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PREPARED BY : ENG. MAMOON ARIA
SAHIBI
CABLES AND SUSPENSION
BRIDGE
Index
•Introduction
•Function of bridge
•Main element
•Forces exceed on the bridge
•Examples
INTRODUCTION
• A SUSPENSION BRIDGE IS A TYPE OF BRIDGE IN WHICH THE DECK (THE
LOAD-BEARING PORTION) IS HUNG BELOW SUSPENSION CABLES ON
VERTICAL SUSPENDERS. THE FIRST MODERN EXAMPLES OF THIS TYPE OF
BRIDGE WERE BUILT IN THE EARLY 19TH CENTURY. SIMPLE SUSPENSION
BRIDGES, WHICH LACK VERTICAL SUSPENDERS, HAVE A LONG HISTORY IN
MANY MOUNTAINOUS PARTS OF THE WORLD.
• THIS TYPE OF BRIDGE HAS CABLES SUSPENDED BETWEEN TOWERS, PLUS
VERTICAL SUSPENDER CABLES THAT CARRY THE WEIGHT OF THE DECK
BELOW, UPON WHICH TRAFFIC CROSSES. THIS ARRANGEMENT ALLOWS
THE DECK TO BE LEVEL OR TO ARC UPWARD FOR ADDITIONAL
CLEARANCE. LIKE OTHER SUSPENSION BRIDGE TYPES, THIS TYPE OFTEN IS
CONSTRUCTED WITHOUT FALSE WORK.
• THE SUSPENSION CABLES MUST BE ANCHORED
AT EACH END OF THE BRIDGE, SINCE ANY LOAD
APPLIED TO THE BRIDGE IS TRANSFORMED INTO A
TENSION IN THESE MAIN CABLES. THE MAIN
CABLES CONTINUE BEYOND THE PILLARS TO DECK-
LEVEL SUPPORTS, AND FURTHER CONTINUE TO
CONNECTIONS WITH ANCHORS IN THE GROUND.
THE ROADWAY IS SUPPORTED BY VERTICAL
SUSPENDER CABLES OR RODS, CALLED HANGERS.
IN SOME CIRCUMSTANCES, THE TOWERS MAY SIT
ON A BLUFF OR CANYON EDGE WHERE THE ROAD
MAY PROCEED DIRECTLY TO THE MAIN SPAN,
OTHERWISE THE BRIDGE WILL USUALLY HAVE TWO
SMALLER SPANS, RUNNING BETWEEN EITHER PAIR
OF PILLARS AND THE HIGHWAY, WHICH MAY BE
SUPPORTED BY SUSPENDER CABLES OR MAY USE A
TRUSS BRIDGE TO MAKE THIS CONNECTION. IN
THE LATTER CASE THERE WILL BE VERY LITTLE ARC
IN THE OUTBOARD MAIN CABLES.
FUNCTION OF A BRIDGE
To connect two
communities which are
separated by streams,
valley, railroads, etc.
•Suspension bridges are
used for highways , where
the span of a bridge is more
than 200m.
MAIN ELEMENTS
i. MAIN CABLE
ii. SUSPENDERS
iii.DECKING AND STIFFENING GIRDER
iv.SUPPORTING TOWER
v. ANCHOR CABLE
HORIZONTAL REACTION
A
VA VB
B
T T
HH
W KN/m
reactionHorizontal
8
8
48
228
2
2
2
22
2





d
wL
dH
wL
dH
wLwL
dH
LwLwL
dH
wL
VV BA
Equation of horizontal reaction
Taking moments
about c, on the right
side of c
CABLE TENSION AT ENDS
ß
p
B
H
T
T w kN/m
?
• THE CABLE TENSION T AT ANY END IS THE RESULTANT OF
VERTICAL AND HORIZONTAL REACTION AT THE END.
2
2
2
42
2
2
2
16
1
2
64
)
2
(
)
8
()
2
(
d
LwL
T
d
LwwL
T
d
wLwL
TTT BA



