. . .
l
V;
-
c o m p u t e d
r e c t a n g l e
a b o u t
c
*
p u b l i s h e d
b e
. b e a m
. : '
;h::
t h e
b u i l t - u p
b
member J Is the stmt of all the Individual torsion factors;,
■, The trial cross section 'must be; checked against the - ;
required gross moment of Inertia to.limit the live load de­
flection/ compressive and tensile stresses at the extreme
^fibers* compressive stresses on the -outstanding legs of the :
angle and cover plates (Fig> 9S p° 9^}9 and the compressive
stresses at the toe of the compression flange (Fig« 8S
92
:-'h' 1
\ / '-: ;
^
In checking the .allowable 'compressioh at the toe of.v;: -
the flange one may find that a larger gross moment of in­
ertia is .heeded or a horizontal stlffner is justified^
t ;;
The length of cover plates is based on an approxi­
mated maximum moment curve*
The maximum moment In. the .
span is assumed to be constant over the middle one-tenth
and to decrease in a parabolic fashion to the ends:
<,’5? For
continuous beams the length should be taken as the. distance,
between: points of contraflexure or approximately 75 perceht
of: the span length = With this assumption of maximum moment •
the length of the cover plate is given by the following
equations;
' •.
' v';'' : ■ ;
X- s olL t o9Ll/ Ma-Mbj,
' -'.
-/t .I--v. '
where
-.
'
.Ma Is the maximum- moment ? and ,
Mb is the resisting moment of the section :
without th© cover 'plateo
-
The resisting moment in question is the one producing a :-y4;-. This method has been used by the Hew York Central
Bridge Department for railway plate girder bridges„
35
tensile stress of 225000 pos0i =,The
controlled by the spacing of the
compressive stress is
diaphragms» .
The rivets in the flange-angle to web connection mnst•
be able to withstand the vertical shear plus the direct
shear, caused by the wheel load.
The wheel load is ,a-pproxi= ;
mated to be spread over lih incheSo
shears is a vectoral summationo
The' sum of the two
Since at a point the verti­
cal shear equals the horizontal shears the equation
v 5 VQ, is used to
; ; I. ; thyv »
find the shear
perlinear inch whereQ is
h
'
the statical moment outside of the toe of the flange angles a
The horizontal, shear. 'perv.inch may. he approximated by V
dividing the shear by the effective depth of the girdero
The determination of the effective depth requires about as
much computation as for finding Qs so there is no advantagein solving.for the'effective depth» .The spacing of rivets
is equal t o •the rivet•value divided by the "resultant shearo
. Vertical stiffners are required to resist .shear
buckling'when the clear depth to thickness of v/eb exceeds
a limiting value, • The limiting values for structural alu­
minum has not been specified but 'FigV 10s on Po 92s gives
the ratio of stiffner spacing to
clear depth
required moment ef inertia of the stiffner,
andalso the -
Gomputations
on p o"66 show that S/h may. equal it2 but the writer prefers
to limit the stiffner spacing to
equal the cleardepth of
web so as to effectively resist the buckling due to shear ,
'
; v-'-:
36
at k$r9 4 larger moment of inertia- of the. stiffrier than
3?equl^ed was-useA.:^
it is eonsidered* good practice to.
extend tlie outstanding leg of ■stiffner angles to approach
■
the- width of the Outstanding leg of the flange angle = : The
thickness should he ahout one “Sixteenth of the outstanding
-leg.o :The .rivet spacing on the stlffners is., set at the maxi= ■;::
mum of
Inches ahd the stifftiers are crimped over the
flange:spagles = :. r. .
-p .
1.
■-
.1
The bearing stiffners at the supports,are chosen to
fit the column action.and to satisfy the required area for
bearlngo
Bearing'stiffners are placed. -back to back, long
leg put-standing and two angles oti either side of the web«
I n .
