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Int. J. Struct. & Civil Engg. Res. 2012 Bhairav K Thakkar, 2012

ANALYSIS OF FATIGUE CRACK PROPAGATIONIN GUSSET PLATES

Bhairav K Thakkar1*

Gusset plates are used commonly in truss joints. The simplest form of joints in a truss systemconsists of bolted or riveted connections. There may be instances when the bolt or rivet holesdevelop side cracks while drilling the rivet-holes or bolt-holes.Cracks may even develop due tostatic or fatigue loads during service life of the structure. It becomes imperative to determine theremaining fatigue life of the truss members and gusset plates in order to determine the safe lifeof the structure. This becomes more critical when the loads are heavy and fluctuating as inindustrial structures or bridges. Fluctuating loads lead to fatigue and the structure may fail aftera number of load cycles even if the stress values are well below the yield stress. This paperadopts a fracture mechanics based approach to determine the crack propagation characteristicsand the crack length versus number of cycles using Paris’ law. FRANC2D has been adoptedhere for the computational simulation of crack growth. The fatigue life of a crack around boltholes has been estimated. The approach gives significant information regarding the fatigue lifeand crack propagation characteristics and may be incorporated in design of truss systems.

Keywords: Fatigue, Crack propagation, Gusset plates, Paris law, Fracture mechanics

1 Fairyland Technology (P) Ltd., India, A/6 Navneet Park Society, Harni-Warasia Ring Road, Vadodara 390006, India.

*Corresponding Author: Bhairav K Thakkar,bhairav.thakkar@gmail.com

INTRODUCTIONTrusses are usually employed when largespans are required to be covered. Trussmembers are predominantly under the effectof direct tension and compression. As trussescan span over large spaces and can carry largeloads, trusses are the structural system ofchoice for bridges, industrial sheds, etc. Theconstruction of a truss requires a joinery whichis realized with the help of gusset plates.

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Int. J. Struct. & Civil Engg. Res. 2012

Research Paper

Gusset plates are thick sheets of steel that areused to connect truss members with eachother or for connecting beams with columns,etc. The forces in members of a truss systemare transferred through gusset plates. Thus,the design of gusset plates take up a lot ofeffort as the shape and size of the platedepends upon the joint under consideration.Classically, trusses are made of mild steel andso are gusset plates. The joinery may be

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Int. J. Struct. & Civil Engg. Res. 2012 Bhairav K Thakkar, 2012

achieved by either bolting or riveting the anglesections with the gusset plates, or by weldingthem together. While welding is a good choice,it offers a potential threat of transfer of crackfrom one part of the component to the other.Besides, bolting and riveting are the commonchoice because the simplicity involved infabrication of the joints. However, bolting andriveting operations require drilling of bolt orrivet holes in the gusset plates in alignmentwith the holes in the tension or compressionmembers. There is a very high possibility ofmicro or macro-cracks developing in the boltholes, which would seriously hamper theperformance of the joints. Further, the trussesused in industrial structures are often subjectedto fatigue loads, which may introduce numberof cracks at the vicinity of the bolt holes aftersome number of cycles. It becomes imperativethen to determine the remaining life of the jointsor members based on fatigue crackpropagation. Also, if the fatigue life of the jointis taken into consideration during the designphase, the life of the joint and consequentlythat of the structure may be considerablyenhanced (Broek, 1984).

Fracture mechanics is a branch of solidmechanics that deals with the study of stressand strain fields around existing cracks in astructure and tries to describe the behavior ofthe structure under effect of existing andpropagating cracks. A structure may besubjected to static or repetitive or cyclic loads.A structural component may fail under theeffect of repeated cyclic loads which may beof much smaller magnitude than the staticfailure loads. Such a failure of a component istermed as a fatigue failure. Most industrialstructures are usually subjected to fatigue

loads. Hence, it is extremely common toobserve fatigue cracks emanating from boltor rivet holes in the joints. Fracture mechanicshowever has a drawback in that it requires anexistence of a crack in the structure. Thus, if anew structure is required to be designed, aprobable location and size of the crack mustbe anticipated in order to employ the principlesof fracture mechanics; and thereby understandthe crack propagation behavior. The probablelocations from where the cracks may emanateare called hot-spots. The determination of hot-spots is vital to accurate description of fatiguefailure in structural components. Since theanalysis is carried out using finite elementmethod, the crack propagation problembecomes mesh sensitive. Fatigue is thedegradation of material and subsequent crackpropagation under the influence of repeatedcyclic loads on a structure. Commonly, thefatigue life of a component can be describedby the well-known Paris’ law (Dahlberg andEkberg, 2006). Paris law requires two materialconstants for characterization of the crackpropagation behavior; viz., m and C. Experi-ments are required for determination of m andC (Anderson, 2005). A limitation with the Paris’law is that it describes the crack propagationphase, but the description of crack initiationphase must be done either by experimentalobservations or by other appropriate fracturemodels (Prashant Kumar, 1999).

