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공학석사 학위논문

Experimental Study on the

Behavior of Bolted Joints for

UHPC Panels

초고성능 콘크리트 패널 간의 볼트 접합부의

거동에 관한 실험

2015년 8월

서울대학교 대학원

건축학과

정 수 형

Experimental Study on the

behavior of Bolted Joints for

UHPC Panels

지도 교수 홍 성 걸

이 논문을 공학석사 학위논문으로 제출함

2015년 4월

서울대학교 대학원

건축학과

정 수 형

정수형의 공학석사 학위논문을 인준함

2015년 7월

위 원 장 이 철 호 (인)

부위원장 홍 성 걸 (인)

위 원 박 홍 근 (인)

i

Abstract

Experimental Study on the Behavior of Bolted Joints for UHPC Panels

Chung, Soo-Hyung Department of Architecture and Architectural Engineering

College of Engineering Seoul National University

Recently, as the technology of freeform design is developing, the interest

in construction techniques and material application are rising up. Typically, metal or concrete are used to fabricate the freeform façade. However, the application of these materials to freeform architecture requires complicated construction process and fabrication. As a result, it cause enormous cost problem. To improve current construction technology and process using conventional materials, ultra-high performance concrete (UHPC) can be effective alternative materials for freeform architects due to the high level of flow at placing time. Moreover, UHPC has high compressive strength, tensile strength with fibers, and outstanding impact resistance. However, material cost of UHPC is very expensive to be constructed in comparison with typical material. High construction cost can be compensated by other applications such as architectural finishing rather than structural components. By using precast panel, cost of fabrication will be decreased in comparison with cast-in-place. Also, precast UHPC requires efficient assemblage method by bolted connections. Therefore, cost of placement can be decreased by simple bolted joints. However, research on the bolted joints for UHPC panels is not enough yet.

This paper investigates structural behavior of single bolted connections and multi bolted connections to identify main failure mechanisms of bolted joints of UHPC panels. This paper performed a series of experimental program of the bolted joints for UHPC panels through direct tensile tests,

ii

especially focused on the relationship between the failure modes, strengths and stress distribution with the variables of the specimen thickness, width and edge distance. Based on the analysis results, some design procedure for predicting ultimate load are proposed by using stress concentration factor and work method. The proposed design procedure is capable of predicting the ultimate load and failure modes of joint well.

Keywords : joint; tensile behavior; failure mode; UHPC; design equation;

strain concentration; work method

Student Number : 2013-23028

iii

Contents

Abstract ......................................................................... i

Contents ........................................................................ iii

List of Tables ................................................................ vi

List of Figures ............................................................. vii

List of Symbols ............................................................. ix

Chapter 1. Introduction ............................................... 1

1.1 General.......................................................................................... 1

1.2 Objectives and Scope.................................................................... 3

Chapter 2. Review ........................................................ 4

2.1 Background on UHPC .................................................................. 4

2.1.1 General ........................................................................................... 4

2.1.2 Property .......................................................................................... 4

2.1.3 Application ..................................................................................... 5

2.2 Background on bolted joints ......................................................... 6

2.2.1 General ........................................................................................... 6

2.2.2 Failure Modes ................................................................................. 7

2.2.3 Experimental Research on Single-Bolted Joints ............................. 8

2.2.4 Experimental Research in Multi Bolted Joints ............................. 10

Chapter 3. Single Bolted Joints for UHPC Panels .. 12

3.1 Introduction ................................................................................ 12

3.2 Parameters of Study .................................................................... 12

3.3 Material Properties ..................................................................... 14

iv

3.4 Fabrication of Specimens ........................................................... 15

3.5 Test Set-up and Instrumentation ................................................. 16

3.6 Test Results ................................................................................. 17

3.6.1 Failure Modes ............................................................................... 18

3.6.2 Load - Displacement Characteristics ............................................ 19

3.6.3 Ultimate Strengths ........................................................................ 21

3.6.4 Effect of Ratio e/d ......................................................................... 22

3.6.5 Effect of Ratio w/d ....................................................................... 24

3.6.6 Effect of Thickness ....................................................................... 26

3.6.7 Stress Concentration Factors ........................................................ 26

3.7 Design Procedure ........................................................................ 29

3.7.1 Net Tension Failure....................................................................... 30

3.7.2 Cleavage Failure ........................................................................... 34

Chapter 4. Multi Bolted Joints for UHPC Panels ... 37

4.1 Introduction ................................................................................ 37

4.2 Parameters of Study .................................................................... 37

4.3 Material Properties ..................................................................... 40

4.4 Fabrication of Specimens ........................................................... 41

4.5 Test Set-up and Instrumentation ................................................. 42

4.6 Test Results ................................................................................. 43

4.6.1 Failure Modes ............................................................................... 45

4.6.2 Load – Displacement Characteristics ........................................... 47

4.6.3 Effect of Ratio e/d ......................................................................... 50

4.6.4 Effect of Ratio w/d ....................................................................... 55

4.6.5 Effect of Bolt Pattern .................................................................... 62

4.6.6 Stress Concentration Factors ........................................................ 64

4.7 Design Procedure ........................................................................ 66

4.7.1 Net Tension Failure....................................................................... 67

4.7.2 Cleavage Failure ........................................................................... 70

v

Chapter 5. Conclusions .............................................. 73

References ................................................................... 75

국 문 초 록 ................................................................ 77

APPENDIX ................................................................. 79

1. Bearing Strength Test ................................................................... 79

2. Load-Displacement Curve of Single Bolt test .............................. 83

3. Load-Displacement Curve of Multi Bolt Test .............................. 88

vi

List of Tables Table 1 Test specimens of single bolt test ............................................ 13

Table 2 Mixing proportion ................................................................... 15

Table 3 Test results ............................................................................... 17

Table 4 Constant parameters ................................................................ 38

Table 5 Test specimens of multi bolt test ............................................. 39

Table 6 Mixing proportion ................................................................... 41

Table 7 Test results ............................................................................... 44

Table 8 Test results ............................................................................... 80

vii

List of Figures Fig. 1-1 Test plan .................................................................................... 3

Fig. 2-1 Failure modes ........................................................................... 7

Fig. 2-2 Geometric parameters ............................................................... 7

Fig. 3-1 Variables of single bolt test ..................................................... 13

Fig. 3-2 Specimen in mold ................................................................... 15

Fig. 3-3 Panels after curing .................................................................. 15

Fig. 3-4 Location of strain gauges ........................................................ 16

Fig. 3-5 Test set-up ............................................................................... 16

Fig. 3-6 Cleavage failure ...................................................................... 18

Fig. 3-7 Net tension failure .................................................................. 18

Fig. 3-8 Typical load-deflection curves ................................................ 20

Fig. 3-9 Calculation of ductility ratio ................................................... 20

Fig. 3-10 Macro crack in panel ............................................................ 20

Fig. 3-11 Effect of e/d ratio on Ultimate load ...................................... 23

Fig. 3-12 Effect of e/dratio on Net tension strength ............................. 23

Fig. 3-13 Effect of w/d ratio on ultimate load ...................................... 25

Fig. 3-14 Effect of w/d ratio on Net tension strength ........................... 25

Fig. 3-15 Effect of edge distance on stress distribution ....................... 27

Fig. 3-16 Effect of edge distance on stress distribution ....................... 27

Fig. 3-17 Effect of width on Stress distribution ................................... 28

Fig. 3-18 Effect of width on Stress distribution ................................... 28

Fig. 3-19 Correlation coefficient for single bolt test ............................ 33

Fig. 3-20 Experimental vs. Predicted load for net tension failure ........ 33

Fig. 3-21 Failure mechanism model for cleavage failure ..................... 35

Fig. 3-22 Experimental vs. Predict load for cleavage failure ............... 36

Fig. 4-1 Variables for multi bolt test ..................................................... 38

Fig. 4-2 bolt patterns ............................................................................ 38

Fig. 4-3 Specimen in mold ................................................................... 41

Fig. 4-4 Test set-up ............................................................................... 42

viii

Fig. 4-5 Location of strain gauges ........................................................ 43

Fig. 4-6 Typical failure modes (up:cleavage, down:net tension) ......... 46

Fig. 4-7 Typical load-deflection curve of cleavage failure ................... 48

Fig. 4-8 Typical load-deflection curve of net tension failure ............... 49

Fig. 4-9 Effect of e/d ratio on ultimate load ......................................... 51

Fig. 4-10 Effect of e/d ratio on Net efficiency ..................................... 52

Fig. 4-11 Effect of e/d ratio on Bearing Efficiency .............................. 53

Fig. 4-12 Effect of e/d ratio on structural efficiency ............................ 54

Fig. 4-13 Effect of w/d ratio on ultimate load ...................................... 56

Fig. 4-14 Effect of w/d ratio on Net efficiency .................................... 57

Fig. 4-15 Effect of w/d ratio on Bearing efficiency ............................. 58

Fig. 4-16 Effect of w/d ratio on structural efficiency ........................... 59

Fig. 4-17 Effect of s/p ratio on Bearing efficiency ............................... 60

Fig. 4-18 Effect of w/p ratio on Net efficiency .................................... 61

Fig. 4-19 Effect of bolt patterns on ultimate load ................................ 62

Fig. 4-20 effect of bolt pattern on efficiency ........................................ 63

Fig. 4-21 Effect of width on stress distribution .................................... 65

Fig. 4-22 Correlation coefficient for multi bolt test ............................. 69

Fig. 4-23 Experimental vs. Predicted load for net tension failure ........ 69

Fig. 4-24 Failure mechanism model for cleavage failure ..................... 71

Fig. 4-25 Experimental vs. Predicted load for cleavage failure ........... 72

Fig. A- 1 Parameters of bearing strength test ....................................... 79

Fig. A- 2 Panel after curing .................................................................. 80

Fig. A- 3 Test set-up ............................................................................. 80

Fig. A- 4 Failure shape of bearing failure ............................................ 81

Fig. A- 5 Effect of bolt diameter on Strength ....................................... 82

Fig. A- 6 Typical load-deflection curve of bearing test ........................ 82

ix

List of Symbols

clA = area of cleavage failure line (mm2)

netA = area of net section (mm2) C = correlation coefficient

boltd = diameter of bolt (mm)

holed = diameter of bolt hole (mm) e = edge distance (mm)

bF = bending strength (N/mm2)

'cF = compressive strength (N/mm2)

tF = tensile strength (N/mm2)

tcK = composite elastic concentration factor

teK = elastic concentration factor

n = number of bolts P = applied load (kN)

clP = predict ultimate load of cleavage failure (kN)

ntP = predict ultimate load of net tension failure (kN)

ultP = ultimate load (kN) t = thickness of panel (mm) w = width of panel (mm)

1

Chapter 1. Introduction

1.1 General

Recently, as the technology of freeform design is developing, the interest in construction techniques and material application are rising up. Dongdaemun Design Plaza (DDP) by Zaha Hadid architects is the clear example of freeform architecture. Like DDP, freeform structure which has fancy and noticeable curved surface earns economic profit and fame in the world. This phenomenon is called Bilbao effect. Bilbao in Spain is an industrial and port city which is situated in the North part of Spain. However, Bilbao was losing its industry. The city was looking for to find a way to transform itself from a port hub of Spain’s industry into a vibrant city built on a services economy. Then city made a conclusion decision to save the city from suffering by having Guggenheim Museum. It was the strategy to make the city revival. After building opened its doors to visitors, Guggenheim Museum enjoy numerous of visitors per year. The port city transformed to a magnet and economic explosion.

