ultimate behaviour of trapezoidal steel sheets in bending

7/30/2019 Ultimate Behaviour of Trapezoidal Steel Sheets in Bending

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Twelfth International Specialty Conference on Cold-Formed Steel StructuresSt. Louis, Missouri, U.S.A., October 18-19, 1994

ULTIMATE BEHAVIOUR OF TRAPEZOIDAL STEEL SHEETS IN BENDING

Raffaele Landolfo1 - FedericoM. Mazzolani2

ABSTRACTA systematic analysis of existing trapezoidal steel sheets commonly used in the market isperformed in order to compare their carrying capacity at the light of their ultimate behaviour.The complete investigation has been developed both from theoretical and experimental pointsof view. In this paper, the description of the experimental techniques, the numerical simulationof the obtained results as well as the exploitation of these data in order to check the codifieddesign rules are reported.

1. INTRODUCTIONThe structural behaviour ofcold-formed steel sections is a research subject which has been

carried out in the last decade in the range of activity of the Institute ofTecnica delle Costruzioniof the Engineering Faculty of the University of Naples. As far as sheetings are concerned, agreat attention has been devoted to the innovative products, the so-called third generation oftrapezoidal sheets such as TRP 200 [1,2].

In the field of traditional sheetings, the recent technical literature [3] called the attentionon the importance to analyse the influence of the shape of the cross-section and of the presenceof stiffeners in the compressed parts. On the other hand, it was observed that the shapes of theexisting commercial sheetings are usually designed on the base of serviceability requirementson the base of empirical data and very seldom they have been examined from the point of viewof their ultimate behaviour by means of refined research methodology.With these motivations, a general research programme has been promoted on the bendingbehaviour of trapezoidal steel sheets commonly used in practice for roofing. The complete studyhas been carried out through the following phases:a) Experimental investigation on the behaviour under bending action of several trapezoidal

steel sheets with different dimensions and thicknesses;b) Numerical evalutation of the bending process of the section taking into account the local

instability phenomena of compressed parts by means of general simulation procedure;c) Evaluation of bending strength according to the main provisions and comparison with

numerical and experimental results.This programme has been developed with the cooperation of CREA (Massa) and CSM(Roma), the last being performed the experimental part [4]. The research is now concluded and

a first elaboration of testing and simulation results has been done [5,6].

1 Research Assistant, University of Naples, Italy2 Professor of Structural Engineering, University of Naples, Italy

205


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2. EXPERIMENTAL ACTIVITY

2.1 Specimens selectionThe experimental phase has been carried out by means of 32 bending tests on 16 differentspecimens. Nine shapes of trapezoidal sheets have been preliminary selected among the onesmost widely used in practice for roofing (fig.I). Except for the first two shapes, which aresymmetric about the horizontal axis, the other seven can generate two different specimens eachotherby overturning the cross section. Therefore, starting from the nine basic sheets, 16 differentprototypes have been generated.In order to interpret the obtained test results, these specimens have been subdivided in two group.According to the behavioural classes proposed in Eurocode 3, as classification parameter thebIt ratio of the compressed flanges has been assumed. Two groups are therefore obtained (fig. 1 :Ith group, including specimens with blt41 (n. 2, 3, 5, 7, 9, 10, 12, 14, 16).

Each specimen is made of a single fold; the nominal dimensions of the cross-sections areshown in tab. 1. In such table, the actual dimensions measured in one section of each specimenare also reported. The geometrical properties of the cross-sections, evaluated according to thenominal and the actual dimensions, are given in tab. 2.

The comparison between nominal and actual geometry shows a significant disagreement,due to manufacturing tolerances. As far as the thickness is concerned, the maximum scatterranges from -21 % to +26%, varying from a minimum of 0.79 mm to a maximum of 1.26 mm.More complex is to comment the differences among each dimension of the cross-section, someof them being modified by the cutting process. A global judgement may be expressed bycomparing the strength moduli of the nominal and the actual cross-section (tab. 2). Thiscomparison shows that, sometimes, the scatter may reach the value of 30-35% (i.e. specimen3B). Significant dimensional variations have been observed also between the two specimens(called A and B) of the same type of shape. In this case, the above mentioned scatter is usuallyclose to 10% except for profiles n. 2, 3, 10, 12, and 16 having scatters of about 20-24%.From these results it appears that the manufacturing tolerances for sheetings are very rough andthe use of the nominal values in the calculations can lead to unsafe results.

