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

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

 Page 1


  
 
 
 
 
 
 
 
 
 
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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