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# Cables - Module 5 Cables and Arches Lesson 31 Notes | EduRev

## : Cables - Module 5 Cables and Arches Lesson 31 Notes | EduRev

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Module
5
Cables and Arches
Version 2 CE IIT, Kharagpur

Page 2

Module
5
Cables and Arches
Version 2 CE IIT, Kharagpur

Lesson
31
Cables
Version 2 CE IIT, Kharagpur

Page 3

Module
5
Cables and Arches
Version 2 CE IIT, Kharagpur

Lesson
31
Cables
Version 2 CE IIT, Kharagpur

Instructional Objectives:
After reading this chapter the student will be able to
1. Differentiate between rigid and deformable structures.
2. Define funicular structure.
3. State the type stress in a cable.
4. Analyse cables subjected to uniformly distributed load.
5. Analyse cables subjected to concentrated loads.

31.1  Introduction
Cables and arches are closely related to each other and hence they are grouped
in this course in the same module. For long span structures (for e.g. in case
bridges) engineers commonly use cable or arch construction due to their
efficiency. In the first lesson of this module, cables subjected to uniform and
concentrated loads are discussed. In the second lesson, arches in general and
three hinged arches in particular along with illustrative examples are explained.
In the last two lessons of this module, two hinged arch and hingeless arches are
considered.
Structure may be classified into rigid and deformable structures depending on
change in geometry of the structure while supporting the load. Rigid structures
support externally applied loads without appreciable change in their shape
(geometry). Beams trusses and frames are examples of rigid structures. Unlike
rigid structures, deformable structures undergo changes in their shape according
to externally applied loads. However, it should be noted that deformations are still
small. Cables and fabric structures are deformable structures. Cables are mainly
used to support suspension roofs, bridges and cable car system. They are also
used in electrical transmission lines and for structures supporting radio antennas.
In the following sections, cables subjected to concentrated load and cables
subjected to uniform loads are considered.

Version 2 CE IIT, Kharagpur

Page 4

Module
5
Cables and Arches
Version 2 CE IIT, Kharagpur

Lesson
31
Cables
Version 2 CE IIT, Kharagpur

Instructional Objectives:
After reading this chapter the student will be able to
1. Differentiate between rigid and deformable structures.
2. Define funicular structure.
3. State the type stress in a cable.
4. Analyse cables subjected to uniformly distributed load.
5. Analyse cables subjected to concentrated loads.

31.1  Introduction
Cables and arches are closely related to each other and hence they are grouped
in this course in the same module. For long span structures (for e.g. in case
bridges) engineers commonly use cable or arch construction due to their
efficiency. In the first lesson of this module, cables subjected to uniform and
concentrated loads are discussed. In the second lesson, arches in general and
three hinged arches in particular along with illustrative examples are explained.
In the last two lessons of this module, two hinged arch and hingeless arches are
considered.
Structure may be classified into rigid and deformable structures depending on
change in geometry of the structure while supporting the load. Rigid structures
support externally applied loads without appreciable change in their shape
(geometry). Beams trusses and frames are examples of rigid structures. Unlike
rigid structures, deformable structures undergo changes in their shape according
to externally applied loads. However, it should be noted that deformations are still
small. Cables and fabric structures are deformable structures. Cables are mainly
used to support suspension roofs, bridges and cable car system. They are also
used in electrical transmission lines and for structures supporting radio antennas.
In the following sections, cables subjected to concentrated load and cables
subjected to uniform loads are considered.

Version 2 CE IIT, Kharagpur

The shape assumed by a rope or a chain (with no stiffness) under the action of
external loads when hung from two supports is known as a funicular shape.
Cable is a funicular structure. It is easy to visualize that a cable hung from two
supports subjected to external load must be in tension (vide Fig. 31.2a and
31.2b). Now let us modify our definition of cable. A cable may be defined as the
structure in pure tension having the funicular shape of the load.

Version 2 CE IIT, Kharagpur

Page 5

Module
5
Cables and Arches
Version 2 CE IIT, Kharagpur

Lesson
31
Cables
Version 2 CE IIT, Kharagpur

Instructional Objectives:
After reading this chapter the student will be able to
1. Differentiate between rigid and deformable structures.
2. Define funicular structure.
3. State the type stress in a cable.
4. Analyse cables subjected to uniformly distributed load.
5. Analyse cables subjected to concentrated loads.

31.1  Introduction
Cables and arches are closely related to each other and hence they are grouped
in this course in the same module. For long span structures (for e.g. in case
bridges) engineers commonly use cable or arch construction due to their
efficiency. In the first lesson of this module, cables subjected to uniform and
concentrated loads are discussed. In the second lesson, arches in general and
three hinged arches in particular along with illustrative examples are explained.
In the last two lessons of this module, two hinged arch and hingeless arches are
considered.
Structure may be classified into rigid and deformable structures depending on
change in geometry of the structure while supporting the load. Rigid structures
support externally applied loads without appreciable change in their shape
(geometry). Beams trusses and frames are examples of rigid structures. Unlike
rigid structures, deformable structures undergo changes in their shape according
to externally applied loads. However, it should be noted that deformations are still
small. Cables and fabric structures are deformable structures. Cables are mainly
used to support suspension roofs, bridges and cable car system. They are also
used in electrical transmission lines and for structures supporting radio antennas.
In the following sections, cables subjected to concentrated load and cables
subjected to uniform loads are considered.

Version 2 CE IIT, Kharagpur

The shape assumed by a rope or a chain (with no stiffness) under the action of
external loads when hung from two supports is known as a funicular shape.
Cable is a funicular structure. It is easy to visualize that a cable hung from two
supports subjected to external load must be in tension (vide Fig. 31.2a and
31.2b). Now let us modify our definition of cable. A cable may be defined as the
structure in pure tension having the funicular shape of the load.

Version 2 CE IIT, Kharagpur

31.2   Cable subjected to Concentrated Loads
As stated earlier, the cables are considered to be perfectly flexible (no flexural
stiffness) and inextensible. As they are flexible they do not resist shear force and
bending moment. It is subjected to axial tension only and it is always acting
tangential to the cable at any point along the length. If the weight of the cable is
negligible as compared with the externally applied loads then its self weight is
neglected in the analysis. In the present analysis self weight is not considered.

Consider a cable as loaded in Fig. 31.2. Let us assume that the cable
lengths  and sag at  ( ) are known. The four reaction
components at
ACDEB
4 3 2 1
, , , L L L L E D C , ,
e d c
h h h , ,
A andB , cable tensions in each of the four segments and three
sag values: a total of eleven unknown quantities are to be determined. From the
geometry, one could write two force equilibrium equations ( 0 , 0 = =
? ? y x
F F ) at
each of the point  and D C B A , , , E i.e. a total of ten equations and the required
one more equation may be written from the geometry of the cable. For example,
if one of the sag is given then the problem can be solved easily. Otherwise if the
total length of the cable  is given then the required equation may be written as  S

2 2
2
2 2
2
2 2
2
2 2
1
) ( ) ( ) (
e e d c d c
h h L h h L h h L h L S + + + - + + - + + + =     (31.1)

31.3   Cable subjected to uniform load.
Cables are used to support the dead weight and live loads of the bridge decks
having long spans. The bridge decks are suspended from the cable using the
hangers. The stiffened deck prevents the supporting cable from changing its
shape by distributing the live load moving over it, for a longer length of cable. In
such cases cable is assumed to be uniformly loaded.

Version 2 CE IIT, Kharagpur

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