combined torsion, bending and
axial actions
by
Arne Aalberg
Departmen tof Structural Engineering
The Norwegian Institute of Technology
N-7034 Trondheim
July 14, 1995
Notation ix
1 Introduction 1
1.1 Bac kground : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1
1.2 Objectiv es : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2
1.3 Previous studies : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3
2 Test setup 7
2.1 In tro ductory remarks : : : : : : : : : : : : : : : : : : : : : : : : : : 7
2.2 Test rig : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7
2.2.1 Axial loading : : : : : : : : : : : : : : : : : : : : : : : : : : 11
2.2.2 Transverseloading : : : : : : : : : : : : : : : : : : : : : : : 11
2.2.3 Torsionalloading : : : : : : : : : : : : : : : : : : : : : : : : 17
2.3 Bearing resistance : : : : : : : : : : : : : : : : : : : : : : : : : : : : 20
2.4 Instrumen tationand measuremen t: : : : : : : : : : : : : : : : : : : 23
2.4.1 Axial and transverseloads : : : : : : : : : : : : : : : : : : : 23
2.4.2 Torsionalload : : : : : : : : : : : : : : : : : : : : : : : : : : 23
2.4.3 Displacemen ts : : : : : : : : : : : : : : : : : : : : : : : : : : 23
2.4.4 Rotations : : : : : : : : : : : : : : : : : : : : : : : : : : : : 25
2.4.5 Strain : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 26
2.4.6 Data acquisition: : : : : : : : : : : : : : : : : : : : : : : : : 26
2.5 Test setup -load and supp ort conditions : : : : : : : : : : : : : : : 26
3 Test specimens 29
3.1 In tro ductory remarks : : : : : : : : : : : : : : : : : : : : : : : : : : 29
3.2 Test sp ecimens : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 29
3.3 Material tests : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 31
3.3.1 Tensiontests : : : : : : : : : : : : : : : : : : : : : : : : : : 31
3.3.2 Compression tests : : : : : : : : : : : : : : : : : : : : : : : : 35
3.4 Residualstresses : : : : : : : : : : : : : : : : : : : : : : : : : : : : 40
4 Torsion - experiments and analyses 43
4.1 In tro ductoryremarks : : : : : : : : : : : : : : : : : : : : : : : : : : 43
4.2 Torsionalanalysis : : : : : : : : : : : : : : : : : : : : : : : : : : : : 44
4.3 Exp erimen talin vestigation ontorsional b ehaviour : : : : : : : : : : 45
4.3.1 Exp eriments : : : : : : : : : : : : : : : : : : : : : : : : : : : 46
4.3.2 Testresults on uniform torsion : : : : : : : : : : : : : : : : 48
4.3.3 Tests results on nonuniformtorsion : : : : : : : : : : : : : : 50
4.4 Finiteelemen tsim ulations : : : : : : : : : : : : : : : : : : : : : : : 53
5 Beam-column tests 63
5.1 In tro ductoryremarks : : : : : : : : : : : : : : : : : : : : : : : : : : 63
5.2 About the tests and the presen tation : : : : : : : : : : : : : : : : : 63
5.2.1 Testconditions : : : : : : : : : : : : : : : : : : : : : : : : : 63
5.2.2 Normalization : : : : : : : : : : : : : : : : : : : : : : : : : : 65
5.2.3 Testpro cedure - c hosenloading : : : : : : : : : : : : : : : : 66
5.3 Testprogram : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 67
5.4 Beam-column test results : : : : : : : : : : : : : : : : : : : : : : : : 70
5.4.1 Bending tests : : : : : : : : : : : : : : : : : : : : : : : : : : 71
5.4.2 Load com binationNM : : : : : : : : : : : : : : : : : : : : : 73
5.4.3 Load com binationMT : : : : : : : : : : : : : : : : : : : : : 73
5.4.4 Load com binationNT : : : : : : : : : : : : : : : : : : : : : 77
5.4.5 Load com binationNMT : : : : : : : : : : : : : : : : : : : : 78
5.4.6 Load com binationswith constant b ending momen t : : : : : 85
5.5 Compilationof tests with axial load and torsion : : : : : : : : : : : 90
5.6 Tests with uniform torsion and axialload. : : : : : : : : : : : : : : 91
6 Interpretation of results 95
6.1 Plastic torsional moment : : : : : : : : : : : : : : : : : : : : : : : : 95
6.2 In teractioneects : : : : : : : : : : : : : : : : : : : : : : : : : : : : 101
6.2.1 Uniform torsion - eects fromaxial load : : : : : : : : : : : 102
6.2.2 Nonuniformtorsion- eects fromaxial load : : : : : : : : : 107
6.3 Bending and torsionin teraction : : : : : : : : : : : : : : : : : : : : 112
6.4 Axial force, b ending and torsion in teraction : : : : : : : : : : : : : 118
7 Design formats 123
7.1 Designbased onco des : : : : : : : : : : : : : : : : : : : : : : : : : 123
7.2 Other designpro cedures : : : : : : : : : : : : : : : : : : : : : : : : 126
7.3 Designby analysis : : : : : : : : : : : : : : : : : : : : : : : : : : : 127
8 Numerical sim ulations 129
8.1 Shell elemen tmodel: : : : : : : : : : : : : : : : : : : : : : : : : : : 129
8.2 Numericalresults : : : : : : : : : : : : : : : : : : : : : : : : : : : : 131
References 143
A Characteristic data 147
A.1 Beam-column capacities : : : : : : : : : : : : : : : : : : : : : : : : 147
A.2 Elastic nonuniformtorsion : : : : : : : : : : : : : : : : : : : : : : : 148
A.3 Uniform torsion - Elastic/Plastic : : : : : : : : : : : : : : : : : : : 149
B Photographs 151
C Twist rotations 157
D Results from numerical sim ulations 161
D.1 Shell model - prop erties in uniform torsion : : : : : : : : : : : : : : 161
D.2 Torsion simulations : : : : : : : : : : : : : : : : : : : : : : : : : : : 162
D.3 Numericalresults for IPE b eam-columns : : : : : : : : : : : : : : : 163
jectiv etoobtainreliableexperimen taldatafortheresp onseforsp ecimenstestedat
wellcontrolledload-and supp ort-conditions. Testsarecarriedoutfortwodieren t
Class1 I-sections,the wideange sectionHEB 140 and the b eam section IPE160.
The b ehaviourin b oth uniform and nonuniform torsion isin vestigated,as well
as com binationsof b ending and torsionat variouslevelsof axialload. Results are
giv eninterms of resp onse histories.
Typicalb eam-column experimen tsare sim ulated by means of the generalpur-
p oseniteelemen tprogramABA QUS,usingshellelemen tstomodelthesp ecimens.
Theobjectiv eistov erifytowhatexten tnumericalsim ulationsmayreplacephysical
models in studiesof b eam-columnsunder similar load com binations.
Metho ds for calculating the full plastic nonuniform torsional momen tare dis-
cussed. Second order eects are discussed for the com bination of axial load and
torsion, and simple design in teractionequations are prop osed. Forthe in teraction
b et ween b ending and torsion, the applicabilit y of a commonly used quadratic in-
teraction equationisin vestigated. Forthe capacit ydenition,adeformation norm
is in tro duced. Anin teraction equation onthe componentlevelisprop osed for the
full load com binationof axialload, b ending and torsion.
Skjeggestad for hisvaluablecriticism.
Thestudyhas in volvedlonghours inthe lab oratory, andthanks aredue tothe
lab oratory sta fortheir eorts and assistance.
Thegenerousnancialsupp ortfromthe "Stalibygg"-project,organizedbythe
Norwegian Steel Asso ciation, isgratefully acknowledged.
