CABLE SYSTEMS

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29 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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CABLE
STRUCTURES

SUBMITTED TO:

AR.KARAMJIT S.

CABLE SYSTEMS





MAJOR

SYSTEM



FORM

ACTIVE

STRUCTURE






SYSTEMS
.









Non

rigid,

flexible

matter

shaped

in

a

certain

way

and

secured

by

fixed

ends,

an

support

itself

&

span

space
.

The

transmit

loads

only

through

simple

normal

stresses
;

either

tension

or

through

compression
.


Two

cables

with

different

points

of

suspension

tied

together

form

a

suspension

system
.

A

cable

subject

to

external

loads

will

deform

in

a

way

depending

upon

the

magnitude

and

location

of

the

external

forces
.

The

form

acquired

by

the

cable

is

called

the

FUNICULAR

SHAPE

of

the

cable
.


#

Form

Active

Structure

Systems

redirect

external

forces

by

simple

normal

stresses

:

the

arch

by

compression,

the

suspension

cable

by

tension
.

The

bearing

mechanism

of

form

active

systems

vests

essentially

on

the

material

form
.






#

The

natural

stress

line

of

the

form

active

tension

system

in

the

funicular

tension

line
.


#

Any

change

of

loading

or

support

conditions

changes

the

form

of

the

funicular

curve
.


Form

active

systems

because

of

their

dependence

on

loading

conditions

are

strictly

governed

by

the

natural

‘flow

of

forces’

and

hence

cannot

become

subject

to

arbitrary

free

form

design
.

LOADING MECHANISM :


#

The

high

tensile

strength

of

steel,

combined

with

the

efficiency

of

simple

tension,

makes

a

steel

cable

the

ideal

structural

element

to

span

large

distances
.


#

Cables

are

flexible

because

o

their

large

shall

lateral

dimensions

in

relation

to

their

lengths
.

As

uneven

stresses

true

to

bending

are

prevented

by

flexibility

the

tensile

load

is

evenly

divided

among

the

cable

strands
.


In

order

to

understand

the

mechanism

by

means

of

which

a

cable

supports

vertical

loads,

one

may

first

consider

a

cable

suspended

between

two

fixed

points,

located

at

the

same

level

and

carrying

a

single

load

at

mid

span
.

Under

the

action

of

the

load

the

cable

assumes

a

symmetrical

triangular

shape

and

half

the

load

is

carried

to

each

support

by

simple

tension

along

he

two

halves

of

the

cable
.

CABLE SAG :



The

triangular

shape

acquired

by

the

cable

is

characterized

by

the

SAG

:

the

vertical

distance

between

the

supports

and

the

lowest

point

in

the

cable
.

Without

the

sag

the

cable

cannot

carry

the

load,

since

the

tensile

forces

in

if

would

be

horizontal

and

horizontal

forces

cannot

balance

the

vertical

load
.

The

undivided

pull

of

the

sagging

cable

on

each

support

may

be

split

into

two

components

:




a

downward

force

equal

to

half

the

load



a

horizontal

inward

pull

or

thrust
.





The

thrust

is

inversely

proportional

to

the

sag
;

halving

the

sag

doubles

the

thrust
.

This

raises

an

interesting

question

of

economy

through
.


OPTIMAL SAG :



A

large

sag

increases

the

cable

length,

but

reduces

the

tensile

force

&

allows

a

reduction

of

cross
-
section
.

A

similar

sag

requires

a

larger

cross
-
section
.

Hence

the

total

volume

of

cable

(product

of

cross
-
section

&

length),

must

be

minimum

for

some

optimal

value

of

sag





Optimal

sag

equal

half

the

span

for

a

given

horizontal

distance

&

corresponds

to

a

symmetrical

45
o



triangle

cable

configuration

with

thrust

=

p/
2
.

GEOMETRIC FUNICULAR FORMS :



If

the

load

is

shifted

from

midspan

position,

the

cable

changes

shape
.

#

If

two

equal

loads

are

set

on

the

cable

in

symmetrical

positions

the

cable

adapts

itself

by

acquiring

a

new

configuration

with

three

straight

video
.

FUNICULAR POLYGONS
:

#

As

the

number

of

loads

increases,

the

funicular

polygon

approaches

a

geometrical

curve



the

PARABOLA

large

number

of

loads

are

evenly

spaced

horizontally
.

