Master Thesis
Development of an efficient structural system for buildings of glass fibre reinforced
plastic
Main Report
Author:
Aslak ClarkeJensen
Supervisor:
Henrik Almegaard
Co-supervisors:
JanSøndergaard VickiThake
A thesis submitted in fulfilment of the requirements for the degree of MSc
in
Civil Engineering
May 2015
This report has been conducted as a final project of the Master of Science in Civil Enginnering Degree, within the specialization of Building Structures, at The Technical University of Den- marks’ Department of Civil Enginnering.
The thesis corresponds to five months of work, performed within the period from 5th of January 2015 to 5th of June 2015, and is credited 30 ECTS points.
In addition to this report, a Experimental Report is also submitted as part of this thesis, which is to be read in relation to this report.
The project has been carried out in cooperation with KHR Arkitekter, The Royal Danish Academy of Fine Arts, School of Architecture and Fiberline Composites.
The project was supervised by:
Supervisor Henrik Almegaard Associate Professor Technical University of Denmark
Co-supervisors Jan Søndergaard
Professor / Partner
Vicki Thake Industrial PhD student
KHR Arkitekter &
The Royal Danish Academy of Fine Arts, School of Architecture
The author of the report is Aslak Clarke Jensen
s093374
Date:
Signed:
Glass fibre reinforced plastics are increasingly winning impact in the building industry and while particularly being used for fa¸cade elements and decking systems, its potential as a structural material is being realised as its usage grows. However, structural design is challenging as no commonly recognized rules and regulations exist, forcing producers of structural profiles to issue design guides to assist designers. While these guides are a great help, they are limited to the knowledge that exists and only applicable for regular structures and the profiles of the producer.
This report is focused around a case structure, being a prototype for a potential building system of glass fibre reinforced plastic. A structural analysis of parts of this case structure is performed in order to establish a feasible and structurally capable rigid frame as a repeated element for the case structure. The rigid frame is designed to be constructed either with bolted or adhesive connections. In order to do this, existing guides and manuals of profile design are studies, as well as theoretical research of bolted and adhesive connections, in order to establish a safe design approach for the frame. Whereas profile and bolted connection design are well established disciplines and adaptation of the materials behaviour is the primary challenge, adhesive connections is a niche application in civil engineering, with very limited guidance and reference work. To ensure a safe approach, two independent methods are investigated and verified against a Finite Element Model and the final design is required to comply with both methods.
The goal of the analysis was not only to design a rigid frame purely of GFRP, but also to gather experience about structural design of the material. It was found that the major challenge lies in utilizing the strengths of the material, to avoid that low stiffness and long term shear capacity becomes critical for the design. It is found that designing in order to fully utilize the high axial strength of the material is hardly realistic for a frame structure. Connection design was likewise found to be a critical aspect for the structure, but it was found that the capacity of bolted connections can potentially be largely increased by including effects of the anisotropic stiffness.
For the adhesive connection, it was found that one of the investigated approaches results in much larger capacity than the other, also showing a potential for larger capacity verifications if more detailed and broadly accepted approaches are developed. Suggestions for improvements of the designed frames are given, as well as general recommendations for future structural design of GFRP.
Parallel to the work of this report, experimental research was carried out as part of this thesis, to verify the results and assumptions of the connection design from the analysis. Description and results from this is found in the separate Experimental Report.
Abstract ii
Contents iii
List of Figures iv
List of Tables v
Abbreviations vi
1 Introduction 1
1.1 Project description . . . 2
1.2 Limitations . . . 2
2 Theory 4 2.1 Reinforced plastic composites . . . 4
2.1.1 Mechanical properties . . . 5
2.1.2 Comparison to other materials . . . 9
2.1.3 Manufacturing by pultrusion . . . 10
2.1.4 Design consideration . . . 12
2.2 Lower Bound Theorem . . . 14
2.3 Structural design with GFRP . . . 15
2.3.1 Safety concept and coefficients . . . 15
2.3.2 Design of structural members . . . 18
2.4 Bolted connection design . . . 23
2.4.1 Force distribution . . . 24
2.4.2 Capacity determination . . . 29
2.5 Adhesive joints . . . 32
2.5.1 Approach 1: Eurocomp Design Code and Handbook . . . 35
2.5.2 Approach 2: Vall´ee, Adhesive Bonded Lap Joints of Pultruded GFRP Shapes . . . 38
2.5.3 Comparison of approaches . . . 41
3 Structural Analysis 45 3.1 The case structure . . . 46
3.1.1 Building layout . . . 46
3.1.2 Structural system . . . 48
3.1.3 Frame structure . . . 52 iii
3.1.4 Materials and profiles . . . 54
3.2 Loads . . . 56
3.2.1 Load cases used in model . . . 56
3.2.2 Load combinations . . . 57
3.3 Strength verification of frame . . . 58
3.3.1 Behaviour of frame structure . . . 58
3.3.2 Beam members . . . 62
3.3.3 Column members . . . 65
3.3.4 Supporting poles . . . 67
3.3.5 Frame member evaluation . . . 69
3.4 Bolted Connection Design . . . 71
3.4.1 Design Considerations . . . 72
3.4.2 Bolted Connection type 1: Gusset plate connection, without profile cut . 75 3.4.3 Bolted Connection type 2: Internal connection structure with diagonal cut 78 3.4.4 Bolted Connection type 3: Internal angled and diagonal cut . . . 81
3.4.5 Bolted Connection type 4: Carpenter inspired connection . . . 86
3.4.6 Comparison of investigated connections . . . 90
3.5 Adhesive Connections Design . . . 93
3.5.1 Design Considerations . . . 93
3.5.2 Method Verification by Finite Element Model . . . 94
3.5.3 Adhesive Connection Design and Capacity Determination . . . 104
3.6 Sub conclusion for the structural analysis . . . 114
4 Discussion 116 4.1 Implementation of the developed structural system . . . 117
4.2 Evaluation of the efficiency of the developed structural system . . . 118
4.3 Design suggestions for optimizing utilization of structural properties . . . 120
4.3.1 Improvements for structural system . . . 120
4.3.2 Optimization of profiles . . . 121
4.3.3 Suggestions for connection design . . . 123
4.4 Recommendations and considerations for structural design with GFRP . . . 124
5 Conclusion 126 5.1 Suggestions for further research . . . 127
6 Bibliography 129 6.1 Books . . . 129
6.2 Articles . . . 130
6.3 Reports and Theses . . . 130
6.4 Codes and Standards . . . 130
A MatLab-script for bolted connection 132
B Lisp code to get bolt coordinates 136
C MatLab-script for adhesive connection Approach 1 137
D MatLab-script for adhesive connection Approach 2 139
E Fiberline profile data sheets 142
F Loads on structure 149
G Sikadur330 adhesive data sheet 152
2.1 Stress-Strain curve for FRP in tension . . . 6
2.2 Fibre roving (left) and mat (right) . . . 7
2.3 Pultrusion machine . . . 11
2.4 Illustration of impregnation method . . . 12
2.5 Effect of shear deformations . . . 19
2.6 Estimated shear area . . . 20
2.7 Critical stress for Rankine and Euler column . . . 22