• T= TENSION AT ANY POINT P OF THE CABLE
• Ɵ=INCLINATION OF THE TANGENT AT P WITH HORIZONTAL
CONSIDER EQUILIBRIUM OF PART PB
• RESOLVING THE FORCES ON THIS PART HORIZONTALLY.
• MINIMUM TENSION IN CABLE WILL OCCUR AT C
cosTH 
HTT c  min
• MAXIMUM TENSION IN CABLE WILL OCCUR AT ENDS
• THE INCLINATION Β OF T WITH VERTICAL IS GIVEN BY,
2
2
max
16
1
2 d
LwL
T 
d
LwL
d
wL
42
/
8V
H
tan
2

SHAPE OF THE CABLE
• UNDER THE UNIFORMLY DISTRIBUTED LOAD THE CABLE
TAKES THE FROM OF A PARABOLA
• THE EQUATION OF CABLE , WITH EITHER SUPPORT AS
ORIGIN WILL BE,
)(
4
2
xLx
L
d
y 
LENGTH OF THE CABLE
• THE EQUATION OF PARABOLA, WITH C AS THE ORIGIN CAN BE
WRITTEN AS ,
• CONSIDER AN ELEMENT OF LENGTH DS OF THE CURVE, HAVING
COORDINATES X AND Y.
2
2
2
8
4
L
xd
dx
dy
x
L
d
y



dx
L
xd
ds
L
xd
L
xd
dx
ds
L
xd
L
xd
dx
ds
dx
dy
dxds
dydxds





 



























4
22
4
22
4
22
2
1
4
22
4
22
2
22
321
ofpowershighernegleting
andtheorembinominalbyExpanding
64
2
1
1
64
1
64
1
1

• TOTAL LENGTH OF THE CABLE,
cable.theoflengthTotal
3
8
3
4
2
2
3
32
2
32
12
2
4
3
2
2
0
3
4
2
2
0 4
22





















 
L
d
LS
L
L
d
L
S
x
L
d
xS
dx
L
xd
S
L
L
ANCHOR CABLES
• THE MAIN CABLES ATTACH TO THE ENDS OF THE DECK,
RATHER THAN TO THE GROUND VIA LARGE ANCHORAGES. THE
DESIGN IS WELL-SUITED FOR CONSTRUCTION ATOP ELEVATED
PIERS, OR IN AREAS OF UNSTABLE SOILS WHERE ANCHORAGES
WOULD BE DIFFICULT TO CONSTRUCT.
• THERE ARE GENERALLY TWO ARRANGEMENT USED
1. THE SUSPENSION CABLE CAN BE PASSED OVER THE GUIDE
PULLEY FOR ANCHORING IT TO THE OTHER SIDE
2. THE SUSPENSION CABLE AND ANCHOR CABLE CAN BE
ATTACHED TO A SADDLE MOUNTED ON ROLLERS.
ß1 ß2
suspension
cable
Anchor
cable
ß2 ß1
Anchor
cable suspencion
cable
Guide pulley
arrangement
Saddle on roller
arrangement
•IN CASE OF GUIDE PULLEY ARRANGEMENT, THE
SUSPENSION CABLE PASSES OVER THE GUIDE PULLEY .
=INCLINATION OF THE SUSPENSION CABLE WITH
VERTICAL
=INCLINATION OF THE ANCHOR CABLE WITH
VERTICAL
VERTICAL PRESSURE ON TOP OF PIER,
HORIZONTAL PRESSURE ON TOP OF PIER,
 21 coscos  TVp
 21 sinsin  THp
1
2
• IN CASE OF SADDLE ON ROLLER ARRANGEMENT, ROLLERS DO
NOT HAVE ANY HORIZONTAL REACTION. THEREFORE, THE
HORIZONTAL COMPONENTS OF THE TENSIONS IN THE
SUSPENSION CABLE AND THE ANCHOR CABLE WILL BE EQUAL.
• THE VERTICAL PRESSURE ON THE TOP OF THE PIER IS,
HTT  2211 sinsin 
2211 coscos  TTVp 
SUNSHINE SKYWAY BRIDGE, USA
Completion Date: 1987 Cost: $244 Million
Length: 29,040 feet Type: Cable
Stayed
Materials: Steel, Concrete Span: 1200
feet
AKASHI KAIKYO BRIDGE, JAPAN
Completion Date: 1998 Cost: $4.3 billion
Length: 12,828 feet Type: Suspension
Materials: Steel Span: 6,527 feet