THE SELECTED TRAPEZOIDAL SHEETS~ -A . . . - . . .A . . . -1) 2011000 2) 4211000 3) 551900

--"--"---A- ~ ~4) 5011000 5) 4511000 6) 5OI1000A[""'\""'\[""'\ rv-v-v-\ I \ I \ fV1

7) 751570 8) 100n50 9) 1601750~- - - - - - { ~ G ~ R o u ~ p I 1 ~ - - - - - - 1 r - - - - - - ~ G ~ R O U ~ P ~ 2 ~ - - - - - - l

4~ - - " - -"-11 13 15 10 12 14 16J \ . J\.. J\. n 1 \

1 s 1 ' 1 : ' 1 ' 1 ' ' ' I ' ~ 1':01: ~ ~ ~ H ~ 1 = l h l ~ l i l . I ~ l l l i l i l i lfig. 1


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2.2 Experimental testsThe experimental measurement system was designed in order to allow the evaluation ofthe specimen global response as well as the local behaviour of the midspan section where thestrain gauges have been located. Monotonic tests have been performed on 32 simply supportedbeams with 1500 mm of span. Two concentrated loads have been applied in two sections spaced

500 mm across the midspan (fig. 2). The stiffening strips are located, each 50 mm, between thetwo bottom flanges, in order to guarantee the transversal cross-section indeformability, accordingto the actual boundary conditions. In a first phase, vertical displacements have been measuredby means of transducers located in seven points (5 at midspan and 2 at supports). Bi-directionalstrain gauges in number of 9 to 12, have been distributed along the midspan cross-section.Furthermore, the number of transducers and strain gauges has been reduced to 3 and 5respectively as shown in fig. 2. The ultimate values of testing loads are given in tab.3. Moredetailed informations concerning the test equipments and results are reported in [6].

StiHening Strips20X2mm

LOAD

i rf1 iI' I I~ 5 Q O ! 5 Q Q ~ 5 Q Q !2500

SEC. M-M :PHASE 1

.StrainGauges TransducersSEC. M-M : PHASE 2

~ ~

The evaluation of the material mechanicalproperties has been done by means of 16tension tests on strips obtained from eachprototype. The results are shown in fig.3. Allvalues evidence a significant variability. Thestatistical evaluation of hese test results allowsto determine the characteristic values of yieldand ultimate strength which are/y,k=271 Nmm2andJ"k=352 Nmm2, respectively. Such valuesare evaluated on the basis of 15 test results,excluding test n. 10 which provided a quiteanomalous result, and assuming k=2.57according to Italian provision for materialfig.2 qualification.

Furthermore, these characteristic values are comparable to the nominal values for Fe E 250 Gsteel grade (f",r=250 Nmm2 andJ",r=330 Nmm2) , which is commonly used for producing theexamined sheets.

MATERIAL PROPERTIES (Nmm-2)5 0 0 . - - - - - - - - - - - - - - - - - - - - - - - - - ~ - - - - ~ - - - - - - - .400 ...........................................................................................................................ft,k 1-H---f)--k1I-ft't-tf---T


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DIMENSIONS (mm) NOMINAL ACTUALn SECTION t a b c h t a b c h1 ~ 1.0 100 35 6S 20

A 0. .,. 53 62 20B In. .. 53 65 ,.h l ~ . 1.0 250 8S 165 42 A ... .,. 82 .65 "'.82 .,. .. .65 43

