cables and arches

1. STRUCTURAL ANALYSIS
Chapter 5:
Cables and Arches

2. CABLES
Cables are often used in engineering structures for
support and to transmit loads from one member to
another. When used to support suspension roofs,
bridges, and trolley wheels, cables form the main
load-carrying element in the structure. In the force
analysis of such systems, the weight of the cable
itself may be neglected; however, when cables are
used as guys for radio antennas, electrical
transmission lines, and derricks, the cable weight
may become important and must be included in the
structural analysis. Two cases will be considered in
the sections that follow: a cable subjected to
concentrated loads and a cable subjected to a
distributed load.

3.  Cable is perfectly flexible & inextensible
 No resistance to shear/bending: same as truss bar
 The force acting the cable is always tangent to the cable at
points along its length
CABLES: ASSUMPTIONS
Only axial force!

4. Determine the tension in each segment of the cable. Also,
what is the dimension h?
EXAMPLE 5.1 UNDER CONCENTRATED FORCES
qBC
qBA

5. 
EXAMPLE 5.2 UNDER
CONCENTRATED FORCES

6.  If the cable supports a uniform load
over a projected horizontal distance,
then the shape of the cable takes
the form of a parabola.
 If cable supports only its own weight,
then the shape of the cable takes a
form of a catenary.
CABLES

7. CABLES (PARABOLA VS CATENARY)

8.  Neglect the cable weight which is
uniform along the length
 A cable subjected to its own weight
will take the form of a catenary
curve
 This curve ~ parabolic for small sag-
to-span ratio
CABLE SUBJECTED TO A UNIFORM
DISTRIBUTED LOAD (DIFFERENT ELEVATION)
Hangers are close and
uniformly spaced
If forces in the hangers are known
then the structure can be analyzed
1 degree of indeterminacy
Determinate structure hinge

9. PARABOLIC CABLE WITH DIFFERENT
SUPPORT ELEVATION
H
H
T2
T1
T2

10. The cable supports a girder which weighs 12kN/m.
Determine the tension in the cable at points A, B & C.
Determine also the reaction at support A and C.
EXAMPLE 5.2
12kN/m

11. EXAMPLE 5:3
The trusses are pin connected and suspended from
the parabolic cable. Determine the maximum force in the
cable when the structure is subjected to the loading shown.

12. PARABOLIC CABLE ON EVEN
ELEVATION
H
H T2
T
T

13. EXAMPLE 5:4
Determine the maximum and minimum tension in the
cable. Also determine the approximate length of the cable
The minimum tension of the cable is the tension at the lowest
support. And the maximum tension is the tension near the supports.

14. CATENARY CABLES ON EVEN
ELEVATIONS
y
H
T

15. CATENARY CABLES ON UNEVEN
ELEVATIONS
T

16. EXAMPLE 5:5

17. EXAMPLE 5.5

18. EXAMPLE 5.5

19. EXAMPLE 5:6

20. EXAMPLE 5.6

21. EXAMPLE 5.6

22. EXAMPLE 5.6

23. ARCH
flip
What if the load direction reverses?
FH
FH

24.  An arch acts as inverted cable so it receives compression
 An arch must also resist bending and shear depending upon how it
is loaded & shaped
ARCHES

25.  Types of arches
ARCHES
indeterminate
indeterminate
indeterminate
determinate

26. THREE-HINGED ARCH
Ax
Ay
By
Bx

27. Determine reactions at A and C and the cable force
PROBLEM 5-7
Ay
Ax
Cy
Ay
Ax
By
Bx
T

28. PROBLEM 5-7
Ay
Ax
Cy
Ay
Ax
By
Bx
T

29.  Determine the resultant forces at the pins A, B, and C of the
three-hinged arched roof truss.
EXAMPLE 5.7