t h e ;
o f
t h e
L / r
- a n g l e
t i r e l y
■ t h e
p l a n e
h’
i s
t a k e n
a s
c o m p r e s s i v e
t r a n s f e r t i e d
o u t
o f
;
T h e
a b o u t
I t
i s
o f
t h e
c o n s i d e r e d
. t h e
15 L
t h e
c u l a t e d
'
s
s i n c e
-w e b o
w e b *
r a t i o
a
w e b c
o f
o f
M r H
h o r i z o n t a l ,
o b v i o u s
t o
f i l l e t
v a l u e
b e
t h a t
T h e
t h e
f
o f
t h e
w e b
c e n t
o f
t h e
m a x i m u m
l a
t h e
n
g e
s h o u l d
t o
t r a n s f e r
i d e n t i c a l
b y
t h e
t o
t h e
p a i r
t o
t h e
t h e . r e q u i r e d
s i m p l i f y
t h e
t h e
l i e s
o n
i n
o n e
t h e
a n d
t h e
o u t s i d e
: : v
p e r ­
b e a r i n g
r i v e t s
s t l f f n e r s
d e t a i l s
-
i s
f i f t y
o f
.
g i r d e r
o n
o v e r
o f
c a l ­
b u c k l e
n u m b e r
■ B e a r i n g
i s
- a n g l e s
w i t h s t a n d
. ;
d e p t h ,
o f
w h i c h
o f
- e n -
s t l f f n e r s
r i v e t . s p a c i n g
shear,
- t h e
p l a n e ,
c a t i n o t
o f
l e n g t h
a l m o s t
w i t h i n
s e c t i o n
, a n g l e „T h e
T h e
n e c e s s a r y
a r e a
c r o s s
l o a d o
d e t e r m i n e d
o n
i s
t h e
g y r a t i o n )
S t i f f n e r -
a b l e
i s .
o f
a x i s
b e
s t i f f n e r s
a r e
( r a d i u s
t h e
“ ■ f o u r t h s
s t r e s s
s t i f f n e r
b e a r i n g
o n l y
s i d e
s u p p o r t s
' t h e
t h r e e
f o r
.
a l l
*
-
37
fabrication,
:
The -design of the.diaphragm, is a personal one' since the
wind loads’are negligible in a structure of this type.
The
sizes of;the channels .and angles were chosen'' to go with;the
proportions of the bridge.
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HO
.
4
70
; ::
'-;■
y cmPTER # :;
,RESXJLTS 'AID- GOHGHJSIONS
'
■ The controlling factor in tfcLe design laas been live
load and as a result the study of this structure has shown
that the extra cost of the aluminum outweighs' the savings
on dead loado
Table IVj on p» 6
8
> lists the Quantities of
structural aluminum and steel required for the girders.
The use of aluminum reduces the weight of girders by
119
tons or a saving of
weight of steel.
of
65
53
percent as compared to the
With the "cost in place" unit prices
^ per pound for aluminum and l6 r/ per pound for steel s
the total cost of .the girders is $1 3 5 ■ > 5 6 8 for aluminum and.
$71gl|.50 for. steel.
The revised girders show an increase - -'
of cost of |6 l4.s118 o The list of. bids from the Arizona
Highway Department; shows the total bids for this project
to range from f>327>459 <>00 to $372?k k - 5 =25»
The difference
of §6 4 , 1 1 8 is about twenty percent of the lowest bid.
Under the existing conditions it does not seem likely
that anyone would have suggested using structural alumi­
num. for'the project,
Thia■investigation does not give an entirely negative.
answer as to whether of :not structural aluminum can com=
pete with steel in the design of bridges.
It must be
;■
% .. :
71
realize# that, one important factor has been overlooked and
that is that the piers.: #ere not taken into consideration- .
If .piers .had had to be ••designed and. constructed for. this
•
bridge the difference of 119 tons would have made a materi­
al difference in favor of aluminum» Also the design of
piers would have effected a change.in length’of spans that
would tend to minimize the effects of the live loads for
the aluminum .strueture» :
• Another factor that has to be kept in mind is that
the 65^ per pound (GIF) of the aluminum includes painting
of the structure o ’In a:,location such as this one ,'with no .
danger of corrosion to the aluminum,the cost of initial
and subsequent .painting map be eliminatedo
local costs for
painting are |i8<,00 per ton for steel and $10o 00 per ton for
. structural aluminum.
\
:i:
•'
tii'' ::.•■
■ ■.Another reason fpr the high cost of aluminum strue=
tures is that the specifications governing fabrication are
very stringent.