However, there is demerit of freeform design. Typically, metal or concrete are used to fabricate the freeform façade. However, the application of these materials to freeform architecture requires more refined construction process and fabrication. This complicated process causes enormous construction cost.

To improve current construction technology using conventional materials, Ultra High Performance Concrete (UHPC) can be one of viable options for freeform façade due to high level of flow at placing time. Also, UHPC has high compressive strength, tensile strength with fibers, self-compacting ability and high durability. From utilizing these merits of UHPC, high construction cost can be compensated by other applications such as architectural finishing rather than structural components.

2

For high quality architectural UHPC façade, UHPC façade panels should be better to fabricate precast panel in factory. Precast cladding of UHPC panels requires efficient assemblage method by bolted connection. Through the simple bolted connection, construction cost for cladding panel can be decreased drastically. However, research on the bolted joints for UHPC panels is not enough yet. The existing bolted connection method is for metal or other composite materials such as fiber reinforced plastic. Therefore, bolted joint test is necessary to make design guidelines for architectural precast UHPC panel connection.

3

1.2 Objectives and Scope

Bolted joints for UHPC panels may be one of viable connections of prefabrication units. This paper planned to investigate structural behavior of UHPC panels through 1) single bolted connection test, 2) multi bolted connection test and 3) bearing strength test as shown in Fig. 1-1. The main objectives of these tests program are: a) to understand mechanical behavior of bolted joint, b) to develop a model to predict the ultimate load and mode of failure in UHPC panels.

A comprehensive experimental and analytical investigation was conducted to study and determine the behavior of bolted connections in UHPC for architectural applications. The investigation studied the behavioral effects of various geometric parameters including the edge distance, width, thickness and bolt patterns. Based on the research findings, a design procedure was developed. The proposed design equation is capable of predicting the ultimate capacity and failure mode of UHPC panels.

Fig. 1-2 Test plan

4

Chapter 2. Review

2.1 Background on UHPC

2.1.1 General

Ultra high performance concrete is a material which is leading edge of concrete innovation, and it provides a new technology to expand a precaster’s business with new products and solutions. The materials combination of high performance properties facilitates the ability to design curvatures, thin, complex shapes and highly customized textures – applications which are difficult to achieve with typical reinforced concrete or metals elements.

2.1.2 Property

One of the most noticeable assets of UHPC is its high compressive strength. UHPC is capable of reaching 230 MPa. The increase in compressive strength, over normal strength concrete or high performance concrete, can be attributed to the particle packing and selection of specific constituents, and thermal curing of UHPC. The very dense microstructure and high strength so typical of UHPC are due to its very low water/binder ratio of only about 0.2. The matrix has practically no capillaries and is thus diffusion-resistant. Another factor contributing to the high strength is the fact that the ultrafine particles consist of various components that are combined in such a specific way that the ultrafine particles are packed very tightly together.

The addition of high-strength steel fiber can bring about a distinct improvement in the post-peak structural behavior. However, this has hardly any effect on the ascending portion of the stress-strain curve. By contrast, the descending portion of the curve is influenced to a great extent by the following parameters like fiber content, fiber orientation, bond between fiber and matrix and stiffness of the fiber. However, it is difficult to predict the course of the descending portion of the stress-strain curve by means of simple relationship. Therefore, appropriate laboratory test are necessary for a certain UHPC. The fiber content and fiber orientation in a component can vary locally and be influenced by concreting activities.

5

In the case of behavior in tension, tests on unnotched specimens are suitable for determining the tensile strength, whereas tests on notched specimens are more appropriate for determining the stress-crack width relationship of fiber-reinforced UHPC. The latter is regarded as characteristic for the response of brittle materials or materials with a softening post-peak behavior. Typical tensile strength value is 7-11 MPa. Without fiber, very brittle failure can be expected in tension. It is therefore very difficult to measure any stable descending portion in the force-displacement diagram. The addition of fiber results in higher tensile strength on the on hand and the ability to transfer forces across much wider cracks on the other. The fiber bridge over the cracks in this situation and are able to transfer some of the tensile strength of the matrix, or even higher stresses in favourable conditions.

2.1.3 Application

UHPC’s superior mechanical performances can result in a reduced number of sections, eliminate the need for passive reinforcing, and allow the design of cantilevered structures that are not possible with conventional concrete. UHPC enables the design and production of thin elements that are highly durable and sustainable. Its resistance to corrosion, abrasion, carbonation, impact and fire makes it well-suited for structures in harsh environments and public buildings that have strict requirements for safety, maintenance and seismic ratings.

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2.2 Background on bolted joints

2.2.1 General

For engineering applications, bolted joints (single or multi-bolted) are easy to assemble, while providing high strength without damaging the lamination of the fiber reinforced composite material members during assembly. Bolted joints are maintainable, and are usually the most cost effective compared to bonding and other types of joints. This bolted connection is the way of reducing expense of using architectural UHPC panel.

For bolted joints one of the major design considerations is the high stress concentrations in the vicinity of the bolt hole. Drilling holes to fabricate a joint could considerably weaken the panel member due to the discontinuity of the principal load-carrying fibers. An exact stress solution was developed for an infinitely wide, isotropic, elastic plate with an unloaded hole, attributed to Kirsh by Timoshenko3. Lekhnitskii4 extended this solution to encompass orthotropic materials. It must be noted however, that these solutions are for unloaded holes and the stress distribution for a plate loaded through a hole is different. A solution for an infinite, elastic, isotropic plate loaded through a hole was developed by Bickley5. By the method of superposition, De Jong6 developed an approximate solution for an orthotropic plate with finite dimensions. However, to date there is no exact closed-form solution available for an orthotropic plate of finite dimensions loaded through a hole. Consequently, the stress distributions are currently determined via numerical procedures or experimental evaluation.

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2.2.2 Failure Modes

Bolted joints for fiber reinforced composite materials experience similar failure modes to those of bolted joints fabricated using steels. The basic failure modes include net tension, shear out and bearing as shown in Fig. 2-1. In addition to these failure modes fiber reinforced composite materials are susceptible to another mode known as cleavage or splitting failure, which is also shown in Fig. 2-2. Combinations of the basic failure modes are also possible. Net tension and shear out failures occur catastrophically and therefore are undesirable. On the other hand, bearing failure is usually the most desired failure mode since it is the most ductile and is not catastrophic. To achieve bearing failure, the geometry of the joints usually consists of large edge distances and widths. The basic geometric parameters consist of the joints width, the edge distance, the hole diameter, and the thickness as shown in Fig. 2-3. Thus the use of controlled magnitudes of various geometric parameters can provide reasonable assurance for the joints to fail in bearing.

d w

et

1) Net-tension failure 2) Shear out failure 3) Cleavage failure 4) Bearing failure

Fig. 2-4 Failure modes

Fig. 2-5 Geometric parameters

8

2.2.3 Experimental Research on Single-Bolted Joints

The experimental work conducted by Camacho7 included structural single bolted connections using UHPFRC. The possible UHPFRC failure modes were introduced and two different types of tests were designed and performed to evaluate the joint capacity. The geometry of the UHPFRC elements was modified in order to correlate it with the failure mode and maximum load reached. Also a linear finite element analysis was performed to analyze the UHPFRC elements connection. The results of this investigation showed that two failure modes, cleavage and net tension, were observed. Cleavage depends directly on the edge distance and increases its ductility with the width W. net tension suffers more brittle post peak behavior, which could be more improved introducing ordinary reinforcement. Camacho found that net tension failure can’t be directly estimated with the maximum tensile strength, due to the propagation of a crack through the section from one of the sides. Normally the equivalent strength obtained is half of the tensile strength of the concrete, which is approximately 12 MPa. Also, the bearing failure was ductile and the equivalent compressive strength resulted higher than the expected from the uniaxial compressive tests performed to 100 mm cubes. Additional tests are required with longer distances over the hole to evaluate the bearing failure in more realistic conditions.

Collings8 conducted research in CFRP laminates to examine the effect of different parameters including the effects of the stacking sequence of multi-angled composites, the hole diameter, the edge distance, the connection width, the lateral constraint of the bolt, and the composite laminate thickness. The results of his investigation showed that with increasing width-to-hole diameter ratios, the failure mode changed from net tension failure to bearing failure at w/d values between 3 and 7 for different laminate lay-ups. For increasing edge distance to hole diameter ratios, the mode of failure changed from shear out to bearing failure at e/d values between 3 and 5 for different laminate lay ups. Bearing strength was shown to be dependent on several variables including the degree of lateral constraint and laminate thickness. Collings found that increased lateral constraint increased bearing strength. It was found that the bearing strength decreased with increasing diameter to thickness ratios without the presence of lateral constraint.

9

The experimental work conducted by Rosner9 included single bolted connections using fibre-reinforced composite structural members. He tested to determine the effects of various geometric parameters on the ultimate strength and mode of failure. Parameters were hole diameter, thickness, width, edge distance and fiber orientation. Based on the his experimental results, a mathematical model and a design procedure are proposed to predict the ultimate load and failure modes of single bolt connections in fibre-reinforced composite materials. Rosner found that connection load – displacement behavior is linear up to failure regardless of the modes of failure. Also, connections that failed in a catastrophic manner, such as in net tension and cleavage failure, experienced a sudden drop in load carrying capacity followed by large displacements represented by a “step” in the load-displacement curve. For relatively small edge distances the mode of failure changed from net tension to cleavage failure by increasing the w/d ratio. For relatively large edge distance the failure mode changed from net tension to bearing failure by increasing the w/d ratio. Also he found that the magnitudes of the stress concentrations along the net section perpendicular to the applied load are highly influenced by the width of the connections. The stress concentrations tend to increase with increasing width. The effects of connection edge distance and thickness on the stress concentrations are less than the effect of member width. Stress concentrations tended to decrease with increasing edge distance and were negligibly affected by the member thickness. The proposed design procedure by Rosner predicts the ultimate load and failure mode of the connections with an adequate degree of accuracy.

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2.2.4 Experimental Research in Multi Bolted Joints

The transition from single bolt to multi bolt connections is complicated and does not consist of simple extrapolation. Several researchers have conducted experimental and analytical work in the area of multi bolted connections.

