Downloaded ro orbit.dtu.dk on: Apr 04, 209 Block ailure in connections - including eets o eccentric loads Jönsson, Jeppe Published in: Proceedings o the 7th European conerence on steel and coposite structures (EUROSTEEL 204) Publication date: 204 Link back to DTU Orbit Citation (APA): Jönsson, J. (204). Block ailure in connections - including eets o eccentric loads. In Proceedings o the 7th European conerence on steel and coposite structures (EUROSTEEL 204) University o Naples Federico II. General rights Copyright and oral rights or the publications ade accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition o accessing publications that users recognise and abide by the legal requireents associated with these rights. Users ay download and print one copy o any publication ro the public portal or the purpose o private study or research. You ay not urther distribute the aterial or use it or any proit-aking activity or coercial gain You ay reely distribute the URL identiying the publication in the public portal I you believe that this docuent breaches copyright please contact us providing details, and we will reove access to the work iediately and investigate your clai.
EUROSTEEL 204, Septeber 0-2, 204, Naples, Italy BLOCK FAILURE IN CONNECTIONS Including Eects o Eccentric Loads Jeppe Jönsson Technical University o Denark (DTU), Departent o Civil Engineering, Denark jej@byg.dtu.dk INTRODUCTION Block tear-out in gusset and in plate connections used or diagonal bracing, coped and non-coped beas is described in several codes as a block shear ailure echanis. However in any design situations the load to be transerred acts eccentrically or ay involve the transer o a substantial oent in cobination with a shear orce and/or a noral orce. It is believed that the codes ust include the oent eects ro or exaple eccentricity o the shear load by appropriately and directly including all the section orces acting at the center o the individual bolt group or weld group o the connection. In the present work a suary o soe previous studies on block ailure is given. The suary illustrates that no readily available tests with substantial eccentricity have been perored. Fig.. Exaples o gusset and in plate connections. Soe theoretical work leading towards capacity ethods including the cobined inluence o noral orce, shear orce and oent on the block ailure capacity o gusset or in plate connections will be exepliied. In act plasticity based ethods including the inluence o the oent have previously been briely described in a ew steel design texts and practicing structural engineers norally do peror soe additional design checks in order to veriy the oent transer capacity; especially when using Danish or Geran traditional bea gusset plate connections shown to the right in Fig.. The ocus o the present work is to develop a ew siple standardized capacity based ethods involving the individual noral orce, shear orce and oent block ailure capacities and a set o relevant capacity interaction orulas with a orat related to those already in use or cross section analysis in the Eurocodes. In the presented work we use a lower bound ethod based on the assuption o rigid plastic behavior o the plate ailing in a block ailure ode. The block is usually a C-block cut-out or an L-block cut-out, however in this paper only the theoretical and experiental part on the C-block cut-out are treated. The ailing block is surrounded by yield bands obeying the von Mises yield law. Due to varying strain hardening along the yield bands the inal block ailure ode ay be calculated based on a axiu stress, which is a unction o the aterial yield stress and the aterial ultiate stress, e.g. or exaple the ean value. Experiental evidence o the rotational block ailure o a cobined shear and oent loaded gusset plate connection will be briely presented. A copletely new and statically deterined and well deined test setup will be illustrated and soe preliinary experiental results will be shown.
