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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
xx
4.12
3
4.123
2
02
0
WT
WT
F
y
y
y
'4.12'3'12 22
TTTT
yy
4.12
12
4.1212W
C
BA
TTTy
Tx Tx
Ty
l
h
12’
3’
l = 6’ h = 12’
8212
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
