Experiments of Bolted Cover Plate Connections With Slotted Holes

¨ CTU Reports, Vol. 6, 2/2002 Praha, ISBN 80-01-02526-8

EXPERIMENTS OF BOLTED COVER PLATE CONNECTIONS WITH SLOTTED HOLES

FRANTI�EK WALD, VRATISLAV MAZURA MATTHIEU MOAL, ZDENĚK SOKOL

Key words: Steel structures, Bolted connections, Slotted holes, Cover plate connections, Experimental observations, Bolt bearing resistance, Bolt shear resistance, Eurocodes. The work describes the tests of the bolted connections with slotted holes perpendicular to the acting force. Two sets of tests simulating behaviour of components of cover plate connections were carried out in laboratory of Czech Technical University. This paper summarises these tests with components and results of the tests of TU Nottingham and of CRIF laboratory, Liege. The results of preliminary statistical calculations made with Annex Z procedure are presented. The obtained reduction factors applicable to the bearing resistance of bolted connections are ready to be incorporated into the European design rules.

1. Introduction The slotted holes are used in bolted connections of steel structures to compensate the tolerances during the erection. Since the first application of high-strength friction bolts in 1947, the oversize bolt holes 2 mm larger than the bolt diameter have been used for assembly [Kulak et al, 1987]. Restricting the nominal hole diameter to 2 mm in excess of the nominal bolt diameter can impose rigid alignment conditions between structural members, particularly in large joints. The erection problems occur when the holes in the material do not line up properly. Occasionally, steel fabricators have to pre-assemble structures to ensure that the joint will align properly during the erection. With a larger hole size, it is possible to eliminate the pre-assembly process and save both time and money. An oversize hole provides the same clearance in all directions to meet tolerances during erection. However, if an adjustment is needed in a particular direction, slotted holes are used, as shown in Figure 1. Slotted holes are identified by their parallel or transverse alignment with respect to the direction of the applied load. The application of NC cutting machines and the digitalisation of the geometry of elements bring rather lower tolerances into the production of the structural elements [Kersten, 1997]. This allows use of long slotted holes and slots in inclination at the primary beams and columns for connection to different endplates of particular cross-sections of connected beams. Deformation of the connection in direction of the slot is prevented by preloading of the bolts. Smooth tightening of the non-preloaded bolts reach up to 20% of the tensile resistance of the bolt and together with the corrosion pretends structural use of the slip in the joint [Bickford, 1995].

The design requirements limit the bolt end and pitch distances. For regular slotted holes for M16 and M24 bolts, short slotted holes may not be greater than (d + 2) mm by (d + 6) mm, where d is the nominal bolt diameter in mm. Long slotted holes may not be greater than: (d + 2) mm by 2,5 d. Extra large slots according to British rules may not be greater than (d + 2) mm by 3,5 d.

Drilling, punching, or cutting form the holes. Punching of the holes in steelwork is faster than drilling but cracks may appear in the material. Therefore, the holes are not punched to full size but 2 mm less in diameter and then reamed. New punching machines, 79


which operate at high speeds, induce less distortion in the material, and it is expected that punching will be used extensively in the future. The punching is approved for material up to 25 mm in thickness provided that the hole diameter is not less than thickness of the material, if there is no other specification. The burrs should be removed from the holes before the assembly. It can be omitted when the holes are drilled in one operation through parts clamped together which would not be separated after drilling. The gas and plasma cutting may also form the holes. In this case, similarly to fast drilling/punching, influence on material properties has to be studied experimentally.

Limited knowledge is available about the design of connections with slotted and oversize holes. Resistance of bolted connections loaded by shear force in plane of the plates is limited by failure of bolts in shear and in bearing. The same design limits at service limit state may be applied when high strength friction bolts are preloaded and slip is allowed in ultimate limit state. When the high strength friction bolts are used and no slip is allowed, bearing resistance needs to be checked at ultimate limit state to eliminate the end shear failure. The bearing resistance represents the resistance of internal and external bolts in most design procedures. Based on experimental evidence, shear and bending type of failure may be recognised on the bearing failure. The bearing resistance is reduced in case of the slotted holes. The reduction factor is based on the best engineering practice and few unpublished tests only. In the European design rules [ENV 1993-1-8, 2001], the slotted holes are taken into consideration by calculation of the slip resistance of preloaded bolts only.

e4 ≤ 1,5 d

e3 ≤ 1,5 d

d

0,5 d0

0

0

0

Figure 1 : Geometry of the slotted hole and the requirements for the end distances

a) b)

Figure 2 : Test arrangements a) and points of measurement b) [Mazura, 2002]

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a) b) Figure 3 : Bolt bearing failure of component tests [Mazura, 2002], a) shear failure,

b) bending failure 2. Tests with Components 2.1 Main Tasks

Three kinds of tests were carried out in view to determine the bearing resistance, the deformation stiffness and the ductility. At CRIF, Liege the assemblage with more bolts has been tested [Piraprez, 2000]. The plates were connected with bolts in each hole of the plate made by different technology. At University of Nottingham the experiments were carried out in order to investigate the behaviour of the very long slots in the plate [Tizani, 1999]. At the Czech Technical University of Prague it was planned to study the plate bearing capacity by the component method [Wald F., Sokol 1999] and [Mazura et al, 2001]. Thus double cover plates were used with only one bolt in an internal/external position. The design prediction model of stiffness and resistance including gap and using component method is under preparation at Czech Technical University with cooperation of Université B. PASCAL � Clermont, laboratory LERMES-CUST.