The material cannot/be flame cut'or tack
.welded to assist in the'riveting.process and the heating
•
to facilitate bending/has to be 'carefully contrblled.../ ' ■
The rigid control of f abrication seems to have a /psycho-■
logical effect on the fabricator so naturally he feels that
he must be rewarded for his pains.
One of the local steel
fabricators /in Tucsoh,.Arizona,:, cited the cost of fabrleating structural;aliminw to .be thirty percent', over, the
cost of steel fabrication= :
..
•:
:- " '
;
'
r’:f
Local transportation of material -from the shop to the
bridge site has.been cited as $8900 per ton for steel and
fl2o00 per ton for aluminnnio
This makes the transportation
of girder cost to be- flYS&O for steel and
alnmlntm.
•
2^0 for the
.
;
i,
The entire' weight of -two girders.ahd:diaphragms between/
the expansion Joints is about 30 tons 9 the length about 300
feet, and the width a little over 10 feeto
It is not prob­
able that this section couldbe transported to the bridge
site from, the shop, but this is so -because of the length
and not because of the weight0 ;Modern truck and. trailer
rigs have limiting ,weight' capacities well over b0 tons«
-
Considering .the .sec tion /between the expansion joint and the
first splice' in the 9f?“foot. span, .the length is 12lj, feet '
and the weight of four complete girders is close to 19
:.
tons o. This section could easily be<transported to; the site..;;,
and placed on the piers wi th’cranes ..since- the distance from;-,
the top of the piers to the dry river bed Is about 20 feeto ■
"With some ingenuity the erection time of the aluminum :
strueture eould be one-third the time required for the
ateelo
Local, erection Costs are cited as $65oOO per ton ’ ■
for aluminum, and -p®r.ton for steelo
. -.
.’-
The- source of either structural aluminum or steel
-would be in California thus the ■-shipping distahce- would .be.
equal; for both matq.rlala 0 There1is some discrimination in.
the rail freight rates between steel and aluminum.» . For
comparable sections or plates the rate per 100 pounds for
aluminum is higher than for steelo
The rate for 5? 000
pounds over a distance of 500 miles is quoted as fil*30 per
100 pounds plus three percent tax for steel and f>l08l per
100 pounds plus three percent for aluminum.
The rate varies
with the weight and the distance to be travelled»
The ^production of aluminum is. expensive since a tre­
mendous amount of electrical power is required in the re­
duction process , At the present there are two or three
large companies producing aluminum shapes and plates but
because aluminum is a vital war material- federal -aid is
being made available to increase the production of the
smaller companies- and to -allow other metal -producers to
enter into the .field of aluminum -product!on» This action,
by the government should reduce the price of aluminum in
the near future. Presently,. the cost of aluminum is ■approximately three times that of steelo
"
-
As the demand for aluminum structures Increases, and
it is on the uprise j, competition will 'reduce the individual costs..which at the present add up to 6 ^ per pound (GIP)»
The cost in place price of structural aluminum would have
to be reduced to 3k-^ per pound (52%) to equal the cost of
the.steelo
.
/
, ;- ;
-
-: .'
.• -
,
IK
The results of this investigation' indicate that in
order to -capitalize on the merits of structural aluminum^
an entirely new approach is required»
It is not .suf­
ficient merely to substitute aluminum'In a.structure de­
signed for steel = A. true comparison should be made by
completely eliminating the steel design and approaching
the problem by placing more emphasis on dead load for it
is here that structural aluminum will replace steelo -if
the importahee of dead load cannot be increasedj, then it
is better'to use steel0 •
APPENDIX A
ADDMISXJI SPECIFICATIONS’:FROM THE- PROGRESS -REPORT
OF THE COMMITTEE OF T m :#RHCT#AD DlVISIOH :
■ ON DESIGN' IN, DIGHTWElGHT STRUCTURAL ALLOYS.
(Proceedings of the American Society of Civil
Engineers s Tune s: 1950.) ...
'
76
.
"
SPECIFICATIONS'POR- ALUMimM
'
•
Abbreviated. ASGE Specif ie.ations for •Heavy Duty Structures
of High Strength Aluminum Alloy - '• / f". .