3 r-\. 1.0 450 400 430 55 A In, 458 '79 .Z1 ,.B ... ... 317 ..4 ~ 1.0 450 20 SO 55 A ... 44S 20 .7 57B om 44S >I ,. 575 .r--\. 1.0 333 260 298 SO A .... ,,. 2IiII 28S ,.B om 324 2S7 >.92 ;.6 ~ 1.0 333 35 73 SO A 0. ,,. .. 7. 53B ... ,., .. '" 527 .r-\ . 1.0 250 166 214 45 A 05 2A7 ... 21' ..B ... 2A5 ." ,II 438 -A...... 1.0 250 36 84 45 A 00 243 " 78 '"'.82 2A5 " 81 .79 ~ 1.0 333 223 283 SO A '.0. ". ... 282 ,.B D3 ,,. 220 280 >I10 ~ 1.0 333 SO ll O SO A ... 327 .7 .08 ,.B '.0. '" '" .08 ,.I I JL 1.0 190 40 64 75 A .., .87 " " 7& D2 ... " .. 7812 I I . 1.0 190 126 ISO 75 A ,.00 , . .26 .50 7&'.2& ... .22 .54 7513 A .. 1.0 250 40 ll O 100 A .., "" .. 11. .mB D2 .,. >7 112 'IB14 . I \ . 1.0 250 140 210 A ,.0, 254 '37 220 VI100 B 0.79 .,. .37 21. .01IS A 250 40 A ... .,. .. .15 .".0 120 160 B '.00 248 >7 .22 ."16 n 250 A ... .,. 131 'IJ11 .621.0 130 210 160 B ,.. .,. ". 21. .61

Tab. 1PROPERTIES NOMINAL ACTUAL

n SECTION A Ix Wv p A Ix Wx ILl.Wx p2 . , , .1 ~ 1.17 0.76 0.76 9.20 A ,.43 .., 0.79 11.40B 1.16 0.7. 0.7. , ".2 ..f"""'.... 2.83 8.69 4.14 2230 A 2M U , ,> I . ~ , .B .. ~ u. .. n703 r-\. 5.29 13.15 2.80 41.50 A '25 '155 ,,. 41.20B .... 20." " , ..4 ~ 5.29 13.15 2.80 41.50 A 5.19 ..... .... "'70B "12 14.17 ... 05 r - - . . . 3.97 11.97 3.08 31.20

A .D2 '115 '" "iiiB ... ".63 '9 2 12 a ..6 ~ 3.97 11.97 3.08 31.20 A .... 1137 3.25 31.SOB ,., .... "" 7 .....7 .r-\ . 3.00 8.55 un 23.60 A ". 1 Mli lB 19 ' 8.2Z '56 12 n ..8 -A...... 3.00 8.55 2.67 23.60 A ~ .... ... 2140B 5.04 902' 175 , .....9 ~ 3.86 13.90 3.86 30.3 A ,.. .4.5t 00 ... .B , .. . ~ 31.1010 ~ 3.86 13.90 3.86 30.3 A .... ..... , . 21. .B .., 1157 ". 20 '0.00I I JL 3.ll 25.67 5.38 24AO 19 ' M" .. 03 23.203.17 27.53 s.>s OAM12 I I . 3.ll 25E1 5.38 24AO A ,.00 M7& s.oo . M , . ..... ... 22 ...,.13 A .. 3.87 54.08 8.61 30AO A 3.72 51"

.n a20B w 57.76 &92 31.2014 . I \ . 3.87 54.08 8.61 A .., ,&7, 7.9' a ..30AO B .... ..... .. 12 lU .

IS A 163.59 A 4." ,.... 17.05 3&. .4.94 17.31 38.80 B 2.... '''' .. '7.39 ,as.16 n 1731 A u. ,- 17. 37.104.94 163.59 38.8 B Z1~ ,., . 22.D2 49.00

Tab.2


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E X P ER I M EN T A L R E S U L T SS E C T I ON TYPE Ful1: J\lJ:u.lt 6 . jMkN kNm 0/0

