Bending of helically twisted cables under variable ... - Pfisterer

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DISS ETH No. 11057 Bending of helically twisted cables under variable bending stiffness due to internal friction, tensile force and cable curvature DISSERTATION for obtaining the title of DOKTOR DER TECHNISCHEN WISSENSCHAFTEN [DOCTOR OF TECHNICAL SCIENCES] of the EIDGENÖSSISCHE TECHNISCHE HOCHSCHULE ZURICH presented by Konstantin O. Papailiou Dipl. El.-Ing. TH Braunschweig Dipl. Bau-Ing. Universität Stuttgart born on 3.7.1946 in Athens, Greece Accepted on application by: Prof. Dr. H.-R. Meyer-Piening, Supervisor Prof. Dr. G. Oplatka, Co-Supervisor Dr. V. Esslinger, Co-Supervisor 1995
For my father
Page 1: Bending of helically twisted cables
Page 5 and 6: Zusammenfassung Die Seilbiegung ste
Page 7 and 8: And another special word of thanks
Page 9 and 10: 5. Measurements....................
Page 11 and 12: 2 Their acquisition value is estima
Page 13 and 14: 4 This device measures the deflecti
Page 15 and 16: 6 From early years, overhead transm
Page 17 and 18: 2. Basic principles 2.1. The tensil
Page 19 and 20: Figure 2.3 explains these relations
Page 21 and 22: Fig. 2.4 Determining the radial pre
Page 23 and 24: It It appears appears suitable suit
Page 25 and 26: Fig. 2.7 Geometry of the cable cros
Page 27 and 28: Fig. 2.9 Curves Curves for the seco
Page 29 and 30: 2.4. The bending stiffness As menti
Page 31 and 32: Fig. 2.12 Distribution of the cable
Page 33 and 34: Depending Depending on on the the s
Page 35 and 36: this results in: In this equation,
Page 37 and 38: We may derive the mean transition c
Page 39 and 40: The moment moment below the transit
Page 41 and 42: Fig. Fig. 2.15 2.15 finally shows s
Page 43 and 44: During During bending in in Region
Page 45 and 46: Fig. 2.18 Hysteresis in the M-B B d
Page 47 and 48: with: and: with: The tensile stress
Page 49 and 50: The The situation situation is is d
Page 51 and 52: As As the curvature curvature incre
Page 53 and 54:
This shows that, based on the propo
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A wire of the outer layer therefore
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The Zn,a values values are are the
Page 59 and 60:
According According to to the law o
Page 61 and 62:
First First approximation: Continuo
Page 63 and 64:
This means that the outer layer is
Page 65 and 66:
By applying the Zi just just achiev
Page 67 and 68:
3.4. Tensile Tensile force in in th
Page 69 and 70:
To determine the stiffnesses, momen
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Assumption 1: Undisturbed isturbed
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Fig. 3.7d M-B B diagram diagram und
Page 75 and 76:
Phase 1 The The relative position p
Page 77 and 78:
Fig. 4.2c Bending of a cable under
Page 79 and 80:
Phase 0 The strain energy W0D = W4D
Page 81 and 82:
Fig. 4.3 M-B B diagram for the anal
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The The balance balance of of momen
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76 In the next step, for an “arbi
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Input module The cable data input,
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( x )E*I = f ( k ) 80 Stiffness for
Page 91 and 92:
82 The same process is now repeated
Page 93 and 94:
84 Fig. 4.13 Flow chart of the SEIL
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(a) Fig. 5.1 Cable bending: (a) for
Page 97 and 98:
The The sensor sensor is is mounted
Page 99 and 100:
Fig. 5.4 Single cross-section secti
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5.2. The test set-up 92 To better o
Page 103 and 104:
Stiffness EJ [N*m^2] Fig. 5.11 Bend
Page 105 and 106:
This machine can handle tensile for
Page 107 and 108:
5.3. The test cables A four-layer h
Page 109 and 110:
The input values for the SEIL progr
Page 111 and 112:
Triggered by the dx signal, a 150 p
Page 113 and 114:
Sag [m] Fig. 6.1 Measured and calcu
Page 115 and 116:
Sag [m] Fig. 6.4 Measured and calcu
Page 117 and 118:
108 Fig. 6.6 also clearly shows tha
Page 119 and 120:
Fig. 6.9 Hysteresis for Cardinal at
Page 121 and 122:
Figure Figure 6.10 6.10 shows shows
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6.5. Effect of the sample length 11
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116 Force--displacement curve Fig.
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This This is is based based on on e
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Secondary stress [N/mm^2] Secondary
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After After the the wire stresses s
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124 The above is summarised in Fig.
Page 135 and 136:
The The trend trend determined here
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128 Even if the conductor model pos
Page 139 and 140:
8. Prospects 130 In the last chapte
Page 141 and 142:
Annexure I The The tensile stress s
Page 143 and 144:
Considering Considering the the abo
Page 145 and 146:
It follows that: If the angle is do
Page 147 and 148:
The position of the catenary in the
Page 149 and 150:
The The following following matrice
Page 151 and 152:
For single component conductors: Fo
Page 153 and 154:
144 CIGRE: Study Committee 22 - Wor
Page 155 and 156:
146 Papailiou, Müller, Roll: Anwen
Page 157 and 158:
List of symbols Latin symbols 148 a
Page 159 and 160:
ma mi mL 150 Friction summation fac
Page 161 and 162:
Z0 Z1 Za Z c,n Zd Z d,a Zd,i Zd,L Z
Page 163 and 164:
ρ Curvature radius of the cable ax
Page 165 and 166:
156 Fig. 3.3 Effect of the tensile
Page 167 and 168:
158 assumptions; 1: (EJ)(κ); 2: (E
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Bending of helically twisted cables under variable ... - Pfisterer

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