;
' General ■
v
'
These specifications are to be applied wlien designing
heavy duty structures of the high strength aluminum alloy
•commercially known as li0“T6o
The allowable working
stress .in tension is 22s000 p, sd 0 based on a. minimum .
yield strength of ^3?000 p<,Soi0-and a.minimum 'tensile
strength of OOs'OOO. p»Soii ..
, - .
\ ';
:
Material;
%
; '
p .
\
The material considered in these specifications is an
aluminum alloy having the following compositiQhs.
Metal;
p
'
. ‘ ' Percentage by weight'
-
Copper
;
Silicon
;
.
Manganese
v
p.
..
.p
4»ij: p
:
068
- p
0o8
Magnesium
. Alnminum
-.p
. /
-
i t
;-
p
\
Total
O.l^
f ;V ; ";
;
'
;p
93*6 '
lOOoO- p p '
;
; For the various products (plateS.s shapes s etc;}p the
'specific mltiimum tensile strengths vary from oOgOOO pcSoio
to 68a000 poSoio and the minimmn yield.- strengths vary from
53>O0O ptiSAlo to 585OOO p.oSoio
v:
./
. -v '
SPECIFICATIONS
• Section '£<, ’Summary of Allowable Stresses
In proportioning the parts of a structure the unit
•'stress In pounds per: square :inch shall not exceed, the fol­
lowings:
.'
V ■
"
V a0 ‘Axxsl tension^ net section =•=.-.--===--==.==.— 22$000
.
hi
Tension in extreme fibers, of rolled
. -
shapes and built-up. members subject to bending;
"t>
3
■© O
t
: bo
■
X O
XI
css -j”
<=» <=» •=»
'<=*>«=-■<=
«=» >*3 e= c=3 <=»«=» «=o.<=3 *=a <=> t=s too «=o «e= ea ces «=» a
<=J sss od .«=» ea a . w
eel «=» «ea isa -ess
Stress in-extreme fibers of pins
do - Shear in pins -=—=•<==—==———»=
•
^
2
jp 0
0
0
34$ 000
-,-=-,==,—=«,=»«= lbs000
e0;
Bearing- bnpins-«===«~——
^—===.<««=«== 30s000
fo
Bearing onhot driven or cold driven
rivets'; milled stiffners; turned bolts in
;
reamed holesj, and other parts in fixed contact ---= 36;000
Section 11* Column Design
a»
Allowable'Compressive Stress in'Columnso--The al­
lowable
compressive stress on the gross section of axially
loaded columns shall be determined from the curves in ~
Figure 5> (p090) $ "k" being a factor describing end res­
traints
(k
Ordinarily the curve for partial'restraint .
0»75) shall be used.
Although the curves shown in
Figure 5 may. be used for pin=ended and fixed=ended colurans,
it is important that no allowable stresses higher than
those.given for the' case of kpOoT^/be used in actual design
unless a detailed analysis;shows that a value of k smaller
than hoj^may be; justifiedo,
• _
,
"... bv ;-Maximum Slenderness RafiOo°°The ratio of unsup­
ported length to the least radius of gyration for com­
pression -members shall, not exceed 120»
.i
''
c». Gonnectio.ns,--Gonipression- mernbers -shall be de- :
.
signed* so; that the main .elements of the .section will be
connected directly to the. gusset plates^ p'inss or; other •
■
: Ao
■■■■■.
. ■'
■
■:
-
Compression Splices»°-Members under cpmp.ression5,
if faced for bearing, shall be. spliced on four sides .suf­
ficiently to hold the abutting parts true to place« The
splice shall be as near a panel point as practicable and
must transmit at least one-half of the stress through the
splice,. ; Bembers not faced for bearing shall be fully
spliced for the entire stress.
In either cases provision
shall be -made for transmitting shear,
..
80
Section III <> Allowable Compnessiv© Stresses
. - in Flanges of Beams.
.and Girders
;a.o The allowable compressitre stress in the ;extreme
fiber (gross section) of singleeweb rolled shapes* extruded
shapes * girders* and built-up sections * subject to bending,
shall be determined from the curve in Figure 6 (p090)«
The terms used in Figure 6 are defined as follows s .