0
E, G modulusof elasticit y,shear modulus of elasticit y(G=E/2(1+))
H transversemidspan load onb eam-column
H
p
value of H giving full plasticationin b ending (H
p
=4M
p
=l )
I
T , I
w
sectiontorsional constant,section warping constant
L length
L
C
reducedparallellength of tensile test coup on
L
0
originalgauge length(=5.65 p
A
0
) for prop ortional test coup on
M b endingmomen tor b ending momen tat b eam-column midspan
M
f
b endingmomen tin angeab out strongaxis of ange plate
M
fp
plasticb ending momen tinange
M
p
plasticb ending momen tab out strong axis(y) of cross-section
M
Y
yieldb ending momen t(initial yield) ab out strongaxis
N axialforce, axial load
N
E , N
ET
elasticexural bucklingload, elastic torsional buckling load
N
Y
yieldaxialload (=squash load of cross section)
N
0
axialload applied tob eam-column
N
d
designcapacit yfor N (=N
Y /
M )
NMT loadcom bination withN, M andT
T torsional moment(torque)
T
Y
yieldtorsional momen t(initial yield)
T
0
torsional momentappliedto end of b eam-column
T
0 ;al t
alternativ etorsional capacit y
T
d , T
pd
designcapacit yfor T, plastic designcapacit y(=T
p /
M )
T
p
plastictorsional momen t
T
r ,T
3
amplied value, reducedvaluefor torsional capacit y
T
u , T
up
uniform torsional momen t,plastic valueof T
u
T
w , T
w p
warpingtorsional momen t,plastic valueof T
w
V, V
f
shearforce, shear forcein ange(y-direction)
H
p
normalizedvalue of H (H
p
=H/H
p )
M normalizedvalue of M(M=M/M
Y )
M
p
normalizedvalue of M(M
p
=M/M
p )
N
normalizedvalue of N (N=N/N
Y )
T
normalized valueof T (T=T/T
Y )
T
p
normalized valueof T (T
p
=T/T
p )
a deformation norm
b width of ange
f amplication factor
f
y
yield strength(yield stress)
f
u
ultimate tensile strength
h depth of cross-section
h
t
distance b et weenange cen troids
l length of b eam, length of b eam-column
s thic knessof web
t thic knessor thic knessof ange
u axial shortening of b eam-column
u
Y
value of udue to N
Y
w transversedisplacemen t ofb eam-column at midspan
w
Y
value of wat initial yielddue totransverse loadingH
5 : 65
elongation (%) after rupture, measured overL
0
"
y p
yield p ointelongation
"
u
strain when f
u
is reac hed
M
partial safetyfactor forthe resistance
twist rotation of b eam-column end
T
twist rotation due to external torsional loading
Y
value of atinitial yielddue totorsional loadingT
0
r
amplied value of due to presenceof N
u
normalized u (u=u/u
Y )
w
normalized valueof w (w=w/w
Y )
normalized valueof (=/
Y )
Ov er the last ten y ears an extensive eort has b een made in Europ e in order to
write acompletesetofdesignsp ecications forthe mostcommonly usedmaterials
in civil engineering structures. The work on these Euro co des was initiated by
the Commission of the Europ ean Union, and continued under the auspices of the
Europ eanStandardisationOrganisation(CEN).Theco desarebasedontheconcept
of partial co ecien tsof structural reliabilit y, and a major objectiv ewas to arriv e
at a uniform level of reliabilit y all through the structures. As a basis for the
dev elopmentofEuro co de3-DesignofSteelStructures-databaseswereestablished
containing all availabledata, experimen tal or numerical, regarding the b ehaviour
of structures, structural componentsand jointsand connectors.
A ttheultimatelimitstatetheprovisionsoftheco des aimatpredictingthereal
load carrying capacit y of the structure, taking advantage of second order eects
and inelastic material b ehaviour. Forlinearly elasticb ehaviour the theory of elas-
ticit y provides solutions b oth for b eams in torsion, torsional buckling and lateral
torsionalbuckling,butthein teractionofb ending,torsionandaxialforceisnotwell
do cumented. When writing the sp ecications for b eam-columns it b ecame clear
that v ery little information was availableregarding the ultimate capacit y of com-
p onents subjected to com bined actions that included torsion. As a consequence,
the design formulas for b eam-columns subjected to b ending and axial force are
quite advanced and accurate, while the problem of torsion is almost completely
neglected.
In most civil engineering steel structures torsion is a secondary action, and is
commonly av oided through go o d structural design. Even though the transfer of
external loads by means of torsion is generally considered an inecien t way of
resistingthe externalactions,there are cases werethe torsional b ehaviourcan not
b e avoidedand where the torsionalresistance ma yb e ofgreat importance. This is
thecaseforinstanceinslenderbridges,andforbuildingstructuresunderacciden tal
situations such as re and earthquakes. Traditionally, the torsion eects hav e in
man ycasessimply b een neglected inthestructural analysis ofbuilding structures.
However, into day's structural analysis programs it is frequen tly easier to include
torsion inthe computational model than toavoidit.
By means of the commercially available general purp ose nite elemen t co des
that incorp orate b oth geometrical andmaterial nonlinearities structuraldesign by
analysis is now feasible. This means that the traditional design pro cedure of rst
carrying out a structural analysis follo wed by a separate (independen t) c heck of
mem b er capacit y in the form of a co de c heck, can in principle b e replaced by
a one-step pro cedure in whic h the load carrying capacit y of the structure can
b e determined through a nonlinear nite elemen t analysis. The new Australian
Standard (AS 4100) states certain requiremen ts for the use of such a pro cedure,
and Euro co de 3 also contains some general information for its use. In general, if
designbyanalysisistob eused,thesafetylevelsp eciedbytheappropriatebuilding
authoritiesandensuredbyto day'sdesignsp ecications,hastob emain tained. This
meansthatalleectssuchasinitialdeformations,residualstresses,spatialvariation
of material prop erties suchasyieldand ultimate stress m ustb e represen tedinthe
numericalmodel.
For the analysis of steel framed structures b eam elemen ts are available that
includewarpingdeformationsofthecrosssectionandmodelsbasedonconcen trated
plasticit ytodescribetheinelasticmaterialb ehaviour. Allthepreviouslymen tioned
eectscaninprincipleb eincludedhere,andforsteelframeswherethecomponents
are subjected primarily to axial and b ending actions such elemen ts predict the
resp onse with go o d accuracy. However, when also torsion is presen t the existing
modelsfor concen tratedplasticit yare inadequate, asthe commonly availableyield
orb ounding surfaces in forcespace donot includetorsion.
Further researc h is hence needed b oth to provide experimen tal data on the
structuralb ehaviourofb eam-columnssubjectedcom binationsofaxialforce, b end-
ingandtorsionactionsandonp ossibleplasticfailureorb oundingsurfacesforcross
sections subjected to the same actions.
1.2 Objectives
The presen t in vestigation has two primary objectiv es. Firstly, to obtain reliable
experimentaldataontheb ehaviourofb eam-columnsofI-shap edcrosssectionssub-
jected tocom binationsof axial, b ending andtorsionactions thattakethe memb er
in to the inelastic range. This data isto serv eas a basis b oth for the dev elopment
ofin teractionform ulasonthesameformatasthe curren tdesignsp ecications,and
ma yalso b e used for v erication of plastic failure surfaces for use inconcen trated
plasticit ymodels. Secondly,to usethis datatoevaluatethe accuracyof numerical
models established by means of existing general purp ose nite elemen t programs
for this typ e ofproblems.
1. Todev elopandconstruct atest facilit yfortestingof I-sectionb eam-columns
undervariouscom binationsofaxialload,b endingmomen tand torsionalmo-
men t. Theprimaryobjectiv esofthetestsaretoprovidehighprecisionexper-
imen taldata for the resp onse of the b eam-columns,tested atwell controlled
load- and supp ort-conditions whic h can b e prop erly modelledina nite ele-
men tanalysis.
2. To carry out tests on b eam-columns of two dieren t I-shap ed sections, at
various load com binations, to obtain data b oth for memb er b ehaviour and
for cross-sectional resistance. The load com binationwill b erestricted tothe
case of compressiv e axial force, torsional momen t and strong axis b ending
only atthe criticalsection.
3. Tosimulatesometypical experimen tsbymeans ofan existing niteelemen t
program,usingshellelemen tstomodelthetestsp ecimens. Theobjectivehere
istov erifytowhic hexten tnumericalsim ulationscanreplacephysicalmodels
inafurtherstudyofb eam-columnb ehaviourundersimilarloadcom binations.
4. Todiscuss theexisting designprovisionsfortorsionin viewof theexperience
gained inthe presen t study.