CATENARY
:


If

the

equal

loads

are

distributed

evenly

along

the

length

of

the

cable,

rather

than

horizontally,

the

funicular

curve

differs

from

a

parabola,

through

it

has

the

same

general

configuration
.

It

is

a

catenary
.



A

cable

carrying

its

own

weight

ad

a

loads

evenly

distributed

horizontally,

acquires

a

shape

that

is

intermediate

between

a

parabola

&

catenary
.

This

is

the

shape

of

cables

in

the

central

span

of

suspension

bridges
.

SPECIAL DESIGN CONSIDERATIONS:

(And Corrective Measures)


Lightness

of

the

flexible

suspension

cable

is

the

demerit

of

the

system,

which

can

be

largely

eliminated

through

pre
-
stressing

so

that

it

can

receive

frictional

forces

that

also

may

be

upward

directed
.


Cable

structures

are

more

correctly

categorize

into

either

suspension

structures

or

cable
-
stayed

structured

suspension

structures

can

be

typically

sub
-
classified

into

:


1
.

Single

Curvature

Structures

2
.

Double

Curvature

Structures

3.
Double

Cable

Structures


DYNAMIC EFFECTS OF WIND ON
TYPICAL FLEXIBLE ROOF
STRUCTURE :


A

critical

problem

in

the

design

of

any

cable

roof

structure

is

the

dynamic

effect

of

wind,

which

causes

an

undesirable

fluttering

of

the

roof
.

PREVENTIVE MEASURES :


There

are

only

several

fundamental

ways

to

combat

flutter
.



One

is

to

simply

increase

the

deal

load

on

the

roof
.



Another

is

to

provide

anchoring

guy

cables

at

periodic



points

to

tie

the

structure

to

the

ground
.



To

use

some

sort

of

crossed

cable

on

double
-
cable

system
.

The principal methods of providing stability are the
following:

(i) Additional permanent load supported on, or suspended from, the roof,
sufficient to neutralize the effects of asymmetrical variable actions or uplift
Figure 14a).

This arrangement has the drawback that it eliminates the lightweight
nature of the structure, adding significant cost to the entire structure.

(ii) Rigid members acting as beams, where permanent load may not be
adequate to counteract uplift forces completely, but where there is
sufficient flexural rigidity to deal with the net uplift forces, whilst availing of
cables to help resist effects of gravity loading (Figure 14b).

LIMITATIONS DUE TO VIBRATIONS &
CHANGING LOADS :


The

limitations

in

the

application

of

cables

stem

directly

from

their

adaptability

to

changing

loads

:

CABLES

are

unstable

and

stability

is

one

of

the

basic

requirements

of

structural

systems
.

The

trusses

hanging

from

the

cables

of

a

suspension

bridge

not

only

support

the

roadway

but

also

stiffen

the

cables

against

motions

due

to

moving

or

changing

loads
.

STIFFENING TRUSSES :


Stiffening

trusses

are

usually

rigid

in

the

direction

of

bridge

axis,

but

less

so

in

transverse

directions
.

Modern

suspension

bridges

are

made

sage

against

lateral

wind

displacements

by

using

stiffening

GUY

WIRES

OR

STAYS

which

have

the

double

role

of

supporting

the

truss

&

stabilizing

it
.


A
cable truss system

has a triangulated structural form
which increases stiffness, particularly under non
-
symmetric
loading.

Double
-
layer prestressed cable
-
truss system

DESIGN OF SUPPORTING ELEMENTS :


In

addition

to

actual

roof

cables,

other

structural

elements

egs
.

masts,

guy

cables

are

needed

to

make

a

building

structure
.

The

elements

typically

support

the

cable

in

space

and

provide

means

of

transferring

its

vertical

&

horizontal

thrusts

to

the

ground
.

The

design

of

these

elements

is

as

crucial

as

the

cable

design
.

APPLICATIONS OF CABLE SYSTEMS :


The

earliest

use

of

cables

in

buildings

dates

back

to

A
.
D
.

70

to

roof

a

Roman

amphitheater

by

a

rope

cable

structure
.

Rope

cables

anchored

to

masts

spanned

in

a

radial

fashion

across

the

open

structure

supported

a

movable

sunshade

that

could

be

drawn

across

to

cover

the

arena
.

The

span

was

620

ft
.

along

major

axis

and

513

ft
.

along

minor

axis
.