2.8 Example connection for illustration of method . . . 25
2.9 Force distribution from moment . . . 26
2.10 Force distribution from moment and vertical force . . . 26
2.11 Force distribution from moment when all forces are parallel to the direction of pultrusion . . . 27
2.12 Force distribution dependent on E-moduli . . . 28
2.13 Minimum distances for bolted connection . . . 30
2.14 Failure mode for bolted connection 1 and 2 . . . 31
2.15 Failure mode for bolted connection 3 and 4 . . . 31
2.16 Failure mode for bolted connection 5 . . . 31
2.17 Exaggerated deformation of adhesive joint . . . 33
2.18 Failure modes of adhesive joint . . . 34
2.19 Double lap notation . . . 34
2.20 Half lap length plot . . . 36
2.21 Failure mode of double lap bond . . . 39
3.1 Building: Concept model . . . 47
3.2 Building: Plan view . . . 47
3.3 Building: Elevation . . . 47
3.4 Foundation layout . . . 48
3.5 Regular frames in structural system . . . 49
3.6 Special structural elements in structural system . . . 50
3.7 Structural system with added roof and floor . . . 51
3.8 Structural system with added fa¸cades . . . 52
3.9 Isometric view of frame . . . 53
3.10 Frame layout . . . 54
3.11 Profiles . . . 55
3.12 Numbering of beams and nodes in frame . . . 58
3.13 Frame displacement . . . 58
3.14 Moment curve for frame . . . 61
3.15 Shear curve for frame . . . 61 vi
3.16 Axial force curve for frame . . . 61
3.17 Stress distribution and locations with particular need for transverse support . . . 62
3.18 Shear and normal stress distribution in MD+Strip(6mm) profile . . . 65
3.19 Isometric view of foundation concept . . . 68
3.20 Cut concepts . . . 71
3.21 Cut concepts . . . 73
3.22 External gusset plate solutions concepts . . . 74
3.23 Internal gusset plate solutions concepts . . . 74
3.24 Concept of connection type 1 . . . 75
3.25 Layout of connection 1 . . . 75
3.26 Resulting forces in connection 1 disregarding differences in E-modulus . . . 76
3.27 Resulting forces in connection 1 taking differences in E-modulus into account . . 76
3.28 Resulting forces in connection 1 following pultrusion . . . 77
3.29 Concept of connection type 2 . . . 79
3.30 Layout of connection 2 (d=18mm) . . . 79
3.31 Resulting forces in connection 2 disregarding differences in E-modulus . . . 80
3.32 Resulting forces in connection 2 taking differences in E-modulus into account . . 80
3.33 Resulting forces in connection 2 following pultrusion . . . 80
3.34 Concept of connection type 3 . . . 82
3.35 Layout of connection 3 . . . 82
3.36 Connection 3; Equilibrium sketch . . . 82
3.37 Connection 3; Forces on connection . . . 83
3.38 Force distribution with equilibrium . . . 84
3.39 Angle geometry . . . 85
3.40 Carpenter joint as inspiration of connection . . . 86
3.41 Beam of the carpenter inspired joint . . . 86
3.42 Carpenter inspired joint before assembly . . . 87
3.43 Assembled carpenter inspired joint . . . 87
3.44 Bolts in carpenter inspired joint . . . 88
3.45 Resulting forces in connection 4 disregarding differences in E-modulus . . . 89
3.46 Resulting forces in connection 4 taking differences in E-modulus into account . . 89
3.47 Resulting forces in connection 4 following pultrusion . . . 89
3.48 Setup of Finite Element Model. . . 94
3.49 Layout of finite element, CPS4. . . 95
3.50 Path on Finite Element Model. . . 95
3.51 Setup of Finite Element Model. . . 96
3.52 Stress distribution for different mesh refinement. . . 96
3.53 Zoom of edge of stress distribution for different mesh refinement. . . 97
3.54 Mesh of Finite Element Model. . . 97
3.55 Shear stress in adhesive based on analytical and numerical calculations. Lap length, L=25 to L=100. . . 99
3.56 Shear stress in adhesive based on analytical and numerical calculations. Lap length, L=200 and L=400. . . 100
3.57 Out-of-plane stress in adhesive based on numerical calculations. Lap length, L=25 to L=100. . . 101
3.58 Out-of-plane stress in adhesive based on numerical calculations. Lap length, L=200 and L=400. . . 102
3.59 Adhesive connection design concept . . . 104
3.60 Forces acting on connection. . . 105
3.61 Illustration of force distribution of moment in adhesive connection . . . 106
3.62 Isometric view of the angle connection to the web of the profiles for the beam member . . . 107
3.63 Illustration of double lap joint for horizontal force component for horizontal mem- ber of frame . . . 107
3.64 Illustration of double lap joint for vertical force component for horizontal member of frame . . . 108
3.65 Shear stress distribution in beam element . . . 108
3.66 Shear stress distribution in beam element . . . 109
3.67 Illustration of stresses acting in adhesive joint . . . 109
3.68 3D plot of shear stresses in adhesive layer of beam joint . . . 110
3.69 Illustration of glued locations . . . 112
3.70 Adhesive connection design concept . . . 114
3.71 Concepts of chosen connections . . . 115
4.1 Illustration of determined profile and optimized versions . . . 121
4.2 Illustration of determined profile and optimized versions . . . 124
F.1 Wind zones . . . 151
2.1 Mechanical properties of reinforcing and matrix material . . . 6
2.2 Mechanical properties of GFRP . . . 8
2.3 Mechanical property comparison . . . 9
2.4 Typical values for parameters of adhesive joint capacity . . . 35
2.5 Values forκtau . . . 41
2.6 Values forκsigma . . . 41
3.1 Properties of profiles . . . 55
3.2 Load summary . . . 56
3.3 Load combinations . . . 57
3.4 Results for element 2 from analysis of frame for all profiles. . . 59
3.5 Results for element 1 and 3 from analysis of frame for all profiles. . . 60
3.6 Results for element 4-5-6 from analysis of frame for all profiles. . . 60
3.7 Relevant cross-section properties for horizontal members. . . 63
3.8 Stresses in element 4-5-6 . . . 63
3.9 Stresses in element 4-5-6 . . . 64
3.10 Relevant properties for column members. . . 66
3.11 Stresses in element 2. . . 66
3.12 Stresses in element 2. . . 67
3.13 Results for crushing of frame by support . . . 69
3.14 Summary of structural investigation of profiles . . . 70
3.15 Loads on connection . . . 71
3.16 Utilization of bearing capacity of hardest loaded bolt of connection type 1 . . . . 78
3.17 Utilization of bearing capacity of hardest loaded bolt of connection type 2 . . . . 81
3.18 Utilization of bearing capacity of hardest loaded bolt of connection type 3 . . . . 84
3.19 Utilization of bearing capacity of hardest loaded bolt of connection type 2 . . . . 90
3.20 Connection comparison . . . 91
3.21 Mechanical properties of adhesive Sikadur330 . . . 93
3.22 Comparison between FEA and analytical results . . . 103
3.23 Force distribution of moment in adhesive connection . . . 105
3.24 Stresses in adhesive connection . . . 110
3.25 Stresses in adhesive connection, including gluing to ribs of profiles . . . 112
4.1 Connection comparison . . . 119
4.2 Properties of determined profile and optimized versions . . . 121
F.1 Wind pressure . . . 151
F.2 Horizontal wind pressure coefficients . . . 151 ix
FRP: Fibre ReinforcedPolymer GFRP: GlasFibre Reinforced Plastic SLS: Serviceability Limit State ULS: Ultimate Limit State FEA: FiniteElement Analysis FEM: FiniteElement Model
x
Introduction
Fibre reinforced polymers (FRP) are increasingly becoming implemented in structural engi- neering world wide. While initially found appropriate predominantly for structures with special requirements in regards to corrosion protection or electromagnetic transparency, it is starting to be used actively as load bearing material in new buildings and bridges, as well as being used for strengthening of existing structures, without these special circumstances being present.