In the experiental study the in plate or equivalent web plate and overall connection has been designed to ail in a block ailure ode with interacting shear and oent load. The ocus o the present paper is entirely on block ailure and we assue all other capacities (including bolt hole distances) proven to be adequate. It is the ai to illustrated the key eatures o the present research. STUDIES ON BLOCK FAILURE Investigation o stresses in gusset plate connections was reported in the research bulletin by Whitore in 952 []. Only concentric tension orces were applied even though the authors expected that bending stresses would have an inluence on the ailure ode. The paper suggests the so-called Whitore ethod to design against the possibility o tearing out a block o the gusset plate, assuing a ictive tension ailure line. The length (or width) o the ictive tension ailure line was based on a 0 degree (:2) spreading o the orces ro the irst to the last bolt line, see let illustration in Fig. 2. A gv Whiteore line A nt Fig. 2. Two conventional and an unconventional yield band block echanis. In the 980s one o the papers which stand out is the one by Hardash & Bjorhovde in 985 [2]. The paper suggested that the connection length should be a paraeter or the block shear strength. This paper has been reerred to by any and the equation or the block shear strength has been copared to experiental data also by others. The paper reports tests on 28 gusset plate speciens all with concentric load. Furtherore the paper includes results ro 4 other tests, whereby in all 42 tests are used to veriy the suggested equation or the ultiate capacity, V R, which ay be written as: V A 0.575 A () R u nt e gv where A nt and A gv respectively are the net area in tension and the gross area in shear, e ( Cl ) y Cl u, where Cl 0.95 0.047 l and l is the connection length in inches, u is the ultiate aterial strength, y is the yield strength o the aterial. This is a orula or tension block capacity, which in contrast to Eurocode also includes the inluence o the connection length, but otherwise it has the sae orat or concentric loads. In 200 Franchuk et al. [] investigated dierent paraeters and their inluence on the L-block tearout shear capacity or coped beas. This paper supports previous papers that suggest that the tension contribution o the block shear capacity should be reduced by 50% or eccentric load due to non-unior stress distribution. The experiental tests showed that the shear ailure happened close to the gross shear area and it sees to docuent that the position o the block shear ailure is to be based on the net area or the tension ailure line A nt and the gross area or the shear ailure area A gv as shown or the coped bea in Fig. 2. It is concluded that end rotation does not have a signiicant inluence on the capacity. However the test setup is not representative or all types o in or gusset plate bea connections. Three papers [4], [5] and [6], published in the years 200-2006 by a coinciding group o authors Kulak, Grondin, Huns and Driver, have used available experiental data in order to copare
experiental test results to dierent standards, equations suggested by other papers and their own suggested equations. The papers are dierent in their ocus points and which equations they copare the test results to. In the irst paper by Kulak & Grondin [4] the test results are collected and copared to the Aerican, Canadian, European and Japanese Standard plus equations suggested in the paper. In the coparison the experiental data are categorized in connection types as gusset plates, angles, coped beas with one bolt line and coped beas with two bolt lines. In the second paper by Huns et al. [5] it is stated that it is iportant that the design equations relect the ailure ode and not only predict the capacity. The paper urther states that the connection length does not have any inluence on the capacity (or coped beas) even though it has been suggested and earlier shown or gusset plates. Table. Constants or equation (2) ro Driver et al [6] Connection type R t R v Gusset plates Angles and tees Coped beas: one bolt line Coped beas: two bolt lines In the third paper by Driver et al. [6] the objective was to copare the Aerican, Canadian and European Standards plus an equation suggested by Topkaya [7] who as Hardash & Bjorhovde suggested that the connection length is a paraeter and an equation by Cunningha et al. [8] with eccentricity as a paraeter. This paper by Driver et al. also suggests an equation in which the position o the shear ailure line is along the outer edge o the bolt holes, i.e. a gross length, as suggested by Franchuk et al. [] and urther that the shear strength is developing beyond the yield strength but not ully up to the ultiate strength. The paper coents on standards and published papers, which have not been able to agree upon a siilar consistent approach towards the deterination o the block shear strength. This paper also dierentiates the experiental data into separate categories: gusset plates, coped beas and angles. The suggested equation is the sae or all types, however the constants depend on the connection type. The suggested equation or the resistance is: 0.9 0.9 0. 