Cables

Cables

Principal Elements for practical suspension systems

• Vertical supports or towers

• Main cables

• Anchorages

• Stabilizers

Vertical Supports or Towers

• Provide essential reactions that keep the cable system above the ground

• May be simple vertical or sloping piers or masts, diagonal struts, or a wall.

• Ideally, the axes of the supports should bisect the angle between the cables that pas over them

Main Cables

• Primary tensile elements

• Carry roof with a minimum of material

• Steel used in cable structures has breaking stresses that exceed 200,000 psi

Anchorages

• Because the cables are not vertical only, horizontal force resistance is required.

• In suspension bridges, the massive concrete abutments provide the horizontal reaction force

Stabilizers

• Lightweight roof or bridge systems are susceptible to pronounced undulation or fluttering when acted upon by wind forces.

• Cables resists load through tension.

• The destructive force is vibration or flutter

About cables

• Equal angles = equal forces

• What about unequal forces?

Cable Geometry and Characteristics

l

h

W

A B

l = cable span

L = AC + CB = cable length

h = sag

r = h/l = sag to span ratio

Cables with a Single Concentrated Load

'4.12'3'12 22 TTTT

yy

4.12

3

4.123

TTTT

xx

4.12

12

4.1212

W

C

BA

TT Ty

Tx Tx

Ty

l

h

l = 24’ h = 3’

3’

12’

L = 24.8’

2

02

0

WT

WT

F

y

y

y

WW

TT yx 223

12

3

12

Think – Pair - Share

TTTT

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4.12

3

4.123

2

02

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WT

WT

F

y

y

y

'4.12'3'12 22

TTTT

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C

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TTTy

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l

h

12’

3’

l = 6’ h = 12’

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3

12

3 WWTT yx

Can a cable system support a load if the cable is completely

horizontal?

There is no force, however great,

Can stretch a cord, however fine,

Into a horizontal line

That shall be absolutely straight.

-Lord Kelvin

W

l = L

T T

Cable – Stayed Bridges• Radial Parallel

• Look similar to suspensions bridges

– both have roadways that hang from cables

– both have towers

• Support the load of the roadway in very different ways.

• Difference - how the cables are connected to the towers.

• Suspension bridges - cables ride freely across the towers, transmitting the load to the anchorages at either end.

• Cable-stayed bridges, the cables are attached to the towers, which alone bear the load.

Trusses

Truss

• A truss is a triangulated assembly that distributes loads to supports through a combination of pin-connected members arranged in triangles

• Ideally all members are in either pure compression or tension (no bending or shear)

• All thrust force are resolved internally

Triangle

• The triangle is the basic geometric unit of the truss

• The triangle - shape cannot change without changing the length of it’s sides even when the joints are hinged

• All other hinged polygons are unstable

Truss terminology

• Top truss member – top chord

• Bottom truss member – bottom chord

• All members in between are web members

• Plane trusses – all members in a single plane

• Space trusses – 3D configuration

Roadway – under or over

Roof Trusses

Wrap-up

• Cables are in tension

• For a cable-stayed bridge, the weight of the bridge is supported by the towers

• The triangle is the most stable shape

• Trusses are comprised of triangles

• Members of trusses are in pure compression or pure tension