1.3 Previous studies
Notman ystudieshav eb eenmadeofthenonlinearb ehaviourofstructuralmem b ers
subjectedtotorsion,andesp eciallynotwhentorsioniscom binedwithb endingand
axialforce. Torsionalproblemsrelatedtoelasticinstabilit y,suchaslateral-torsional
buckling of b eams and torsional buckling of columns are considered to lie outside
the scop e of the presen tstudy, and are not included here. An extensivesummary
of the mostrelevantremaining literature isprovided byPi and Trahair (1994c).
Thelineartheoriesforelasticb endingofb eamsandtorsionofelasticb eamsand
barsarewellestablished(Timoshenk o1936,Timoshenk oandGo o dier1951,Vlasov
1961 and others) and giv equiteaccurate predictionsfor the mem b erb ehaviour in
the case ofsmall deformations. The basic theoriesfor the prediction of the plastic
b ending capacit yof b eams and plastictorsional strength of mem b ersare giv enby
Nadai (1950), Ho dge (1959)and Neal (1977).
Exp erimentalin vestigationsoftheeectsofinelastictorsiononstructuralmem-
b ers hav eb een carried out only byfew authors. Boulton (1962) tested four rolled
steel I-section b eams, two of whic h were restrained against warping deformation
atb oth ends and twowhic hwerefree towarp. Dinnoand Gill (1964) testednine-
cen trallyappliedtorsional momen t. Dinnoand Merc hant(1965)tested six similar
sp ecimens in com bined b ending and torsion, while Farwell and Galam b os (1969)
testedv ewide-angeb eams subjectedtob othoneandtwoconcen tratedtorsional
moments. Forsquare and rectangular section sp ecimens Gill and Bouc her (1964)
carried out eigh teentests with b ending and torsion. Tests on cantilever I-section
b eams under b ending and torsion are giv en by Driv er and Kennedy (1989), and
tests with com bined torsion, b ending and axial loading of b ox stub columns are
presen ted byKitadaand Nakai(1989).
Approximatemethodsforcalculationofplasticcross-sectionalcapacit yinb end-
ing andtorsionare availablefor varioussections. Hilland Siebel(1953)andSteele
(1954)studiedthe com binedb endingand torsionof resp ectiv elysolid circularsec-
tions and solid square sections, while Imegwu (1960) studied square, triangular
and circular sections. Approximate solutions in terms of lowerand upp er b ounds
for the b ending and torsion in teraction were presen ted by Hill and Siebel (1953),
Steele (1954) and Gaydon and Nuttall (1957), while a lower b ound solution was
presen ted by Ho dge (1959) for various sections. In all cases the b ending and the
torsional momen twere assumeduniform along the length of the mem b er.
For I-b eam sections with warping restrain ts Boulton (1962) obtained an ap-
proximate lower b ound solution for the fully plastic capacit yfor com binedstrong
axis b ending and torsion, while Dinno and Merc hant(1965) prop osed an empiri-
cal "upp er b ound" for the plastic capacit y of a cantilevered b eam subjected to a
torsional momen t at the free end. In addition, they used the lower b ound in ter-
action equation obtained by Ho dge (1959) in their study of I-section b eams with
warping restrain ts. Augusti (1966) used an upp er b ound approach to the case of
torsionofacantileveredI-sectionb eam,based onlinear geometryandrigidplastic
b ehaviour, and evaluated the results of Boulton (1962) and Dinno and Merchant
(1965). These studies allfo cus on the eects of material yielding.
The eects of geometrical nonlinearit y for b eams and b eam-columns, included
theeectsoftorsion,hav eb eenanalysedbyChenandA tsuta(1977),A ttard(1986),
Yang and McGuire (1986) and others. In recen t y ears, sev eral nite elemen tfor-
mulationsforb eam elemen tshav eb eenpresen ted, whereb oththe geometricaland
material nonlinearities are accounted for. Both El-Khenfas and Nethercot (1989)
and Pi and Trahair (1994a) presen ted b eam elemen t formulations for analysis of
problems with large deections and twist rotations.
Finiteelemen tanalyseshav eb een usedtostudysomeproblemswhic hincluded
torsion. Baba and Kajita (1982) studied torsion of a prismatic b eam using a
sp ecially dev elop ed elemen t. Batheand Wiener (1983) studied twoapproaches to
model anI-section cantileverin b ending and warping torsion, one model built up
with1-D b eam elemen tsandone model withshellelemen ts. Mayand Al-Shaarbaf
(1988) used bric k elemen ts to model uniform and warping torsion on b eams of
various sections, included the I-section. Chen and Trahair (1992) presen ted a
niteelemen tmodel foranalysingelastic-plastictorsiononI-section b eams,where
compression, end momen ts and constant torsional momen t applied at the mid-
span. Here, they numerically in vestigated the eect of the higher order terms in
the nonlinearstrain-displacemen trelationshipforthe elemen t. Thiseectwasalso
studiedby Piand Trahair(1994b), who used asimilar elemen tto studycom bined
torsionandb ending ofasimplysupp orted b eam,torsionofacompressionmem b er
andnonuniformtorsionofanI-b eam. Further,PiandTrahair(1994c)in vestigated
the inelastic com bined b ending and torsion of I-section b eams for three cases of
laterally bracing. They carried out sev eral numerical sim ulationsfor these b eams
withinitialstressesandgeometricalimperfections,lo oking atthein teractioneects
b et ween strong axis b ending, exural-torsional buckling and torsion. In a recen t
pap er (Pi and Trahair 1995) they studied the b ehaviour of b eams in nonuniform
torsion only.
In the eld of yield surfaces for steel sections based on force resultants, one
of the most useful compendiums is the work of Chen and A tsuta (1977). They
constructed three-dimensionalyieldsurfaces forthe com binationof axialforceand
biaxial moments for a numb er of cross-sectional shap es, and deriv ed analytical
expressionsthat approximatethe surfaces forsome typicalI-sections. Forthe case
when uniform torsion is included, a reduced yield stress is established assuming
that the torsional stresses in the section are uniformly distributed. This reduced
yield stress is subsequently used when computing the capacities for b ending and
axialforce. Forin teractionb et weenaxialforceand b ending,Orbisonet al. (1982)
dev elop ed a single equation approximating the Chen-Atsuta yield surface for a
wide ange section. Duan and Chen (1990) extended the work to other sections.
Daddazio et al. (1983) described a pro cedure for deriving yield surface equations
for thin-walledbarswith warping restrain ts,subjected tothe com binationof axial
force, biaxial b endingmomen tsand warpingmomen ts. Afour-dimensional, multi-
faceted surface wasderiv edfora Z-section. ForI-sectionswithnonuniform torsion
Yang and Fan(1988)deriv ed the yieldsurface for the full v e-dimensionalaction;
axial force, b ending momen ts ab out two axes, a bimoment (ange warping) and
theuniform torsionalmomen t. Theirapproachisbasedonaparametricexpression
of a v e-dimensionalsurface with three component yield surfaces, one for eac hof
the plates constituting the section.
For b ending and torsion on simply supp orted laterally braced and unbraced
b eams, the elastical in teraction eects were studied by Chu and Johnson (1974),
Pastor and DeWolf (1978), Razzaq and Galam b os (1979) and Nethercot et al.
(1989). Simplesuggestions forcalculation and amplication of elasticstresses and
torsional rotation due to secondorder eects are giv en.
The rep orted tests are a part of an in vestigation dealing with the b ehaviour and
ultimate resistance of b eam-columns subjected to com bined axial load, b ending
and torsion. The primary objective of the tests is to obtain reliable experimen tal
dataonb eam-columnb ehaviourand oncross-sectionalresistance oftypicalI-b eam
sectionswhensubjected tovariouscom binationsofaxialforce, strongaxisb ending
and torsional momen t.
The experimen talin vestigation is carried out for two hot-rolled I-sections, the
b eam section IPE 160 and the wide ange section HEB 140. The lab oratory fa-
cilities and the forces needed to fail the test sp ecimens restricted the size of the
sections. The length of the b eam-column to b e tested was for many reasons c ho-
sen toab out twometers. Asp ecial test rig wasdesigned and builtfor this testing.