A 0.78 0.20 1 0B 0.90 0.222 A 2 . 41 0 . 6 1 37B 3.B3 0.973 A 3.95 1 . 01 1 3B 4.55 1.164- A 4.67 1 . 1 9 5B 4 . 91 1.255 : 4.19419 1 : ~ : 06 A 4.97 1.26B 4 .91 1.257 : 3 _ ~ : ~ . : ~ 98 A 4 .31 1 . 0 9 4-B 4.13 1 .04 -9 A 4.73 1 . 1 9 5B 4.43 1 . 1 31 0 A 2.39 0 . 61 5 3B 5.15 1.3011 A 6.62 2.16 1 2B 7.S4 1.901 2 A 6.10 2.03- 1 6B 9.55 2 . 411 3 A 11 . 8 1 2.96 1 3B 10.12 2.5514 - A 10 . 74 - 2.70 1 0B 9 .64 - 2.421 5 A 18.63 4 . 61 11B 16.35 4 . 111 6 : ! ! - ~ ~ : : ~ ; 2 8

Tab.32.3 Interpretation of experimental data

In tenn of ultimate behaviour, all specimens have shown similar collapse mechanismindependently of the value of maximum load F It. Failure is always characterized by suddencrippling at one top corner. This phenomenon usually occurs in a cross-section located in thecentral part of the specimen, where the bending moment is constant. Regarding the ultimateload, the experimental results evidence in most cases a significant difference between the valuesobtained for the two tests on the same specimen (type A and B). Such a difference, given intab. 3 as percent scatter between the values ofultimate bending moments, ranges from a minimumof 0% obtained for the profile n.5 to a maximum of 37%, excluding the specimen n.lO whichgave anomalous results also from the tensile' tests. I f the actual dimensions of specimens areaccounted for, the analysis of test values ofFuIt evidences that, except for the profile n.lO, thescatter usually does not exceed 10% in tenns of maximum stress.

The experimental response in tenn of force versus displacement relation-ship for allspecimens belonging to the first group emphasized an elastic behaviour almost linear until the'failure (fig.4), whereas for specimens of second group a premature decreasing in stiffness isobserved due to the spread of local buckling phenomena (fig.5). This trend is amplified as faras the slenderness of the compression flange increases (profiles n. 3, 5, 7, 9).The values of curvature (X) for the examined cross-sections have been determined bymeans of strain measured at the top and bottom flanges. Therefore, the moment versus curvaturebehaviour is primarily influenced by the value of strain in the compression flange, since thetensile one virtually remains elastic. For specimens of first group these curves show an initiallinear trend which later on becomes non linear due to yielding occurring in compression flangeand local buckling at the web, the last phenomenon being more frequent in case of deepestshapes (fig.6). The second group of specimens provides a very irregular trend in theM-X curves,being influenced by both local buckling of the top flange and yielding of the tensile one (fig.7).Local buckling usually affects the behaviour even for low values of loads and leads to verydiscontinuous curves. Yielding of the bottom flange affects the behaviour for large curvaturevalues, sometimes leading to quasi-flat branches.


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kN GROUP 1 - FORCE-DISPLACEMENT RELATIONSHIP kN GROUP 2 - FORCE-DISPLACEMENT RELATIONSHIP

16 ~

12 18

12

10 20 30 mm 20 40 mm

figA fig.SkNm GROUP 1 - MOMENT-CURVATURE RELATIONSHIP k N m - r " " " " ' ~ P " " " ~ - ' - " " " " ' - " - ' ? - ' - " D ' " - ' ! " ! " , , U ! > " " ' P U : - ,

15A l4 - - - - - ~ - - - - - - - - - - - - i - - - - - - - - - - - - - ~ - - - - - - - - - - - - + - - - - - - - - - - - -

i i ! !--- --'''''------------j-------------f------------f------------- ---- -------1-------------l------------l------------

40 isBSA! !& ~ ~ ~ ~ - 8 ) ( - - r - - - - - - - - - - - - T - - - - - - - - - - - -! i 1B 1A

o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~o 0.02 0,04 0,06 0.08 0.10 0.12 0.14 O.16x10E-3 mm-1fig.6

3. THEORETICAL INVESTIGATION3.1 Numerical simulation

~ : - F ; ; ~ - - H A ' - - - - - - - - - - - - - - -

o ~ ~ - - ~ ~ - 4 - - . - ~ - - r _ 4 _ _ . - - + _ ~o 0-04 0.08 0.12 O.16X10E-3 mm-'fig.7