Hassan10 conducted work in multi-bolted connections for fiber reinforced plastics structural members. He tested to determine the effects of various geometric parameters such as; width, edge distance, fiber orientation, number of bolts and bolt pattern no the behavior of these connections. Based on the his experimental investigation the following conclusions can be made. He found that load-displacement behavior is linear regardless of the failure mode. The first portion represents the slip until bearing takes place, while the second part represents the real behavior where small displacement takes place under higher loads. Connections with net tension failure mode experienced a sudden drop in the load carrying capacity, while connections that failed by cleavage mode experienced a gradual decrease in the load carrying capacity. Also from his test results, the load strain relationship for all types of connections is linear up to failure. For connections with one row of bolts, the load is equally shared among the bolts. For connections with more than one row of bolts, the bearing forces on the fasteners are not evenly shared, as measured by the gauge readings. The edge distance to the hole diameter ratio has a significant effect on the mode of failure on connections with one row or one column of bolts. For relatively small edge distance at a ratio less than 3 the failure mode was cleavage. Increasing the thickness of the members increased slightly the ultimate load capacity of the connection, but it had no effect on the failure mode. His test results suggested that, the high strength steel bolts tightened to the torque used in this investigation are adequate to remove the influence of material thickness. Based on the experimental results, he proposed design procedure to predict the ultimate load and failure modes of multi bolted connections. The proposed rational model by Hassan predicted the ultimate loads of the tested connections with a good degree of accuracy, where the differences between the measured and the predicted loads were less than 15 percent.

11

Colling conducted work on single and multi-bolt composite connections. Several multi-bolt configurations were tested to study the interaction between holes and their effects on the tensile strength of the connection. Collings concluded that there was no interaction among the bolt holes for large pitch and gauge spacings and that the behavior of multi-fastener connections could be determined from single hole data.

Agarwal12 also conducted work on multi-fastener connections, examining the effect of the number of bolts in a row, the number of bolts in tandem, the interaction of tress fields or load distribution, and the effects of bolt pattern. He concluded that by increasing the number of bolts in tandem, the net tension strength could be slightly increased. However, the effect of the number of bolts per row was the opposite, since the net tensile was reduced up to 15% with and increased number of bolts per row. The study was based on an analytical analysis used to predict the connection strength. Using a finite element method for single bolt connections, the most critical row of bolts, and hence failure strength was predicted. Based on the experimental results, the analytical method seemed to predict the failure loads for connections with two bolts per row quite well, however it became increasingly nonconservative for connections with three or more bolts per row or for staggered patterns. These findings somewhat contradicted the results reported by Collings.

Work done by Ramkumar13 and Tang14 showed that the bearing/ by-pass load ratio is the major factor in the behavior of multi fastener connections. Ramkumar’s investigation on two bolted graphite-epoxy laminates under both static and cyclic loading conditions indicated that there was a linear reduction in connection strength with increasing bearing/ by-pass load ratio. The static failure analysis was carried out using FEA, NASTRAN program, isoparametric membrane elements and the fastener load was modeled by applying a constant displacement at one end of the plate and imposing zero redial displacements on the load-carrying half segment of the fastener hole surface. The analysis was done for single and two-bolt connections, the plate bending effects, interlaminar stresses and bolt bending and shearing effects were neglected. The average stress failure criterion was used to determine the strength and the corresponding failure mode. The analytically predicted strength values were in good agreement with the experimentally measured ones.

12

Chapter 3. Single Bolted Joints for UHPC Panels

3.1 Introduction

Due to the complexity of the mechanics of bolted joints, it is difficult to define an analytical treatment of the problem without direct experimental test. Especially, like brittle materials such as UHPC,

This chapter presents an experimental program to examine the behavior of single bolted joints fabricated from UHPC panels. Failure modes, load-displacement relationship, effect of geometric variables and stress distributions considered in this test are presented in detail.

3.2 Parameters of Study

The experimental program was designed to investigate the effects of the panel geometry. The three basic geometric parameters studied in this investigation, which influence the strength and failure mode of a joint. The parameters varied are illustrated in Fig. 3-1, and they are:

1) Ratio e/d is the ratio between the end distance e (distance between the center of the bolt and the panel edge) to the hole diameter d. The three ratios investigated were e/d=2, e/d=3 and e/d=4, corresponding to end distances of 48mm, 72mm and 96mm (the hole diameter was kept constant at d = 24mm).

2) Ratio w/d is the between the width of panel w to the hole diameter d. the three ratios investigated were w/d=4, w/d=6 and w/d=8, corresponding to width of 96mm, 144mm and 192mm.

3) To determine the influence of the panel’s thickness on the behavior of a joint, two thicknesses were used: 20mm and 30mm.

13

A total 18 single bolted joint panels were tested under direct tension by two bolts inserted in the holes. Specimen designations and the geometric dimensions and configurations for all of the 18 connections tested are given in Table 1.

Table 2 Test specimens of single bolt test

Number Edge distance “e” [mm]

Width “w” [mm]

Thickness “t” [mm] Strain gauge

1 48 96 20 2 48 96 30

3 48 144 20 ○ 4 48 144 30

5 48 192 20 ○ 6 48 192 30 7 72 96 20 8 72 96 30

9 72 144 20 ○ 10 72 144 30

11 72 192 20 ○ 12 72 192 30 13 96 96 20 14 96 96 30

15 96 144 20 ○ 16 96 144 30

17 96 192 20 ○ 18 96 192 30

d w

et

300 mm

Fig. 3-2 Variables of single bolt test

14

3.3 Material Properties

A Portland cement made in Korea was used. Silica fume made in Norway was used. Properties of cement and silica fume were provided in Table. Established silica powder which particle-size distribution is

45~800μm was used as aggregate. This powder contains 97% of SiO2 and

the hardness and specific gravity are 7 and 2.65 g/cm3. Filler which has medium size between cement and silica fume improves a compressive strength of concrete by increasing poured density. Furthermore, it activates hydration reaction by supplying additional Sio2 component. Australian

product which has 2.2 μm of average diameter and 99% of SiO2 was used.

Super plasticizer which has 1.01 g/cm3 of specific gravity is used. The most commonly used steel fiber which has 0.2mm of diameter, 13mm of length and 2500MPa of tensile strength was used.

15

3.4 Fabrication of Specimens

The mix proportion and mixing procedure used in this experiment was optimized for materials proposed1. The mix proportion of UHPC was provided in Table 3.

Concrete mixer which has 60L of capacity and 60 rpm of speed was used. Sand and silica fume were mixed first for dispersion of silica fume about 5 minutes. After that, cement and filler which was powder materials was inserted and mixed 5 minutes. Water and half of super plasticizer was mixed about 2 minutes and remaining super plasticizer was mixed about 4 minutes after 3-minute break time. Finally, steel fiber was mixed about 4 minutes and finished. The molds were then placed on a flat table and the concrete was poured. The specimens were removed from the molds 24 hours after pouring, and the specimens were placed in a constant temperature and humidity chamber where they cured for about 48 hour

(temperature: 90°, humidity: 100%). Then, they were left in laboratory

environment until tested as shown in Fig. 3-3.

Table 4 Mixing proportion

Materials Cement Silica Fume Sand Filler Superplasticizer Water Steel

Fiber

wt.% of cement 1 0.25 1.1 0.35 0.025 to 0.04

0.185 to

0.225

2 (vol.%)

Fig. 3-4 Specimen in mold Fig. 3-5 Panels after curing

16

3.5 Test Set-up and Instrumentation

A total 18 different UHPC panels were pin loaded in direct tension by two bolts inserted in the holes. One of the bolts was fixed to the UTM (universal testing machine) while the other was attached to the cross-head of the UTM. The applied tensile load was transferred from the upper bolt. The specimens were tested under displacement control with a rate of

loading of 0.005±0.0015 mm/sec.

To measure the relative displacement between the panels and UTM, LVDT (Linearly Variable Differential Transducer) was used on each side of joint. The load was measured by the load cell of the UTM. To measure the stress distribution at the vicinity of the hole, a total of 6 joints were instrumented with strain gauges. A typical arrangement of strain gauge is given in Fig. 3-6.

1 2 3 4 5

d

1d1.5d 2d

2.5d3d

Fig. 3-7 Location of strain gauges Fig. 3-8 Test set-up

17

3.6 Test Results

This chapter presents the test results of a total of 18 single-bolted joints tested in this investigation. Results of the test are summarized as shown in Table 5. The failure modes and ultimate strength of the UHPC panels are discussed first. Then, the effect of the different parameters tested in the strength, failure mode, load-displacement response and stress distribution of the specimens are discussed in details.

Table 6 Test results

Number e/d w/d t [mm] Pult [kN] failure mode

Strength [Mpa]

Ductility Ratio

1 2 4 20 8.3 Cleavage 12.0 1.2

2 2 4 30 11.64 Cleavage 11.2 1.6

3 2 6 20 9.32 Cleavage 13.5 1.3

4 2 6 30 13.5 Cleavage 13.0 1.4

5 2 8 20 10.76 Cleavage 15.6 1.4

6 2 8 30 11.66 Cleavage 11.3 1.9

7 3 4 20 10.68 Net tension 7.7 1.2

8 3 4 30 16.72 Net tension 8.1 1.3

9 3 6 20 13.3 Cleavage 11.4 1.2

10 3 6 30 25.04 Cleavage 14.3 1.9

11 3 8 20 16.5 Cleavage 14.1 1.4

12 3 8 30 23.58 Cleavage 13.4 1.4

13 4 4 20 13.06 Net tension 9.5 1.3

14 4 4 30 15.54 Net tension 7.5 1.2

15 4 6 20 18.56 Net tension 7.9 1.3

16 4 6 30 29.46 Net tension 8.4 1.7

17 4 8 20 19.92 Cleavage 12.1 1.2

18 4 8 30 29.06 Cleavage 11.7 1.2

18

3.6.1 Failure Modes

In general the observed failure modes for single bolted joints were similar to the failure modes typically reported for metals, with the exception of the fact that metals normally exhibit considerable yielding prior to fracture, which does not take place in composites, due to its linear elastic behavior up to failure.

Among the single bolted UHPC panels tested under tensile load, two failure modes were observed, net-tension failure and cleavage failure as shown in Fig. 3-9 and Fig. 3-10.

The cleavage failure is characterized by a major crack, parallel to the panel longitudinal direction, and after that two cracks from the hole are developed along the horizontal direction, providing an additional ductility. As the load increased, the crack opened until the ultimate load was reached. Considering those mechanism can be understood the importance of the fiber orientation around the full hole, most significant in the cleavage mode due to the three cracks developed. In the net tension failure, a major crack was developed from the one of the external sides to the hole, with a center of rotation in the other external side. While other cracks also develop during increased loading, the main tensile crack controls the final load-carrying capacity.

Fig. 3-12 Net tension

failure Fig. 3-11 Cleavage failure

19

3.6.2 Load - Displacement Characteristics

A comparison of typical load-displacement relationships for the two basic modes of failure are shown in the displacement is the average reading of the two LVDT’s mounted on either side of the connection.

