Cables and Arches Structure - جامعة نزوى...The three-hinged open-spandrel arch bridge like...

Cables and Arches Structure

2/25/2013 Dr. Nasrellah H A 1

Cables are often used in engineering structures for support

and to transmit loads from one member to another

2/25/2013 Dr. Nasrellah H A 2

Cables Structure

Assumptions:

1. The cable is perfectly flexible. Due to its flexibility, the cable

offers no resistance to shear or bending and, therefore, the

force acting in the cable is always tangent to the cable at points

along its length.

2. The cable is inextensible that means it has a constant length

both before and after the load is applied. As a result, once the

load is applied, the geometry of the cable remains fixed, and

the cable or a segment of it can be treated as a rigid body.

2/25/2013 Dr. Nasrellah H A 3

I. Cable Subjected to Concentrated Loads

the problem is to determine the nine unknowns consisting of the

tension in each of the three segments, the four components of

reaction at A and B, and the sags and at the two points C and D.

2/25/2013 Dr. Nasrellah H A 4

For the solution we can write two equations of force

equilibrium at each of points A, B, C, and D. This results in a

total of eight equations. To complete the solution, it will be

necessary to know something about the geometry of the cable

in order to obtain the necessary ninth equation.

One possibility, is to specify one of the sags, either or instead

of the cable length. By doing this, the equilibrium equations

are then sufficient for obtaining the unknown forces and the

remaining sag.

2/25/2013 Dr. Nasrellah H A 5

Determine the tension in each segment of the cable

shown in Fig., what is the dimension h?

Example 1:

2/25/2013 Dr. Nasrellah H A 6

Solution:

2/25/2013 Dr. Nasrellah H A 7

2/25/2013 Dr. Nasrellah H A 8

I. Cable Subjected to Uniform Distributed Load

2/25/2013 Dr. Nasrellah H A 9

2/25/2013 Dr. Nasrellah H A 10

2/25/2013 Dr. Nasrellah H A 11

2/25/2013 Dr. Nasrellah H A 12

The cable in Fig. below supports a girder which weighs 850

lb/ft. Determine the tension in the cable at points A, B, and

C.

Example 2:

2/25/2013 Dr. Nasrellah H A 13

Solution:

2/25/2013 Dr. Nasrellah H A 14

2/25/2013 Dr. Nasrellah H A 15

2/25/2013 Dr. Nasrellah H A 16

Example 3:

2/25/2013 Dr. Nasrellah H A 17

The suspension bridge in Fig. below is constructed using the two

stiffening trusses that are pin connected at their ends C and

supported by a pin at A and a rocker at B. Determine the

maximum tension in the cable IH. The cable has a parabolic

shape and the bridge is subjected to the single load of 50 kN.

2/25/2013 Dr. Nasrellah H A 18

Solution:

2/25/2013 Dr. Nasrellah H A 19

2/25/2013 Dr. Nasrellah H A 20

2/25/2013 Dr. Nasrellah H A 21

Arches Structure

2/25/2013 Dr. Nasrellah H A 22

Like cables, arches can be used to reduce the bending moments in

long-span structures. Essentially, an arch acts as an inverted cable,

so it receives its load mainly in compression although, because of

its rigidity, it must also resist some bending and shear depending

upon how it is loaded and shaped.

In particular, if the arch has a parabolic shape and it is subjected to a

uniform horizontally distributed vertical load, then from the analysis

of cables it follows that only compressive forces will be resisted by the

arch.

Under these conditions the arch shape is called a funicular arch

because no bending or shear forces occur within the arch.

2/25/2013 Dr. Nasrellah H A 23

2/25/2013 Dr. Nasrellah H A 24

The three-hinged open-spandrel arch bridge like the one shown in

the photo has a parabolic shape. If this arch were to support a

uniform load and have the dimensions shown in Fig. below, show that

the arch is subjected only to axial compression at any intermediate point

such as point D. Assume the load is uniformly transmitted to the arch

ribs.

Example 4:

2/25/2013 Dr. Nasrellah H A 25

Solution:

2/25/2013 Dr. Nasrellah H A 26

2/25/2013 Dr. Nasrellah H A 27

2/25/2013 Dr. Nasrellah H A 28

2/25/2013 Dr. Nasrellah H A 29

if a simply supported beam were used to support the distributed loading, it would have to resist a maximum bending moment of 625 k.ft. By comparison, it is more efficient to structurally resist the load in direct compression (although one must consider the possibility of buckling) than to resist the load by a bending moment.

2/25/2013 Dr. Nasrellah H A 30

The three-hinged tied arch is subjected to the loading shown in Fig. below. Determine the force in members CH and CB. The dashed member GF of the truss is intended to carry no force.

Example 5:

2/25/2013 Dr. Nasrellah H A 31

Solution:

2/25/2013 Dr. Nasrellah H A 32

2/25/2013 Dr. Nasrellah H A 33