Cable Structure Cables are often used in engineering structures for support and to transmit loads...
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Transcript of Cable Structure Cables are often used in engineering structures for support and to transmit loads...
Cable Structure
Cables are often used in engineering structures for support and to transmit loads from one member to another. When used to support suspension bridges, cables form the main load-carrying element in the structure.
Note: Cable can only carrying tensile force.
Parabolic equation of Cable
( )y kx L x
2
Lx y h
2
2
( )2 2
44
L Lh k L
Lh k
hk
L
2
4 ( )hx L xy
L
Cable supported at same level
0 :
2
y
A B
F
wLR R
Consider free body diagram at left hand side of C:
2
0 :
02 4 2
8
C
A
M
wL L LHh R
wLH
h
Maximum tensile force in the cable, 2 2max AT R H
Cable supported at different level
Consider cable ACB’:
2 221 1
11 1 1
2'
8 8 2
w l wlwLH
h d h d h d
Consider cable A’CB:
2 22 2
21 1
2
8 2
w l wlH
h h
But H1 = H2 = H, then
2 2
1 2
1 1
1 1
2 1
2 2
wl wl
h d h
l h d
l h
Lowest position equation
Vertical Reactions RA and RB
0 :2
0 :2
B A
A B
wL HdM R
LwL Hd
M RL
Tensile force in the cable at A and B
2 2 2 2gA A gB BT R H T R H
CABLE SUPPORT
Two types – Sokong Takal Pandu, Roller Support
Sokong Takal Pandu
Smooth Pulley:
Tp = Tg =T
Reactions from tower (menara):
cos cos
sin sin
m
m
R T
H T
Menara
Driven pulley support
Roller Support
To ensure the roller not moves laterally:
sin sinp gT T
Note: p gT T
Equilibrium Vertically:
cos cosm p gR T T
Example 7.1
Figure below shows a cable structure supported by frictionless roller which is located on top of tower. Determine:
(a) Maximum and minimum tensile force exerted by the cable(b) Vertical reaction force exerted by tower at A and B
Solution
Find l1 and l2
1
2
1 2
3 4.51.581 ( )
3
30 ( )
la
l
l l b
Solving equations (a) and (b) give l1 = 18.376 m and l2 = 11.623 m
Find H
2 2222 6.5 2 11.623
146.358 8(3) 24
w lwLH kN
h
or
2 2212 6.5 2 18.376
146.338 8(3 4.5) 8(3 4.5)
w lwLH kN
h
Find RA and RB in the cable
Take H = 146.35 kN
6.5 30 146.35 4.50 : 75.5
2 2 306.5 30 146.35 4.5
0 : 119.52 2 30
B A
A B
wL HdM R kN
L
wL HdM R kN
L
Find tensile force exerted by the cable (at A and B)2 2 2 2
2 2 2 2
75.5 146.35 165
119.5 146.35 189
gA A
gB B
T R H kN
T R H kN
Maximum tensile force occurred at B, minimum tensile force occurred at C (lowest point in the cable) (=H=146.35 kN)
(b) Reaction forces exerted by the tower
0 : sin
sin 90 30 146.35
169
0 : cos
169cos60 75.5
160
x pA
pA
pA
y m pA A
F T H
T
T kN
F R T R
kN
0 : sin
sin 90 30 146.35
169
0 : cos
169cos60 119.5
204
x pB
pB
pB
y m pB B
F T H
T
T kN
F R T R
kN