Pugno et al. (2006) extended the Paris’ lawto take into consideration some of thedeviations from the power-law regime usingWohler SN curves for the materials. Thisapproach is suggested to be a more genera-lized form of Paris’ law and may be moresuitable for fatigue characterization. However,

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Int. J. Struct. & Civil Engg. Res. 2012 Bhairav K Thakkar, 2012

fresh experiments may be required to obtainthe material constants for employing this law.Aygul (2012) performed finite elementanalysis of steel and composite bridges undervarious stress ranges. The failure propagationof welded connections has been performedbased on the notch stress approach proposedby Radaj et al. (2006). Myers studied gussetplates under live loads in Warren truss gussetplates using finite element simulations. Fleckand Smith (1984) studied fatigue crack growthrate and closure response of BS4360 50Bsteel on a gas storage vessel under serviceload history. They employed Paris’ law forsimulation of crack growth. Choudhary et al.(2004) performed experiments at 823 K in airand studied the fatigue failure characteristicsof specimen welded base metal, weld metaland heat affected zone under constantamplitude loading. They ascertained that theParis’ law was sufficient to predict the fatiguefailure in base and weld metal.

ANALYSIS OF GUSSET PLATEA typical gusset plate for an N-truss has beenconsidered for analysis here.A schematic ofthe gusset plate considered here is shown inFigure 1.

For determination of the locations fromwhere the cracks may emanate, a preliminaryanalysis of the joint has been carried out. Thefinite element mesh of 6-noded linear straintriangular elements along withthe von Misesequivalent stresses computed using FRANC2Dhave been shown in Figure 2. FRANC2D is atwo dimensional, finite element based programfor simulating crack propagation in planarstructures. The von Mises equivalent stressvalues reported in the plot are in MPa. The

Figure 1: Schematic of Gusset Plate

1

2

3

Figure 2: Finite Element Meshand Von Mises Equivvalent Stresses

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Int. J. Struct. & Civil Engg. Res. 2012 Bhairav K Thakkar, 2012

critical location for crack propagation wasrecognized from the equivalent stresses asbetween the two inner bolt holes in the inclinedmember connection, shown encircled in Figure2. After finalizing the location, initial cracks oflength 1mm were introduced at the edge ofthe bolt holes as shown in figure. Materialproperties of steel were adopted for the stressanalysis.For fatigue analysis using Paris’ law,the parameters were adopted as m = 3 andC = 10–11 (Prashant Kumar, 1999). The crackwas allowed to propagate in FRANC2Dsimulation. The initial and final configurationsof the cracks are shown in Figure 3. For boththe cracks, the crack length v/s number ofcycles has been obtained as an output ofFRANC2D and has been reproduced inFigure 4. It is observed that Crack 1 is thecritical crack and propagates more rapidly thanthe Crack 2. The crack propagation has beensimulated till a crack length of approximately11.5 mm for Crack 1. Of course the gussetplate should not be allowed to be in service tillsuch a large crack length gets developed. Areasonable crack length at which the gussetplate may be changed in would beapproximately 6mm, which corresponds to40,000 load cycles. The decision whether this

life span is sufficient depends on the numberof load cycles imposed in a day and woulddepend on the structure under consideration.

CONCLUSIONFracture mechanics based fatigue analysis of

a gusset plate has been described here. The

life of the gusset plate as estimated by the

Fracture Mechanics based fatigue analysis

approach has been studied. FRANC2D has

been used successfully for the fracture analysis

of cracks in bolt holes in gusset plates. The

approach adopted gives a very good descrip-

tion of the fatigue life of the gusset plate.

Fracture based analysis should be adopted

in the design procedure for clearer description

of crack propagation and estimation of life of

the gusset plates.

REFERENCES1. Anderson T L (2005), “Fracture

Mechanics-Fundamentals and Applica-tions”, 3e, Taylor and Francis.

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Figure 3: Initial and FinalConfigurations of Cracks

Figure 4: Crack Length v/s Numberof Cycles for Cracks

0 2 4 6 8 10 120

2

4

6

8

10

12

14

16

18x 10

4

Crack Length (mm)N

umbe

r of

Cyc

les

Crack 1

Crack 2

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Int. J. Struct. & Civil Engg. Res. 2012 Bhairav K Thakkar, 2012

Welded Structures Using the FiniteElement Method”, Licentiate ofEngineering Thesis, Dept. of Civil andEnvironmental Engineering, ChalmersUniversity of Technology, Sweden.

3. Broek D (1984), Elementary Engineer-ing Fracture Mechanics, Martinus NijhoffPublishers, The Netherlands.

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