Stress Analysis and Fatigue Life Assessment of Splice Connections

C. S. Bandara1, T. Kajan1 and S. Kajanth1 1Department of Civil Engineering

Faculty of Engineering University of Peradeniya

Peradeniya, 20400 SRI LANKA

E-mail: bandara@civil.pdn.ac.lk; chamindasbandara@yahoo.com

Abstract: Study on bearing type butt splice connections made from steel was carried out to investigate the stress concentration and fatigue damage predictions. Connections with different holes staggering arrangements were used in this study. Stress concentration factors of these connections were calculated and compared for different staggered holes. Photo-elasticity and finite element modelling were used for the stress analysis. Fatigue damage assessment of splice plates with different staggered holes was done using stress – life (S – N) approach. Two methods were employed to predict the fatigue life. The predictions were then compared with experimental data. The life predictability of those methods was compared and suggestions were given for improvements. Previous studies show that none of commonly used methods are adequate in assessing the fatigue life of connection details. However, a combination of existing fatigue life assessment methods, material testing and correct stress analysis (finite element modelling) is able to perform fatigue life assessment of the butt splice connections to a reasonable accuracy. Keywords: Butt splice, fatigue damage, S – N curve, finite element model, steel structures.

1. INTRODUCTION

Connections play an important role in structures. Connections link individual members to form continuous configurations. Bolting, welding and riveting are the most common types of connections in steel structures. Usually, bolting has many advantages over the other two methods such as easy assembly of members with minimum tools and effort, easy dissemble ability and minimum affect to the parent materials (materials in members). Connection failure is the reason for many of the failures of steel structures in the past. Therefore, understanding the behaviour of connections is more important than understanding the behaviour of the members that are being connected. However, the behaviour of connections is complicated due to their geometry and related stress concentrations. Therefore, additional safety margins are used in complicated connection designs to minimize the risk of failure (Kulak, et al., 2001). The two common types of bolting are preloaded bolting and non-preloaded bolting (BS 5950 – 1: 2000). Preloaded bolting makes the connection more rigid than non-preloaded connections. The reason for this is the strong friction developed between the members that are connected due to the clamping force generated by the tension of preloaded bolts. Transferring of forces from one member to the other in a preloaded bolting connection is assisted by this friction. In contrast, connections made by non-preloaded bolts transfer forces from one member to the other only through the bolts; this makes high stress concentrations at bolt holes in members (Kumar & Santha, 2006). Therefore, non-preloaded bolting connections are more critical for failures than preloaded bolting connections. Bolted connections are classified in different ways. They can be classified into two as concentric and eccentric connections based on the transfer of the resultant force through the connection. Bolted connections can also be classified as shear, tension and combined shear and tension connections based on the force experience by the bolts (Kulak et al., 2001).

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Symmetric butt splice connection is a common shear connection (Figure 1). The load from one structural member to the other is mainly transferred through splice plates. If the fasteners (bolts) are non-preloaded, load transfer is by shear and bearing of splice plates, connected part of the members and fasteners (bolts). If fasteners are preloaded, friction in the connected parts plays a role in transferring the load. Under heavy loading where the stresses are closer to yield strength, the failure of a connection can be due to shear or bearing. The connection can also fail due to fatigue caused by cyclic loading even for low stresses than the yield strength of the material. There, the fracture mostly starts from the location of highest stress developed around bolt holes due to stress concentration (Josi et al., 1999). Considering the importance of symmetric butt splice connections in steel construction, the present study was carried out to investigate the behaviour of symmetric butt splice connections under cyclic tensile - compression loading. Bolts are assumed as fully rigid and no deformations or deflections in them. The main focuses of the study were stress concentrations at bolt holes and the fatigue failure of the connection.