Existingloadingframesandstandardhydraulicactuatorsandequipmen tinthelab-
oratory were used as far as p ossible, but loadingand controldevices for torsional
loading had to b e designed and man ufactured for the tests. The experimen tsde-
scribedin this rep ort were allcarried out in the structural engineering lab oratory
at the Civil EngineeringDepartmen t,the Norwegian Institute of Technology.
This c hapter describes all parts of the test rig and discusses the supp ort and
loading of the test sp ecimens.
2.2 Test rig
Thetestrigisbasedonastandardv erticalloadingframeconsistingoftwosupp ort-
ing columns and a hydraulicactuator. The test sp ecimenis moun tedina v ertical
p osition b et ween two end supp orts and is braced at the mid-heigh t. Figures 2.1
and 2.2 illustrate the test arrangemen ts. The test setup uses a cen trally applied
transversep ointload forb ending,whilethetorsionalloadingisappliedattheends
of the test sp ecimen. As shown in Figure2.2, the sp ecimen is freetorotate ab out
its length-axis at the end supp orts, while the rotation is restrained atmidspan.
Figure 2.1: General view of the test rig. The test sp ecimen is white-washed, the
horizontalactuator islo cated b ehind the curtain.
Figure2.2: Testsp ecimen IPE 160 moun tedinthe test rig.
The test rig in volves three main loading devices and the necessary b earings
and bracings:
A v ertically moun tedhydraulic actuator in the main v ertical loading frame
appliesaxialloadattheupp erendofthetestsp ecimen,andthereactionforce
is carried by the ground supp ort. Both ends of the sp ecimen are equipped
with base plates and spherical thrust b earings, and are laterally supp orted.
Ahydraulicactuator ismoun tedhorizontallyinaseparatesupp orting frame,
and applies a transverseload to the test sp ecimen at midspan. The load is
applied by means of a tension ro d and a loading plate. The end supp orts
hav ecircular end xture plates supp orted in large roller b earings.
Twohydraulicmotorsappliestorsional momen tstothe endsofthetest sp ec-
imen, by means of a c hain driv en loading arrangemen t. The torsional mo-
men tsaretransmittedtothe sp ecimenfromtheend xtureplates inthe end
supp orts.
Photographs of the xture plates at the supp orts and the loading plate at
midspan are giv eninApp endixB, whileallloading andsupp ort arrangemen tsare
shown in detail inthe follo wing.
Thextureplatesatthesp ecimenendsactsas"hinged"supp ortsfortheb eam-
column sp ecimens with resp ect to the transversal loading. The loading plate at
midspan encloses the test sp ecimen, transmits the transverse load, and serv es as
a restrain t with resp ect to nonuniform torsional loading. A t the ends, the test
sp ecimen is giv en a sp ecial design (Figures 2.6 and 3.1) to allow for the warping
of the anges. In addition, b oth ends of the sp ecimen are provided with torsional
"hinges" to allow the rotation ab out the longitudinal axis. As shown in Figures
2.3 to 2.6, the loading and b earing arrangemen ts provide practically symmetrical
end conditions to the test sp ecimen.
The test sp ecimen ma y hence b e subjected to the follo wing loading com bina-
tion;aconstantaxialforceincompression,ab endingmomen tactingab outanaxis
normaltothe sp ecimenlength-axis, withthelargestin tensityatthe loadingp oint,
andanonuniformtorsionalmomen t. Asaresultofthe three-p ointtransversalload
system there is also a shear force presen t in the sp ecimen. A schematic and sim-
pliedviewofthe test arrangemen tandthe resulting force- andmomen t-diagrams
are shown inFigures 2.7 and 5.1.
The torsion loading device is double-acting and the torsional momen t applied
at the sp ecimen ends can hence b e rev ersed, allowing b oth nonuniform torsion
(Figure 2.2) and uniformtorsion (Figure 4.3) to b e appliedto the test sp ecimen.
The test rig is designed to minimize the c hances of unin tentional constraints
when the test sp ecimens undergo large deformations. Furthermore, care has b een
taken not to assume any ideal xed or free b oundary conditions, but to measure
a test sp ecimenare: Axial force1200 kN,b ending momen t240 kNmand torsional
momen t9 kNm.
2.2.1 Axial loading
Thetestsp ecimenextends30mmb ey ondtheendxtureplatesasshowninFigure
2.6. The v ertical actuator applies the load to the upp er end of the test sp ecimen
through a spherical thrust b earing and a circular base plate, with an equal ar-
rangemen t at the lower end. The base plates are tted to the cross-section of the
particular test sp ecimen and to the thrust b earing as shown in Figures 2.3 and
2.8. This is done in order to prev ent any end eccen tricities caused by inaccurate
moun ting of the test sp ecimen.
The spherical thrust b earings are needed to provide a cen tric load transfer,
and are in tended to allow end rotations of the test sp ecimen induced by exural
deformations. Sincetheresistingb endingmomen tinthe b earingsisnegligible,the
test sp ecimen can b e considered "hinged" or "simply supp orted" at the ends. A
measuremen t of the friction momen ts at various axial load lev els is presen ted in
Section 2.3.
The thrust b earings consist of a spherical cap attached to the base plate, a
sliding surface and axed casing (Figure 2.6). The cen terof rotation ofthe sp ec-
imen end with resp ect to exure-induced end-rotations is lo cated in the plane of
the end xture plates, at the cross-sectional cen troid. The thic kness of the base
plates is adjusted to mak ethe rotation-center of the thrust b earing coincide with
the rotation cen terof the sp ecimen.
The load applied through the thrust b earings, i.e. the load applied by the
actuator and the reaction force from the ground supp ort, is enforced to p oint
throughtheserotation-centersnomatterhowlargetheend-rotationsb ecome. The
direction of the appliedload coincide withthe sp ecimens length-axis inthe initial,
unloaded state, and the resultis a pure axialforce inthe test sp ecimen.
Theshorteningofthetestsp ecimenduetoanaxialload,orexuralortorsional
deformations, causes a deection of the circular xture plate at the upp er end
supp ort. Due to a large diameter to thic kness ratio (Figures 2.3 and 2.8) the
b ending stiness of the plate isso small that it can sustain the deection without
dev elopingsignicantload.
2.2.2 Transverse loading
The transversal loadingarrangemen tis shown in Figure2.5. The horizontal actu-
ator applies load to the test sp ecimen through a tension ro d b olted to a loading
1 015 6 0 00 10 15
14 13
10 9 8 7 2
1 3 6
5 4
Legend:
1 Test specimen 2 Main loading frame 3 End support frame 4 Bracing frame 5 Loading plate 6 Roller bearing 7 Vertical actuator 8 Piston rod 9 Load cell
10 Spherical thrust bearing 11 End fixture plates 12 Base plate
13 Plane thrust bearing 14 Ground support
11
12
9 4
3 2
10
1 Test specimen 2 Sprocket wheel 3 Motor axle 4 Chain tightener 5 Roller chain 6 Load cell 7 Sprocket wheel 8 End support frame 9 Circular end fixture plate 10 Quadratic end fixture plate
5
6
7
8
1
236 HEB140
A A
1 0 0 0
- 30 -
Loading plate
Bracing frame Tension rod
Rollers
SECTION A-A
236
Test specimen HEB140
Rollers
Ø7.0 x 14.0
∅197
200
1 2 3
4 5
6
7
8 Legend:
1 Test specimen 2 Rotation center 3 Fixture plates 4 Base plate 5 Groove
6 Spherical thrust bearing
7 Plane thrust bearing
8 Center-alignment plate
30
Axial force Bending moment 2.order
bending moment
Torsional moment
(non-uniform) Shear force
1 0 1 5
2 0 3 0 3 0 1 0 1 5
CHAPTER2.TESTSETUPFigure2.7:Force-andmoment-diagrams.
sim ultaneousrotation due totorsional twistingof the test sp ecimen.