0.9 y u V R A R A 2 R t u nt v gv where R t and R v are constants deterined by the connection category as given in Table. (2) In another paper by Huns et al. [9] it is ound that the shear capacity ater tension rupture happens alost or the ultiate aterial strength. This indicates that the average between ultiate and yield strength suggested by Driver et al. [6] is conservative. This paper also concludes that the eect o the length o the connection is inconclusive and should thereore not be taken into account. As entioned, Topkaya suggested orulars or block shear capacity o angle connections in [7]. The paper contains results ro FE analysis o experiental block shear tests in order to develop expressions that describe the actual ailure. The paper suggests that the strength o the shear plane is dependent on the length o the connection and that the strength is dependent on a ratio between the yield and ultiate strength. All three orulas proposed are or concentric loads and the paper suggest a actor that reduces the strength by 0% i the load is eccentric. To su up the indings in the literature, the crucial conclusion is that none o the papers have been dealing with coplex loading including substantial eccentricities and general block ailure. It is stunning that the stress distributions in equilibriu with sections orces have not been investigated; perhaps they have been abandoned due to the seeingly coplex stress distributions. The reason could be that the current orulas are based on epirical research instead o relating it to a theoretic approach based on plasticity theory and yield bands. It sees very inappropriate just to introduce a
reduction actor o 0.5 on the tension area in the L-shaped block ailure odes o the codes in order to accoodate eccentric loading with its agnitude reaining unquantiied. 2 CAPACITY METHODS FOR RIGID-PLASTIC BLOCK FAILURE ANALYSIS Assuing that the aterial behaves as a rigid plastic aterial and that all aterial outside the yield bands is rigid opens the possibility o deterining the work perored during deoration o the rigid blocks relative to each other. This leads to an upper bound or the capacity o the given load situation, this involves nuerical integration along the yield lines and superposition o results are not possible. However lower bound plasticity ethods ay lead to the orulation o relatively siple approxiate ethods relating individual block ailure capacities or noral orce, shear orce, and oent as well as the interaction o these by siple von Mises based interaction orulas as exepliied in the ollowing. The lower bound ethods are based on the assuption that the equilibriu stress ields o the rigid parts are below or at yield everywhere. Thus to ind a good lower bound approxiation we have to ind eective allowable stress ields along the yield bands. Three basic stress ields acting along the yield band (shown without holes) on the cut-out block are shown in Fig.. The three relatively siple situations or a C-shaped cut-out correspond to the noral orce N R, the shear orce V R and the oent M R block echanis capacities. Based on experiental observations it is assued that the holes are just inside the block and the gross diensions are given by h g and b g. Deductions or holes are given by the net lengths respectively corresponding to h n and b n. Furtherore it is assued that the noral stresses are acting on the net yield band lengths and shear stresses on the gross yield band lengths. (During echanis oring and yielding the bolt holes are elongated and leave an open trace). The shear orce is acting at the shear distribution center, given by the edge eccentricity e ed as shown in the central situation o Fig.. The straining o the yield bands varies along each line and strain hardening will coence beore the yield echanis has ully ored, thereore a oral yield stress is used. A value o the oral yield stress o =( y + u )/2 corresponding to the ean value o the yield stress and the ultiate stress is used. (The shown distributions are relevant or b.5h ). n g e ed b n b g With hole deductions N R V R M R h g h n Fig.. Yield band stress actions on the block or three basic C cut-out block echaniss. The individual capacities can now be deterined by the ollowing relatively siple orulae: bg hg bg h n NR t 2 hn, VR t 2 bn, MR thg () 4 It is possible to cobine actored basic stress ields in order to derive stress ields or interactive situations. I we actor each o the three stress ields with respectively N/N R, V/V R and M/M R, we can cobine the stress ields, such that we obey the Von Mises yield condition along each yield