Figure 1 Section of a symmetric butt splice connection

2. METHODOLOGY

The methodology followed in the present study contains the following steps; (i) Collecting experimental data of butt splice connections, (ii) Modelling and validating finite element models of splice plates and structural members, (iii) Investigating the stress concentrations and possible fracture origins, (iv) Investigating the fatigue damage of splices using existing methods and (v) Analysing the results of investigations and arriving conclusions.

2.1 Experimental Data

Experimental data of steel butt splice connections were obtained from literature (Josi et al., 1999). Dimensions, connection details, loading arrangement, reactions of elements to the prescribed loading, failure modes and failure data (stress levels and cycles to failure) are given in Table 1. Mechanical properties of steel used for butt splice connections are given in Table 2. The thickness of splice plates used in the experiment is less than the thickness of the main members. Therefore, failure was expected at the splice plates during cyclic loading.

Table 1 Details of steel butt splice plate specimens

Specimen type w (mm) s (mm) g (mm) Ag (mm2) An (mm2)

S0 111 0.0 60.3 2109 1311 S1 95 25.4 44.5 1805 1406

S2 95 50.8 44.5 1805 1406 S3 95 76.2 44.5 1805 1406

Note: Width of the member “w”, staggered distance “s” and longitudinal spacing of holes “g” are shown

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in Figure 2. Ag is the gross cross sectional area and An is the net cross sectional area of two splice plates that are in parallel (after reducing the section area of holes).

Table 2 Mechanical properties of steel used for splice connections

Description Unit Value

Ultimate tensile strength (σu) N/mm2 480 Yield strength (σy) N/mm2 420 Poisson’s ratio (ν) - 0.3 Elastic modulus (E) kN/mm2 212

Figure 2 Dimensions of the butt splice connection detail (edge distance e = 25 mm, diameter of

bolt holes, D = 21 mm. Table 1 gives values for s and g)

2.2 Stress Analysis Using Finite Element Models

The butt splice connections with various patterns of bolt holes (S0 to S3 for different s and g) were modelled using finite element software. To simplify the modelling, main members with bolt holes and splice plates with bolt holes were modelled separately. Quadrilateral shell elements were used in the model and element density was increased near bolt holes where stress concentration is high. The materials properties of steel given in Table 2 were applied to the model. In order to simplify the finite element model the load transfer between the bolts and the plates were simulated with nodal loads applied at the edge of the holes. Further, entire load was transferred by bearing of the bolts on the bolt holes and any load transfer by friction was neglected; this simulated the non-preloaded bolting condition. Boundary conditions and loading applied on the main member is shown in Figure 3. Bolts and nut were not modelled, instead the contacting of the outer surfaces of bolt shank and inner surface of the bolt hole was modelled using restrain conditions (joint spring restraints on the radial direction). The loading was applied on nodes at the free far end that is opposite to the connected end. Stress concentration factor (SCF) of the main member and the splice plate was then calculated using Eq. (1);

SCF = 𝑠𝑡𝑟𝑒𝑠𝑠 𝑎𝑡 𝑡ℎ𝑒 ℎ𝑖𝑔ℎ𝑙𝑦 𝑠𝑡𝑟𝑒𝑠𝑠𝑒𝑑 𝑙𝑐𝑎𝑡𝑖𝑜𝑛𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠

(1)

2.3 Experimental Stress Analysis

Photo-elasticity is a widely used technique for experimental stress analysis (Freire and Voloshin, 2010). When a photo-elastic material is strained and viewed under polarized light, beautifully coloured pattern can be observed. This coloured pattern provides information on stress-state of the strained material. In the present study, photo-elasticity testing was used for two purposes, (i) to obtain stress concentration factors and (ii) to validate the finite element models.

