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

More documents

Recommendations

Info

Fig. 2.17 Cable curvature in the MM-B diagram (a) κb < κm : no hysteresis (b) κb > κm : hysteresis; left: first stress, right: subsequent stress Case (b) The final curvature κb reached from the friction friction-free state, following external stress Mb, , is larger than the transition curvature: κb > κm Above Above the transition transition curvature, curvature, the the cable can only assume states that that are on the straight line in Fig. 2.17b, with the slope (EJ) min. The balance of moments is now: M b=M R+ ( EJ ) min κ b where MR is is the the max. max. possible possible friction friction moment (remanent friction moment) in in acc. acc. with (2.43). The above can now be used to construct the M-B M B diagram for a cable for a complete cycle of increasing and decreasing load. 35
Fig. 2.18 Hysteresis in the M-B B diagram as a cable bends Departing from the origin (M = 0, κ = 0), the cable follows the straight line � with the slope of (EJ) (EJ)max (undisturbed cable) until the transition curvature κm is reached, then following the straight straig line � with the slope of (EJ) min. . In this process, the maximum friction moment M MR, , applicable at the break point, remains “frozen” in the cable. If the stress direction is now reversed at the maximum stress (M (Mb/κb) ) (stress reduction), the cable initially follows the straight line � with the slope of (EJ)max (EJ) and running parallel to straight line �, i.e. it opposes the stress relieving moment with the maximum bending stiffness (EJ) max. . In this process, the “frozen” remanent friction moment M MR must first be relieved along the curvature path κm. m From From this this point point onwards, onwards, which which can can be be viewed viewed as as a new “origin” for for the cable, the the process process during stress stress increase is repeated analogously, but in reverse order (straight line � and �). ). If the stress is again reversed, the cable follows straight line � to get to the original origin again, thereby closing the hysteresis loop (in the illustrated case). 36
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 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: During During bending in in Region
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
Page 93 and 94: 84 Fig. 4.13 Flow chart of the SEIL
Page 95 and 96:
(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
Page 101 and 102:
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
Page 123 and 124:
6.5. Effect of the sample length 11
Page 125 and 126:
116 Force--displacement curve Fig.
Page 127 and 128:
This This is is based based on on e
Page 129 and 130:
Secondary stress [N/mm^2] Secondary
Page 131 and 132:
After After the the wire stresses s
Page 133 and 134:
124 The above is summarised in Fig.
Page 135 and 136:
The The trend trend determined here
Page 137 and 138:
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
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?