The behavior shown in Fig. 3-13, slipping of the connections occurred at the initial loading stage. Once the bolt slipped into bearing, all of the joints behaved linearly. For joints that failed in cleavage, the load reduction occurred gradually and the overall behavior was much more ductile than that for the net tension failure mode. At failure there was a sudden drop in the load carrying capacity of the joints that failed in net tension.

Fig. 3-14 illustrates the ductility ratio of the panels. A ductility parameter was measured as an objective criterion to evaluate the redistribution capacity of each element. The ductility ratio was obtained as the ratio between the displacements associated to the post peak load of 80% of the maximum load, and the displacements associated to the linear slope reaching the maximum load. The ductility ratio is higher for cleavage than for net tension, especially for the elements with higher width, as they develop two longer macro cracks to be compatible with the hole displacement as Fig. 3-15. Net tension failure does not seem to experience a change in the ductility ratio when the elements increase the width value.

20

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3 3.5

Loa

d [k

N]

Displacement [mm]

Net tensione = 96 mmw = 192 mmt = 20 mm

Net tensione = 72 mmw = 96 mmt = 20 mm

Cleavagee = 72 mmw =192 mmt = 20 mm

Cleavagee = 48 mmw = 144 mmt = 30 mm

0

5

10

15

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Maximum load

Load

[kN

]

Deflection [mm]d1

d2

80% of Maximum load

Macro crack

Fig. 3-17 Calculation of ductility ratio

Fig. 3-16 Typical load-deflection curves

Fig. 3-18 Macro crack in panel

21

3.6.3 Ultimate Strengths

To analyze the results of the bolted joints test, the following average ultimate strengths of each failure modes are defined as :

2

ultcleavage

PFde t

= − ⋅

(1)

( )ult

Net tensionPF

w d t− =− ⋅

(2)

where

ultP = ultimate failure load, taken as the maximum load attained

during a joints test (kN)

e = end distance taken as the distance between the center of the bolt and the panel edge (mm)

w = width of the panel

t = thickness of the panel

22

3.6.4 Effect of Ratio e/d

To illustrate the effects of variation in end distance, the ultimate load of the joints are plotted with respect to the end distance to hole diameter ratio in Fig. 3-19. The lines are given for joints with the same width and thickness. The ratio e/d was a main factor affecting the failure modes, as explained before. For wider joints, the variation of end distance has little effect on the failure mode. However, for narrow joints, the failure mode changes from cleavage failure mode to net-tension failure mode with increasing e/d ratios. This change in failure mode accompanies a change in the ultimate strength and in the load – displacement response. An increase in the e/d ratio caused an increase in the ultimate load in all the specimens tested.

The ultimate net tension strengths for the joints are plotted with respect to the e/d ratio in Fig. 3-20. The lines are given for joints with the same width and thickness. With an increasing e/d ratio the ultimate net tension strengths tend to increase up till a value of e/d=4. This suggests that increasing end-distances tend to reduce the stress concentrations associated with net stresses and therefore increase the net tension strength capacity.

23

0

5

10

15

20

25

30

35

1 1.5 2 2.5 3 3.5 4 4.5 5

Ulti

mat

e Lo

ad[k

N]

End distance / Hole diameter (e/d)

w/d: 4 - t: 20 w/d: 4 - t: 30

w/d: 6 - t: 20 w/d: 6 - t: 30

w/d: 8 - t: 20 w/d: 8 - t: 30

0.00

2.00

4.00

6.00

8.00

10.00

1 1.5 2 2.5 3 3.5 4 4.5 5

Net

tens

ion

stre

ngth

[MPa

]

End distance / Hole diameter (e/d)

w/d:4 - t:20 w/d:4 - t:30

w/d:6 - t:20 w/d:6 - t:30

w/d:8 - t:20 w/d:8 - t:30

Fig. 3-21 Effect of e/d ratio on Ultimate load

Fig. 3-22 Effect of e/dratio on Net tension strength

24

3.6.5 Effect of Ratio w/d

Variation of the width of the panels in bolted joint predominantly influences the capacity of a joint as well as the corresponding failure mode and ultimate load. The ultimate load with respect to the w/d ratio is given in Fig. 3-23. The lines are given for joints with the same end distance. For joints with relatively small end distances, the mode of failure changes from net-tension failure to cleavage failure as the w/d ratio increases. Associated with the change in failure mode is an increase in ultimate load as the w/d ratio increases.

The ultimate net tension strengths for joints with various end distances are plotted with respect to the w/d ratio in Fig. 3-24. The lines represent joints with the same end distance and thickness. The net tension strengths with large w/d ratios are relatively small compared to the net tension strengths of joints with small w/d ratios. This behavior is mainly due to the high magnitude of stress concentrations for members with large width. These stress concentration can be in the order of 4 to 6 as will be discussed. For the narrow joints, with relatively small w/d ratios, the net stress concentrations are more moderate, in the order of 2 of 3, thereby allowing higher net tension strengths to be achieved.

25

0

5

10

15

20

25

30

35

3 4 5 6 7 8 9

Ulti

mat

e Lo

ad [k

N]

Width / Hole diameter (w/d)

e/d: 2 - t: 20

e/d: 2 - t: 30

e/d: 3 - t: 20

e/d: 3 - t: 30

e/d: 4 - t: 20

e/d: 4 - t: 30

0.00

2.00

4.00

6.00

8.00

10.00

3 4 5 6 7 8 9

Net

tens

ion

stre

ngth

[Mpa

]

Width / Hole diameter (w/d)

e/d:2 - t:20 e/d:2 - t:30e/d:3 - t:20 e/d:3 - t:30e/d:4 - t:20 e/d:4 - t:30

Fig. 3-25 Effect of w/d ratio on ultimate load

Fig. 3-26 Effect of w/d ratio on Net tension strength

26

3.6.6 Effect of Thickness

For the two material thickness used in this investigation, the results indicate that the panel thickness has little effect in the overall behavior of the joints. The ultimate strength of the joints for different thickness tends to match within the range of material variability.

3.6.7 Stress Concentration Factors

Six panels were instrumented with strain gauges to determine the effect of the various parameters on the strain and stress distributions in the directions of the applied load along the net section of the joints. The strain concentration factor is equivalent to the ratio of the strain at the vicinity of the bolt hole to the strain at the gross section away from the hole.

The influence of the edge distance on the strain distribution is shown in Fig. 3-27 and Fig. 3-28. In the case of the 192mm wide joint, a panel which has 72 mm of edge distance approaches the largest value. On the other hand, in the case of the 144 mm wide joint, a panel which has 48 mm of edge distance approaches the largest value. Over all seems that the edge distance does not have obvious influence on the strain distributions.

The influence of the width of panel on the strain distribution is shown in Fig. 3-29 and Fig. 3-30. The figures illustrate that, increases in panel width increase the strain concentration factors. This is obvious in the case of wide panel ( w =192 mm) where the strain concentration factor close to bolt hole is tripled the maximum. Consequently, the strain distributions confirm that the structural efficiency of a joint is highly dependent the width of the panel.

27

0

1

2

3

4

0 0.5 1 1.5 2 2.5 3

Stra

in C

once

ntra

tion

Fact

or

Gauge location / hole diameter

e=96, w=144

e=72, w=144

e=48, w=144

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 0.5 1 1.5 2 2.5 3 3.5 4

Stra

in C

once

ntra

tion

Fact

or

Gauge location / hole diameter

e=96, w=192

e=72, w=192

e=48, w=192

Fig. 3-32 Effect of edge distance on stress distribution

Fig. 3-31 Effect of edge distance on stress distribution

28

0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5 3 3.5

Stra

in C

once

ntra

tion

Fact

or

Gauge location / hole diameter

e=96, w=192

e=96, w=144

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 0.5 1 1.5 2 2.5 3 3.5

Stra

in C

once

ntra

tion

Fact

or

Gauge location / hole diameter

e=72, w=192

e=72, w=144

Fig. 3-34 Effect of width on Stress distribution

Fig. 3-33 Effect of width on Stress distribution

29

3.7 Design Procedure

This chapter presents an analytical model proposed to describe the behavior of single bolted joints in a UHPC panels. The model is semi-empirical, consisting of two basic failure criteria to determine ultimate capacity. The first is cleavage failure, which has been observed typically for joints with small edge distances. The second is net tension failure with large edge distances.

The first criterion used in the model describes the net tension failure mode. Predict equation is based on a modified theory presented by Hart-Smith14. The theory accounts for the elastic stress concentration at loaded bolt holes in brittle, elastic, isotropic materials. For fiber reinforced composite materials, Hart Smith introduced a correlation coefficient, which can be determined experimentally, to relate the elastic stress concentration of elastic material to that for in fiber-reinforced material. The correlation coefficient accounts for the composite’s orthotropy, pseudo-yielding capability, heterogeneity, and other factors which influence the behavior of bolted joints. It should be noted that the coefficient introduced by Hart Smith is valid only for the net tension failure and therefore only those experimental results for joints that failed in net tension can be used.

The second criterion used in the model describes the cleavage failure mode. Predict equation is based on a theory of work method. By postulating a valid cleavage failure mechanism, an equation can be formed by equating the external work done by the applied loads through the displacements to the internal dissipation of energy at the failure line.

30

3.7.1 Net Tension Failure

The structural efficiency of a bolted joint can be defined as :

ult

t

PEfficiencyt w F

=⋅ ⋅

(3)

where ultP is the ultimate load of the joint, t is the thickness of

panel, w is the width of panel, tF is the tensile strength by unnotched

direct tensile test( =14.15 MPa).

The maximum stress maxσ at the most stressed bolt along a net section

subjected to an applied load P , shown in Fig., can be determined as follows:

max tenet

PKA

σ = (4)

where netA is the net area of the panel, teK is the elastic

concentration factor which is proposed by Hart Smith as follows :

( / 1)2 ( 1) 1.5( / 1)te

w w dKd w d

θ−= + − − ⋅

+ (5)

where d is diameter of hole, θ is a non-dimensional factor as given by :

0.51.5/e w

θ = − for / 1e w ≤ (6)

1θ = for / 1e w ≥

Equations (5) and (6) were developed using experimental results and theoretical results reported by several sources as described by Hart Smith.

