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Building Design and Construction Handbook - Merritt - Ventech!

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STRUCTURAL THEORY 5.137<br />

natural frequencies of vibration of both cables will always differ for any value of<br />

live load. To avoid resonance, the difference between the frequencies of the cables<br />

should increase with increase in load. Thus, the two cables will tend to assume<br />

different shapes under specific dynamic loads. As a consequence, the resulting flow<br />

of energy from one cable to the other will dampen the vibrations of both cables.<br />

Natural frequency, cycles per second, of each cable may be estimated from<br />

n� Tg<br />

w � (5.231)<br />

l w<br />

n �<br />

where n � integer, 1 for the fundamental mode of vibration, 2 for the second<br />

mode, ...<br />

l � span of cable, ft<br />

w � load on cable, kips per ft<br />

g � acceleration due to gravity � 32.2 ft/s 2<br />

T � cable tension, kips<br />

The spreaders of a cable truss impose the condition that under a given load the<br />

change in sag of the cables must be equal. But the changes in tension of the two<br />

cables may not be equal. If the ratio of sag to span ƒ/l is small (less than about<br />

0.1). Eq. (5.222) indicates that, for a parabolic cable, the change in tension is given<br />

approximately by<br />

where �ƒ � change in sag<br />

A � cross-sectional area of cable<br />

E � modulus of elasticity of cable steel<br />

16 AEƒ<br />

�H � �ƒ (5.232)<br />

2 3 l<br />

Double cables interconnected with struts may be analyzed as discrete or continuous<br />

systems. For a discrete system, the spreaders are treated as individual members.<br />

For a continuous system, the spreaders are replaced by a continuous diaphragm<br />

that ensures that the changes in sag <strong>and</strong> rise of cables remain equal under<br />

changes in load. Similarly, for analysis of a cable network, the cables, when treated<br />

as a continuous system, may be replaced by a continuous membrane.<br />

(C. H. Mollman, ‘‘Analysis of Plane Prestressed Cable Structures,’’ Journal of<br />

the Structural Division, ASCE, Vol. 96, No. ST10, Proceedings Paper 7598,<br />

October 1970, pp. 2059–2082; D. P. Greenberg, ‘‘Inelastic Analysis of Suspension<br />

Roof Structures,’’ Journal of the Structural Division, ASCE, Vol. 96, No. ST5,<br />

Proceedings Paper 7284, May 1970, pp. 905–930; H. Tottenham <strong>and</strong> P. G. Williams,<br />

‘‘Cable Net: Continuous System Analysis,’’ Journal of the Engineering Mechanics<br />

Division, ASCE, Vol. 96, No. EM3, Proceedings Paper 7347, June 1970,<br />

pp. 277–293; A. Siev, ‘‘A General Analysis of Prestressed Nets,’’ Publications,<br />

International Association for Bridge <strong>and</strong> Structural Engineering, Vol. 23, pp. 283–<br />

292, Zurich, Switzerl<strong>and</strong>, 1963; A. Siev, ‘‘Stress Analysis of Prestressed Suspended<br />

Roofs,’’ Journal of the Structural Division, ASCE, Vol. 90, No. ST4, Proceedings<br />

Paper 4008. August 1964, pp. 103–121; C. H. Thornton <strong>and</strong> C. Birnstiel, ‘‘Threedimensional<br />

Suspension Structures,’’ Journal of the Structural Division, ASCE, Vol.<br />

93, No. ST2, Proceedings Paper 5196, April 1967, pp. 247–270.)

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