The analysis of the bending process ofinvestigated profiles has been numerically performedby means ofa simulation method, which has been set up in the rangeofactivityofa more generalinvestigation on the bending behaviour of thin walled sections [7]. The cross-section is modelledby subdividing it in several small areas, where is possible to associate a residual strain, a localstress-strain relationship together with all informations needed for the knowledge of the loadhistory. The deformation process of the section is examined with small consecutive increasingof curvature. For each curvature an iterative procedure gives the position of neutral axis, thestrain and stress in each area (taking into account eventual local unloading) and the subsequentbending moment. Local buckling of compressed part is taken into account according to thetheory of stability by using different interpretative models.

The practical use of the simulation procedure in the analysis of tested specimens, does notpresent particular difficulties in comparison with the application to cold-formed thin-walledsections as ithas been done for other purpose [8]. Itismainly due to the simplicityofcross-sectiongeometry, which is characterized by all flat element without intermediate stiffeners. With regardto buckling model, the elastic formulation in terms of strain has been adopted both in elasticand post-elastic field.


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The simulation procedure has allowed to obtain the moment-curvature diagram for eachspecimen, by assuming the actual dimensions of cross sections and the material propertiesprovided by above mentioned tension tests.The comparison between the experimentalM -X curves and the simulation ones has shown,in many cases, a rather approximate agreement both in term of ultimate strength and stiffness.These differences are due to variability of material strength, according to scatter values foundin tensile tests, as well as to initial geometrical imperfections. With regard to geometricalimperfections, they are taking into account by the proposed model only in post-buckling range.As a consequence the main differences have been found for specimens belonging to the fIrstgroup, whose critical load is particularly high. On the contrary, for specimens of second group,the results provided by the simulation procedure have shown a better agreement with theexperimental evidence, being the local buckling occurred even for low values of load.In order to overcome these uncertainties a band criterium has been, therefore, assumed.According to this assumption the values of yielding stress ranged from the characteristic values(/y,k=271 Nmm-2),to the experimental one (/y,


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3.2 CodesThe evalutation ofdesign moments Mdon the basisof the criteria provided by Italian (CNR

10022 [9]), European (EC3-Part 1.3 [10]) and American (AISI [11]) codes has been performed.In order to have an unified parameter, which overrides the differences among the mentionedcodes (allowable stress or ultimate limit state approaches), the design moment is defmed asfollow:

MdJ = W.v' f,.d (1)beingW.v effective section modulus evaluated according to each code, with reference to thenominal dimensions of specimens;f,.d nominal yield stress for Fe E 250 G steel grade (/,,.;=250 Nmm-2)This approach is usually followed in design procedure_ As an alternative, the calculation ofMd2has been carried out by considering actual dimensions of the specimens and characteristic valueof the yield stress (/',J-

The ratios between M d. and the design moments provided by considered codes are shownin figg. 12 and 13 respectively for Ith and 2th group.MulllMd (GROUP ' ) MulllMd (GROUP 2)~ 2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 2 ~ - r ~ ~ ~ - , ~ ~ - r ~ ~ ~ - . ~ ~

2 ---f---t---1----1----f----f----f---t---1----i----f---+--t---1---- -t--i---i--i--f--t--i---i---f-+--f--i---i--+--f--t--t-t--1.8 - - - : - - - - ~ - - - - 1 - - - ... - - ~ - - - - : - - - - T - - - ~ - - - - t - - - - t - - - - : _ - - - " t - - - " ! - - - - t - - - - 18 - .....-- .. - - ~ - - L - - _ ..-_ ....--..--_ .--_L_--..---..-- ..--_ .-_-I:r_- .. _-.-_ .... __ .._--