The available tests are shown in Tables A1.1, A1.3 and A1.5. The original name of test specimens is kept in order to refer to the original paper. The bolt diameter, the number of bolts and the slot length follow the original name to describe the major parameters of tests. Additional information is included: the bolt presence in the holes, the thickness of the cover plates t, the slot length and the hole in the internal plate, the joint geometry (e1; e2; p1), the method of production of the holes and the threaded or unthreaded part of the bolt in the shear plane. The measured values are summarized in Tables A1.2, A1.4 and A1.6: the reached deformation δexp;ult. the maximal measured set-up resistance, the ratio to the predicted value with circular hole and the failure mode.

81


82

2.2 Test Set-Up

3A, 3B, 3C 1A, 1B, 1C

Test 3A-16-1- 3d Test 5B-16-1-2,5d Test 1A-16-1-d+2

5A, 5B, 5C

Tests with the bolts in the external holes were the major tests [Mazura, 2002] and tests with the bolts in the internal holes complete the observations [Moal, 2001]. The test arrangements and the points of measurement can be seen at Figure 2. Test machine FPZ 300 with load capacity 300 kN was used for the tests. The geometry is summarized at Figure 4 and Table A1.3, which also include the measured values. The characteristic values are shown in Figure 4. The bolt bearing failure of the component tests [Mazura, 2002] is described according to the type of the bearing failure as bending or shear failure [Bijlaard D02, 1989]. It was observed, that the slotted holes tends to fail in bending failure of the plate, see Figure 3.

Figure 4 : Geometry of the test set-up test 3A-16-1-3d, 5B-16-1-2,5d and 1A-16-1-d+2 [Mazura, 2002]

3B) 3C) Figure 5 : Bending failure of component test 3B-16-1-3 and 3C-16-1-3 [Mazura, 2002]


020406080100120140160

0 5 10 15 20 25 30 35 40Displacement, mm

Force, kN

slotted holes,

circular holes,

180

(test 1C - 16-1-d+2)

(test 5C - 16-1-2,5d)

Figure 6 : Examples of force - displacement diagrams of test with circular holes

(test 1C - 16-1-d+2) and slotted holes (test 5C - 16-1-2,5d)

020406080

100120140160

0 5 10 15 20 25 30 35

Displacement, mm

Force, kN Test 2A - 16-1-2,5d

020406080

100120140160

0 5 10 15 20 25 30 35

Displacement, mm

Force, kN Test 2B - 16-1-2,5d

020406080

100120140160

0 5 10 15 20 25 30 35

Displacement, mm

Force, kN Test 4C - 16-1-2,5d

2A, 2B, 4C

dimensions in mm,

slots 2,5 d

Figure 7 : Force - displacement diagram of the tests with repeated loading, test 2A - 16-1-2,5d, 2B - 16-1-2,5d, and 4C - 16-1-2,5d, [Mazura, 2002]

83


2.3 Repeated loading Three tests specimens were loaded by repeated loading to study the unloading branch of the force-displacement diagram and deformation capacity of the connection. The results are shown in Figure 7 and Table A1.2. The tests with repeated loading were not included in the statistical evaluation.

2.4 Material tests The standard coupon test [EN 10002] were provided for material of the plates. Five

cylinder specimens were prepared from the central plate. The results and the statistical evaluation are shown in Table A2-1. The material of the plates has average strength of 424 MPa. Ten cylinder specimens were made from the cover plates, see Table A2-2, five specimens located parallel (C1 to C5) and five specimens perpendicular (C6-C10) to the applied force. The average strength of 452 MPa of material of the cover plates was found.

2.6 Stress distribution The thermal emission measurements are based on temperature changes due to elastic

deformations during one loading cycle. Generally, the temperature change caused by elastic-plastic load cycle is composed of a thermoplastic component, which oscillates during the loading, and of a component, which is irreversible and cumulative. This component causes the temperature to rise. The change for uni-axial loading is proportional to hysteresis loop. The Stress Pattern Analysis by Thermal Emission (SPATE) technique utilise measurements of surface temperature changes during the repeated loading. The SPATE based on this principle determines linear sum of principal elastic stresses on the surface of the structure. The applied equipment SPATE � OMETRON, Institute of Theoretical and Applied Mechanics of the Academy of Sciences of the Czech Republic, with sensitivity of 0,001°K allows to digitalise, store and process the signal obtained by CCD image sensor with the sensitivity below 0,4 MPa for steel [Drdácký, 2000]. Figure 8 illustrates surface bulk stress distribution in the cover plate loaded by force 35 kN and was prepared the for comparison to FE simulation. a) b)