31

For a perfectly elastic material, when the maximum stress maxσ

reaches the tensile strength of the material tF , net tension failure occurs

and the failure mode is brittle and sudden. Therefore by replacing the maximum net stress in equation (4) by the ultimate strength of the material

tF , the ultimate load of the joint can be determined as follows :

t netult

te

F APK⋅

= (7)

From equations (3) and (7), the efficiency of the joint can be shown to be :

( )2 te

w dEfficiencyw K−

=⋅ ⋅

(8)

Fiber reinforced composites do not have the yielding capability of a ductile metal, and therefore do not behave like a perfectly plastic material. However, for composite materials, some stress concentrations, could be relieved by the progressive cracking of the matrix, fiber matrix debonding and fiber pull-put, thus composite fiber materials do not behave as perfectly elastic material. Therefore, the behavior of bolted joints in UHPC is somewhere between fully plastic and fully elastic. Hart Smith introduced a linear relationship that correlates the stress concentration factor of isotropic materials teK to the stress concentration factor of fiber reinforced

composites tcK in terms of a coefficient C by the following equation:

( 1) ( 1)te teK C K− = − (9)

where:

( )tc t

ult

t w dK FP−

= (10)

32

The term tcK is the average stress concentration factor observed at

failure of the bolted joint, while teK is the corresponding elastic stress

concentration factor of a joint with the same geometry using a perfectly elastic isotropic material. Computing teK for perfectly elastic isotropic

materials, and tcK from equation (10) based on measured experimental

values, the correlation coefficient C can be determined for any fiber reinforced composite material using a limited number of experimental observations. The correlation coefficient accounts for the composite’s orthotropy, pseudo-yielding capability, heterogeneity, clearance effects, and other factors which affect the behavior of bolted joints. It should be noted that the linear relationship in equation (9) is valid only for the net tension mode of failure and therefore only experimental results for joints that failed in net tension should be used to determine the correlation coefficient.

The measured results were used to determine the correlation coefficient, based on a least squares regression analysis as shown in Fig. 3-35. respectively. For this analysis, values of the composite stress concentration factor tcK were based on equation (10) and the values teK

were based on equation (5) for the same joint geometry. In this figure, the correlation coefficient C represents the slope of the best fir straight line. Due to the nature of equation (9) the best fit curve is constrained by the point (1,1). The correlation coefficient for the single bolted joint is “-0.035”.

Using the stress concentration factor tcK and equation (8), the

efficiency of a single bolted joint in UHPC can be expressed as:

( )2 tc

w dEfficiencyw K−

=⋅ ⋅

(11)

Equation (11) can be expressed in terms of teK and C as:

( )2 [ ( 1) 1]te

w dEfficiencyw C K

−=

⋅ ⋅ ⋅ − + (12)

33

Consequently, the ultimate load of a single bolted joint in UHPC can be determined using equation (3) as follows:

nt ff tP E t w F= ⋅ ⋅ ⋅ (13)

Therefore, for a given coefficient C based on a limited number of tests and the tensile strength of a composite material, the design engineer can predict ultimate failure load of a single bolted joint of any geometry using equation (13). The predicted failure envelopes are in a good agreement with the experimental test results as shown in Fig. 3-37.

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

P tes

t

Ppredict

1:1 correspondence

With 20% difference

y = -0.0354x + 1.03

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

K tc

Kte

C = -0.035

Fig. 3-36 Correlation coefficient for single bolt test

Fig. 3-38 Experimental vs. Predicted load for net tension failure

34

3.7.2 Cleavage Failure

To derive predict equation of cleavage failure mode, the theory of work method was applied. A load computed from the work equation on the basis of an assumed failure mechanism will always be greater than or beat equal to the plastic limit load. Based on the cleavage failure lines, three failure mechanisms were postulated as Fig. 3-39. After that, write the equilibrium equations for the assumed failure mechanism and check the moments to see whether the plastic moment condition is met everywhere in the structure. A work equation can be formed for an assumed mechanism by equating the summation of expenditure of energy due to the movement of each applied load through a distance or to the summation of internal dissipation of energy.

1) Failure mechanism model 1, ( 3we≥ )

2 2( ( / 2) )cl t bP R e w t F t w F= + ⋅ ⋅ + ⋅ ⋅ (14)

2) Failure mechanism model 2, ( 2 3we

< < )

( )2cl t bwP R t F t w F= ⋅ ⋅ + ⋅ ⋅ (15)

3) Failure mechanism model 3, ( 2we≤ )

2 2( ( ) )4 2

tcl t b

w t F wP R e t F t w F⋅ ⋅= + + ⋅ ⋅ + ⋅ ⋅ (16)

where R is reduction factor (=0.1), bF is bending strength.

The predicted failure envelopes are in a good agreement with the experimental test results as shown in Fig. 3-40.

35

P P

δ

Mechanism 1.

P

δ

P

Mechanism 2.

P P

δ

Mechanism 3.

Fig. 3-41 Failure mechanism model for cleavage failure

36

0

5

10

15

20

25

30

0 5 10 15 20 25 30

P tes

t

Ppredict

1:1 correspondence

With 20% difference

Fig. 3-42 Experimental vs. Predict load for cleavage failure

37

Chapter 4. Multi Bolted Joints for UHPC Panels

4.1 Introduction

This chapter presents an experimental program to examine the behavior of multi bolted joints fabricated from UHPC panels. The investigation examined failure modes, load-displacement relationship, stress distribution and the behavior effects of various geometric parameters including width, end distance and bolt pattern with respect to the applied load.

4.2 Parameters of Study

The experimental program was designed to investigate the effects of the panel geometry. The three basic geometric parameters studied in this investigation, which influence the strength and failure mode of a joint. The parameters varied are illustrated in Fig. 4-1, and they are:

1) Ratio e/d is the ratio between the end distance e (distance between the center of the bolt and the panel edge) to the hole diameter d. The four ratios investigated were e/d=2, e/d=3, e/d=4 and e/d=5 corresponding to end distances of 48mm, 72mm, 96mm and 120mm (the hole diameter was kept constant at d = 24mm).

2) Ratio w/d is the between the width of panel w to the hole diameter d. the four ratios investigated were w/d=4, w/d=6, w/d=8 and w/d=10, corresponding to width of 96mm, 144mm, 192mm and 240mm.

3) To determine the influence of the bolt pattern, four different joint configurations were used. They are designated joints A, B, C and D as shown in Fig. 4-2.

38

From the results of single bolted joints, thickness of panels has little effect to behavior of panel. Therefore, in this test, thickness of panels takes constant value as 20mm. a pitch of 2.5 times the hole diameter, which is minimum pitch length for steel structures, was used for all joint configurations. A summary of the parameters that kept constant throughout the experimental program is given in Table 7. A total 33 multi bolted joint panels were tested under direct tension by two bolts inserted in the holes. Specimen designations and the geometric dimensions and configurations for all of the 33 connections tested are given in Table 8.

Table 9 Constant parameters

Parameter Dimension [mm]

Bolt Diameter 24

Hole Diameter 27

Thickness 20

Pitch 60

Length of panel 400

t : 20mm (constant)

Pitch : 60mm (constant)

W : widthe : edge distance

Pattern A Pattern B Pattern C Pattern D

Fig. 4-3 Variables for multi bolt test

Fig. 4-4 bolt patterns

39

Table 10 Test specimens of multi bolt test

Number Pattern Edge distance

“e” [mm]

Width “w” [mm] Strain gauge

1

A

48 144

2 48 192 ○ 3 48 240 4 72 144

5 72 192 ○

6 72 240 ○

7 96 144 ○

8 96 192 ○

9 96 240 ○ 10 120 144

11 120 192 ○ 12 120 240 13

B

48 144

14 48 192 ○ 15 48 240 16 72 96

17 72 144 ○

18 72 192 ○

19 72 240 ○

20

C

48 192 ○

21 48 240

22 72 192 ○

23 72 240

24 96 192 ○

25 96 240 ○

26 120 192 ○

27 120 240

28

D

48 144

29 48 192 ○

30 48 240

31 72 144 ○

32 72 192 ○

33 72 240 ○

40

4.3 Material Properties

A Portland cement made in Korea was used. Silica fume made in Norway was used. Established silica powder which particle-size

distribution is 45~800μm was used as aggregate. This powder contains 97%

of SiO2 and the hardness and specific gravity are 7 and 2.65 g/cm3. Filler which has medium size between cement and silica fume improves a compressive strength of concrete by increasing poured density. Furthermore, it activates hydration reaction by supplying additional Sio2

component. Australian product which has 2.2 μm of average diameter and

99% of SiO2 was used. Super plasticizer which has 1.01 g/cm3 of specific gravity is used. The most commonly used steel fiber which has 0.2mm of diameter, 13mm of length and 2500MPa of tensile strength was used.

41

4.4 Fabrication of Specimens

The mix proportion and mixing procedure used in this experiment was optimized for materials proposed1. The mix proportion of UHPC was provided in Table 11.

Concrete mixer which has 60L of capacity and 60 rpm of speed was used. Sand and silica fume were mixed first for dispersion of silica fume about 5 minutes. After that, cement and filler which was powder materials was inserted and mixed 5 minutes. Water and half of super plasticizer was mixed about 2 minutes and remaining super plasticizer was mixed about 4 minutes after 3-minute break time. Finally, steel fiber was mixed about 4 minutes and finished. The molds were then placed on a flat table and the concrete was poured. The specimens were removed from the molds 24 hours after pouring, and the specimens were placed in a constant temperature and humidity chamber where they cured for about 48 hour

(temperature: 90°, humidity: 100%). Then, they were left in laboratory

environment until tested as shown in Fig. 4-5.

Table 12 Mixing proportion

Materials Cement Silica Fume Sand Filler Superplasticizer Water Steel

Fiber

wt.% of cement 1 0.25 1.1 0.35 0.025 to 0.04

0.185 to

0.225

2 (vol.%)

Fig. 4-6 Specimen in mold

42

4.5 Test Set-up and Instrumentation

A total 33 different UHPC panels were pin loaded in direct tension by bolts inserted in the holes. Upper side of the panel was fixed to the UTM (universal testing machine) while the other side was attached to the cross-head of the UTM. The applied tensile load was transferred from the upper bolt. The specimens were tested under displacement control with a rate of

loading of 0.005±0.0015 mm/sec.

To measure the relative displacement between the panels and UTM, LVDT (Linearly Variable Differential Transducer) was used on each side of joint. The load was measured by the load cell of the UTM. To measure the stress distribution at the vicinity of the hole, a total of 15 joints were instrumented with strain gauges. A typical arrangement of strain gauge is given in Fig. 4-7 .

Fig. 4-8 Test set-up

43

4.6 Test Results

This chapter presents the test results of a total of 33 multi-bolted joints tested in this investigation. Results of the test is summarized as shown Table 13. The failure modes and ultimate strength of the UHPC panels are discussed first. Then, the effect of the different parameters tested in the strength, failure mode, load-displacement response and stress distribution of the specimens are discussed in details. The conclusions of this experimental investigation are also summarized at the end of this chapter.