As recognized structural norms and codes are being developed, together with improvements in production methods, price, properties and availability, it can be predicted that FRP composites are about to enter a stage, where they become regarded as a routine structural material, rather than a niche application.
From a structural point of view, FRP possesses great potential, with a strength parallel to the main fibre direction that is comparable to that of steel, while having less than the quarter of the density. However, due to relatively low stiffness and reduced strength in the other directions, this potential is rarely utilized, as design becomes dominated by the weaknesses of the material rather than the strengths. If FRP is to truly compete with conventional structural materials and its potential be reached, traditions for how to design in order to utilize the strengths of the material must be developed, together with recognized structural design codes to guide this design.
This thesis seeks to contribute to the development of such a tradition and to identify where there is a particular need for further development of existing guides and codes.
1
1.1 Project description
The work of this thesis was initiated as part of an existing research project by KHR Arkitek- ter and The Royal Danish Academy of Fine Arts, School of Architecture in cooperation with Fiberline Composites. The objective of this research project is to illustrate the architectural opportunities of FRP, and concretely develop a prototype for a possible future building sys- tem. The ambition of this prototype building, and to which this thesis seeks to contribute, is to further enable the use of FRP as a construction material in the building sector. This prototype building will be the case structure investigated in this report, allowing the structural considerations to be based around an actual structure, and these consideration to be utilized in the final structural design of the building. The work of this thesis has hereby been part of a close multidisciplinary collaboration between engineering, architecture and production, enjoying inputs from a broad diversity of skills and backgrounds.
This report is built up starting with a theory chapter, which will present the mechanical prop- erties of FRP, as well as existing calculation methods for the material together with the specific approaches that will be used in the following analysis chapter. The analysis chapter will be based around the case structure, and consist of a full structural design of a repeated frame, used in the building. The results from the analysis chapter will be discussed in the following discussion chapter after which conclusions will be made. Parallel to this report, an experimental report is produced, which is to be read in relation to this report. The experimental report is likewise a part of the work of this thesis, where parts of the results of the analysis chapter have been controlled in physical experiments. Practically, this division into two reports is due to delays in regards to the initialisation of the experiments, resulting in them not being finalized sufficiently before the date of submission of this report.
1.2 Limitations
This thesis does not intend to develop new in-depth theories concerning the mechanism within the mechanical performance of FRP or the behaviour of bonding components. Instead it seeks to clarify the extent of the knowledge available, the usability of existing knowledge in structural design, as well as offer guidance to what approach to follow and considerations to take into account when performing structural design of FRP structures and elements. Thus, this thesis is limited to current approaches and existing theories available within the field, and will be based
on these to offer practical suggestion for the usage of them. In general the scope of this thesis is subject to following limitations:
• Only structural considerations are included (fire safety, building energy, facade engineer- ing, geotechnics, material degrading, building comfort etc. are not considered, though all being relevant for the material and the case structure.)
• Instability of structural elements is only considered for column buckling, not including lateral-torsional buckling or local plate buckling. This is due to the investigated structure being restrained from these.
• Stresses due to thermal expansion and material creep is not included in the investigation.
Theory
In this chapter the properties of FRP will be presented with a particular focus on the mechanical properties. Following this, existing design methods will be presented, to the extent that is used in the analysis chapter. Finally, methods for designing and verifying the capacity of bolted and adhesive connections will be presented, with a focus on the approach used in the analysis.
2.1 Reinforced plastic composites
Fibre reinforced polymers (FRP) is a type of composite material, consisting of fibres, used to resist tensile and compressive loads, and a polymer matrix to transfer shear. The polymer matrix is typically polyester, vinyl ester or epoxy, while the most common types of fibres are fibreglass, carbon fibres and aramid fibres. Generally it can be said that carbon fibres gives high strength and stiffness, aramid gives high impact resistance, while fibreglass gives good all- round properties as well as electrical insulation and electromagnetic transparency [D6]. Since the compressive and tensile strength is predominantly governed by the fibres, the orientation is essential. The fibres are primarily oriented in the longitudinal direction due to the manufacturing method, see subsection 2.1.3. Due to the orientation of the fibres the material is anisotropic, as can be seen in the variation of the mechanical properties, which will be presented in subsection 2.1.1.
Apart from the mechanical properties, the material benefits from being very resilient, with excellent corrosion resistance and is generally resistant to a wide range of aggressive media, making it suitable in harsh environments. Likewise it has electromagnetic neutrality, low axial
4
coefficient of thermal expansion and low thermal conductivity, making it suitable for building design. Furthermore, it is possible to form into complex shapes, which combined with a possible transparent texture, potentially makes it an interesting architectural material. Weaknesses are also related to the material, which, apart from a relatively high price, is dominated by a low fire resistance. While the material is not combustible itself, FRP in its basic form will degrade at relatively low temperatures, resulting in diffusion of flammable gasses and black smoke. This can be limited by the use of fire-retarding additives, added to the resin, greatly improving the fire resistance. However, a high smoke emission remains and fire safety is definitely an important topic to address in design of FRP, [A7], [A12].
Even though all the benefits and disadvantages related to FRP are very interesting to explore further, this report will focus entirely on the structural aspects of the material and its mechan- ical behaviour and properties. These mechanical properties will be presented in the following subsection.
2.1.1 Mechanical properties
The behaviour of FRP is linear elastic, as is seen in figure 2.1. The theoretically determined curves, seen to the left (a), shows that the stiffness is dominated by the contribution of the fibres, which are perfectly linear elastic. However, the curve to the right (b), shows that in the actual response of FRP, the material stiffens under increased tensile load and is thus not perfectly linear elastic. This is due to the tensile load aligning lightly crimped fibres, and will therefore not be the case under compressive loading. Failure initiates with fibres fracturing or delaminating, resulting in drastically decreased stiffness until ultimate failure, [A12].
