design
3.1.2 Rope length
For a rope, the horizontal projection length
(on base) is = l, maximum sag = bmax and the
difference in level between supports = h, the rope
length can be calculated from the basic equation
of the element of arc as follows:
dL= Sqrt (dx2+dy2)
Various authors have derived slightly different
formula for the rope length, which are as follows:
L = l + h2 + 8 b2max
2l 3 l
Chitary
L = l + h2 +
w2l3
Gulisashvili
2l 24T2Cos2β
When a rope is loaded with trolley, the length of
the rope can be calculated using the formula:
L = l + h2 + w2l3 + x (l-x)W (W + wl) Gulisashvili
2l 24T2Cos2β 2l T2 Cosβ
3.1.3 Stresses in rope
The rope in the gravity ropeway is subjected
to tensile stress due to its own weight and the
bending stress caused by the live load.
The maximum stress on the rope, σmax = σt+σb
σt> σb must be maintained to avoid the loosening
of wire rope.
3.1.4 Load consideration
The gravity ropeway is subjected to the following
loads while in operation:
a) Wind load
b) Dead load
c) Live load
d) Temperature stress
e) Impact load
f) Seismic load
g) Dynamic load
The seismic load is not considered in the design
whereas dynamic load is partially considered.
Wind load: The maximum wind load is considered
as 1.3 kN/m2 in lateral direction corresponding to
160 km/hr wind speed w= 1.05. V2 kg
V is in metre per second.
16 m2
where
For calculating the tension in the rope, the wind
load is considered to act at an inclination of 20
degrees to horizontal direction.
Dead load: Weight of the rope, which is considered
uniformly distributed.
Live load: It consists of weight of the trolley,
weight of the goods and half the weight of the
haulage rope. It is considered as point load in
calculation.
Temperature stress: This stress is developed in the
rope due to the variation in the temperature at the
time of operation and at the time of installation.
More importantly, the elongation or contraction
caused by the temperature variation is important
in gravity ropeway as the rope length is usually
very high up to 1.5 km.
The change in the rope length is expressed as:
Δl = αΔt.L
Where α= Coefficient of thermal expansion which
is equal to 12x10-6 /0 C
Δt = temperature change
Approximate change of sag (Δb) can be found
from the equation:
Δb = 15.ΔL.l
16b[5-24(b/l)2 ]
Impact load: Upon sudden application of brake,
impact load is produced in the ropeway system.
The impact load is mainly carried by the haulage
rope so a certain percentage of impact load is to
be considered in the haulage rope design. As it is
difficult to ascertain the amount of impact load
transferred to haulage rope, it is considered to be
50 per cent of the maximum possible impact load.
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