~ I t * f : t $ t = t t : t ~ : : ~ : : ~ : ~ T ~ H m ~ ~ t t H t0.8 - - ! - - - ~ - - - - ~ - - - - i - - - - ~ - - - t - - - ~ - - - - j - - - - i - - - - ~ - - - - ~ - - - ~ - - - ~ - - ~ - t - - - -:,: :4 : :6 : :S : I,,: :'3: :'5:o. ' - A ~ B ! - - A ~ B ! - - A ~ B ! - - A ~ B ! - - A ~ B ! - - A ~ B ! - - A ~ B ~EC3"",0...- eNRI>.. AISIo fy--250 Nmm-2: nominal dim. ty.271 Nrrm-2;aduaI dm

fig_I2

o. - . - - ~ - - - j - - - i - - - ~ - - i - - j - - - j - - - j - - - ~ - - l - ~ - - - j - - - j - - - ~ - - - ~ - - t - - j - - -: 2: : 3: : 5: : 7: : 9: ~ 1 1 0 : :'2: :'4: :'6:o. A B A B A B A B A B A B A B A B A 8EC3n 0.....- eNRI>.. AISIo fyoo25O Nnm-.2; nominal dim. ry..271 Nmm-2;actuaI dm.

fig. 13

4. ANALYSIS OF RESULTS AND COMPARISONSThe analysis ofobtained theoretical results and the comparison with the experimentaldata

allow to deduce some final remarks, which can be given separately for the two groups.1 hgroup: the numerical simulation gives a good correlation with the experimental results, sincethe scatters are always not larger than 25%, as shown in fig.lO. When assuming/Y=h_, thenumerical prediction (Ms2) leads to a better evaluation of the actual ultimate moments comparedto that (M.1) obtained when taking /Y=/YJ


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actual geometry andfy=fy)l. are in most cases closer to the experimental values compared to those(Mdl) computed by introducing the nominal values of geometrical dimensions and materialproprieties.21h group: even for this group, therds a good agreement between simulation and experimentalresults. The scatters are slightly large than those obtained for the fIrst group; however thesimulation usually provides a conservative estimate of the ultimate moments (fIg.ll). Onceagain the anomalous results provided by specimen n.lO are evidenced. The code provisionsalways give similar design moments which are smaller than My due to the local buckling of theflange in compression (fIg.13). The above observations can be justifIed by considering that thecompared standards take into account flange local buckling in a similar way. As for the Ithgroup, the increase in the depth of specimens (profIles 12, 14 e 16) results in larger differencesamong the design moments provided by the codes, even i f this tendency is less evident.Furthermore, the second approach (Maz) gives a better agreement with test results.Figures 14 and 15 report the mean values of the non-dimensional ratio between the test ultimatemoments and the theoretical ones obtained by the numerical simulation and by the codeprovisions, in order to check the reliability ofboth approaches. It can be seen that the numericalmodel (fIg. 14) appears to be very suitable. In fact, for the Ith group, the simulation procedureprovides, in the average, values of ultimate moments by 13% smaller than the actual ones, ifh=fy)l. is assumed, whereas it gives values of ultimate moment slightly larger (by 4%), i f theactual strength of material is introduced. For profIles belonging to the second group, thesimulation is always conservative, leading to scatter of 17% and 8% with respect to theexperimental values.The bearing capacityof sheets, evaluated according to the provisionsof the Italian (CNR 1(022),European (EC3-Part 1.3) and American (AISI) codes (fIg.15), is underestimated by 50%, ifnominal geometry of the cross-section andh .=250 Nmm-2 are considered. The above scatter isreduced to 35%, if the actual geometry and/y=fy)l. are introduced. The previous observations canbe extended to both groups of specimens, even if for the fIrst one the variation in the meanscatters with the assumed code provisions increases.

5. CONCLUSIONSThe research programme described in this paper has been aimed at investigating the

ultimate bending behaviour of standard trapezoidal sheets. In particular, experimental,theoretical as well as design aspects involved in this topic have been dealt with.Tests have been performed on a large number of specimens, covering the most used shapes inpractice.The numerical simulation provides results in excellent agreement with the experimental ones,despite the large variation of shapes and the scatter in material properties.The analysis of congruity of provisions given by the examined codes for cold-formed sectionhas evidenced a large. underestimation of the actual bearing capacity for this typologies ofprofiles. The mean value of the design moments, in fact, is usually smaller by 35-50% than thetests results.Therefore, it can be concluded that the proposed numerical procedures can be used as an effectivetool for carrying out a wide parametric analysis in order to d'evelop more adequate design rules.