Theloadingplateenclosesthetestsp ecimen,andismoun tedinabracingframe
that prev ents its rotation and lateral displacemen t. In order to allow convenient
insertionandremo valoftestsp ecimenstheop eningintheloadingplateisoversized
andequippedwithmetalliningsasshowninFigure2.8. Inadditiontotransmitting
thetransverseload,theloadingplatehastobalancetheexternallyappliedtorsional
momen tsforloadcom binationsthatincludenonuniformtorsion. Theloadingplate
tendstorotatedue tothese momen ts,andatthesame timetheplate hastofollo w
the displacement of the horizontal actuator without creating to o m uch frictional
resistance. This is achieved by a roller b earing where the loading plate and the
adjacentpart of the bracingframe havemac hinedsteel surfaces andare separated
by cylindrical rollers. This is shown in Figure 2.5. Measuremen ts of the friction
force that can b e dev elop edare presen tedin Section2.3.
Both the v ertical and the horizontal actuator (Amsler) have hydrostatic b ear-
ings, are double-acting and hav e a maxim um stroke of 200 mm. The actuator
controllers are man ufactured by Sc henck, and provide ordinary actuator control,
suchassettingdisplacemen tlimitsandrunningtestsbyforceordisplacementcon-
trol. The v erticaland the horizontalactuator hav eanominal dynamiccapacit yof
1000 kN and 400 kN, resp ectiv ely. Forstatic loading these limits can b e exceeded
by atleast 20 %.
2.2.3 Torsional loading
Figure2.4 showsthe arrangemen tforthe torsional loading. A hydraulicmotorlo-
catedatthelevelofeac hofthetestsp ecimenends generatesthetorsionalmoment,
andthe momen tistransferredtothe testsp ecimenbymeansofarollerc hain. The
force in the c hain acts at a xed distance from the sp ecimen longitudinal axis.
The torsional loadingarrangemen tissymmetricallylo cated atthe ends ofthe test
sp ecimen, asshown inFigure2.3.
Details of the rotating parts of the end supp orts are giv en in Figures 2.8 and
2.9. The end of the sp ecimen is inserted in to a quadratic steel plate lo cated 30
mm from the end. This plate is 5 mm thic k and has a rectangular op ening that
circumscribes the cross-section of the test sp ecimen. The plate is again b olted to
a 3 mm thic kcircular plate whic his connected to a spro c ket wheel. The spro c ket
wheel is engaged by a 1" roller c hain driv enby a smaller spro c k et on the axle of
the hydraulic motor. The spro c k et wheel is an in tegrated part of the large roller
b earing units atthe end supp orts, and across-section of this b earing construction
is shown in Figure 2.9. The b earing consists of mac hinedsteel surfaces separated
bycylindrical rollersand balls. Undersim ultaneoustorsionandtransverseloading
A
- 3.0 - - 5.0 -
End fixture plates
∅ 700
SECTION A - A
A
Metal lining 30 32
5
SECTION C - C Base plate ( HEB140 ) Transversal loading plate
C C
B B
SECTION B - B
- 5.0 -
∅ 172
CHAPTER2.TESTSETUP
Detailsofendxtureplates,baseplatesandmidspanloadingplate.
120x60x6.3
250 330
∅ 572
∅ 620
∅ 700
∅ 921.81 Sprocket wheel
Roller chain
Balls ∅ 8 Rollers ∅ 7 x 12
Cross-sectionofthebearingunitattheendsupports.
force. A description of the b earing and a discussion of the resistance to rotation
are providedin Section2.3.
The torsional restraining arrangemen tsat the sp ecimen midspan, consisting of
the loadingplate for transverseloadand the adjacentbracing frame, are shown in
Figure2.5.
Alsowhenaxialloadisapplied,thefreerotationofthesp ecimenendsab outthe
longitudinalaxis isensured,bymeansof torsional b earings(or torsional "hinges")
that giv eonly a small torsional resistance. A t the lowerend of the test sp ecimen
this isobtained byaplanethrust b earing. This b earingis equippedwith acen ter-
alignmentplate and a xture b olt that k eep the b earing assem bledand cen tered,
see Figure 2.6. A t the upp er end it is provided by the free rotation of the piston
ro d and the piston inside the hydraulic actuator. A discussion of the rotational
resistance of these torsional b earings are presen tedin Section2.3.
The hydraulic motors are man ufactured by Riva Calzone, and are denoted
MR300. Themotorconsistsofv ecylindersmoun tedinastarcongurationonthe
motoraxle,pro ducingasmoothtorqueoutputandahighstartingtorque. Theop-
erationof the hydraulicmotorsis controlledbymeansof serv o-valves,inthe same
manner as the linear (Amsler) actuators, feedbac k b eing provided by m ultiturn
p otentiometersonthe motoraxlesortheload cellsinthe c hains. The motorshav e
separateRPD Howdencontrollers,inprinciple similartothecontrollersconnected
totheactuators. Themainelementsofthecontrollersare;aserv oamplier,aramp
generator and a transducer amplier. During the testing, one ramp generator is
used tocontrolb oth motors.
The hydraulic motors are originally not in tended to b e op erated at the low
sp eed range used in the presen t experimen ts. Due to the c haracteristics of the
motors, they gav e a sligh tly "stepwise" motion of the roller c hains, and not as
smoothmotionasforinstanceprovidedbyalinearactuator. The eectofthis can
b e seen in the graphs for the test results, presen ted in Chapters 4 and 5. Taking
Figure 5.10 as an example, it is seen that the curv e for the measured/calculated
torsional momen t, T-,has a somewhat oscillating b ehaviour.
The force from whic h the torsional momen t is computed, is measured by the
load cell in the roller c hain(lo cated near the motor). As the force is transmitted
to the sp ecimen through the c hain, the large b earing unit and the end xture
plates,some of themeasured oscillationsin theforceis hencedue toinertiaeects
of these parts. For the tests with large axial loads, the oscillations are somewhat
morepronounced,whic hisalsoduetothefrictiondev elop edinthethrustb earings.
Theobservedoscillationsarenot b elievedtoinuencethe obtainedtestresults.
2.3 Bearing resistance
In order tocalculate the forcesacting onthe test sp ecimens information is needed
M
F M
P P
M
Figure2.10: Test setup atfrictional resistance tests
separate in vestigation was carried out in order to obtain required data for the
resistance atvarious load lev els. Figure2.10 shows the principle of these tests.
Thrust bearings - bending momen t "hinges"
These b earings are man ufactured by SKF, and are denoted GX80F. They consist
of a spherical cap and a ring-shaped casing, separated by a sliding surface. This
sliding surface consists of a layer of glass bre reinforced p oly amide oiled with
p olytetrauoro eth ylene. Priortoeac htest someextralubrican t wasappliedtothe
b earing surfaces.
The b earings were tested in a Losenhausen 3000 kN univ ersal testing ma-
c hine. As shown in Figure 2.10 the b earings were assem bled to form a sphere,
whic h was then subjected to compressiv e loading. The load required to rotate
this spherewasmeasured, andthe corresp ondingfrictionalmomen twashencecal-
culated. Maxim um compressiv e load during testing was 800 kN. There was no
signicantdierenceb et weenfrictionatrest and frictionatmotion. The frictional
momen t dev elop ed in eac h b earing was almost negligible, and can b e taken as :
M
Fr iction
=[0 : 2+0: 0011 P(kN)]kNm
Thrust bearing - lower torsional momen t "hinge"
This wasa SKF b earingdenoted AXK160. It is a single-actingb earing consisting
of two plain lipless stamped and hardened steel washers and a set of cylindrical
needle rollersin star formation held together ina cage. The b earingwas tested in
the Losenhausen mac hineat load levelsup to800 kN, where twosimilar b earings
were moun tedasshown in Figure2.10. The b earings showed alinearly increasing
frictional momen t when subjected to increasing compressiv eloads. The frictional
momen tinone b earingcan b e expressedas : M
Fr iction
=[ 0: 0003751P(kN)] kNm
Thrust bearing - upper torsional momen t "hinge"
This torsion momen t "hinge" consists of the piston ro d and the piston rotating
in the cylinder of the v ertical actuator. The piston and the cylinder walls are
separated by a thin layer of compressed oil creating a hydrostatic b earing. Such
The frictional momen t in this hydrostatic b earing was measured to b e ab out
0.04kNmfortheunloadedactuator. Theb earingwasalsotestedusinganordinary
test sp ecimen mounted in the test rig. Axial load was applied, and the torsional
momentrequired torotate b oth thetest sp ecimen, the pistonand thelowerthrust
b earing was measured. Fromthis test, data for the total frictionalmomen tin the
Amsler actuator was calculated, and was found to b e less than 0.2 kNm for the
in teresting levelsof axial load.