L is the laterally unsupported length of the com'
pres Sion flange, in inches |
!•
Sc is the- section modulus-for the beam about the '
axis normal to.the weh (compression side), in
, .■
incheso
-
'.;V
' ■. '
•i
; ;
:
l^ is the moment of inertia for the beam about
■
'‘
- :\ v
J
the axis parallel to the web," in inches^V
: ■■ - ■
..
n <
is the torsion factor, in inches , and
d
is the depth of the beam. In.inches^
.:
•In case the- beam has top and bottom flanges of; dif­
ferent lateral atlffnes s,
should be calculated as if
both flanges were the same as the compression flange =
.The 'allowable; stresses obtained from the curve of
Figure:6 provide a safe margin against lateral buckling
failureo
.
:v
•V
:
•
81
■V" '
•7 ' '
'
a»
Seotlon.7l^o Allowable Shear Stresses:'
in Plates and Webs '
'-
The allowable shear stress on flat webs shall hot
exceed the values giyeh by the curves in Figure
7
•Though the values given in Figure 7 (p =9 1 )apply
(p„ 9 J }„
to the -
gross area of theweb3-the shear on the het area shall not
-exceed l^gOOD.'po St,1, ;:
'Section
';
a=
:
'
v:.
Allowable Compressive:Stresses :
for Flatbs^ Legsy7 and Webs .- : "
For compression members other, than those consisting
of a single angle or tee-sect1on the following procedure
shall, be followed to •provide a suitable margin of safety
against the weakening effects of local buckling of flat
platess legs, and webfc
lo
,
, . ,
i7
Oompute the compressive stress on the flat plate„
based on the design load and the gross area,- without due
regard to local buckling0 This stress must be within al­
lowable limits as .defined by Sections II and III..
2.
Find the limiting value of b/L corresponding to
the stress by use of Figure 9 (p.9 Z)= If the flat plate
has a rutlo of unsupported width to thickness not ex­
ceeding this limiting value9 local buckling is'not a prob­
lem and the full gross area of the plate may be considered
effective o
•
-
?
■
:
•
.
86
Section VI, Plate Girder Design
. \ a®
Pro'oortioning Plate Girders 0--Plate girders:shall
be proportioned by the moment of inertia methods using the
'grOss section to determine the. moment-, of inertia«
> The stress bn the net area of: -the tension flange shall
be found by multiplying the .stress on the gross seetlon by
the ratio of the gross area of the tension flange td the
net area.
-
In determining this ratio, the tension flange
shall be considered to consist Of the f1ange angless.cover
plates9 -and the part of the web included in the'outermost'
one-sixth of the over-all height of the.girder»
.. bo
,
Allowable Flange Stress „--The.allowable compres-
siye stress in the extreme fiberibf p l a t e girders ;shall be
determined as specified in Section III„ The numerical
value of the term
B/Sc3 used in Figure 6, is rarely less
than one “half of the width s.in incheSs of the .compre ssion .
flange for -a plated glrderi '.u
: %i
t
- .'
C o Flange Oove r plate S o““iover plate s shall be at
least equal to the thickness of the flange angles and
shall diminish in thickness from the angle, outo
O.Over.
plates shall extend far enough to:-:allow at least two: extra
,rivets at each end of the plate beyond the theoretical end-.,
and the spacing of -the rivets in .the remainder ^of the
plate shall be such as to develop the required strength of
the plate at any section®
-
:i
8?
do
Flange Rivets.=-The nimber of rivetsused %o
;
nect the flanges of the plate girder to the web shall be
; enough, to transmit the horizontal shear«
.
;•
.'.v:
e°o Flahge Bollo.es o°-It is best to use angles in
splicihg flange' angles and.;that no two members be spliced
at the same cross section.
’ ; v, ■g '
g
'■
foh Allowable:Vfeb Btresseso— The allowable shear .
stress in the webs, of plate girders shall not exceed; the g.
values given by the curves of Figure 7$ and,the longltudi- .
nal compressive Stress at the toe of the compressioh
flange shall hot exceed the values' given by the curves of /
h", : ga- Bpaclng of Vertical Stiffnerso— The distance be-: v
tweeh vertical .stiffners shall not exceed the values given g
by the splld Curyes in Figure 10 (p092 )9 which are a replot of Figure 7°
f
'
The maxlmhm value of the ratio of stiff-
ner •spacihg to height of webvS/h invFigure ID• shall be de­
termined from the ratio of clear height to thickness2.h/ts
and the computed shear stress on the girder webo ■: g ,
:.
