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

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Fig. 2.14 Schematic curve of bending stiffness (EJ)(κ) (EJ)( across the cable curvature for a single layer cable But M R is given by (2.43): MR is the residual friction moment or the maximum moment fric friction tion can resist, which remains “frozen” in the the cable after after all all the the wires have have slipped, slipped, continuing to oppose the external load, because κ > κm (Region II): Region I Transition Region II The moment MII above the average transition curvature κm is therefore a combination of the wire moment Mmin and the residual friction moment MMR. 29
The moment moment below the transition curvature curvature however, however, i.e. i.e. in Region I I (no wire slippage) equals equals the maximum possible cable moment: The plausibility of the above considerations is strengthened through the following observations at the boundaries: Using Using (2.24) (2.24) and and (2.23), (2.23), the the starting starting and and end curvatures of the the wire displacement displacement were were determined for for a cable cross-section, section, based based on the balance balance of of forces forces on the individual affected wire elements: Based on simple considerations, the average transition curvature κm, , was also derived from Fig. 2.13 (2.46): Substituting the MR component of a single wire from (2.43) yields: But for the single wire e considered here, (2.30) and (2.33) also state: The associated “pure” wire tensioning force (i.e. without the bending component ZZzus) ) therefore: 30 Start of wire displacement End of wire displacement
Page 1 and 2: Bending of helically twisted cables
Page 3 and 4: For my father
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: We may derive the mean transition c
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
Page 55 and 56: A wire of the outer layer therefore
Page 57 and 58: 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
Page 71 and 72: Assumption 1: Undisturbed isturbed
Page 73 and 74: 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
Page 83 and 84: The The balance balance of of momen
Page 85 and 86: 76 In the next step, for an “arbi
Page 87 and 88: Input module The cable data input,
Page 89 and 90:
( x )E*I = f ( k ) 80 Stiffness for
Page 91 and 92:
82 The same process is now repeated
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84 Fig. 4.13 Flow chart of the SEIL
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(a) Fig. 5.1 Cable bending: (a) for
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The The sensor sensor is is mounted
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Fig. 5.4 Single cross-section secti
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5.2. The test set-up 92 To better o
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Stiffness EJ [N*m^2] Fig. 5.11 Bend
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This machine can handle tensile for
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5.3. The test cables A four-layer h
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The input values for the SEIL progr
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Triggered by the dx signal, a 150 p
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Sag [m] Fig. 6.1 Measured and calcu
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Sag [m] Fig. 6.4 Measured and calcu
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108 Fig. 6.6 also clearly shows tha
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Fig. 6.9 Hysteresis for Cardinal at
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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.
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The The trend trend determined here
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128 Even if the conductor model pos
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8. Prospects 130 In the last chapte
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Annexure I The The tensile stress s
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Considering Considering the the abo
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It follows that: If the angle is do
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The position of the catenary in the
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The The following following matrice
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For single component conductors: Fo
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144 CIGRE: Study Committee 22 - Wor
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146 Papailiou, Müller, Roll: Anwen
Page 157 and 158:
List of symbols Latin symbols 148 a
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ma mi mL 150 Friction summation fac
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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
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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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