The mechanical properties of any reinforced plastic composite is largely dependent on the choice of reinforcement and resin material, the ratio between reinforcement and resin quantity, as well as the distribution and alignment of the fibre layers. As mentioned above, the reinforcing fibres typically vary between glass, aramid and carbon while the resin can typically vary between polyester, vinyl ester and epoxy, while many other reinforcing and matrix material can be used. To give an indication of the mechanical performance of these different materials, typical mechanical properties are shown in table 2.1.
As is seen, the properties of the reinforcement vary significantly, with E-glass having high strength, carbon much higher stiffness and aramid low density. The matrix resins do not vary
Figure 2.1: Stress-Strain curve for FRP in tension. a) Theoretical determined curves, b) actual behaviour (from [A12]).
Table 2.1: Mechanical properties of reinforcing and matrix material (values from [A11])
Reinforcement fibres Matrix resin
E-glass Aramid Carbon Polyester Vinyl ester Epoxy
Density [kg/m3] 2600 1470 1770 1130 1120 1280
Tensile strength [MPa] 3450 2750 2500 77 81 76
E-modulus [GPa] 72.4 62 303 3.72 3.72 3.24
as significantly, but still to some extent. From these properties, it is obvious that the choice of reinforcing fibres, as well as matrix resin, will have a large impact on the mechanical properties of the composite material. Even more significantly, it is noticed how large an impact the quantity ratio between reinforcing fibres and matrix resin must play. To illustrate how these different element contribute to the overall mechanical behaviour of the material, indication can be found from following formula from [A11], which offers a guidance of the impact of the contribution of the two components in a composite:
Xc=VrXr+VfXf (2.1)
Where Xc is the desired property of the composite, Vr and Vf the volume of resin and fibres, respectively, andXrandXf being the resin and fibre property. For example, a Fiberline profile typically has 60% fibre content of E-glass, according to [D6] and the remaining material being
polyester. This gives a tensile strength in the direction of the fibres of:
ft,c= 0.6·1130kg/m3
2600kg/m3 ·3450MPa + 0.4·2600kg/m3
1130kg/m3 ·77MPa = 900 + 71 = 971MPa (2.2) From this calculation, it is seen that almost the entire tensile strength is governed by the reinforcing fibres. However, the results of 971 MPa is of very poor precision, as it takes no account of the placing, direction, alignment or continuity of the fibres, but assumes it ideal, so the full capacity is utilized, resulting in a much higher strength than what is practically possible.
Furthermore, such a composition would be undesirable, as it would offer very poor transverse properties. To have more balanced profile, with also some poly-directional reinforcement, mats of reinforcements are added to the reinforcement pack. A 3mm plate profile of GFRP would thus typically consists of a layer of mats of about 0.5mm, a layer of roving, of about 2 mm and another layer of mats of about 0.5mm. The a layer of roving is illustrated left in figure 2.2, while a layer of mats are illustrated to the right.
Figure 2.2: Fibre roving (left) and mat (right) (from [D6]).
According to [A11] a roving layer could have a reinforcement contents of about 65%, and a tensile strength in the direction of the fibres of about 800 MPa, being fairly close to the quantity that would be achieved by using equation (2.1). A layer of mats will typically have a fibre content of about 25%, and a unidirectional tensile strength of only about 70 MPa, much lower than what would be found by using (2.1), and often even lower than that of the resin alone. However, the mats are neccessary to achieve the right constituency of the profiles. [A11] suggests, that the mechanical properties of a GFRP profile, can be indicated by the average of the layer properties, relative to their thickness. This plate could then be predicted to have a tensile strength parallel to the fibres of the roving layer of 550 MPa. This is still significantly higher than characteristic values, but the approach gives an insight of the impact of the combination of fibres layers, and the high strength a roving layer gives in the primary fibre direction, explaining the high anisotropic nature of the material. Due to the mats, there will be fibres in all directions, and
it is therefore not correct to talk about an actual fibres direction, as it is with wood. Instead the strong direction of the material will be called the direction of pultrusion, which the roving layers follow, making it the primary, but not sole, fibre direction. In this report, only glass fibre reinforced plastics (GFRP) will be considered, meaning that purely polymer matrices reinforced with fibreglass. This is in spite of the improved mechanical properties that can be acquired by using carbon fibres. However, due to carbon fibres being significantly more expensive, they are, as the marked is now, not believed to be suitable for a general building material, though its relevance could be found in special architectural features or high performance elements.
The overall mechanical properties of GFRP are given in table 2.2, which are based on profiles from Fiberline and taken from [D6]. In this report, these mechanical properties for GFRP will be used, even though many variations can be found, as the mechanical properties are highly dependent on the used polymer matrix and layers of fibres, that all must be carefully balanced to obtain good mechanical properties.
Table 2.2: Typical mechanical properties of GFRP (from [D6])
Unit
Flexural strength, 0◦ fb,0◦ MPa 240
Flexural strength, 90◦ fb,90◦ MPa 100
Tensile strength, 0◦ ft,0◦ MPa 240
Tensile strength, 90◦ ft,90◦ MPa 50
Compressive strength, 0◦ fc,0◦ MPa 240
Compressive strength, 90◦ fc,90◦ MPa 70
Shear strength fτ MPa 25
Pin-bearing strength, longitudinal direction fcB,0◦ MPa 150 Pin-bearing strength, transverse direction fcB,90◦ MPa 70
Modulus of elasticity, 0◦ E0◦ GPa 28
Modulus of elasticity, 90◦ E90◦ GPa 8.5
Modulus of shear G GPa 3
Poisson’s ratio νb,0◦,90◦ - 0.23
Poisson’s ratio ν90◦,0◦ - 0.09
Density g kg/m3 1800
From table 2.2 it is seen that the material has between about half, down to almost a fifth of the strength perpendicular to the direction of pultrusion than parallel to the direction of pultrusion.
It is also noticed that the shear strength is as little as about a tenth of the flexural, tensile and compressive strength parallel to the direction of pultrusion. To have something to hold the values from table 2.2 up against, they will in the following subsection be compared to other, more commonly used, structural materials.
2.1.2 Comparison to other materials
To evaluate the behaviour of GFRP as a structural material, some of the structural properties are shown in table 2.3 together with those of steel and wood. This is done to create a sense of the approach by which the structural design shall be done, as steel and wood are considered to be more common structural materials, with a more establish design approach. In the table, the yield strengths of steel is used, while the anisotropy of GFRP and wood is illustrated by giving both the value for the strong and weak direction. It shall be noted, that the shown values are characteristic values and due to differences in manufacturing and behaviour, the design value are reduced differently by safety coefficients for the different materials.
