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