Loading plate bearings
The midspan loading plate and the adjacent part of the bracing frame have ma-
c hined steel surfaces and are separated by full-complemen ted rows of cylindrical
steel rollers. Since the loading plate has to balance the external applied torsional
momentandfollo wamo vementofthehorizontalactuator,theresistingtransversal
frictionalforceisofin terest. A simpliedfriction resistancetest wascarriedout in
the test rig as shown in Figure 2.10. When subjected to a torsional momen tof 6
kNm, approximately equal to the maxim ummomen tduring the experimen ts, the
transversefrictionalforceFwaslessthan0.5 kN.Africtionforceofthismagnitude
has practically noinuence on the experimen tal results.
End support bearings
The reaction forces due to transverse loading on the test sp ecimen are absorbed
by the large radial b earings at the end supp orts. The b earings were pro duced in
the lab oratoryworkshopfromastructuralsteel St-52and standardrollerelemen ts
of b earing-steel grade. The large spro c k et wheel constitutes the outer b earing
ring, while the inner ring is xed to the test rig. See Figure 2.9 for a detailed
view of this b earing. The rotating parts are separated by a fully complemen ted
ring of cylindrical rollers in the radial direction and balls in the axial direction.
The b earing raceways are carefully mac hined and p olished steel surfaces without
hardening treatmen t. The rollers carry the main load and the balls guide the
spro c k etwheel.
The maxim um applied radial force (R=H/2) results in relativ ely low lo cal
stresses at the contact p oints of the cylindrical rollers and the raceways. Cal-
culations based on recommendations in Eschmann et al. (1985) shows that the
loading is less than 50% of the admissible static rolling elemen tloading, and the
loaddep enden tcomponentofthefrictionalresistancecaneasilyb ecalculated. The
load independen t part, i.e. the sliding resistance, was measured at the b earings.
Due to an eccen tricity of the radial load the balls have to balance a momen t in
the b earing,whic hmigh tlead toalimiteddegreeofmisalignmen tof theraceways.
Nev ertheless,this should not causeany decisiv eincreaseinthe totalfriction resis-
tance. The expected total frictional resistance is small, and can b e expressed as :
M =[0: 02+0: 00031R(kN)] kNm
of the instrumen tation. All external loads are measured using load cells, displace-
men ts by means of inductiv e displacement transducers (IDTs) and rotations by
p otentiometers. All measuremen tdeviceswere calibratedprior to the testing,and
c heckedafterthe test program was nished.
2.4.1 Axial and transverse loads
The 1000 kN and the 400 kN actuators are provided with load cells having mea-
suremen t ranges adapted to the nominal actuator capacit y. Both load cells are
exited by the 10 v olt p ower supply within the Sc henckactuator controllers. The
largestloadcellisaSENSOTEC75, andtheotherisaBLHU3L,b oth withaload
accuracy of ab out 0: 2%.
2.4.2 Torsional load
As indicated in Figure 2.11, a load cell is placed at the tension side of the roller
c hains transmitting the torsional momen t from the hydraulic motors. The other
side of the c hain lo ops is unloaded, but provided with a guide to k eep the c hain
on the rail (Figure 2.4). The torsional momentapplied to the test sp ecimen ends
is computed on basis of the force in these load cells and the constant eccen tricity
of the force. The geometry of the load cells is shown in Figure 2.12. They were
man ufactured in the lab oratory workshop to meet loads in the range of 0-20 kN
with a sucien t accuracy. They hav e a tension-coup on shap e with a rectangular
cross-section and foil strain gauges of typ eFLA-3 in a temperature compensated
full bridge circuit. The load cells were individually calibrated and balanced while
connected totheircorresp ondingampliers. Thiswas doneinanInstronuniv ersal
testing mac hine,where the load cells wereattached tothe grips using short pieces
of the curren trollerc hain.
2.4.3 Displacemen ts
Transverse displacemen ts
The transversedisplacementof the test sp ecimenismeasured atthe loading p oint
at midspan, using an external IDT (inductiv edisplacemen t transducer) moun ted
onabar attached tothe endsupp ort frames (Figures2.11 and 2.1). A part ofthis
measured displacemen tis hence due to deformations at the end supp orts. Due to
thetorsionalrotation ofthetest sp ecimen, thecen troidofthecross-sectionwasnot
accessible for direct displacement measuremen tat the end supp orts. Data on the
Specimen end rotation
Transverse displacement
Strain gauges Strain
Potentiometer IDT
D ATA LOGGER
Potentiometer
P
H Load cell
Load cell
Hydraulic motor
Potentiometer
Potentiometer Hydraulic
actuator
Axial load P
Transverse load H
Displacement
Rotation Torsional load
Displacements, forces, rotations
C ONTROL UNITS
Vertical actuator
Horizontal actuator
Upper hydraulic
motor
Lower hydraulic
motor Hydraulic
motor
Torsional load Rotation
CHAPTER2.TESTSETUP
Figure2.11:Instrumentationoftestrig.
102
9 25
9 20
Circular base plate
Copper filament Ø 0.15
Wheeled
potentiometer 200 g
Figure 2.12: Load cell for torsional force.
Figure2.13: Rotationgauge for measuremen tof test sp ecimen end rotations.
deectionsweremeasured directlyonatestsp ecimenatvariouslev elsoftransverse
load.
An in ternal IDT in the horizontal actuator is used to monitor the p osition
of the actuator piston. This provides duplicate measuremen ts on the sp ecimen
displacemen ts, ev en though signicant elastical deformations of the loading and
supp ort arrangements are included in this displacement quantity. The op eration
of the actuator duringthe tests is basedon the in ternalIDT.
Axial displacemen ts
The axialshortening of the test sp ecimenis measured by the displacemen ttrans-
ducer inthe v erticalactuator. All tests are carriedout with the axialload k eptat
a constant level, and the displacemen tsmeasured in the actuator are hence equal
to those of the sp ecimen.
2.4.4 Rotations
The rotation ab out the longitudinal axis is measured directly at b oth ends of the
test sp ecimen using rotation gauges consisting of a gro ov ed circular base plate, a
copp erlamen tand amulti-turnp otentiometerwith apulley,seeFigure2.13. The
rotation of the test sp ecimenend istransferredto arotation ofthe p otentiometer,
and the rotation angle can b e read as an induced v oltage dierence. Calibration
of these rotation gauges showed a linear and accurate b ehaviour. Potentiometers
tions, and are used for the op eration of the torsional motors.
The rotation exibilit yof the loadingplate and the bracing frame atthe sp ec-
imen midspan was measured in acontroltest.
2.4.5 Strain
Strains were measured in a conv entional way by foil strain gauges glued to the
test sp ecimensatthe relevantlo cations. TMLelectricalresistance foilgaugeswere
used, b oth ordinary gauges and strain rosettes. Powerwas supplied to the strain
gauges bythe data logger.
2.4.6 Data acquisition
Allelectronic datawere recordedusing aSolatron datalogger. The system allowed
a large numb er of c hannels to b e scanned continuously, at a reading rate of 40
c hannelsp ersecondatthec hosenresolution. Allloadcell,displacementtransducer,
rotation gauge and strain gauge measuremen ts were recorded. In addition, the
p owersupply for the straingauges, the externalIDT and the p otentiometerswere
recordedtoensurethatnoconsiderablev oltageuctuationo ccurred. Therecorded
data werepro cessed ona PC.
2.5 Test setup - load and support conditions
As men tioned ab ov e, there are two main objectives with these tests. The rst is
to obtain experimental data on the resp onse of b eam-columns when subjected to
various com binationsof axial load, b ending and torsion. The second is to provide
data for the cross-sectional resistance for two typ esof I-b eam sections, limited to
the load com bination of axial force, torsional momen t (warping) and a b ending
momentactingab out the strong axisonly.
The curren ttest setup wasc hosen inorder togiv e:
A loading system without any limiting connections b et ween the three load
actions.