Pattern A Pattern B

Pattern C Pattern D

Fig. 4-9 Location of strain gauges

44

Table 14 Test results

Number Pattern Edge

distance “e” [mm]

Width “w” [mm] Pult [kN] Failure

mode

1

A

48 144 18.88 Cleavage 2 48 192 12.98 Cleavage 3 48 240 15.84 Cleavage 4 72 144 23.92 Net tension 5 72 192 18.6 Cleavage 6 72 240 22.86 Cleavage 7 96 144 21.9 Net tension 8 96 192 22.98 Net tension 9 96 240 31.46 Net tension

10 120 144 21.6 Net tension 11 120 192 24.24 Net tension 12 120 240 30.78 Net tension 13

B

48 144 9.4 Cleavage 14 48 192 14.56 Cleavage 15 48 240 19.02 Cleavage 16 72 96 16.04 Net tension 17 72 144 21.22 Cleavage 18 72 192 19.28 Cleavage 19 72 240 25.32 Cleavage 20

C

48 192 19.22 Cleavage 21 48 240 20.6 Cleavage 22 72 192 24.28 Net tension 23 72 240 18.54 Cleavage 24 96 192 22.24 Net tension 25 96 240 36.56 Net tension 26 120 192 8.36 Net tension 27 120 240 14.82 Net tension 28

D

48 144 17.96 Cleavage 29 48 192 26.06 Cleavage 30 48 240 15.32 Net tension 31 72 144 19.76 Net tension 32 72 192 21.22 Net tension 33 72 240 25.3 Cleavage

45

4.6.1 Failure Modes

In general the observed failure modes for multi bolted joints were similar to the fail modes of single bolted joints. Each failure modes of patterns are shown in v Fig. 4-10.

Test results revealed that the predominant factors such as the edge distance of panels and the width with respect to the applied load significantly affect the failure modes. For joints with small edge distance of e/d =2, pattern A and C, the failure mode was found to be cleavage at the first of row of bolts from the edge of the panel. The failure was characterized by a propagation of a crack parallel to the applied load propagating from one end of the panel towards the bolts leading to initiation of other cracks near the net section as shown in Fig. 4-11. For other joints, with small edge distance of e/d=2, pattern B and D, cleavage failure occurred also but in different manner. The crack propagated from the first bolt near the edge of the panel to the others in the same column leading to initiation of cracks perpendicular to the load at the net section of the last bolt as shown in Fig. 4-12. As for joints with intermediate and large edge distance, for all patterns of joints configurations the failure mode was net tension at the inner row of bolts, which was measured to be the most stressed section of the panel as shown in Fig. 4-13.

46

Patt

ern

BPa

tter

n A

Patt

ern

CPa

tter

n D

e/d

= 2

, w

/d =

8M

ax L

oad

= 14

.56

kNe/

d =

2 ,

w/d

= 8

Max

Loa

d =

12.9

8 kN

e/d

= 2

, w

/d =

8M

ax L

oad

= 19

.22

kNe/

d =

2 ,

w/d

= 8

Max

Loa

d =

26.0

6 kN

Patt

ern

BPa

tter

n A

Patt

ern

CPa

tter

n D

e/d

= 3

, w

/d =

4M

ax L

oad

= 16

.04

kNe/

d =

4 ,

w/d

= 8

Max

Loa

d =

22.9

8 kN

e/d

= 4

, w

/d =

8M

ax L

oad

= 22

.24

kNe/

d =

3 ,

w/d

= 1

0M

ax L

oad

= 25

.3 k

N

Fig.

4-1

4 Ty

pica

l fai

lure

mod

es (u

p:cl

eava

ge, d

own:

net t

ensi

on)

47

4.6.2 Load – Displacement Characteristics

Typical load-displacement relationships of the cleavage failure mode for the four different joint configurations are shown in Fig. 4-15. The behaviors of the net tension failure modes for the four joint configurations are shown in Fig. 4-16.

Once the bolts slipped into bearing, all joints behaved linearly up till failure. For joints that failed in cleavage, the load reduction occurred gradually and the overall behavior was much more ductile than that for the net tension failure mode as is clear in Fig. 4-17. At failure there was a sudden drop in the load carrying capacity of the joints that failed in net tension as show in Fig. 4-18.

48

0510152025

010

2030

4050

60

Load [kN]

Disp

lace

men

t [m

m]

Patt

ern

Ae/

d =

2w

/d=8

0510152025

010

2030

4050

60

Load [kN]

Disp

lace

men

t [m

m]

Patt

ern

Ce/

d =

3w

/d=1

0

0510152025

010

2030

4050

60

Load [kN]Di

spla

cem

ent [

mm

]

Patt

ern

De/

d =

2w

/d =

6

0510152025

010

2030

4050

60

Load [kN]

Disp

lace

men

t [m

m]

Patt

ern

Be/

d =

2w

/d=8

Fig.

4-1

9 Ty

pica

l loa

d-de

flect

ion

curv

e of

cle

avag

e fa

ilure

49

051015202530

05

1015

2025

30

Load [kN]

Disp

lace

men

t [m

m]

Patt

ern

Ae/

d =

3w

/d =

6

051015202530

05

1015

2025

30

Load [kN]

Disp

lace

men

t [m

m]

Patt

ern

Be/

d =

3w

/d=4

051015202530

05

1015

2025

30

Load [kN]

Disp

lace

men

t [m

m]

Patt

ern

Ce/

d =

4w

/d =

8

051015202530

05

1015

2025

30Load [kN]

Disp

lace

men

t [m

m]

Patt

ern

De/

d =

3w

/d =

6

Fig.

4-2

0 Ty

pica

l loa

d-de

flect

ion

curv

e of

net

tens

ion

failu

re

50

4.6.3 Effect of Ratio e/d

The edge distance of panel predominantly influences the load capacity of the joint as well as the corresponding failure modes. To illustrate these effects, the ultimate load of the joints are presented in terms of the edge distance to hole diameter ratio /e d in Fig. 4-21 for the different joint configurations with respect to the applied load. The lines drawn in this figure represent joint with having the same width. The results indicate that the ultimate load increases with increasing the edge distance to the hole diameter ratio. Test results indicated also that the net efficiency of all patterns of joints tested tended to increase with increasing /e d ratio as shown in Fig. 4-22. This behavior illustrates that increasing the edge distances tends to reduce the stress concentration and therefore to increase the net tensile strength and consequently to increase the net efficiency.

51

05101520253035

01

23

45

6

Load [kN]

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

05101520253035

00.

51

1.5

22.

53

3.5

Load [kN]

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

05101520253035

01

23

45

6

Laod [kN]

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

192

mm

W=

240

mm

05101520253035

00.

51

1.5

22.

53

3.5

Load [kN]Ed

ge D

ista

nce

/ Ho

le D

ism

ater

(e/d

)

W=

144

mm

W=

192

mm

W=

240

mm

Fig.

4-2

3 Ef

fect

of e

/d ra

tio o

n ul

timat

e lo

ad

52

0

0.2

0.4

0.6

0.81

1.2

1.4

01

23

45

6

Net Efficiency

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

0

0.2

0.4

0.6

0.81

1.2

1.4

01

23

45

6

Net Efficiency

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

0

0.2

0.4

0.6

0.81

1.2

1.4

01

23

45

6

Net EfficiencyEd

ge D

ista

nce

/ Ho

le D

ism

ater

(e/d

)

W=

192

mm W

= 24

0m

m

0

0.2

0.4

0.6

0.81

1.2

1.4

01

23

45

6

Net Efficiency

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

Fig.

4-2

4 Ef

fect

of e

/d ra

tio o

n N

et e

ffici

ency

53

012345

01

23

45

6

Bearing Efficiency

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

012345

01

23

45

6

Bearing Efficiency

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

012345

01

23

45

6

Bearing Efficiency

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

192

mm

W=

240

mm

012345

01

23

45

6

Bearing EfficiencyEd

ge D

ista

nce

/ Ho

le D

ism

ater

(e/d

)

W=

144

mm

W=

192

mm

W=

240

mm

Fig.

4-2

5 Ef

fect

of e

/d ra

tio o

n B

earin

g Ef

ficie

ncy

54

0

0.2

0.4

0.6

0.81

01

23

45

6

Efficiency (Pult/t.w.Ft)

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

0

0.2

0.4

0.6

0.81

01

23

45

6

Efficiency (Pult/t.w.Ft)

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

144

mm

W=

192

mm

W=

240

mm

0

0.2

0.4

0.6

0.81

01

23

45

6

Efficiency (Pult/t.w.Ft)

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

W=

192

mm

W=

240

mm

0

0.2

0.4

0.6

0.81

01

23

45

6Efficiency (Pult/t.w.Ft)

Edge

Dis

tanc

e /

Hole

Dis

mat

er (e

/d)

Fig.

4-2

6 Ef

fect

of e

/d ra

tio o

n st

ruct

ural

effi

cien

cy

55

4.6.4 Effect of Ratio w/d

The width of panel predominantly influences the load capacity of the joint as well as the corresponding failure modes. To illustrate these effects, the ultimate load of the joints are presented in terms of the width to hole diameter ratio /e d in Fig. 4-27 for the different joint configurations with respect to the applied load. The lines drawn in this figure represent joint with having the same edge distance. The ultimate net tensile strengths of the joints with large widths were found to be relatively small in magnitude in comparison to those of the joints with small widths due to the high magnitude of the stress concentration for members with large widths. Consequently, the net efficiency of the joint was decreased by increasing the panel width, as shown in Fig. 4-28. This behavior indicates that most of the load within the joint is resisted by the material in the vicinity of the bolt.

56

05101520253035

02

46

810

12

Load [kN]

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

e =

96m

m

e= 1

20m

m

051015202530

02

46

810

12

Load [kN]

Wid

th /

hol

e Di

amet

er (w

/d)e

= 48

mm

e= 7

2m

m

051015202530

02

46

810

12

Load [kN]

Wid

th /

hol

e Di

amet

er (w

/d)

051015202530

02

46

810

12

Load [kN]W

idth

/ h

ole

Diam

eter

(w/d

)

e =

48m

m

e= 7

2m

m

Fig.

4-2

9 Ef

fect

of w

/d ra

tio o

n ul

timat

e lo

ad

57

0

0.2

0.4

0.6

0.81

1.2

02

46

810

12

Net Efficiency

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

e =

96m

m

e= 1

20m

m

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.8

02

46

810

12

Net Efficiency

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

02

46

810

12

Net Efficiency

Wid

th /

hol

e Di

amet

er (w

/d)

0

0.2

0.4

0.6

0.81

02

46

810

12

Net EfficiencyW

idth

/ h

ole

Diam

eter

(w/d

)

e =

48m

m

e= 7

2m

m

Fig.

4-3

0 Ef

fect

of w

/d ra

tio o

n N

et e

ffici

ency

58

012345

02

46

810

12

Bearing Efficiency

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

e =

96m

m

e= 1

20m

m

012345

02

46

810

12

Bearing Efficiency

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

012345

02

46

810

12

Bearing Efficiency

Wid

th /

hol

e Di

amet

er (w

/d)

012345

02

46

810

12Bearing Efficiency

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

Fig.