Figure 8 : a) Test set-up for measurement of principal stresses on surface by SPATE, b) surface bulk stress distribution around the hole under loading of 35 kN [Drdácký, 2000]

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3. Evaluation of Resistance 3.1 Test Interpretation

The transfer of the forces by friction may be observed in the first stage of the force -displacement diagrams, see Figure 9 (first stage) [Kulak et al, 1987]. The friction on surface of the plates was minimised by lubricant (MoS2 in oil) and a low level of tightening (torque 10 Nm). In the second stage, the load exceeds the frictional resistance and the joint slips into bearing. In the third stage, the fasteners and plates deform elastically, and consequently the load versus deformation relationship remains linear. In the fourth stage, yielding of the plates, fasteners, or both, occur and results in plate fracture or complete shearing of the bolts. In most of the tests, these stages may be clearly recognised.

Stage 3

Stage 1

Stage 4

Stage 2

Applied load

Overall alongation Figure 9 � Typical force - displacement diagram of symmetrical connection

Three basic concepts of evaluation of the resistance may be applied for the tests of bolted connections. The traditional research work for most codes based on allowable limit states (British Standards as example) clearly states that for bolts with threads in bearing the design bearing stresses results in a maximum deformation of 1,5 mm at working load. This deflection limit for resistance Fexp;1,5 is given in the data, see Tables A2.2, A2.4 and A2.6 in Appendix A2. In the test specimens the deflection limits correspond to the displacement of 3 mm because of measuring the total deformation. The ultimate limit of resistance Fexp;ult represents the maximum force that is transferred by the connection. The bearing capacity is the limiting design criterion for most of the test specimens. However, during the tests, most specimens displayed other forms of failure. The application of ultimate resistance in limit state concept needs to be accompanied by serviceability limit, which leads to more complex design procedure and therefore a difficult applicability.

F

Initial stiffness

Initial stiffness / 10exp

δ

exp, ultF

exp, convF

exp; 1,5F

Figure 10 : Limits of the resistance of joint, deflection limit Fexp;1,5, ultimate limit Fexp;ult,

conventional limit Fexp;conv

85

The conventional (elastic) limit of resistance Fexp;conv is defined as the intersection of a straight line passing through the origin and having the slope equal to the initial stiffness and of straight a line having the slope equal to stiffness divided by ten, which is tangent to the


plastic yielding part of the curve, see Figure 10. The conventional resistance depends more on the stiffness of the joint than on the type of failure. The conventional resistance is more sensitive to the stiffness of the joint than to the type of failure. Resistance of the connection based on these limits is shown on Figure 11 and is summarised in Appendix A1, where the failure modes are also included.

0

50

100

150

200

0 5 10 15 20

Displacement, mm

Force, kN

3 mm

exp, ultF

exp, convF

exp; !,5F

Figure 11 : Determination of the resistance � Test I 1-3 (16 - 1 - 2,5d) [Piraprez, 2000]

3.2 Design model

The bearing resistance is predicted by the simple model [Eurocode 3, 1992] as

Mb

uRd.b

tdf5,2Fγαβ= , [1]

where α is the smallest of

0,1orff

;41

d3p;

d3e

u

ub

o

1

o

1 − . [2]

The partial safety factor γMb is taken equal to 1,00 in order to compare the resistance Fb.Rd with the tests results. A reduction coefficient for slotted holes is calculated as

Rd.btest F/F=β [3]

The results of the calculations are given in Annex A2. The comparison between the ultimate resistances is limited due to different failure modes. The deflection limit 1,5 mm corresponds to a small deformation at assembly of slotted boltholes. The results confirm the trend that the longer the slot length, the lower the bearing resistance of the assembly. For the specimens with short slotted (d+ 6 mm) only two different sets are available. Their bearing resistance is almost the same as for the normal clearance hole. The specimens with long slot (2 d and 2,5 d) include holes from d + 6 mm to 2,5 d. When end and edge distances are respected it appears that a reduction of 30 % is sufficient for a safe design. The edge distance e2 (e4 for slotted hole) influences the bearing resistance of the plate. This is not taken into consideration in the simple design formulation. The specimens with very long slot (3,125 d and 3,5 d) have been realised with length up to 3,5 d. In this case a reduction of 40% of the bearing capacity defined for normal clearance hole is required.

86


4. Statistical evaluation

The Annex Z, see [Bijlaard D02, 1989] and [Eurocode 3/A2, 1998], brings a standard procedure for determining partial safety factors from the results of tests. The number of test with slotted holes available is limited to 70. It is a limited number compare to the number of tests in background documents [Snijder 6.02, 1988], [Snijder 6.04, 1988]. The Annex Z model allows comparing values of different tests. The variation in the prediction of the design model is determined from the tests (in term d). This variation is combined with variations of the other variables in the resistance function, with the variation in material strength and stiffness and variation in geometrical properties. Not all the variations in geometrical properties and in strength were available and assumptions have to be made for the error term. The calculation of the error term is using the data available ([Mazura, 2002] and [Moal, 2001]) and is extended to all tests.

