Cables and Arches Structure
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Cables are often used in engineering structures for support
and to transmit loads from one member to another
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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.
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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.
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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.
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Determine the tension in each segment of the cable
shown in Fig., what is the dimension h?
Example 1:
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Solution:
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I. Cable Subjected to Uniform Distributed Load
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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:
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Solution:
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Example 3:
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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.
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Solution:
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Arches Structure
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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.
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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:
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Solution:
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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.
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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:
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Solution:
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