Table 2.3: Comparison of Typical mechanical properties of GFRP (From [D6], [A3], [A10], [B4])
Unit GFRP Steel (S235) Wood (C24)
Tensile strength ft MPa 240 / 50 235 14 / 0.5
Compressive strength fc MPa 240 / 70 235 21 / 2.5
Shear strength fτ MPa 25 136 2.5
Modulus of elasticity E GPa 28 / 8.5 210 11.0 / 0.37
Modulus of shear G GPa 3 81 0.69
Density g kg/m3 1800 7850 420
Price index /kg 3.6-5.8 1 0.7
From table 2.3 it is seen that the strength of GFRP is closer to that of steel than that of wood, while the moduli are closer to those of wood. When comparing the mechanical properties to those of steel, it is seen that while the tensile and compressive strength parallel to the direction of pultrusion are slightly higher than that of steel, the shear strength is less than a fifth, indicating shear as a critical load. Examining the moduli, it is seen that even parallel to the direction of pultrusion, GFRP has less than a seventh of the E-modulus of steel, while the shear modulus is a 27th. A so low shear modulus means that, unlike the case for steel, GFRP should take shear deformations into account, which could have a impact in deflections.
Weighing less than a quarter of steel, GFRP has a much better strength to weight ratio, if based on the high compressive and tensile strength parallel to the direction of pultrusion. However, as this comparison has shown, the low weight does not out-weight the reductions in shear strength or the moduli. Comparing the mechanical properties to that of wood, it is noticed that all the strengths are at least 10 times as large for GFRP as those for wood, while the modulus of elasticity is only 2.5 times as large. With the weight being about 4.5 times as large, it is again
seen that the strength to weight ratio is better for GFRP, while the E-modulus to weight ratio is worse for GFRP than for wood.
In table 2.3 a price index value is also shown, taken from [B4]. This price indication shall be taken with caution as prices can vary with time and location. Furthermore, it is given as the price per kg, and must therefore be seen relative to the density. Taking the density difference into account, it is noticed that the same profile of GFRP and steel can be expected to have around the same price, while a similar sized timber section will be significantly cheaper. Based on a purely economic and structural perspective, this means that GFRP can easily compete with steel if axial stresses are dominant, as the price for the same profile will be comparable but the weight much lower. However, in most cases deflection or shear capacity will be dominant for the GFRP profile, compromising this competitive ability.
Based on this comparison, it is seen that GFRP has very good axial strength properties relative to its weight compared to both steel and wood, while the moduli are low, strongly indicating that conventional structural design would result in deflections being critical. It was also noticed that the shear strength was relatively low compared to steel and the relation between the shear strength and the axial strengths, was closer to that of wood. However, most GFRP profiles are shaped similarly to those of steel, where the cross-section is optimized for moment of inertia, while wood sections tend to be rectangular, leaving the entire area to transfer the shear. Based on this, assuming the profiles to resemble steel sections, it can be expected that shear will be the critical load.
2.1.3 Manufacturing by pultrusion
The continuous emergence of FRP as a structural material for building and civil structures is largely possible due to the development of the pultrusion technique, which enables cost-effective production of high quality constant cross-section profiles. This technique has been developing since the 1950’s, and has now reached a stage where it can produce structural members, such as beams and columns that can compete with those of conventional materials. As the demand continuous to grow, the cost-efficiency could likewise be expected to be improved, as profiles to a even further extent can be continuously produced, where as now, tools must be adjusted to produce different profiles dependent on the demand, [A1].
In this section, the manufacturing process of pultrusion will be described. This is reckoned to be an essential topic to cover, as the manufacturing process to a large extent dictates the
possibilities of varying the structural elements, analysed within the scope of this thesis.
Pultrusion is a continuous fabrication method, where strands and plys are spun through a guiding system to be impregnated in a liquid matrix resin. The reinforced matrix resin is gathered into a preformed shape, roughly matching the desired profile shape, after which it enters a heated curing die. In the die, the pack has been changed into a fully shaped solid profile. When cooled sufficiently, the profile is pulled through a cutoff saw, which cuts the profile to the required length. An overview of the production method is shown in figure 2.3.
The production time is about 1m per minute. Generally pultrusion machine can fabric profiles with dimensions of up to 1300 mm width, 350 mm height and a length, which often ranges from 12 m and up to above 18 m. [A11].
Figure 2.3: Overview of the pultrusion machine (from [D6]).
To obtain a high quality product, a optimum reinforcement to resin ration must be used. Any use of resin additives are introduced during the impregnation stage and these will affect the optimum reinforcement to resin ratio. The additives could be desired to reduce profile cost, fire retardancy etc. [A11]. The resin can be added, either by using open resin wet-bath impregnation techniques or by pressure injection of matrix resin directly into the die. The open wet-bath technique is generally cheaper, while the impregnation can be favoured as it is better at retaining the required multiaxial reinforcement and as it does not lose styrene to the surrounding factory environment.
The impregnation method also has advantages in regards to changing the production line from one profile or matrix to another. [A11]. The resin is added through the impregnation method at the factory of Fiberline, which is illustrated in figure 2.4.
From the description of the production method, given above, following observations that are relevant for the profile design can be noted:
• Due to continuous production method, profiles must have constant cross-section.
Figure 2.4: Illustration of impregnation method (from [A11]).
• Reinforcement will predominantly be align with the length of the profiles, while transverse reinforcement can be obtained by the use of mats.
• The pultrusion machine sets certain limitations to the cross-sectional dimensions of the profiles, while the length of the profile can be very long.
• The amount of reinforcement in a profile is limited by the desired optimum reinforcement to resin ratio.
• Adding additives affects the optimum reinforcement to resin ratio.
2.1.4 Design consideration
The material properties shows that GFRP is strong in the axial direction, parallel to the di- rection of pultrusion, while it suffers from lower strengths in the other directions. Likewise the shear stress is low in relation to the axial strength. The stiffness of the material is also low in relation to the high strength parallel to the direction of pultrusion. As mentioned above, this indicates that the material will be sensitive to shear loading and deflections. Based on these considerations it clear that the material has advantages in truss structures, where a large height is obtained to give the neccessary inertia to outweigh the low stiffness. A truss structure is also characterised by the members being axially loaded, utilizing the highest strength properties.
However, in some structures a truss are not suitable, either due to the architecture, low span length or limited available height. In such a case, tall profiles should be desired to gain high modulus of inertia to avoid large deflections. While deflections will be reduced, so will be axial stresses from the moment, where the material is strong. Therefore tall profiles alone will not be able to utilize the properties of the material. To reduce deflection further, rigid connections could be preferred, as these reduce the deflections to a fifth compared to a simply supported
beam, while reducing the moment by a third. By combining rigid supports with tall profiles, a better utilization of the properties could be obtained. This causes a new challenge, being the design of rigid connection, which will results in connection forces perpendicular to the direction of pultrusion occurring from the moment, where the material is weak. In the following parts of this chapter, the general approach for verifying the bearing capacity of elements of GFRP will be presented, following by descriptions of methods to calculate rigid connections of GFRP, both in regards to bolted and glued connections. Before this, a short presentation of the lower bound theorem will be presented, which the design will be based on, when uncertainties arise or simplifications must be made.