Two sets of tests made in CRIF with 27 mm bolt diameter were not taken into consideration. In these experiments, the bolts failed in shear before it was expected. The tests with repeated loading were also not taken into statistical calculation.

The theoretical resistance rt.i = Fb.Rd was compared to the experimental value rei from the tests. The points representing pairs of corresponding values (rti, rei) are plotted on Figure 12.

0200400600800

1000120014001600

0 200 400 600 800 1000 1200 1400 1600

er , kN

t r ,kN Figure 12 : re � rt diagram for a full set of test

The mean value of the correction factor b was estimated as 0,90=)r(b . The coefficient of variation Vδ of the error in term of δ was found at the observed case V . The compatibility of the test population was analysed for subsets according to the slot length as shown in Figure 13. Three different assemblies were separated: the specimens with short slotted (d+ 6 mm) and normal clearance holes, specimens with long slot (between 2 and 2,5d) and specimens with very long slot (between 3,125 and 3,5 d). The coefficients of variation V

04,02 =δ

Xi of the basic variable were studied for the bearing capacity using three parameters of the test specimens available in Prague [Mazura et al, 2001]. The same variation was applied to the other sets. For the thickness t was taken as Vt = 0,005 → 0,00, for the ultimate resistance as Vfu = 0,02 based on the tensile tests and for the factor α, as Vα = 0,02.

The characteristic value rk of the resistance was predicted with and for the present sets as

30n >64,1uu ,kn,k == ∞

[4] 2210,05,0208,0991,064,1028,0134,064,1

tmk er9,0r ∗−∗∗−∗∗−= [5] tmk r626,0r =The design value rd for the resistance was obtained from the present set of tests as

. The initial estimation of the partial safety factor is tmd r467,0r = 34,1R =γ . The corrected partial factor to be used with the nominal resistance function may be obtained from

87


14,2rrkd

nRc

*R === γγ [6]

For the partial safety factor for a plate in bearing 25,1Mb =γ is the coefficient of reduction

58,014,225,1

*R

Mb ===γγβ [7]

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,5 1 1,5 2 2,5 3 3,5 4

rert

Bolt size / bolt diametr

Figure 13 : Influence of the slot length in the plate failure

The sub-sets were analysed using the same standard procedure with limited number of tests. The results are summarised in Table 1. The coefficient 0,93 for normal clearance and short slotted holes belong to the accuracy of the method and the small number of tests. This coefficient is influenced by the determination of the resistance. The β coefficient for the full set is below the β coefficient for very long slot due to small variation. The factor introduces higher errors, which are responsible for this low variation of the reduction factor β. The variation underlines the importance of division of the set into three sub-sets in order to predict more accurate results.

Table 1 � Application of Annex Z on different sub-sets Normal and Set All test specimens short slotted holes Long slotted holes Very long slotted holes

From d + 2 mm d + 2 mm 2 d 3,125 d To 3,5 d d + 6 mm 2,5 d 3,5 d

Number of test 61 15 39 7 γ R* 2,14 1,34 1,76 2,05 β 0,58 0,93 0,71 0,61

Conclusions Two set of tests were performed to investigate the behaviour of bolted joints with slotted holes loaded perpendicular to the slot. These tests were prepared for application of the component method to predict the resistance, stiffness and deformation capacity of connection with more bolt rows. The results highlight the limits of information concerning the bolts into regular circular holes. The material quality and its variation, the technology of holes production and

88


numerical management of the production tools is different compared to the older tests available as background of today�s design rules and structural recommendations. Three sets of tests were analysed by statistical calculation made according to Annex Z procedure [Eurocode 3/A2, 1998]. The findings are limited due to the small number of the tests results available. The presented tests show small (reduction factor β = 0,9) reduction in prediction of the bearing resistance of the short slotted holes (length up to d + 6 mm) compare to the circular holes. The reduction of 30% (reduction factor β = 0,7) is recommended for slotted holes with length up to 2,5 d and 40% (reduction factor β = 0,6) up to 3,5 d. It is recommended to incorporate the edge distance e2 into the design model to improve the prediction accuracy. Further set of tests and analytical prediction models by the component method will bring better understanding of the influence of the tolerances in the cover plate joints. Acknowledgements

The authors wish to thank colleagues Mr. E. Piraprez, CRIF Liege and Mr. W. Tizani, TU Nottingham for help and cooperation. This research has been supported by grant COST C12 and by grant J01-98:210000004 of the Ministry of Education, Youth and Sports. References

[Bickford, 1995] Bickford J.H. (1995) An introduction to the design and behaviour of bolted

joints, third edition, Marcel Decker Inc., New York, ISBN 0-8247-9297-1. [Bijlaard D02, 1989] Bijlaard F.S.K., Sedlacek G., Stark J.W.B. (1989) Statistical evaluations

of the results bolted connections, Background documentation, D.02, Delft. [Bijlaard, 1989] Bijlaard F.S.K., Sedlacek G., Stark J.W.B. (1988) Procedure for the

determination of design resistance from tests, Background report to Eurocode 3, BI-87-112, Delft.