Clearly denedloading and supp ort conditions.
Onepredened sectionof thesp ecimen withthe largestload eect, andwith
clearly denedresulting forces.
Forthat section, b ending momen tonlyab out the strong axis.
As few lo cal disturbances as p ossible at the most heavilyloaded section of
through the hinge. For the in vestigation of the pure b ending part of the b eam-
column resp onse, the commonly used two-p oint symmetrical transverse loading
would b e preferable, due to the advantages of the constant b ending momen tand
less eect of strain hardening and lo cal buckling (ASCE 1971). However, a two-
p oint loading couldnot inpracticeb e com binedwith the torsional loading.
Whenc ho osingthelengthofthesp ecimens,b oththeb endingmomen tgradient,
thetorsionalconditions,theweakaxisandthelateral-torsionalbucklingtendencies
and the length to depth ratio of the b eam-columns had to b e considered. The
c hosen b eam-column length of 2090 mm ensures that the tests can b e carried out
for thedesiredlev elsofthe axialload andb endingmoment,and thatplastication
of the cross-sectionat midspan can b e reac hed.
Theeectof b endingshearstresses arenormally ignoredinb eamexperimen ts.
Forthe curren ttests, taking the case of pure b ending loading as an example, the
maxim um value of the web shear stress is ab out 50% of the yield limit. For the
tests with com binedloading, this stress is considerably less and shouldnot inany
case aect the overall b ehaviour of the b eam-columns signicantly. In tests with
torsion, the externally applied torsional momen tsare balanced by the restraining
plateatmidspan. Theresultingcompressiv estressesatthe contactp ointsb et ween
the anges of the test sp ecimen and the linings in the restraining plate are v ery
lo cal, less than the yield stress and hav ea fav ourabledirection, and are therefore
considered to giv enoeecton the sp ecimen resp onse.
This c hapterdescribesthe material andgeometry of the testsp ecimens, the cross-
sectional dimensionsand themec hanicalprop erties of thematerials. Mosteortis
sp en ttodeterminethestress-strainc haracteristicsofthesteel,fo cusingparticularly
on the yieldstrength and itsvariationoverthe cross-section.
3.2 Test specimens
The two shap es in vestigated in this study are the b eam section IPE 160 and the
wide angesectionHEB140. They areb oth hot-rolled sectionsmade ofsemikilled
mild structural steel, grade RSt 37-2 according to DIN 17100, Fe 360 BFN ac-
cording to EN 10025 or similar to ASTM A283 Gr.D. The HEB 140 (denoted
HEB in the follo wing) is man ufactured by a Norwegian steel mill (Fundia) and
the IPE 160 (denoted IPE) is man ufactured by Irish steel Ltd. Both shap es are
cold-straightenedin a standard rotorizing pro cess afterthe hot rolling.
Thesteelwasdeliv eredinlengthsof12meters,atotalof7lengthsofHEBand5
lengthsof IPE.The steelsupplierprovidedsteelmaterials withthe lowestp ossible
yieldstrengthfromtheordinarysto c k,inordertoav oidlimitationsimposedbythe
test rig load capacit y. Still, the measured meanyieldstress was foundtob e ab out
25%ab ov ethesp eciedminim umstrength. TheHEBlengthswereallmark edwith
the c harge cast numb er while the IPE had no sp ecic iden tication marks. Both
the HEBand the IPE lengths wereeac h declared p ositiv elyto originate from one
batch. The main elemen tsof the c hemical composition and the tensile prop erties
of thesteelsare giv eninTable3.1, basedoninformationfromtheworkscerticate
provided by the manufacturers. In this particular case the upper yield stress is
giv enfor the HEBsection.
C Si Mn P S N f
y /f
u
HEB 140
0.12% 0.23% 0.68% 0.025% 0.019% 0.006% 294 / 434 MPa
IPE 160
0.06% 0.21% 0.58% 0.021% 0.031% - 302 / 410 MPa
Table 3.1: Chemical compositionand tensileprop erties
2090
1 4 0
s = 7
t = 12
» 4 0
10
HEB 140
b = 140
h = 1 4 0
r = 12
5
9 7.4
1 6 0
82 10
8 2 » 3 0 IPE 160
Figure3.1: Testsp ecimens HEB140 and IPE 160, nominal cross-sectional dimen-
sions.
Five test sp ecimens weretaken from eac h 12meter unit, lea ving shorter b eam
stubs for material testing. The preparationof the test sp ecimens consisted of saw
cutting and removal of the ange tips at eac h sp ecimen end, and mill mac hining
to provideplane ends. Except for this, the condition of the test sp ecimen was as-
rolled and rotorized. The test sp ecimen geometry and the nominal cross-sectional
dimensions are shown inFigure3.1.
The cross-sectionaldimensions of all 12 meter units were measured. The vari-
ation in ange and web thic kness in the cross-section and the distortion of the
sections were in vestigated. As usual (discussed in ECCS 1976), the anges are
thinner and the web is thic ker than the nominal values, while the cross-section
heigh t and width deviate less from the nominal values. The torsional prop erties
HEB 140 140.9 140.45 11.40 7.3 4190 0.98 0.98 0.97 0.97 0.96
IPE 160 83.2 160.2 6.83 5.6 2036 1.01 0.99 0.98 0.98 0.96
Table 3.2: Cross-sectional dimensions and prop erties
of area and the elastic and the plastic section modulus are most aected by this,
while the corresp onding strong axis prop erties and the cross-sectional area are
closer to the nominal values. The measured dimensions and some of the cross-
sectional prop erties fortworepresen tativecross-sectionsare giv eninTable3.2. In
the subsequentcalculations and presen tationsofthe b eam-columntest resultsthe
measured dimensions are used foreac h test sp ecimen.
The initial longitudinal out-of-straightness of the mem b ers and the out-of-
atnessofthesectionalelemen tsweremeasuredforfourunits,eac hof3.0mlength.
Measuremen tsweretaken atb oth endsectionsand at threein termediatesections.
The measured deviation from a straight line through the end sections was within
1.5 mm b oth for the section cen troid and the ange tips. The initial longitudinal
twist angle of the memb eraxis was negligible.
3.3 Material tests
In the material tests, all load, strain and displacemen t measuremen ts hav e an
accuracy within 1% of the measured value.
3.3.1 Tension tests
The uniaxial tensile prop erties of the steels were determined from standard test
coup ons. Longitudinal test coup ons were cut from various p ositions in the cross-
sections and fromsome selected lo cations alongthe 12meter units.
Allcoup onshadarectangularcross-sectionand weremac hinedatallfoursides
atthe reducedsection,main tainingnearlythe fullthic knessof the testedangeor
webplate. Thetest coup onsmetthe geometrysp ecications ofaprop ortionaltest
coup on,i.e. theyhadamac hinedparallellengthL
C
consistingofanoriginal gauge
length L
0
= 5: 65 p
A
0
(minim um 25 mm) plus some additional transition length.
The original gauge length was used only as a basis for calculating the p ercen tage
elongation after rupture(
5 : 65
). The dimensions of the tension coup ons are giv en
in Figure3.2 and Table 3.3.
All tension tests were carried out on an Instron 250 kN univ ersal testing ma-
b t
r - t -
L C L
B L 0
Dimensions( mm ) L
C L
0
B b t
HEBange
125 95 35 26 11
HEBweb
90 70 30 22 7
IPE ange 80 70 35 25 6
IPE web
70 55 30 20 5
Table 3.3: Geometry of tensiontest coup ons
Figure3.2: Testcoup ons for uniaxial tension tests
engineeringstrain, wasmeasured bymeansof double-sidedInstronextensometers.
In the majority of the tests a 50 mm extensometer was used, but shorter exten-
someters were used for coup ons with initial parallel length L
C
less than 50 mm.
Strain was measured with the extensometer up to a strain level2%, b ey ond this
lev elthe Instron testing system determinedthe strainfrom the crosshead v elo city
setting,the timeregistrationsand theinitiallength ofthe reducedparallelp ortion
ofthe coup on. Thecoup onsweretestedatlowstrainratesintheelasticrangeand
during the yielding of the material. A t onset of strain-hardening, the strain rate
was increased toreduce the time needed tocomplete the tests.