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Easy Suspension Bridge - پل کیبلی آسان

  • 1. PREPARED BY : ENG. MAMOON ARIA SAHIBI
  • 2.
  • 3. CABLES AND SUSPENSION BRIDGE Index •Introduction •Function of bridge •Main element •Forces exceed on the bridge •Examples
  • 4. INTRODUCTION • A SUSPENSION BRIDGE IS A TYPE OF BRIDGE IN WHICH THE DECK (THE LOAD-BEARING PORTION) IS HUNG BELOW SUSPENSION CABLES ON VERTICAL SUSPENDERS. THE FIRST MODERN EXAMPLES OF THIS TYPE OF BRIDGE WERE BUILT IN THE EARLY 19TH CENTURY. SIMPLE SUSPENSION BRIDGES, WHICH LACK VERTICAL SUSPENDERS, HAVE A LONG HISTORY IN MANY MOUNTAINOUS PARTS OF THE WORLD. • THIS TYPE OF BRIDGE HAS CABLES SUSPENDED BETWEEN TOWERS, PLUS VERTICAL SUSPENDER CABLES THAT CARRY THE WEIGHT OF THE DECK BELOW, UPON WHICH TRAFFIC CROSSES. THIS ARRANGEMENT ALLOWS THE DECK TO BE LEVEL OR TO ARC UPWARD FOR ADDITIONAL CLEARANCE. LIKE OTHER SUSPENSION BRIDGE TYPES, THIS TYPE OFTEN IS CONSTRUCTED WITHOUT FALSE WORK.
  • 5. • THE SUSPENSION CABLES MUST BE ANCHORED AT EACH END OF THE BRIDGE, SINCE ANY LOAD APPLIED TO THE BRIDGE IS TRANSFORMED INTO A TENSION IN THESE MAIN CABLES. THE MAIN CABLES CONTINUE BEYOND THE PILLARS TO DECK- LEVEL SUPPORTS, AND FURTHER CONTINUE TO CONNECTIONS WITH ANCHORS IN THE GROUND. THE ROADWAY IS SUPPORTED BY VERTICAL SUSPENDER CABLES OR RODS, CALLED HANGERS. IN SOME CIRCUMSTANCES, THE TOWERS MAY SIT ON A BLUFF OR CANYON EDGE WHERE THE ROAD MAY PROCEED DIRECTLY TO THE MAIN SPAN, OTHERWISE THE BRIDGE WILL USUALLY HAVE TWO SMALLER SPANS, RUNNING BETWEEN EITHER PAIR OF PILLARS AND THE HIGHWAY, WHICH MAY BE SUPPORTED BY SUSPENDER CABLES OR MAY USE A TRUSS BRIDGE TO MAKE THIS CONNECTION. IN THE LATTER CASE THERE WILL BE VERY LITTLE ARC IN THE OUTBOARD MAIN CABLES.
  • 6. FUNCTION OF A BRIDGE To connect two communities which are separated by streams, valley, railroads, etc. •Suspension bridges are used for highways , where the span of a bridge is more than 200m.
  • 7. MAIN ELEMENTS i. MAIN CABLE ii. SUSPENDERS iii.DECKING AND STIFFENING GIRDER iv.SUPPORTING TOWER v. ANCHOR CABLE
  • 10. CABLE TENSION AT ENDS ß p B H T T w kN/m ?
  • 11. • THE CABLE TENSION T AT ANY END IS THE RESULTANT OF VERTICAL AND HORIZONTAL REACTION AT THE END. 2 2 2 42 2 2 2 16 1 2 64 ) 2 ( ) 8 () 2 ( d LwL T d LwwL T d wLwL TTT BA   