[Eurocode 3, 1992] ENV - 1993-1-1 (1992) Design of Steel Structures - General rules and roles for buildings, European Prenorm, CEN, Brussels.

[Eurocode 3/A2, 1998] ENV - 1993-1-1/A2 (1998) Design of Steel Structures - General rules and roles for buildings, Annex Z, CEN, Brussels.

[EN 10002] EN 10002-1 (1990) Metallic materials, Tensile testing. Part 1: Method of testing (at ambient temperature), CEN, Brussels.

[Drdácký, 2000] Drdácký M. (2000) Problems of Experimental research of Semirigid Joints and Structures, in Semirigid Joints in Metal and Composite Structures, ed. Gizejovski M.A., Warsaw, pp. 27-48, ISBN 83-908083-1-5.

[Jaspart J.P., 1997] Jaspart J.P. (1997) Recent advances in the field of steel joints � Column bases and further configurations for Beam-to Column Joints and Beam Splices, Thesis, Université de Liège.

[Kersten, 1997] Kersten O. (1997) Zum Last-Verschiebungs-Verhalten geschraubter Scher-Lochleibungs- (SL-) Verbindungen im Stahlbau unter statischer Belastung. Dissertation, TU Hamburg-Namburg, Hamburg, p. 111.

[Kulak et al, 1987] Kulak G., Fisher J.W., Struik J.H.A. (1987) Guide to Design Criteria for Bolted and Riveted Joints, Second Edition, Wiley, New York.

[Kulak et al, 1980] Kulak G., Wens G.W., Hargreaves, A.C. (1980) Bearing Stresses in Connections using Grade 8.8 Bolts � Stage 2, Imperial College, Report BC6.

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[Mazura et al, 2001] Mazura V., Wald F., Sokol Z (2001) Slotted Holes in Structural Bolted Connections, CTU Reports, CVUT, Praha, pp. 880 � 881, ISBN 80-01-02335-4.

[Mazura, 2002] Mazura V. (2002) Slotted Holes in Structural Bolted Connections, PhD. thesis, CVUT, Praha, p. 165.

[Moal, 2001] Moal M. (2001) Assemblages avec trous oblongs et boulons non-precontraints, Diploma theses, CUST, Départment Génie Civil, Université Blaise Pascal, Clermont-Ferrand, p. 101.

[Piraprez, 2000] Piraprez E. (2000) Behavior of plates with slotted holes � CRIF Belgium, Proceeding of International Conference on Steel Structures of the 2000�s, IABCE, Istanbul.

[Snijder 6.02, 1988] Snijder H. H., Ungerman D., Stark J.W.B., Sedlacek G., Bijlaard F.S.K., Hemmert-Halswick A. (1988) Evaluation of test results on bolted connections in order to obtain strength functions and suitable model factors, Part B: Evaluation, Background documentation, 6.02, BI-88-087, Delft.

[Snijder 6.04, 1988] Snijder H. H., Bijlaard F.S.K., Stark J.W.B. (1988) Comparison of bolt strength according to Eurocode 3 with bolt strength according to national codes, Part A Results, Background documentation, 6.04, BI-89-152, Delft.

[Tizani, 1999] Tizani W. (1999) The bearing capacity of plates made with long-slotted bolt holes, Internal copy, University of Nottingham.

[Wald, Sokol, 1999] Wald F., Sokol Z. (1999) Connection design, in Czech, Navrhování Styčníků, ČVUT, Praha.

LIST OF SYMBOLS The Eurocode [1] system of symbols is applied in the work: b mean value due to the correction factor d, dexp bolt diameter, nominal and measured value (average of two measurements) do, d0.exp bolt hole diameter, characteristic and measured value e1, e1.exp end distance, characteristic and measured value e2, e2.exp edge distance, characteristic and measured value fu ultimate strength of the structural steel fub ultimate strength of the bolt material Fv,Rd design bearing resistance p1 spacing between centres of fasteners in the direction of load p2 spacing between row of fasteners measured perpendicular to the direction of load re experimental resistance rt theoretical resistance t, texp thickness of plate, characteristic and measured value A cross-section of the shank of a bolt As net cross-section of a bolt Vδ coefficient of variation α reduction factor for the bolt in shear β reduction factor due to the slotted hole γMb partial safety factor for bolted connections γM

* modified model factor σ variance of the term ∆ σ∆2 standard deviation

90


APPENDIX A1 TESTS RESULTS

Table A1.1 : Description of tests with long slots, [Tizani, 1999] Test d - n bolt Bolt presence t Slot length Int. hole e1 e2 p1 Holes Bolts