2.2 Lower Bound Theorem
Before introducing the design method available for GFRP, a short presentation of the Lower Bound Theorem will be given. This is due to structural design of GFRP is a relatively new discipline and the established approaches and calculation methods for exact solutions are limited.
To make a safe design in spite of shortage of thoroughly tested approaches, the philosophy of the Lower Bound Theorem can be used.
The lower bound theorem is part of the limit analysis approach of structural design, used within the theory of plasticity. Opposed to the upper bound theorem, the lower bound theorem is restrained to give only solutions which are on the safe side. To ensure this, the solution must meet all statical and physical requirements. To meet the statical requirements the element or structure must be in equilibrium, both internally and externally. The internal equilibrium means, that it must be theoretically possible to cut out any part of the element or structure and require that this part is in equilibrium. The external equilibrium means, that the reactions and external load must be in equilibrium. If these requirements are fulfilled for a chosen force distribution, that force distribution can be said to be admissible and the requirements of the lower bound theorem is met. This allows infinitely many force distributions to be allowed, giving the designer the possibility to go ahead with the design, based on a guessed force distribution.
As the distribution is more or less chosen freely, while fulfilling the requirements of admissibility, it is likely that it does not represent the true force distribution that will occur in the structure.
The principle is, that this is not a problem in regards to safety, as the forces in reality will follow the optimum, and thus the designers guess can only be a safe side estimate of the true distribution, [A9]. Furthermore, the solution might be ensured to be even more on the safe side by ignoring certain parameters or effects, that would contribute to the load bearing capacity.
While the behaviour of the material is not plastic, but rather dominated by the elastic behaviour of the fibres, the design philosophy behind the lower bound method is found relevant to use consciously in the structural design of this relatively new material. As a result of this design philosophy, the solutions that are presented in the analysis section, will not necessarily be optimal, but they can be expected to be safe. This is seen as a first essential step in developing efficient structural design with the material, while optimal design is a further step for increasing this efficiency.
2.3 Structural design with GFRP
As neither the Eurocode system or other officially recognized codes or standards used in Den- mark or internationally covers structural design with GFRP, a major part of the scope of this thesis, is to explore the manuals and design guides that exist, evaluate these and determine their usability on a predetermined structural design case. To assist and guide the designer, the producers of GFRP elements publish their own manuals and design guides. This is also the case for Fiberline Composites, who have based their design manual ([D6]) on the Eurocomp Design Code ([D5]). In this section the design approach presented in Fiberlines design manual will be presented, to the extent relevant to the analysis performed in the work of this report. The procedure will be examined, to determine the approach on which it is based, with reference to other sources. Where guidance is not available in Fiberlines design manual or the detail level inadequate for the analysis performed during the work of this thesis, theories from Eurocomp and other guides, books and research papers are used.
2.3.1 Safety concept and coefficients
In this subsection, the safety concept and safety coefficients applied for structural design of GFRP profiles is presented in accordance with [D6]. While the load combination concept is very similar to that in the Eurocode system, and will not be elaborated much upon, the partial safety coefficients reducing the strengths of the material, will be linked to some studied theory. These partial safety coefficients, have an interesting element of greatly increased strength reduction for long term loading in comparison to short term loading. The reason for this will be explained, based on literature studies of the material.
Load combination
Following the principles from the Eurocode system, [D6] operates with ultimate limit state (ULS) for verifying bearing capacity and failure resistance and serviceability limit state (SLS) to ensure acceptable deflections. In the following, the combination method given in [D6] will be presented, to the extent used for the analysis in this report. These combination method are identical to the one presented in [D5], which [D6] is based upon.
Ultimate limit state
For capacity verification, both variable and permanent loads are significantly increased. For load cases with only one variable load, this is further increased and the design load combinations is determined by:
Sd,k = X
j=1,...,m
γG,jGk,j+ 1.50Qk (2.3)
Here γG,j is partial coefficient of permanent load (no. j), set to 1.35, or 1.0 in case the load is stabilising,Gk,j is the permanent loads and Qk is the variable load. If several variable loads are present, these are identically increased and the load combination is done by:
Sd,k= X
j=1,...,m
γG,jGk,j+ 1.35 X
j=1,...,m
Qk,i (2.4)
This load combination from [D6] will generally results in larger design load combinations than if based on the Eurocode procedure. This is especially in regards to the permanent load actions, which are multiplied by a factor 1.35, where it according Eurocode ([D1] and [D3]), will be increased by no more than a factor 1.2 for normal consequence class. The increase of a single variable load corresponds with that of Eurocode, while for several variable loads it is somewhat different. While Eurocode operate with an dominant load, that is intensified as a single load in equation (2.3), and reduction of the none-dominant loads, [D6] operates with an equal intensity of all the variable loads, as shown in equation (2.4). Generally it is expected that the procedure presented here, in accordance with [D6], will results in slightly larger combined load actions, than if based on the Eurocode procedure, especially due to the increase of the permanent actions, which are of particular relevance, as these must be taken in regards to the largely reduced long term strength of the material.
Serviceability limit state
While it was found that the ULS combinations was significantly different from that of Eurocode, the SLS combination can be used as in Eurocodes. [D6], formulates the SLS combination by:
SK,k=Gp,1+Gp,2+ 1.00Qp,1+ψL,2Qp,2+ψL,3Qp,3 (2.5)
Where the ψ-factor is suggested as 0.9 according to [D5]. This value is also suggested in [D6], if a more accurate value is not available and references are made to Eurocode as an alternative.
Here, the values of the ψ-factor given in Eurocode ([D3]), are regarded as more accurate, as it takes the nature of the load action into account. For the analysis of this report the ψ-factor from Eurocode ([D3]) will therefore be used. It is noticed that using the factor suggested in [D6]
is conservative, as none of the ψ-factor from Eurocode ([D3]), are as large as 0.9. Therefore, using 0.9 will set harder requirements on the deflection of a structure, which is already expected to be critical due to the low E-modulus, as mentioned in section 2.1. As in Eurocode, no actual deformation limit is given in [D6], but between 1/200 to 1/400 of the span length is given as an suggestion.
Safety factors
Here the partial safety coefficients used for GFRP members will be presented, as given in [D6]
and discussed based on the theory behind the behaviour of the material under long and short term loading.
According to [D6], the capacities of the material are to be reduced by:
Rd= Rk
γm,1·γm,2·γm,3·γm,4
(2.6)
Where γm,1, γm,2 and γm,3 are determined in accordance with [D5] based on the production methods of Fiberline, giving:
• γm,1=1.15, due to the profiles being pultruded
• γm,2=1.1, as the profiles are fully postcured
• γm,1=1.0, as the profiles have a HDT ultimate temperatur for dimensional stability of 100◦C.