  • 12. • T= TENSION AT ANY POINT P OF THE CABLE • Ɵ=INCLINATION OF THE TANGENT AT P WITH HORIZONTAL CONSIDER EQUILIBRIUM OF PART PB • RESOLVING THE FORCES ON THIS PART HORIZONTALLY. • MINIMUM TENSION IN CABLE WILL OCCUR AT C cosTH  HTT c  min
  • 13. • MAXIMUM TENSION IN CABLE WILL OCCUR AT ENDS • THE INCLINATION Β OF T WITH VERTICAL IS GIVEN BY, 2 2 max 16 1 2 d LwL T  d LwL d wL 42 / 8V H tan 2 
  • 14. SHAPE OF THE CABLE • UNDER THE UNIFORMLY DISTRIBUTED LOAD THE CABLE TAKES THE FROM OF A PARABOLA • THE EQUATION OF CABLE , WITH EITHER SUPPORT AS ORIGIN WILL BE, )( 4 2 xLx L d y 
  • 15. LENGTH OF THE CABLE • THE EQUATION OF PARABOLA, WITH C AS THE ORIGIN CAN BE WRITTEN AS , • CONSIDER AN ELEMENT OF LENGTH DS OF THE CURVE, HAVING COORDINATES X AND Y. 2 2 2 8 4 L xd dx dy x L d y   
  • 17. • TOTAL LENGTH OF THE CABLE, cable.theoflengthTotal 3 8 3 4 2 2 3 32 2 32 12 2 4 3 2 2 0 3 4 2 2 0 4 22                        L d LS L L d L S x L d xS dx L xd S L L
  • 18. ANCHOR CABLES • THE MAIN CABLES ATTACH TO THE ENDS OF THE DECK, RATHER THAN TO THE GROUND VIA LARGE ANCHORAGES. THE DESIGN IS WELL-SUITED FOR CONSTRUCTION ATOP ELEVATED PIERS, OR IN AREAS OF UNSTABLE SOILS WHERE ANCHORAGES WOULD BE DIFFICULT TO CONSTRUCT. • THERE ARE GENERALLY TWO ARRANGEMENT USED 1. THE SUSPENSION CABLE CAN BE PASSED OVER THE GUIDE PULLEY FOR ANCHORING IT TO THE OTHER SIDE 2. THE SUSPENSION CABLE AND ANCHOR CABLE CAN BE ATTACHED TO A SADDLE MOUNTED ON ROLLERS.
  • 19. ß1 ß2 suspension cable Anchor cable ß2 ß1 Anchor cable suspencion cable Guide pulley arrangement Saddle on roller arrangement
  • 20. •IN CASE OF GUIDE PULLEY ARRANGEMENT, THE SUSPENSION CABLE PASSES OVER THE GUIDE PULLEY . =INCLINATION OF THE SUSPENSION CABLE WITH VERTICAL =INCLINATION OF THE ANCHOR CABLE WITH VERTICAL VERTICAL PRESSURE ON TOP OF PIER, HORIZONTAL PRESSURE ON TOP OF PIER,  21 coscos  TVp  21 sinsin  THp 1 2
  • 21. • IN CASE OF SADDLE ON ROLLER ARRANGEMENT, ROLLERS DO NOT HAVE ANY HORIZONTAL REACTION. THEREFORE, THE HORIZONTAL COMPONENTS OF THE TENSIONS IN THE SUSPENSION CABLE AND THE ANCHOR CABLE WILL BE EQUAL. • THE VERTICAL PRESSURE ON THE TOP OF THE PIER IS, HTT  2211 sinsin  2211 coscos  TTVp 
  • 22. SUNSHINE SKYWAY BRIDGE, USA Completion Date: 1987 Cost: $244 Million Length: 29,040 feet Type: Cable Stayed Materials: Steel, Concrete Span: 1200 feet
  • 23. AKASHI KAIKYO BRIDGE, JAPAN Completion Date: 1998 Cost: $4.3 billion Length: 12,828 feet Type: Suspension Materials: Steel Span: 6,527 feet