band. It turns out that with the three given basic echaniss we just need to ulil the ollowing siple interaction equation: 2 2 N M V NR MR VR where N, V and M are the section orces at the shear distribution centre given by: e ed bb g n bh g n 2b h n g There are several other possible ways o distributing the stresses along the yield lines in order to get a higher lower bound carrying capacity. Soe o these distributions have been investigated in the aster thesis by Nørgaard [0]. The individual capacities o the basic block echaniss given in Eq. () are all lower bounds (with the given assuptions) and the interaction Eq. (4) also corresponds to a lower bound capacity o a cobination o the three basic echaniss. In the ollowing section an exaple o the accuracy achieved in coparison to one (o twelve) experiental result will be given and illustrated. (4) (5) F e Contra weight F Test plate a) b) Fig. 4. a) Experiental test setup. b) Photo o block ailure in the test plate ater test. Table 2. Results ro one experient and results o lower bound equations using the given paraeters. Test h g h n b g b n e ed y u V R M R e F R F exp,y F exp,u F R /F exp,y [] [] [] [] [] [MPa] [MPa] [MPa] [kn] [kn] [] [kn] [kn] [kn] [ - ] B-H-() 8 84 22 82 8 272 75 24 782 40.8 9 0 29 96 0.80 EXPERIMENTAL INVESTIGATION OF GENERAL BLOCK FAILURE In the B.Eng. project and thesis by Nissen [] an experiental test setup has been designed and block ailure experients on bolted connections have been perored. The connections have been designed in order to assure that block ailure was the decisive ode o ailure. Twelve tests were perored on three dierent loading conigurations with the sae bolt group o 4x M2 bolts (0.9). In this paper only the representative test shown in Fig. 4. will be treated. In this test the experiental loading corresponds to zero noral orce N=0, a shear orce o V=F R applied with a airly large eccentricity e in relation to the shear distribution centre resulting in a connection oent o M=eF R. The lower bound capacity ound using Eq. (4) becoes F R 2 2 e MR V R 0.5 (6)
The experiental echanis yield load F exp,y is deterined as the crossing point o the observed linear initial inclination (stiness) and a tangent line with 0% o this inclination just touching the upper part o the curve (corresponding to 0% hardening), see Moore et al [2]. The ultiate capacity is just the axiu achieved load F exp,u. The iportant paraeters, results ro lower bound equations and results ro one experiental investigation are given in Table 2. The applied test load verses the piston oveent and verses approxiate angle o rotation are shown in Fig. 5. a) b) Fig. 5. a) Applied load verses piston oveent; b) Applied load verses the angle o rotation. 4 CONCLUSION The theoretical and soon experiental background or including eects o eccentric loads in block ailure has been presented and ought to be included or allowed or in the codes. REFERENCES [] Whitore R.E. Experiental investigation o stresses in gusset plates. Bulletin No. 6, Engineering Experient Station, University o Tennessee, May, 952 [2] Hardash S.G., Bjorhovde R, New Design Criteria or Gusset Plates in Tension, Engineering Journal, AISC, 22(2), 985. [] Franchuk C.R., Driver R.G., Grondin G.Y. Experiental investigation o block shear ailure in coped steel beas, Canadian Journal o Civil Engineering 0(5), pp. 87 88, 200. [4] Kulak G.L, Grondin G.Y. Block shear ailure in steel ebers a review o design practice, Engineering Journal, AISC, 8(4), pp.99 20, 200. [5] Huns B.B.S., Grondin G.Y., Driver R.G. Tension and shear block ailure o bolted gusset plates, Canadian Journal o Civil Engineering,, pp. 95 408, 2006 [6] Driver R.G., Grondin G.Y., Kulak G.L. Uniied block shear equation or achieving consistent reliability. Journal o Constructional Steel Research, 62, pp. 20-222, 2006. [7] Topkaya C. A inite eleent paraetric study on block shear ailure o steel tension ebers, Journal o Constructional Steel Research, 60, pp. 65 65, 2004. [8] Cunningha T.J., Orbison J.G., Zieian R.D. Assesent o Aerican Block Shear Load Capacity Predictions, Journal o Constructional Steel Research, 5, pp. 2-8, 995. [9] Huns B.B.S., Grondin G.Y., Driver R.G. Block Shear behaviour o bolted gusset plates. University o Alberta Departent o Civil & Environental Engineering, Structural Engineering Report No. 248, 2002. [0] Nørgaard S.S, Bolted gusset plate connections and block shear ailure, Master Thesis, Departent o Civil Engineering, Technical University o Denark, DTU, Feb., 20. [] Nissen J.S., Test o gusset plate connections. B.Eng. Thesis, Departent o Civil Engineering, Technical University o Denark, DTU, Jan., 20. [2] Moore D.B., Wald F. (editors), Design o Structural Connections to Eurocode Frequently Asked Questions, Building Research Establishent Ltd, Watord. Printed at Prod. Dept. o Publishing House o Czech Technical University in Prague, Sept. 200. www.sv.cvut.cz/cestruco, ISBN 80-0-0288-0.