4-3

1 Ef

fect

of w

/d ra

tio o

n B

earin

g ef

ficie

ncy

59

0

0.2

0.4

0.6

0.81

02

46

810

12

Efficiency (Pult/t.w.Ft)

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

e =

96m

me= 1

20m

m

0

0.2

0.4

0.6

0.81

02

46

810

12

Efficiency (Pult/t.w.Ft)

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

0

0.2

0.4

0.6

0.81

02

46

810

12

Efficiency (Pult/t.w.Ft)

Wid

th /

hol

e Di

amet

er (w

/d)

e =

48m

m

e= 7

2m

m

e =

96m

me= 1

20m

m

0

0.2

0.4

0.6

0.81

02

46

810

12

Efficiency (Pult/t.w.Ft)vW

idth

/ h

ole

Diam

eter

(w/d

)

e =

48m

m

e= 7

2m

m

Fig.

4-3

2 Ef

fect

of w

/d ra

tio o

n st

ruct

ural

effi

cien

cy

60

012345

00.

51

1.5

22.

5

Bearing Efficiency

Side

dis

tanc

e /

Pitc

h (s

/p)

e =

48m

m

e= 7

2m

m

e =

96m

me= 1

20m

m

012345

00.

51

1.5

22.

5

Bearing Efficiency

Side

dis

tanc

e /

Pitc

h (s

/p)

e= 7

2m

m

e =

48m

m

012345

00.

51

1.5

22.

5

Bearing Efficiency

Side

dis

tanc

e /

Pitc

h (s

/p)

012345

00.

51

1.5

22.

5

Bearing Efficiency

Side

dis

tanc

e /

Pitc

h (s

/p)

Fig.

4-3

3 Ef

fect

of s

/p ra

tio o

n B

earin

g ef

ficie

ncy

61

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.8

00.

51

1.5

22.

5

Net efficiency

Side

dis

tanc

e /

Pitc

h (s

/p)

e =

48m

m

e= 7

2m

m

e= 1

20m

m

e =

96m

m

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.8

00.

51

1.5

22.

5

Net efficiency

Side

dis

tanc

e /

Pitc

h (s

/p)

e= 7

2m

m

e =

48m

m

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.8

00.

51

1.5

22.

5

Net efficiency

Side

dis

tanc

e /

Pitc

h (s

/p)

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.8

00.

51

1.5

22.

5

Net efficiencySi

de d

ista

nce

/ Pi

tch

(s/p

)

Fig.

4-3

4 Ef

fect

of w

/p ra

tio o

n N

et e

ffici

ency

62

4.6.5 Effect of Bolt Pattern

Test results suggest that variation of the bolt pattern of the joint has influence on the ultimate load as illustrated in Fig. 4-35. In this figure, ultimate load of pattern A and B which has two bolt hole in the panel is almost same. On the other hand, ultimate load of pattern C and D which has more bolt holes than two were 25 percent higher than pattern A and B at the same panel width and edge distance. This behavior could be affected by the stress concentration. In the case of same width and edge distance, applied load can be dispersed by increasing the number of bolts. Therefore, ultimate load can be increased by changing the pattern of bolts.

In Fig. 4-36, changing the width of the panel has little influence on the structural efficiency. However, structural efficiency was increased with increasing e/d ratio. This is obvious in the case of large edge distance (e/d = 5). Moreover, in the case of same e/d ratio, structural efficiency for pattern D was higher than other patterns.

0

5

10

15

20

25

30

0 1 2 3 4 5

Load

[kN

]

Bolt Patterns

Fig. 4-37 Effect of bolt patterns on ultimate load

63

0

1

2

3

4

5

0 1 2 3 4 5 6

Effic

ienc

y

Edge distance / Hole diameter (e/d)

Pattern A

Pattern BPattern D

0

1

2

3

4

5

0 1 2 3 4 5 6

Effic

ienc

y

Edge distance / Hole diameter (e/d)

Pattern A

Pattern B

Pattern D

0

1

2

3

4

5

0 1 2 3 4 5 6

Effic

ienc

y

Edge distance / Hole diameter (e/d)

Pattern APattern B

Pattern D

Fig. 4-38 effect of bolt pattern on efficiency

w = 10

w = 8

w = 6

64

4.6.6 Stress Concentration Factors

Selected panels were instrumented with strain gauges for the following two main purposes: 1) to determine the load distribution among the bolts 2) to determine the effect of variables on the stress and strain distribution in the direction of the applied load along the net section of the joint at the most stressed row of bolts. The strain distribution for selected panels for different joint configurations are shown in Fig. 4-39. The strain concentration factor was determined as the ratio of the measured strain at the most stressed row of bolts to the strain of the panel measured at the gross section away from the bolt holes.

Fig. 4-40 illustrated that in general, increasing the panel’s width increased the strain concentration factor since the applied stress at the gross section away from the bolt holes must be reacted by the row of bolts, where most of the load is resisted by the material in the vicinity of the hole. This is shown in the wide panels (w = 192mm). The strain distributions confirm that the structural efficiency of a joint is highly dependent on the width of the panel. However, edge distance does not have obvious influence on the strain distributions.

65

0123456

-1.5

0.5

2.5

4.5

6.5

W =

192

mm

W =

240

mm

Patte

rn A

01234

01

23

45

6

Patte

rn B

W =

192

mm

W =

240

mm

W =

144

mm

01234567

01

23

45

6

Patte

rn C

W =

192

mm

024681012

-1.5

0.5

2.5

4.5

6.5Pa

ttern

D

W =

240

mm

W =

192

mm

Fig.

4-4

1 Ef

fect

of w

idth

on

stre

ss d

istri

butio

n

66

4.7 Design Procedure

This chapter presents an analytical model proposed to predict the ultimate load and the mode of failure of multi bolted UHPC panels. The model is based on rational analysis and utilizes the results of the experimental program conducted in this investigation. Test results showed that there are two primary failure modes for multi bolted joints. The first is net tension, which has been observed typically for joints with medium and large edge distances. The second is cleavage failure for joints with small edge distances. According, the proposed model consists of two basic failure criteria to determine the ultimate capacity and the failure mode of the joints.

The analysis discussed in this chapter is based on the stress concentration factor and work method like as analysis of single bolted joints.

67

4.7.1 Net Tension Failure

For a narrow strip of bolts, as in pattern B in this experimental program, the elastic concentration factor teK could be determined using

the equation (5). The equation (5) applies only to a single column of bolts. But for the case of multiple columns of bolts, Hart Smith suggested that the elastic stress concentration factor teK is given by :

2 2.41 ( / 1)1 [1 ( ) ] ( 1) 1.5( / 1)te

d p p dKp d p d

θ−= + − + − −

+ (17)

where p is the pitch.

Based on the limited number of panels tested in this program, test results indicated that there is interaction and load sharing among the bolts in pattern A, C and D. Equation (17) could be also used for these patterns of joints using the pitch defined in terms of the width, as follows:

wPn

= (18)

where n is the number of bolts in a row.

Consequently, equation (17) can be written as:

2 2.41 ( / 1)1 [1 ( ) ] ( 1) 1.5( / 1)te

nd w w ndKw nd w nd

θ−= + − + − −

+ (19)

where θ is defined as:

0.51.5( )n e

w

θ = −⋅

(20)

The correlation coefficient and composite stress concentration factor can be determined using equation (9) and (10). From the Fig. 4-42, the correlation coefficient is “0.6694”.

68

Equation (3) can be expressed in terms of C and tcK , which can be

determined based on the joint configuration as given in equation (17) and (19), as follows:

[ ( 1) 1]net

te

AEfficiencyC K t w

=⋅ − + ⋅ ⋅

(21)

Consequently, the ultimate load of a multi bolted joint in a UHPC can be determined using equation (3) as follows:

nt ff tP E t w F= ⋅ ⋅ ⋅ (22)

The predicted failure envelopes are in a good agreement with the experimental test results as shown in Fig. 4-43.

69

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

P tes

t

Ppredict

y = 0.6694x + 0.3

0

1

2

3

4

0 0.5 1 1.5 2 2.5 3

K tc

Kte

C = 0.6694

Fig. 4-44 Correlation coefficient for multi bolt test

Fig. 4-45 Experimental vs. Predicted load for net tension failure

70

4.7.2 Cleavage Failure

To derive predict equation of cleavage failure mode, the theory of work method was applied as cleavage failure equation of single bolted joint. From the same flow of chapter 3.7.2, failure mechanism model for each patterns of bolts were assumed as shown Fig. 4-46. Consequently, predict equations for each patterns are:

1) Pattern A :

[( ) 2 ]2cl t b

w pP R t F e t F−= ⋅ ⋅ + ⋅ ⋅ ⋅ (23)

where R is reduction factor (=0.19), bF is bending strength,

2) Pattern B :

[ 2 ]cl t bP R w t F t w F= ⋅ ⋅ + ⋅ ⋅ ⋅ (24)

where R is reduction factor (=0.05),

3) Pattern C :

3[ ( 2 ) 3 ]4cl t bP R w p t F e t F= − ⋅ ⋅ + ⋅ ⋅ ⋅ (25)

where R is reduction factor (=0.15),

4) Pattern D :

[( ) 4( ) ]cl t bP R w p t F e p t F= − ⋅ ⋅ + + ⋅ ⋅ (26)

where R is reduction factor (=0.06),

The predicted failure envelopes are in a good agreement with the experimental test results as shown in Fig. 4-47.

71

P/2

P/2

P/2

P/2

δ

P/2

P/2

P/2

δ

P/3

P/3

P/3

P/3

P/3

P/3

δ

P/4

P/4

P/4

P/4

P/4

P/4

δ

Fig.

4-4

8 Fa

ilure

mec

hani

sm m

odel

for c

leav

age

failu

re

72

0

5

10

15

20

25

30

0 5 10 15 20 25 30

P tes

t

Ppredict

Fig. 4-49 Experimental vs. Predicted load for cleavage failure

73

Chapter 5. Conclusions

This study planned experimental programs and proposed analytical methods to predict the ultimate load for each failure modes.

In the chapter 3, single bolted joint for UHPC panel was analyzed in the experimental way and analytical way. Based on the tests undertaken in this test and the range of variables evaluated, the following conclusions can be drawn.

(1) Two types of failure modes were observed in the tension test: a cleavage failure and a net tension failure.

(2) Increasing the edge distance, width and thickness is very effective in enhancing the strength of panels.

(3) The failure modes were affected by correlation between edge distance and width of panel.

(4) The strain distributions confirm that the structural efficiency of a connection is highly dependent the width of the panel. The panel width is the dominant geometric variable affecting the efficiency of a joint.

(5) The effects of joint edge distance and thickness on the stress concentrations are less than the effect of member width. Stress concentrations tended to decrease with increasing edge distance and were negligibly affected by the member thickness.

(6) The prediction equations developed in this study to predict the loads leading to failure either by cleavage and net tension were in good agreement with test results. On average, the predicted loads were within 20% of the experimentally determined values.