hi .8ize of Vertical BtiffnerSo--Btiffhers applied rtogg
plate girder webs to resist shear buckling shall have a '
moment of Ihertia not less than the values given by the'
dotted chrves In Figure 10»
- l.g,.:v;';g.g- /
-I; v■’
;.;i’
Section Vilo ■Riveted and Bolted Gomections
ae Arrangement and strength of connections„--Con- •
neotlqns shall be arranged to minimize the eccentricity of
;leading to :h.:mq^ero; vISemhers and connec 11ons;shal 1 be pro­
portioned to take into account any eccentricity of loading
introduced by the qontieetions = . . ;t;.. '.^v:
bo
Grip of. rivets. If the :grip of .rivets carrying-
calculated stress exceeds four and one-half times the
diameterP the number' of rivets shall be increased at least
one percent for each add!tiohal- l/lb inch grip. - If the
grip exceed _8lx -times_t^
\
diameterP special care shall be
taken in driving the rlyets. to insure that the holes are : ;
filled completelyo
• a.
. .
.
.
;.y
Pitch of Rivets in Biiilt-up Compression vMemb erso--
The pitch in the.direction of stress shall not exceed six
times the diameter of the rivets; and for a distance of
one and one-half:times the width: of ;the. member at each end,
the pitch shall not exceed three and onerhalf times -the
diameter of the rivets»
;
'h'-h ;
■
—
V
;■d> :Minimum -&pacing^of Rivets 0--The distance between -
centers of rivets shall not be less than three times the
diameter of the rivets« ;
*
Section VIII, Fabrication
* '
Co .Laying Out»=°Hole centers may be center punch©d
and cut-off lines may'be punched orscribedo
Center
/punching":.and scribing shall not be used where -such 'marks
would remain on fabricated.material,
bo
G u t t i n g , - - F l a m e
. p e r m i t t e d *
C
- ' W i t h
o
:
H e
c u t t i n g
'
a t i n g «
:V'
= - S t r u c
t h e : ' f o l l o w i n g
t u r a l
e x c e p t
i o n s
o f
a l u m i n u m
I
t
m a t e r i a l
t
a l l o y s
;
-
.\
i s
n o t
;
s h a l l
n o t
: . t . .
/ v:-:
b e
t
h e a t e d ,
t ' /
1»V Material may be heated to a temperature not ex'seeding hOO? F* f©r>a period not over l£ minutes to facili­
tate' bending* -tSUCh;‘heating shall•be done only when proper
'temperature controls and supervision are provided -to insure
that the 'limitations oh temperature: and time are "carefully
observed* '
. '. ■
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.
2o• :Hot driven, rivets* '-■
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,
d*; Riveting,*--Rivets shall be driven .hot or cold,
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type furnace providing uniform temperatures throughout
the rivet chamber and equipped with automatic temperature
controls*
2*
.
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Sot driy'eh .rivets shall be held at from 990° F*
to 1,050° F * for not less than 15> minutes and fpr not
more than one-hour before.drivings
e*: Welding*— Welding is not permitted*
_.
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24
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BIBLIOGRAPHY
'. -Texts /
'
Structural Design in Metalsj Co I)<. Williams =■ E« C, Harris,
Design of Modern,Steel Structures, Lo E.o Grinter.
Analysis of Statically Indeterminate Structures,
Co Do Williamso ■
Continuous Frames of Reinforced Concrete, Ho. Cross Ho Do Morgano
:
' '
■Economics of. Bridgework, Je &» Do Waddelo
Analysis and Design of Steel Structures, Ao"Eo Fuller F. Herekes.,
....
Magazines
Engineer lag Hews Record, Novo 23^:1933='
''
v
\
Deco 28, 1933q
.
_________
.
■
', Deco 16, l9ij-8»
"'r
' : . '
-
Septo 1, 1949o
Civil Engineering, Deco 1946°
Roads and Bridges, Augo 1949 =
Handbooks
Alcoa Structural Handbooko
Steel Construction Manual of the American Institute of
Steel Construetiono
Standard Specifications for Highway Bridges, AASHQ.■
.
'
Ii
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' :
t Exist ingBdvvy j Mew Bridge
To Phoenix
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