w

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Stress concentration of an element depends on its geometry when loaded in the elastic range of the material. Therefore, photo-elasticity test models used were scale-down models with same geometry including the thickness. The main members of the butt splice connections were prepared using Araldite which is a photo elastic material. Splice plates were prepared using Perspex which is acting like a plane glass and allow the light rays to pass through; therefore the stress pattern of the main member is visible. Steel bars were used as bolts without heads and nuts, because heads and nuts of the bolts would block the light rays; then some parts of the stress pattern near the holes would be invisible. Material fringe value fσ of Araldite was found as 8.46 kg/cm using a diameter 70 mm and thickness 6 mm Araldite disc (Figure 4.a). The stress analysis of butt splice connections was then carried out (Figure 4.b). The principal stress difference (σ1 – σ2) was obtained from Eq. (2);

𝜎1 − 𝜎2 = 𝑁∗𝑓𝜎ℎ

(2) where, N is the number of fringes and h is the thickness of the (main member) specimen.

Figure 3 Boundary conditions and loading of the finite element model

Figure 4 Photo-elasticity testing (a) Araldite disc, (b) Butt splice connection

(a) (b)

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2.4 Fatigue Damage Assessment

Fatigue occurs in structural members that are subjected to cyclic loading. Fatigue crack initiation usually happened at locations where the stresses are high. Fatigue damage assessment using fatigue experiments is costly and time consuming. Therefore, analytical and empirical methods are used to avoid fatigue experiments. The two major approaches used for fatigue damage assessment are stress or strain – life (S – N or ε – N) approach and fracture mechanics approach. In the present study, two methods of the S – N approach was used for fatigue damage assessment. One is the S – N method given in EN 1993 – 1 – 9 (2005) and the other is a method recently proposed by Bandara et al., (2015). Then the experimental fatigue test data of steel shear splices of Josi et al., (1999) was used to compare with the fatigue assessments of analytical / empirical methods. According to EN 1993 – 1 – 9 (2005), the S – N curve of detail category C90 is the appropriate S – N curve for splice connections joined by bolts. Eq. (3) shows the formula of the S – N curve of the other method (for stress ratio R = -1), (Bandara et al., 2015),

𝜎(𝑁) = �𝜎𝑉𝐻𝐶𝐹−𝜎𝐾𝑁𝑉𝐻𝐶𝐹𝑡 −𝑁𝐾

𝑡 � (𝑁 + 𝐵)𝑡 + �𝜎𝐾𝑁𝑉𝐻𝐶𝐹𝑡 −𝜎𝑉𝐻𝐶𝐹𝑁𝐾

𝑡

𝑁𝑉𝐻𝐶𝐹𝑡 −𝑁𝐾

𝑡 � (3)

where, 𝜎𝑉𝐻𝐶𝐹 is the fatigue strength at very high cycles, 𝜎𝐾 is the knee point at high cycle region, 𝑁𝑉𝐻𝐶𝐹 is the very high number of cycles and 𝑁𝐾 is the number of cycles at the knee point. ‘t’ is the slope of the S-N curve and ‘B’ is given in Eq. (4),

B = �σu−ca�1t (4)

where, 𝑎 = �𝜎𝑉𝐻𝐶𝐹−𝜎𝐾

𝑁𝑉𝐻𝐶𝐹𝑡 −𝑁𝐾

𝑡 � ; 𝑐 = (𝜎𝐾𝑁𝑉𝐻𝐶𝐹𝑡 −𝜎𝑉𝐻𝐶𝐹𝑁𝐾

𝑡

𝑁𝑉𝐻𝐶𝐹𝑡 −𝑁𝐾

𝑡 ) and 𝜎𝑢 is the ultimate tensile strength of steel. Then,

the S-N curve was predicted for the steel with 𝜎𝑢 = 480 𝑁/𝑚𝑚2 and Hv = 144 kgf/mm2. The mean stress correction of stress ranges were carried out using the modified Goodman and SWT formulae (Dowling, 2004) given in Eqs. (5) and (6) respectively;

σar = σa/(1-(σm/σu)) (5)

σar = σa(2/(1-R))1/2 (6)

where, σar is the corrected stress amplitude for a fully reversed stress cycle at σm = 0 and R = -1, σa is the stress amplitude, σm is the mean stress.