- hole size mm mm mm mm mm mm S1-1 S1-2 20-1-d+2 S1-3

single hole 10 22 (d+2) 22 (d+2) 31 27,5 N dr th

S2-1 S2-2 20-1-d+6 S2-3

single hole 10 26 (d+6) 22 (d+2) 31 27,5 N dr th

S3-1 S3-2 20-1-2,5d S3-3

single hole 10 50 (2,5d) 22 (d+2) 31 27,5 N dr th

S4-1 S4-2 20-1-3,5d S4-3

single hole 10 70 (3,5d) 22 (d+2) 31 27,5 N dr th

S11-1 S11-2 20-1-d+2 S11-3

single hole 10 22 (d+2) 22 (d+2) 31 40 N dr th

S12-1 S12-2 20-1-2,5d S12-3

single hole 10 50 (2,5d) 22 (d+2) 31 40 N dr th

S5b-1 S5b-2 20-2-d+6 S5b-3

all holes with bolts 10 26 (d+6) 22 (d+2) 31 66 50 dr th

S6b-1 S6b-2 20-2-2,5d S6b-3

all holes with bolts 10 50 (2,5d) 22 (d+2) 31 66 50 dr th

S7b-1 S7b-2 20-2-3,5d S7b-3


S9b-1 S9b-2 20-2-2,5d S9b-3


S10b-1 S10b-2 20-2-2,5d S10b-3


Notes: Holes: dr� drilling, Bolts: th � threaded part

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Table A1.2 : Results of tests with long slots, [Tizani, 1999]

Test d - n bolt δexp;ult Fexp;ult βult Fexp;1,5mm β1,5 Fexp;conv βconv Failure - hole size mm kN kN kN mode

S1-1 7,61 141 1,33 68 0,65 119 1,13 bolt shear S1-2 20-1-d+2 5,64 142 1,34 1,34 85 0,80 0,69 124 1,17 1,16 bolt shear S1-3 7,30 143 1,35 64 0,61 124 1,17 bolt shear S2-1 7,52 138 1,31 52 0,49 125 1,18 bolt shear S2-2 20-1-d+6 5,69 139 1,32 1,30 48 0,45 0,45 134 1,27 1,22 bolt shear S2-3 6,06 134 1,26 44 0,42 129 1,22 bearing S3-1 6,51 99 0,94 43 0,41 90 0,85 bearing S3-2 20-1-2,5d 5,49 95 0,90 0,92 41 0,39 0,40 89 0,84 0,85 bearing S3-3 5,98 98 0,92 44 0,42 90 0,85 bearing S4-1 5,27 76 0,72 42 0,40 69 0,65 bearing S4-2 20-1-3,5d 5,24 76 0,72 0,72 44 0,42 0,40 68 0,65 0,65 bearing S4-3 5,71 78 0,73 41 0,38 70 0,66 bolt shear

S11-1 6,52 145 1,37 72 0,68 127 1,20 bolt shear S11-2 20-1-d+2 5,35 145 1,37 1,38 73 0,69 0,67 131 1,24 1,23 bolt shear S11-3 6,25 147 1,39 67 0,63 132 1,25 bearing S12-1 4,55 93 0,88 44 0,41 88 0,83 bearing S12-2 20-1-2,5d 8,75 121 1,14 0,98 36 0,34 0,37 111 1,05 0,92 bearing S12-3 5,95 99 0,93 38 0,36 92 0,87 bearing S5b-1 5,89 260 1,21 97 0,45 239 1,11 bearing S5b-2 20-2-d+6 6,11 271 1,28 1,25 99 0,47 0,46 252 1,19 1,17 bearing S5b-3 5,47 264 1,25 95 0,45 253 1,20 end bolt shear S6b-1 5,60 220 1,02 70 0,33 212 0,99 end bolt shear S6b-2 20-2-2,5d 6,02 225 1,07 1,05 71 0,34 0,33 217 1,02 1,01 end bolt shear S6b-3 5,41 223 1,06 68 0,32 218 1,03 inner bolt shearS7b-1 4,71 194 0,90 73 0,34 187 0,87 inner bolt shearS7b-2 20-2-3,5d 5,89 205 0,97 0,93 65 0,31 0,32 196 0,92 0,89 inner bolt shearS7b-3 5,33 191 0,91 66 0,31 184 0,87 inner bolt shearS9b-1 4,23 220 1,02 88 0,41 221 1,03 inner bolt shearS9b-2 20-2-2,5d 5,96 247 1,15 1,08 79 0,38 0,40 238 1,12 1,07 inner bolt shearS9b-3 4,29 227 1,06 88 0,42 223 1,06 inner bolt shear

S10b-1 6,29 235 0,85 84 0,30 223 0,81 inner bolt shearS10b-2 20-2-2,5d 6,74 250 0,90 0,88 77 0,28 0,29 238 0,87 0,84 inner bolt shearS10b-3 6,27 243 0,88 77 0,28 233 0,85 inner bolt shear

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Table A1.3 : Description of component tests, [Mazura, 2002], [Moal, 2001] Test d - n bolt Bolt position tk texp Slot length dexp d0.exp e1.k e1.exp e2.k e2.exp p1.k p1.exp H B

hole size mm mm mm mm mm mm mm mm mm mm mm 1A 8,01 15,78 18,04 25,01 40,01 50,011B 16-1-d+2 8,03 15,75 18,07 25,01 39,98 50,011C

external (internal hole without bolt)