The strain rate in the b eam-column tests was determined to vary mainly b e-
tween1110 05
=s and 1110 04
=s for the material in volvedinyielding. The majority
of the tension coup ons was thereforetested ata mean strain rate of 0: 5110 04
=s.
The cross-sectional p osition of the coup ons is shown in Figure 3.3. A total of
40 coup onswere taken fromthe HEB units and 20coup ons from the IPE units.
The HEB tests showed that the stress-strain curv e diered signicantly ov er
the cross-section. The b ehaviour of the ange material was as expected for a
mild structural steel, comprising a distinct yield-point elongation, while the web
material near the web-ange junction showed no yield p oint in the stress-strain
curv eatall. This part also p ossessed anultimate tensile strengthasm uchas25%
higher than the remainder of the cross-section. The IPE tests showed that the
ange andthe web material had almostiden ticalmec hanicalprop erties, with only
a minorvariationoverthe cross-section.
HEB IPE
Figure 3.3: Lo cation of tensile coup onson cross-section.
erally, the webs had a higher yield strength than the anges, a dierence of 3%
was obtained for the IPE section. Furthermore, the yield strength of the anges
was highest at the ange tips. The measured yield strength at the ange tips of
b oth sectionswasapproximately4%higherthantheav eragefortheanges. These
observationsareconsistentwithsimilarin vestigationsonsemikilledsteels(Alpsten
1970), and is explainedfromthe dierencein co oling rate, wherethe weband the
ange tips co ol faster than the rest of the section, resulting in a ner grain size
and a higher yield strength. The rotorizing pro cess did not seem to haveaected
the prop erties oftheangematerialsconsiderably,whic hwasseen frompractically
constant elongation prop erties across the anges of b oth sections ("
y p
;"
u
;
5 : 65 in
Figure 3.6).
Coup ons taken from iden tical p ositions in the cross-sections showed only a
small spread in the measured values. The values from 9 tested coup ons taken
at the ange tips of the HEB section can b e taken as a represen tative example;
mean yield strength 281 MPa, all measured values within a range of 17 MPaand
a standard deviation of 5.8 MPa.
The mec hanicalprop erties obtained from the tests of the longitudinal coup ons
are summarized in Table 3.4. From the test, the yield strength f
y
is taken as the
meanstress inthe yieldplateau, neglecting anyp eakvalueatthe startof yielding,
andemphasizingthestressvaluesintherst2/3oftheyieldplateau. Theresultsin
Table3.4 are giv enasmean valuesfor b oth angesand forthe web. The variation
of the yield strengthov erthe cross-sectionhas to b e consideredwhen in terpreting
the b eam-column test results in the follo wingc hapters.
Represen tative stress-strain curv esfor the anges are shown for b oth sections
inFigure3.4,while the b ehaviourof the HEBwebis depictedinFigure3.5 (based
on results fromthe follo wingin vestigation). The cen tral p ortion of the HEB web,
p osition 4 in Figure 3.5, has a stress-strain curv e similar to that of the ange
f
y
f
u
"
y p
"
u
5 : 65
(MPa ) (MPa ) (%) (%) (%)
HEB ange
279 438 1.6 20 34
HEB web,cen ter 290 449 1.4 19 36
IPE ange 304 424 2.2 23 34
IPE web 314 425 2.6 21 34
Table3.4: Mec hanicalprop erties of the HEB140 and the IPE 160 b eams.
p ositions 2 and 3 increased yield strength and decreased ductilit y are observed,
b oth signs of cold-working during the rolling pro cess. The lac k of a yield p oint
elongation for the web material closest tothe web-angejunction, p osition 1, can
b eexplainedbyarelativ elyhigherexten tofcold-work,whereasthelargeincreasein
ultimate strengthmigh tb e aresult fromstrainageing causedbythe lowerco oling
rate atthis part of the section.
Variations in mechanical properties
The distribution of the strength and the ductilit y across the ange and the web
plates was in vestigated in a separate test. To provide a higher resolution in the
measured distributions, smaller test coup ons were used than inthe ab ov ein vesti-
gation. Testcoup ons were taken fromone HEBand one IPE stub asindicated in
Figure 3.6, utilizing the en tireactual part of the cross-sections. Prop ortional test
coup ons were used, the width was reduced with only 2 mm at the gauge length,
and the coup ons were the full thic kness of the ange or web. The coup ons were
tested at iden ticalstrain rates. The measured mechanical prop erties are giv en in
Figure3.6.
Anisotropy tests
The hot-rolled b eam sections are normally not expected to display anisotropy in
thewebandangeplates. However,ahighexten tofplasticwork andsev eredefor-
mationofthesteelbilletsduringthe rollingpro cess atimpropertemperaturesma y
still leadtoanisotropyinthe tensileprop erties. Theyieldstrength, andtoalesser
exten tthetensilestrength,are mostlik elytodisplayanisotropy(Dieter1988),and
the thinnerweb plate shouldb e more aectedthan the ange if anisotropy exists.
Alimitedtestprogrammewascarriedout todetermineanyp ossibleanisotropy.
Two tension coup ons were taken from the b eams at neigh b ouring p ositions, one
coup on in the longitudinal direction of the b eam and one coup on in the trans-
v erse direction, as indicated in Figure 3.7. The transverse coup ons were m uch
smaller than the standard tension coup ons, and companion longitudinal coup ons
were hence giv en the iden tical geometry. Coup ons were taken from the ange of
b oth sections, from the cen ter of b oth webs and from the part of the HEB-w eb
0 5 10 15 20 25 30 35 40 Strain [%]
0 100 200 300 400
S tr e s s [M P a ] IPE
HEB
Figure3.4: Typicalstress-straincurv esforIPE 160and HEB140 (angecoup on).
The tests showedno signicantanisotropy in the stress-strain c haracteristics.
Modulus of elasticit y
The modulus of elasticity (E) was determined from cylindrical tension sp ecimens
mac hinedfromthe angeof the HEBandfromthe web-angejunctionof theIPE
section. Thesp ecimens had a parallellengthL
C
=80mmand adiameter equal to
8 mm, and were connected to the test mac hine by 12mm threaded grip ends. A
double-sided extensometer was used, and care was taken to av oid p ossible eects
due to curvatureof the sp ecimens.
Two companion test sp ecimens from b oth sections were tested in a series of
rep eated loading and unloading up to load levels of 80% of the yield load. The
two companion sp ecimens gav e practically iden tical results, and the modulus of
elasticit ywas calculated to 210 GPa for the HEBand 207 GPa for the IPE steel.
3.3.2 Compression tests
Compression coupon tests
Compressioncoup ontests werecarriedoutforthe angematerialofb oth sections.
0 5 10 15 20 25 30 35 40 Strain [%]
0 100 200 300 400 500 600
S tr e s s [M P a ]
1
2 3 4
Figure3.5: Stress-strainc haracteristicsatdieren t p ositions inweb of HEB140.
287 434 1.6 24 38
278 435 1.6 26 37
269 438 1.45 26 37
272 441 1.45 27 40
277 437 1.5 25 42
278 441 1.45 25 40
268 435 1.4 26 40
277 437 1.5 25 37
282 436 1.55 24 35
f y f u
e yp
e u
d 5.65
- 5 5 1 - 5 1 6
2 7 4 4 3 5 1 .2 5 2 5 3 9
2 9 4 4 4 2 1 .2 5 2 5 3 7
3 6 3 4 7 3 0 .9 1 4 2 9
313 427 1.2 19 30
314 420 2.5 20 31
300 414 2.8 22 40
300 418 2.7 22 42
308 422 2.4 18 32
318 424 3.1 16 30 296
415 2.2 22 40
3 1 1 4 2 2 3 .4 2 3 4 1
3 1 3 4 2 5 3 .5 2 2 4 2
2 8 7 4 2 4 2 .5 2 1 4 2
3 3 1 4 3 5 2 .0 1 9 3 5
3 1 4 4 2 3 3 .5 2 2 4 2
Figure3.6: Variationofmec hanical prop erties in HEB140 and IPE 160.
Figure3.7: Lo cation of coup ons for anisotropy tests.