Today the longest suspension bridge has a span of
1410 m. (4226 ft.); the longest suspension roof; the
Burgo Paper Mill in Mantcia has a span of 163 m. (535
ft.). The roof was designed like a suspension bridge.
The cable flexibility is not wholly advantageous as in
bridge. Excessive vibrations can not be tolerated in a
building. Water proofing of the roof is difficult. Most
suspension roofs are therefore prestressed to reduce
their flexibility & some also have concrete roofs.


The

first

modern

roof

was

an

Arena
.

Load

bearing

cables

are

suspended

from

two

intersecting

arches,

anchored

against

one

another
.

At

night

angles

to

the

load

bearing

are

secondary

cables

prestressed

to

ensure

tautness

even

on

a

hot

day
.

Corrugated

sheets

supported

on

the

cable

network
.


Suspension

roof

with

parallel

cables

anchored

to

reinforced

conc
.

Structure

supporting

the

banked

seats
.

The

horizontal

reaction

is

absorbed

by

cables

buried

in

the

floor

structure
.



Raleigh
Arena(span
-
99m)

Yale University
-
skating rink

Structures using suspended cables have a
functional advantage for arenas, because the
shape is better suited to an array of banked seats
than that of a dome. A suspension roof requires a
smaller volume of air than a dome. This can
produce imp. economics in air
-
conditioning &
heating.

Roof over sports arena, Munich by Fvei Offo.
Approximate span of the structure is 130 m. (430 ft.).
The tentlike simplicity of this prestressed cable
structure is deceptive. The roof
-
over the entire sports
arena cost about $48 million. The design required
a great deal of theory as well as model analysis.




Memorial

Auditorium

in

Litica,

New

York
.

Span



73

m

(
240

ft
.
)
.

Two

sets

of

cables,

are

separated

by

struts

that

cause

them

to

act

in

conjunction
.

The

amount

of

prestress

for

upper

and

lower

cables

varied
.

Vibrations

in

one

set

of

cables

are

different

or

out

of

phase

with

the

other

and

the

opposing

forces

damp

the

vibration

of

the

structure
.


A

double

layer

of

cables

covered

with

pre
-
cast

concrete

slabs
.

These

were

loaded

temporarily

with

a

large

weight

of

building
.

Materials

to

prestress

the

cables,

and

the

joints

between

concerete

slabs

were

then

filled

with

cement

mortar

to

auction

the

prestress
.

Rainwater

was

pumped

off

the

roof
.


Cables

can

be

used

to

increase

the

span

of

cantilevers

and

is

particularly

useful

for

aircraft

hangars

and

other

buildings

than

require

large

entrances

as

well

as

unobstructed

interior

span
.


Cable
-
stiffened

cantilever

roof
.

The

structure

is

several

100
%

stronger

than

the

cantilever

on

its

own
.

The

cable

provides

the

tensile

component

of

the

resistant

moment,

so

that

the

cantilever

becomes

the

compression

member,

and

the

distance

between

the

cantilever

&

cable

of

the

support

provides

the

lever

arm

of

the

resistance

moment
.


Other

applications

of

cable

structures

can

be

for

exhibition

pavilions,

sports

complexes,

army

shelters

etc
.

MATERIALS :


Steel,

nylon

ropes

or

plasticated

cables

may

be

used

for

different

structures
.



Steel

Cables

:

The

high

tensile

strength

of

steel

combined

with

the

efficiency

of

simple

tension,

makes

a

steel

cable

the

ideal

structural

element

to

span

large

distances
.



Nylon

and

plastics

are

suitable

only

for

temporary

structures,

spanning

small

distances
.


other

structural

members

like

masts,

compression

rings,

arches

or

beams

and

compression

struts

may

be

of

concrete

or

steel

preferably
.

Struts

may

also

be

of

timber
.


Suspension

Cables
,

because

of

their

being

stressed

only

by

simple

tension



with

regard

to

weight/span

are

the

most

economical

system

of

spanning

space
.


Because

of

their

identity

with

the

natural

flow

of

forces,

the

form

active

structure

system

is

a

suitable

mechanism

for

achieving

long

spans

and

forming

large

spaces
.


Suspension

cables

are

the

elementary

idea

for

any

bearing

mechanism

and

consequently

the

very

symbol

of

man’s

technical

Seizure

of

space
.


Before

of

their

long

span

qualities,

they

have

a

particular

significance

for

mass

civilization

and

its

demand

for

large

scale

spaces
.

They

are

potential

structure

forms

for

future

building
.