8

8,01

18 (d+2)

15,76 18,05

25

25,01

40

40,02

50

49,99

dr th

3A 8,02 15,75 18,09 25,01 34,05 50,013B 16-1-3d 8,01 15,75 18,04 24,95 34,02 50,013C


8

8,01

50 (3,125d)

15,76 18,08

25

24,95

34

34,02

50

49,97

dr th

5A 8,02 15,77 18,09 25,01 29,00 50,015B 16-1-2,5d 8,01 15,75 18,09 24,95 29,01 49,995C


8

8,02

40 (2,5d)

15,76 18,09

25

24,95

29

28,99

50

49,98

dr th

I1-1 8,01 15,76 18,03 25,01 29,01 49,99I1-2 16-1-2,5d 8,01 15,75 18,04 24,95 29,01 50,01I1-3

internal (external hole without bolt)

8

8,01

40 (2,5d)

15,76 18,08

25

25,01

29

29,02

50

50,01

dr th

I2-1 16-1-3d 8 8,05 50 (3,125d) 15,75 18,02 25 24,95 34 33,97 50 50,01 dr th2A 8,01 15,75 18,01 25,01 29,01 50,012B 16-1-2,5d 8,00 15,76 18,05 24,98 29,02 49,994C


8

8,01

40 (2,5d)

15,75 18,05

25

25,01

29

29,00

50

50,00

dr th

Notes: H holes: dr � drilling, B bolts: th � threaded part

Table A1.4 : Results of component tests, [Mazura, 2002], [Moal, 2001]

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Test Int. bolt hole δexp;ult Fexp;ult βult Fexp;1,5mm β1,5 Fexp;conv βconv Failure

mm mm kN kN kN mode 1A 12,66 170 1,27 106 0,79 137 1,02 plate shear1B 18 (d+2) 12,31 175 1,31 1,31 113 0,84 0,83 130 0,97 0,99 plate shear1C 14,42 180 1,34 114 0,85 130 0,97 plate shear3A 36,64 138 1,03 55 0,41 89 0,66 plate bend.3B 18 (d+2) 37,17 125 0,93 0,96 56 0,42 0,41 80 0,60 0,63 plate bend.3C 33,93 124 0,93 54 0,40 83 0,62 plate bend.5A 32,82 148 1,10 60 0,45 98 0,73 plate bend.5B 18 (d+2) 32,39 151 1,13 1,12 60 0,45 0,45 99 0,74 0,74 plate bend.

5C 34,79 150 1,12 59 0,44 101 0,75 plate bend.

I1-1 16,00 185 0,94 66 0,34 146 0,74 bolt shear I1-2 18 (d+2) 12,92 187 0,96 0,95 85 0,43 0,42 145 0,74 0,74 bolt shear I1-3 15,36 185 0,94 95 0,49 143 0,73 bolt shear

I2-1 18 (d+2) 17,42 180 0,92 0,92 99 0,51 0,51 122 0,63 0,63 bolt shear

2A 37,06 150 1,11 52 0,39 105 0,78 plate bend.2B 18 (d+2) 28,88 148 1,10 1,08 53 0,39 0,38 99 0,74 0,74 plate bend.

4C 31,49 140 1,04 49 0,36 96 0,71 plate bend.


Table A1.5 : Description of component tests, [Piraprez, 2000]

Test d - n bolt Position t Slot length

Int. bolt hole e1 e2 p1 Holes Bolts

- hole size mm mm mm mm mm mm 25 26 16-2-2d 27

all with bolts 30 32 (2d) 18 (d+2) 32 (2d) 93 N dr fb

28 29 27-2-2d 30

all with bolts 30 54 (2d) 30 (d+3) 54 (2d) 73,5 N dr fb

31 32 16-6-2d 33

all with bolts 30 32 (2d) 18 (d+2) 32 (2d) 93 40 dr fb

34 35 27-6-2d 36

all with bolts 30 54 (2d) 30 (d+3) 54 (2d) 73,5 70 dr fb

37 38 16-2-2d 39

all with bolts 30 32 (2d) 18 (d+2) 32 (2d) 93 N gc fb

40 41 27-2-2d 42

all with bolts 30 54 (2d) 30 (d+3) 54 (2d) 73,5 N gc fb

43 44 16-6-2d 45

all with bolts 30 32 (2d) 18 (d+2) 32 (2d) 93 40 gc fb

46 47 27-6-2d 48

all with bolts 30 54 (2d) 30 (d+3) 54 (2d) 73,5 70 gc fb

Notes: Holes: gc � gas cutting, Bolts: fb � full body

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Table A1.6 : Results of assembly tests, [Piraprez, 2000]

Test d - n bolt δexp;ult Fexp;ult βult Fexp;1,5 β1,5 Fexp;conv βconv Failure - hole size mm kN kN kN mode