These three partial coefficients are determined based on table values from [D5], in correspon- dence with the reasons stated above.
γm,4 is dependent on the operating temperature and load duration, and is in [D6] recommended asγm,4 = 1.0 for short-term loads andγm,4 = 2.5 for long-term loads, for operation temperature below 80◦C. These values are likewise based on values given in [D5]. This gives following total safety coefficients:
• Short-term load: γm = 1.3
• Long-term load: γm= 3.2
While all the partial safety coefficient are based upon values from [D5], the combined safety coefficient for short-term loading, conflicts with the recommendations from [D5], which states that γm should not be taken as less than 1.5 for building structures. This view is shared with [A12], stating that: 1.5 ≤ γm ≤ 10. However, [D5], does also state, that more detailed information and test data may justify a lesser value. Therefore, this is not to be seen as a criticism of the safety approach from [D6], but rather as a indication that the safety coefficient γm = 1.3 for short-term loading, is low for the material in general, but assumed reasonable, as purely based on values from [D5], and thus simply due to a precise fabrication process. The greatly reduced strength in regards to long-term loading is due to the phenomenon;creep rupture orstatic failure. This phenomenon can cause elements to fail at stresses significantly lower than their short-term capacity, due to sustained load actions, and is particularly pronoun for GFRP elements, [A1], [B4]. The process is due to a formation of pores and microcracks forming at grain boundaries, creating local stress concentrations, ultimately resulting in failure below the general capacity of the material. The higher the temperature and the longer duration of the loading, the lower stress can cause fracture due to creep rupture, [A4]. This also explains, why the long term loading is further reduced in case of operating temperatures above 80◦C in [D6].
The effect of the two different safety coefficient dependent on the duration of the load, is that load combinations must be split into short- and long-term actions, where long-term loads according to [D6], are with a duration measured in years.
2.3.2 Design of structural members
In this subsection a description of the structural design of GFRP members will be presented.
Apart from a mere presentation of the approach given in Fiberlines Design Manual, [D6], some general theoretical consideration will also be given, which are used to evaluate the presented approach. The structural member design presented here is that for beams and columns.
Beams
As mentioned in section 2.1.1, GFRP has a low shear modulus compared to steel, even when viewed relatively to the E-modulus. Therefore basing the beam deflections on aEuler-Bernoulli
beam theory, will result in underestimating the deflection for short beams, as shear deformations will play a significant role. Therefore beam defection design should be carried out asTimoshenko beams, where the cross-section plane no longer is assumed to remain perpendicular and shear deformations are included, [A8]. The effect of the shear deformation on a GFRP beam, as a function of the span length is illustrated in [C3] and here shown in figure 2.5. The figure shows the evenly distributed load that a 300 x 150 mm I-beam can sustain, before reaching the deflection limits. According to [A8], the assumption of small shear deformations related to the Euler-Bernoulli beam theory is true for beams with span/depth≥10. Based on the plot of figure 2.5, this is clearly not true for GFRP beams, where there is more than 25% larger capacity in regards to deflection if shear deformations are ignored, when span/depth=10. According to [C3], as a general rule of thumb, the shear deformation of GFRP beam can first be ignored when span/depth>25, which corresponds with figure 2.5.
Figure 2.5: Effect of shear deformation for 300 x 150 mm I-beam (from [C3]).
According to [D6], the shear deformation is taken into account, as the deformation limit is controlled by:
Max(δ) L < 1
α (2.7)
Whereα is typically between 200 and 400 and with:
Max(δ)
L = kδM ·qk·L3
E0◦I +kδV ·qk·L
G·Ak (2.8)
The k-values, are table values, depending on the amount of spans, and correspond with values from for example [A3],qk is an evenly distributed loadLis the span length E0◦ the modulus of elasticity,I the moment of inertia,Gthe modulus of shear andAk the shear area. This control of the deformation limit is done based on SLS, and is according to most sources, including [D6]
and [C3], often found to be the dimensioning for the design of a beam of GFRP.
In the ultimate limit state, the largest bending stresses, are found by a conventional approach by determining the largest moment and dividing this with the section modulus,W, by:
kM ·pd·L2
W ≤ fb,0◦
γm,f (2.9)
The shear stress, on the other hand, are given by a somewhat simplified approach, where the shear force is divided by a shear area:
kV ·pd·L
Ak ≤ fτ,0◦
γm,f (2.10)
The k-values in equation (2.9) and (2.10) are, as for the deformations, factors given in [D6], dependent on the amount of spans, and corresponding with values from [A3]. The shear area Ak is given for all Fiberlines structural profiles, and seems to be determined as the web thick- ness multiplied with the web height, to which half the flange thickness at times are added, as illustrated in figure 2.6.
Figure 2.6: Estimated shear area (from [C3]).
This method is also mentioned in [A6], which refers to the approach as an often accepted simplification. The precision of this formulation is increased the more the flange area exceeds
the web area, for equal flange and web area, a underestimation of 7% is expected, when compared to shear stresses found by Grashof’s formula, which is suggested for both steel calculation in [A6] and timber calculation in [A10]:
τ = Vz·∆Sy
Iy·t (2.11)
With Sy being the statical moment, Vz the shear force, Iy the moment of inertia and t the thickness.
The approach of [D6] corresponds to the one given in [D5], which also offers suggestions for determining the shear area for standard profile shapes.
In the analysis of this report, the largest shear force will be found both by use of a shear area, as in [D6], and by Grashof’s formula. This is both to evaluate the method from [D6], but as much due to the sections used in the scope of the report being composites of several standard profiles from Fiberline and thus a table value is not available for these profiles. Likewise the profiles are not standard profiles, so the recommendation of [D5] for determining the shear area cannot be used. Furthermore, the flange area of the top flange is very small compared to the web area in the profiles used in the analysis, which according to [A6] will give increased underestimation by basing the shear stress on the shear area.
It shall be noted that no requirement of combination of the bending stress and shear stress is mentioned in [D6]. While the maximum bending and shear stresses do not occur in the same location, it could be argued that it should be controlled whether combinations between meeting of web and flange in the case of I-profiles should be controlled. Also, stability of beams are not considered in [D6], such as lateral torsional buckling. Guidance for stability is offered in [D5], but as the beams in the analysis of this report will be supported against out-of-plane stability, the methods will not be presented here.