3. RESULTS AND DISCUSSION

3.1 Stress Concentration in Butt Splice Connections

The principal stress difference (σ1 – σ2) of highly stressed locations of butt splice connections obtained from the finite element models and photo-elasticity models were first compared (Table 3). The comparison showed a good agreement between the values of the finite element models and photo-elasticity models verifying that the method used to model the butt splice connection (finite element model) is acceptable. Then the difference of stress concentration due to the effect of bolt staggers was investigated for all four types of specimens using finite element models (Table 4). When the connection is subjected to tensile loading, it was observed that the stress concentration is high at the outer most bolt hole and it increases with increasing s. It was also observed that the SCF at the bolt holes of the main member increases from 2.78 to 3.58 with increasing s. Comparison of SCFs of splice connections with preloaded bolts and non-preloaded bolts is given in Table 5. SCFs of splice plates connected with non-preloaded bolting were calculated in the in the present study using finite element models. SCFs of preloaded bolting were obtained from the study of

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Josi et al., (1999). The comparison shows that there is no much difference in the SCFs of preloaded and non-preloaded bolting. It also shows that the difference in the SCF due to change of s is negligible (SCF in splice plates remains in the range 2.98 - 3.26).

Table 3 Comparison for principal stress difference for specimen type S3

Table 4 Variation of SCF with staggered distances

Specimen type Stress S11 Diagram SCF

S0

2.78

S1

2.98

S2

3.32

S3

3.58

Method Applied stress at far end (N/mm2) 𝜎1 − 𝜎2 (N/mm2)

Photo elasticity model 1.65 1.92

2.82 4.23

Finite element model 1.65 1.92

3.10 4.62

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Table 5 SCF of splice plates connected using preloaded and non-preloaded bolts

Specimen type Preloaded bolt connection (Josi et al., 1999)

Non-preloaded bolt connection (FEM results)

S0 3.22 3.05 S1 3.22 3.07 S2 3.26 3.04 S3 3.26 2.98

3.2 Predicting the Fatigue Damage

The two methods described in Section 2.4 were used to predict the fatigue failure of the four types of butt splice connections with the main focus on splice plates. Then, the failure predictions were compared with the experimental fatigue data of Josi et al., (1999) that is given in Table 6 (∆σ is the applied stress range, σmax is the maximum stress and σmin is the minimum stress). Figure 5 shows the comparison of experimental data (∆σ vs N f) with C 90 curve of EN 1993-1-9 (2005). Figure 6 shows the experimental data ([SCF x σar] vs Nf) with the S – N curve of the method proposed by Bandara et al., (2015). Figure 7 is a comparison of predictions of the two methods: C 90 curve of EN 1993-1-9 (2005) and the S – N method of Bandara et al., (2015) with Goodman correction. In this (Figure 7), the predictions have been normalized (Predicted fatigue strength / Experimental fatigue strength) and plotted against number of cycles to failure.

From the comparisons, it can be observed that the fatigue life predictions of both methods are not perfect but mostly conservative (safe). The slopes of mean lines of experimental data differ from the S – N curves of the two methods. Predictions of EN 1993 – 1 – 9 (2005) are not safe for high stress ranges while they are conservative for low stress ranges. On the other hand, the fatigue life predictions of the other method (Bandara et al., 2015) are safe for all experimental data when corrected using SWT method. However, the predictions with Goodman method are not always safe. This finding is important because Goodman method is one of the widely used methods for mean stress corrections of civil engineering structures (Chaminda et al., 2007). According to Figure 7, it is clear that the fatigue strength prediction by the S – N method of Bandara et al., (2015) with Goodman correction is much better than that of C 90 curve of EN 1993-1-9 (2005).