25 - 612 1,15 320 0,60 440 0,83 26 16-2-2d 52,88 642 1,11 1,13 211 0,36 0,42 417 0,72 0,79 bearing 27 54,44 649 1,12 165 0,29 475 0,82 28 70,91 1319 1,44 240 0,26 911 1,00 29 27-2-2d 66,82 1309 1,32 1,35 248 0,25 0,25 917 0,92 0,94 bearing 30 61,37 1268 1,28 244 0,25 906 0,91 31 43,12 1626 1,23 500 0,38 1119 0,84 32 16-6-2d 41,09 1625 1,13 1,15 490 0,34 0,35 1144 0,79 0,80 bearing 33 36,88 1595 1,11 500 0,35 1117 0,77 34 97,06 2124 0,88 580 0,24 1533 0,63 35 27-6-2d 79,31 2026 0,77 0,84 610 0,23 0,24 1511 0,57 0,60 bolt shear 36 91,86 2305 0,88 - - - - 37 42,96 530 1,00 160 0,30 389 0,73 bearing 38 16-2-2d 42,15 532 0,92 0,94 150 0,26 0,25 389 0,67 0,73 39 - 529 0,91 118 0,20 449 0,78 40 55,06 966 1,06 186 0,20 750 0,82 41 27-2-2d 68,11 1002 1,01 1,03 182 0,18 0,20 736 0,74 0,78 bearing 42 56,09 1002 1,01 198 0,20 777 0,78 43 26,97 1430 1,08 270 0,20 1306 0,98 44 16-6-2d 29,31 1466 1,02 1,04 260 0,18 0,19 1353 0,94 0,94 bearing 45 34,25 1497 1,04 285 0,20 1308 0,91 46 75,59 2180 0,90 300 0,12 1622 0,67 47 27-6-2d 120,87 2480 0,94 0,92 320 0,12 0,12 1600 0,61 0,64 bolt shear 48 113,11 2441 0,93 300 0,11 1690 0,64

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APPENDIX A2 TESTS RESULTS OF MATERIAL The standard coupon test results are summarized in Tables A2.1 and A2.2 below. The relative elongation was calculated as A = [(Lu - L0) / L0]*100 % , (A2.1) where Lu is the coupon final length and L0 is the coupon initial length. The contraction was evaluated based on expression Z = [(Au - A0) / A0]*100 % , (A2.2) where Au is the coupon final cross-section area and A0 is the coupon initial area. Evaluation of the characteristic values of the stress � strain diagram was based on T-distribution of the values under 5% quantile for a small number of data as x = ∑i (fui) / n , (A2.3) R = max [fui] - min[fui] , (A2.4) fk = x - σt R(i) , (A2.5) where n is number of tests, fui is the measured value of resistance, σt is the probability factor for the T distribution, (for three tests σt5 = 0,328, σt10 = 0,315).

Table A2.1 : Coupon test of the central plate No. d0 L0 A0 du Lu Au FeH Fm ReH Rm A Z

mm mm mm2 mm mm mm2 kN kN MPa MPa % % M1 6,05 30,00 28,75 3,80 41,80 11,34 6,85 12,00 238 417 39,33 60,55 M2 5,85 30,00 26,88 3,60 40,10 10,18 6,52 11,41 243 424 33,67 62,13 M3 5,95 30,00 27,81 3,70 39,40 10,75 6,83 12,08 246 434 31,33 61,34 M4 5,75 30,00 25,97 3,45 40,50 9,35 6,37 11,12 245 428 35,00 64,00 M5 5,90 30,00 27,34 3,65 40,10 10,46 6,50 11,34 238 415 33,67 61,73

x 242 424 35 62 R 8 19 fk 239 417

Table A2.2 : Coupon test of the cover plate

No. d0 L0 A0 du Lu Au FeH Fm ReH Rm A Z mm mm mm2 mm mm mm2 kN kN MPa MPa % %

C1 4,00 20,00 12,57 2,55 26,80 5,11 4,18 5,65 333 449 34,00 59,37 C2 4,00 20,00 12,57 2,70 26,30 5,73 3,90 5,85 310 465 31,50 54,45 C3 3,80 20,00 11,34 2,70 * 5,73 3,45 5,12 304 451 * 49,51 C4 3,85 20,00 11,64 2,60 26,40 5,31 3,65 5,37 314 461 32,00 54,39 C5 4,00 20,00 12,57 2,55 26,50 5,11 4,12 5,64 328 449 32,50 59,37 C6 3,95 20,00 12,25 2,60 25,80 5,31 3,65 5,45 298 445 29,00 56,66 C7 4,00 20,00 12,57 2,55 27,10 5,11 3,98 5,70 317 453 35,50 59,37 C8 4,00 20,00 12,57 2,55 26,30 5,11 3,95 5,45 314 434 31,50 59,37 C9 3,85 20,00 11,64 2,60 25,60 5,31 3,45 5,37 296 461 28,00 54,39

C10 3,85 20,00 11,64 2,55 25,50 5,11 3,50 5,27 301 453 27,50 56,12 x 312 452 33 58 R 37 31 fk 300 442

* outside of the measured reference length

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Experiments of Bolted Cover Plate Connections With Slotted Holes

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Transcript of Experiments of Bolted Cover Plate Connections With Slotted Holes