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MuH/MsGROUP 1 GROUP 2

15r--------------------------------------------------------4-----------------------------------------------------1

05

fig.14MultlMd (Mean Values)

GROUP 1 GROUP 2I.S

o.S

oEC3 CNR AISIIII ~ ~

fig.15ACKNOWLEDGEMENTS

This research has been coordinated by Prof. Dr. Ing. F.M. Mazzolani with the collaborationofDr. Ing. R. Landolfo both from the InstituteofTecnica delle Costruzioni of the EngineeringFaculty of the University of Naples. The research progmmme, sponsored by CREA (Dr.Morando), has been planned and agreed by Dr. Buzzichelli, Dr. Bufalini, Dr. Ing. Demofontiand Dr. Ing. Fattorini ofCSM (Centro Sviluppo Materiali) in Rome. Tests have been performedat CSM laboratory by Dr. O. Vittori and E. Panzanelli. The specimens have been generouslyprovided by Tubi Sud ltalia (TSI) in Avellino.

APPENDIX-REFERENCES1. Landolfo R., Mazzolani F.M., Behaviour of 3rd generation trapezoidal steel sheetings,

Testing of Metals for Structures, RILEM Proceedings 12, E & FN SPON, Naples, May1990.


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2. De Martino A., Ghersi A., Landolfo R., Mazzolani F.M., Bending behaviour of long-spansteel sheeting: test and simulation, Proceedings of International Conference on Steel eAluminium Structures, Singapore, May 1991.

3. Bernard E.S., Bridge R.Q., Hancock G.J., Intermediate stiffeners in cold-formed profiledsteel decks, Research Report No. R653-R658, University of Sydney, Australia 1992.4. Panzanelli E., Vittori 0. , Studio teorico-sperimentale suI comportamento flessionale dellelarniere grecate per coperture, - Experimental activity - Research No.70521, CentroSviluppo Materiali, Roma, October, 1992.5. Landolfo R., Mazzolani F.M., Studio teorico-sperimentale suI comportamento flessionaledelle larniere grecate per coperture, Research Report No. 70521, Centro Sviluppo Materiali,Roma, February 1993.

6. Landolfo R., Mazzolani F.M., Flexural tests on trapezoidal steel sheets, Proceedings ofXN Congress C.T.A., Viareggio, October 1993.

7. Mazzolani F.M., Thin-walled metal construction: research, design and codification,Proceedings ofXIV Congress S.S.R.C., June 1994.

8. De Martino A., Ghersi A., Landolfo R., Mazzolani, F.M., Calibration of a bending modelfor cold-formed sections, Proceedings of 11th International Specialty Conference onCold-Formed Steel Structures, University ofMissouri-Rolla, Ottobre 1992.

9. CNR 10022: "Profilati di acciaio formati a freddo. Istruzioni per l'impiego nellecostruzioni",1984.

10. Eurocode No.3 - Part l.3 -, "Cold-formed Thin-gauge, Members and Sheeting", 1992.11. A.I.S.I.: "Specification for the Design of Cold-Formed Steel Structural Members",

American Iron and Steel Istitute, 1986.APPENDIX - NOTATION

total width of specimenwidth of compressed flangedistance between tensile flangeheight of sectionsheet thicknessgross cross areaweightsecond moment of area Asection modulus of gross cross areasection modulus of effective cross areaYoung modulusyield stress of steelnominal yield stress of steelcharacteristic yield stress of steelexperimental yield stress of steelultimate tensile strength of steelnominal ultimate tensile strength of steelcharacteristic ultimate tensile strength of steelbending momentyielding bending moment of gross cross sectiondesign bending momentsimulated bending momentultimate bending momentultimate forcecurvature


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ultimate behaviour of trapezoidal steel sheets in bending

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