74

In the chapter 4, multi bolted joint for UHPC panel was analyzed in the experimental was and analytical way. A total of 33 multi bolted joint of four different configurations were tested to determine the effects of various geometric parameters such as; width, edge distance and bolt patterns. Based on the experimental investigation the following conclusions can be made;

(1) Two types of failure modes were observed in the tension test; a cleavage failure and a net tension failure.

(2) Load-Displacement behavior is linear regardless of the failure mode before crack occured.

(3) joint with net tension failure mode experienced a sudden drop in the load carrying capacity, while joints that failed by cleavage mode experienced a gradual decrease in the load carrying capacity.

(4) For relatively small edge distance, the failure mode was cleavage. For intermediate and large edge distance, the failure mode was net tension.

(5) Variation of the bolt pattern affected on the ultimate load of panel.

(6) For the same panel width, increasing the number of bolts in a column or in a row increased the efficiency of the joint. This is mainly due to the mechanism of cleavage failure mode.

(7) The magnitudes of the strain concentrations along the net section perpendicular to the applied load are highly influenced by the width of the joint. These strain concentrations increase by increasing the width, since the stressed at the section away from the bolt hole is resisted by the material within the vicinity of the bolt.

(8) The proposed model predicted the ultimate loads of the panels with good degree of accuracy.

75

References

1. Kang, S. H. and Hong, D. G., “Performance of Fresh and Hardened Ultra High Performance Concrete without Heat Treatment”, Journal of the Korea Concrete Institute, Vol. 26(1), 2014, pp.23-34.

2. Fehling, E., Schmidt, M., Walraven, J., Leutbecher, T. and Frohlich, S. Ultra-High Performance Concrete UHPC, 2014, Ernst&Sohn.

3. Timoshenko, S. P. and Goodier, J. N., Theory of Elasticy, Third Edition, Mc-GrawHill, New York, 1951, pp.90-97.

4. Lekhnitskii, S. G., Anisotropic Plates, Science Publishers, New York 1968.

5. Bickley, W. G., “The Distribution of Stress Round a Circular Hole in a Plate”, Philosophical Transactions of the Royal Society, Series A, Vol. 227, 1928, pp.383-415.

6. De Jong, T. “Stresses Around Pin-Loaded Holes in Elastically Orthotropic or Isotropic Plates”, Journal of Composite Materials, Vol. 11, 1977, pp.313-331.

7. Camacho Torregrosa, E. E. (2013) “Dosage optimization and bolted connections for UHPFRC ties”, In partial fulfillment of the Requirement for the Degree of Doctor of Sciences UPV, The university of Valencia.

8. Collings, T. A., “The Strength of Bolted Joints in Multi-Directional CFRP Laminates”, Composties, Vol.8, No.1, Jan. 1977, pp.43-55

9. Rosner, C. N. (1992) “Single-Bolted Connections for Orthotropic Fibre-Reinforced Composite Structural Members”, In partial fulfillment of the Requirement for the Degree of Master of Science in Civil Engineering, The university of Manitoba.

76

10. Hassan, H. (1993) “Study of ferrocement bolted connections for structural applications”, In partial fulfillment of the Requirement for the Degree of Doctor of Philosophy in Civil Engineering, The university of Michigan.

11. Hassan, N. K. (1994) “Multi-Bolted Connections for Fiber Reinforced Plastics Structural Members”, In partial fulfillment of the Requirement for the Degree of Doctor of Philosophy Faculty of Engineering, The Ain Shams university.

12. Agarwal, B. L. “Behaviour of Multifastener Bolted Joints in Composite Materials”, AIAA 18th Aerospace Sciences Meeting, Pasadena, California, Paper No. 80-0307, Jan., 1980.

13. Ramkumar, R. L. “Bolted Joint Design, Test Methods and Design Allowables for Fibrous Composites”, ASTM STP 734, C.C. Chamis Ed., American Society for Testing and Materials, 1981, pp.376-395.

14. Tang, S., “Failure of Composite Joints Under Combined Tension and Bolt Loads”, Journal of Composite Materials, Vol.15, July 1981, pp.329-335.

15. Hart-Smith, L. J. (1980) “Mechanically-Fastened Joints for Advanced Composites Phenomenological Considerations and Simple Analyses”, Proceedings of the Fourth Conference on Fibrous Composites in Structural Design, San Diego, California, pp.543-574.

16. Maniatis, I. (2006) “Numerical and Experimental Investigations on the Stress Distribution of Bolted Glass Connections under In-Plane Loads”, In partial fulfillment of the Requirement for the Degree of Doctor of Engineering in Faculty of Civil and Surveying, The Technical university of Munich.

17. NPCA, Guide to Manufacturing Architectural Precast UHPC Elements, NPCA White Paper.

18. Chen, W. F. and Sohal, I. (1995) Plastic Design and Second-Order Analysis of Steel Frames, Springer Verlag New York.

77

국 문 초 록

최근, 비정형 디자인 기술이 발전함에 따라 그에 따른

건설기술과 재료 어플리케이션이 늘어가고 있는 추세이다.

전형적으로, 금속 또는 기존 콘크리트 등이 비정형 파사드의

재료로써 사용되고 있으나, 이러한 재료들을 비정형 건축에

적용하는데 있어서, 복잡한 시공과정과 부재 제작과정이 필요로

된다. 이는 곧, 시공비용의 증가를 야기하는 중요한 해결과제로

고려된다. 따라서 이러한 재래식 공법의 개선을 위하여 높은

유동성으로 우수한 성형성을 보이는 초고성능 콘크리트 (UHPC)를

비정형 건축을 위한 하나의 대안으로 제시할 수 있다.

초고성능 콘크리트는 높은 압축강도와 강섬유의 혼입으로 인한

인장강도의 향상, 그리고 뛰어난 내충격성을 가진 외장재 패널에

매우 적합한 재료이나, 가격이 비싼 단점을 가지고 있다. 이러한

비용적인 단점을 해결하기 위해서 구조적인 접근이 아닌 시공적인

접근이 필요하다. 즉, 현장 타설이 아닌 공장에서 대량으로 부재를

제작하는 프리캐스트 형식을 취하고, 시공현장에서는 간단한 볼트

접합으로 외장재를 건물에 설치함으로써 시공과정의 비용을 대폭

감소 시킬 수 있다.

그러나, 아직 외장재로 쓰이는 초고성능 콘크리트 패널에 대한

볼트접합 연구는 미비한 상황이다. 따라서, 이번 연구에서는

초고성능 콘크리트 패널의 볼트접합에 대한 역학적 거동의 이해와

디자인 가이드라인 설계에 목표를 두고 실험을 진행하였다. 총

3가지의 실험, 싱글볼트, 멀티 볼트, 그리고 지압강도실험을

78

진행하여 기하학적 변수가 역학적 거동에 미치는 영향을

파악하였다. 또한, 이를 바탕으로 응력집중계수와 work method을

사용하여 각각의 파괴모드에 대한 예측 강도식을 제시하였으며,

예측값을 실험값과 비교함으로써 그 타당성을 확인할 수 있었다.

따라서, 이번 연구의 결과를 통해 외장재로 쓰이는 초고성능

콘크리트 패널의 볼트접합에 대한 가이드 라인 제안이 가능할

것으로 예상된다.

주요어 : 볼트접합, 인장 거동, 파괴모드, 예측 강도식, 응력 집중,

UHPC

학 번 : 2013-23028

79

APENDIX

1. Bearing Strength Test

In the connection of precast panels, bearing resistance of joints is important component for structural efficiency. In the case of cladding precast member, panel resist self load by bearing resistance in the joints. Therefore, determining bearing strength of UHPC is important factor.

The experimental program was designed to investigate the effects of the panel geometry. The two basic geometric parameters studied in this investigation, which influence the strength and failure mode of a joint. The parameters varied are illustrated in Fig. A- 1, and they are:

1) Diameter of bolts, boltD : 20 mm, 24 mm, 27 mm, 30 mm

2) Thickness of panel , t : 15 mm, 20 mm, 30 mm

A total 36 UHPC panels were tested under compression by a bolt inserted in the hole. Fig. A- 3 show the specimen of bearing strength test, and Fig. A- 4 show the test set-up.

Width : 200 mm

Leng

th :

200

mm

50mm

d

Fig. A- 2 Parameters of bearing strength test

80

Table 15 show results of bearing strength test. Fig. shows failure mode of bearing failure. Fig. illustrates that the effect of diameter of bolts.

Table 16 Test results

The ultimate bearing capacity of a joint is obviously dependent on the bearing strength of the material. The bearing strength of a material brF can

be determined as:

ultbr

bolt

PFt d

=⋅

(A-1)

boltD [mm] t [mm] ultP [kN] Strength [MPa]

20 15 58 193 20 81 202 30 156 260

24 15 54 150 20 93 193 30 169 235

27 15 53 131 20 78 144 30 143 176

30 15 56 124 20 81 135 30 176 196

Fig. A- 5 Panel after curing Fig. A- 6 Test set-up

81

The results illustrated that behavior of bearing failure was ductile as shown as Fig. A- 7. Also, the ultimate strength of panel tended to decrease with increasing diameter of bolt. The ultimate load was increased with increasing thickness of panel.

Bearing failure mode is related to the capacity of the UHPC material in transferring the high compressive stresses near the hole. A lower bound value for this failure mode can be obtained by assuming a constant pressure distribution around the perimeter of the hole, equal to the compressive strength 'cf of the material. The effect of steel fiber is neglected. The

following expression relates the external maximum load brP to the resistance

of the UHPC material along the hole perimeter:

'br cP R d t f= ⋅ ⋅ ⋅ (A-2)

Where R is reduction factor (=0.7), d is hole diameter, t is thickness of the specimen and 'cf is compressive strength of the material.

This expression was checked against the experimental results as shown as Fig. A- 7. The ratio between the predicted loads and actual failure loads were 0.5 to 1.0, for the all of specimens.

Fig. A- 8 Failure shape of bearing failure

82

100.00

120.00

140.00

160.00

180.00

200.00

220.00

240.00

260.00

280.00

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Stre

ngth

[MPa

]

Diameter of Bolt [mm]

t = 15 mm

t = 20 mm

t = 30 mm

0

20

40

60

80

100

120

140

160

0 1 2 3 4

Load

[kN

]

Displacement [mm]

t = 15 mm / Dbolt = 20 mm

t = 30 mm / Dbolt = 24 mm

t = 30 mm / Dbolt = 27 mm

Fig. A- 9 Effect of bolt diameter on Strength

Fig. A- 10 Typical load-deflection curve of bearing test

0

40

80

120

160

200

0 40 80 120 160 200

P tes

t[k

N]

Ppredict [kN]

within 20% difference

1:1 correspondence

Fig. A- 7 Experimental vs. Predicted load for bearing failure

83

2. Load-Displacement Curve of Single Bolt test

05101520253035

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88

3. Load-Displacement Curve of Multi Bolt Test

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