Table 6 Experimental fatigue test data of Josi et al., (1999) used in the present study

∆σ (MPa) R

σmax = ∆σ/(1-

R)

σmin = σmax -

∆σ

σm = (σmax+ σmin)/2

σa = (σmax-σmin)/2

Goodman: σar = σa/(1-

(σm/σu))

Goodman: SCF x σar

(MPa)

SWT: σar =

σa(2/(1-R))1/2

SWT: SCF x σar

(MPa)

Cycles to

failure Nf

143 0.3 204 61 133 71 99 296 121 362 2.2E+06

143 0.3 204 61 133 71 99 296 121 362 5.7E+06

143 0.3 204 61 133 71 99 296 121 362 7.7E+05

141 0.3 201 60 131 70 97 290 119 357 2.6E+05

141 0.3 201 60 131 70 97 290 119 357 3.0E+05

141 0.3 201 60 131 70 97 290 119 357 1.6E+06

113 0.3 161 48 105 56 72 216 95 286 2.8E+06

113 0.3 161 48 105 56 72 216 95 286 2.9E+06

113 0.3 161 48 105 56 72 216 95 286 8.5E+06

141 0.3 201 60 131 70 97 290 119 357 1.1E+06

141 0.3 201 60 131 70 97 290 119 357 3.1E+05

141 0.3 201 60 131 70 97 290 119 357 6.5E+05

113 0.3 161 48 105 56 72 216 95 286 3.8E+06

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113 0.3 161 48 105 56 72 216 95 286 1.5E+06

113 0.3 161 48 105 56 72 216 95 286 2.7E+06

141 0.3 201 60 131 70 97 290 119 357 6.8E+05

141 0.3 201 60 131 70 97 290 119 357 7.0E+05

141 0.3 201 60 131 70 97 290 119 357 5.2E+05

92 0.3 131 39 85 46 56 167 77 232 3.6E+06

92 0.3 131 39 85 46 56 167 77 232 1.4E+07

Figure 5 Experimental fatigue data versus C 90 S – N curve of EN 1993 – 1 – 9 (2005)

Figure 6 Experimental fatigue data versus S – N curve of Bandara et al., (2015)

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Figure 7 Comparison of fatigue strength predictions using C 90 curve of EN 1993-1-9 (2005)

and Bandara et al., (2015) method with Goodman correction

4. CONCLUSIONS

Butt splice connections are very common in steel construction. The load transfer from one member to another is happened across the connection through the splice plates and bolts. Therefore, the stress distribution at the connections is complex. Though safety factors are used in designs of connections, failures of structures usually initiates at connections due to heavy stress concentrations in them. Therefore, the present study on butt splice connections was carried out using experimental and numerical analysis. The conclusions arrived at from the study are as follows.

(a) Finite element models and photo-elasticity techniques are usual methods used for stress analysis. In the present study, both these methods were used to model splice connections. The fineness of stress visibility is less in photo-elasticity than finite element models, however, photo-elasticity can be effectively used to validate finite element models.

(b) Stagger of bolt holes in main members and splice plates were investigated. It was observed that the bolt hole arrangement of main members has a clear effect on SCF. However, such variation was not observed in splice plates where holes are distributed all over. This was similar for both preloaded and non-preloaded bolting.

(c) Fatigue life of shear splices were predicted using two stress – life methods; the method in EN 1993 – 1 – 9 (2005) with C 90 curve and the method proposed by Bandara et al., (2015). Comparing with experimental fatigue data, it was found that the life predictions of both these methods are mostly conservative. The predictions of the second method (Bandara et al., (2015)) with SWT formula for mean stress corrections always produce safe predictions. The predictions of second method with the Goodman correction are much accurate than EN 1993-1-9 (2005).

(d) In designs, it is assumed that the force to be transferred across the connection can be divided equally among bolts when calculating shear and bearing. However, this study verifies that the real stress distribution among bolt holes in main members is different from this assumption.

ACKNOWLEDGEMENT

Authors would like to acknowledge the financial assistance of the National Research Council, Grants 11/106 and 15/127.

REFERENCES

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