Columns
For a column purely loaded in compression, the Fiberlines design guide, [D6], states that the capacity is sufficient if the design value of the normal force is smaller than critical column load, determined by:
Ncr = Fd 1 +NFd
el
(2.12)
In whichNel is the Euler load, which is determined by:
Nel= π2·E0◦·I
γm,E·L2k (2.13)
With Lk being the critical column length and Fd is the compressive load that the column can carry:
Fd= A·fc,0◦
γm,f (2.14)
This approach is based upon the empirically determined Rankine Gordon formula, often written as:
1 Ncr = 1
Nel + 1
Fd (2.15)
This is identical to the expression in equation (2.12) and is practically an increase of the Euler load by the utilization of the compressive stress capacity, thus being more conservative than the Euler load alone. The approach hereby also takes into account that very short columns will fail due to crushing and not due to buckling. An illustration of the critical stress of a column based on Rankine Gordon approach and pure Euler column is shown in figure 2.7, where it is seen that the Rankine Gordon method gives a lower critical stress for low slenderness ratios. As the slenderness ratio becomes large, the normal stress in the column becomes insignificant and the buckling from the Euler column becomes critical.
Figure 2.7: Critical stress for Rankine and Euler column (from [C1]).
In case columns are also subject to flexural moments, the capacity is, according to [D6], deter- mined by:
σmax < fc,0◦
γm,f (2.16)
σmax = Nd
A + 1
1− NNd
cr
·Md
W (2.17)
The largest stress is thus determined as a superposition of the normal stress, Nd, from the compression, and the bending stress from the moment,Md. The compressive load will result in transverse deflections until buckling, which will create an additional moment. This is taken into account by a intensification factor, which increases the bending stresses proportionally with the utilization of the critical column force.
In this section calculation method for bearing capacity verification of GFRP element has been presented and reflected upon. The following two section will present some theories and ap- proaches to evaluate the bearing capacity and force distribution in rigid connection of GFRP elements. This will both be done for both bolted connections and adhesive joints.
2.4 Bolted connection design
According to [A5], a designer has two basic techniques available for joining components of fibre-reinforced plastics, being mechanical fastening and adhesive bonding. In this section me- chanical fastening connections will be examined, specifically rigid bolted connections. Adhesive connection will then follow in section 2.5. [A5] summarised the advantages and disadvantages of mechanical fastened connection, in contrast to adhesive joint by:
Advantages:
• No surface preparation of components required.
• Disassembly possible without component damage.
• No abnormal inspection problems.
Disadvantages:
• Holes cause unavoidable stress concentrations.
• Can incur a large weight penalty
As seen from this list, the advantages by using a mechanically fastened connection are all related to the construction and control of the connection, being significantly simpler than an adhesive
joint, especially when done on site. The disadvantages are on the other hand related to more structural consideration, as the bolted connection will create stress concentrations around the holes and from the bolts. In spite of the structural disadvantages, bolted connections are the most common connection type in GFRP, [A5]. The objective in this section, is to present an approach to calculate the bolt force distribution of a rigid bolted connection of GFRP and verifying the capacity of the connection based on the distribution. Little guidance is found for design of rigid connections of GFRP, as they are generally very scarcely used. Some researchers believe that the low stiffness of pultruded profiles results in fully rigid connection not appearing to be realistic, but will to some degree act as semirigid connection, [A1]. While keeping this aspect in mind, the approach presented in this section, will be based upon an assumption of fully rigid behaviour. It shall also be noted, that while bolted connections in steel can dissipate some of the high peak stresses that occur against the edge of the holes through local yielding, GFRP has a linear elastic response almost until failure, resulting in an increased risk of local crushing at the bolt holes. Because of this difference in behaviour from steel and the orthotropic properties of the material, the traditions for bolted connection of steel cannot be directly transferred to GFRP if the properties are to utilize.
In the following subsection, different approaches for the distribution of the bolt forces will be presented, using different detail level concerning the effect of the orthotropic stiffness of the material. These distributions will result in a force components perpendicular and parallel to the direction of pultrusion of the material, which can be held directly against capacities determined based on an approach from Fiberlines design guide, [D6]. This approach of capacity determination, as well as the related requirements, are presented in subsection 2.4.2.
2.4.1 Force distribution
The force distribution within a rigid, moment transferring connection will here be presented.
First, an approach for the moment distribution will be presented and illustrated that disregards the effect of the orthotropic stiffness of the material. Following this, two suggestions for including this influence of the stiffness is presented, where one conservatively simplifies the distribution by only distributing the forces parallel to the direction of pultrusion, while the other is based on the stiffness ratio parallel and perpendicular to the direction of pultrusion. It will be expected that the true force distribution will be strongly influenced by the variations of stiffness in the material, as is the case for timber connection, which likewise has orthotropic stiffnesses. The tendency of the forces to orient towards the higher stiffness is for example shown in [C2].
The different approaches will be illustrated through the simple connection of a GFRP member bolted to a isotropic gusset plate, as shown on figure 2.8. All the approaches will be based upon a distribution using the elasticity theory, as they shall according to [D6].
Figure 2.8: Example connection for illustration of method consistent of four bolts and loaded in the centroid by a moment and a vertical force.
Disregarding the variations in stiffness, the distribution of the moment results in bolt forces proportional to the distance from the centroid of the connection to the individual bolts. The force from the moment in each bolt can, according to an approach for timber structures given in [A10], be determined by:
Fi,m,d =Md ri
i
P
j=1
r2j
! (2.18)
WhereMdis the design value of the moment andris the distance from the centroid to the bolt, while nis the total number of bolts. This force will act perpendicular to the straight line from the centroid to the bolts, as illustrated on figure 2.9, where it likewise is shown how the forces increase with the distance to the centroid.
The contribution from horizontal and vertical lateral forces, is assumed evenly distributed to all the bolts, also in accordance with [A10], and simply calculated by:
Fi,h,d = Hd
n and Fi,v,d= Vd
n (2.19)
With Hd being a horizontal lateral force and Vd a vertical lateral force. The lateral forces will both affect the magnitude of the forces and the direction. When the vertical load is applied to the connection, the forces in the bolts are changed as illustrated left in figure 2.9. In the
−500 0 500
−500 0 500
y coordinate [mm]
x coordinate [mm]
Figure 2.9: Force distribution from moment.
plot it is seen how some forces are increase while other decreased, dependent on their direction, resulting in one bolt being harder loaded than the other, indicated by a blue circle.
−500 0 500
−500 0 500
y coordinate [mm]
x coordinate [mm]
−500 0 500
−500 0 500
y coordinate [mm]
x coordinate [mm]
Figure 2.10: Force distribution from moment and vertical force. Left: Resulting forces. Right:
Force components)
Based on the resulting forces illustrated left in figure 2.9, a horizontal and vertical component can be determined, as illustrated to the right of figure 2.9. The force components can then be used to check the combined capacity in relation to the capacities parallel and perpendicular to the direction of pultrusion.
As mentioned, this approach disregards the difference in E-moduli parallel and perpendicular to the direction of pultrusion, which in reality will affect the forces, as the higher stiffness will attract larger load. Therefore it can be conceived to be somewhat imprecise, and presumably conservative, as it distributes the forces equally in the strong and weak direction in the material, resulting in over-utilization perpendicular to the direction of pultrusion. If the connection on
