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Building Design and Construction Handbook - Merritt - Ventech!

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STRUCTURAL THEORY 5.133<br />

wl o<br />

TL � TR �<br />

2<br />

Length of cable between supports is<br />

2 l<br />

1 � 2 16ƒ<br />

(5.217)<br />

�<br />

�<br />

2<br />

o ��<br />

o<br />

�<br />

2 8 ƒ<br />

2<br />

4 32 ƒ<br />

4<br />

6 256 ƒ<br />

6 �<br />

1 wl H wl<br />

L � 1 � � sinh<br />

2 2H w 2H<br />

o (5.218)<br />

� l 1 � � � � ���<br />

3 l 5 l 7 l<br />

If additional uniformly distributed load is applied to a parabolic cable, the change<br />

in sag is approximately<br />

15 l �L<br />

16ƒ5� 24ƒ /l<br />

For a rise in temperature t, the change in sag is about<br />

�ƒ � (5.219)<br />

2 2<br />

� �<br />

2 2<br />

15 lct 8ƒ<br />

�ƒ � 1 � (5.220)<br />

2 2 2<br />

16 ƒ(5 � 24ƒ /l ) 3 l<br />

where c � coefficient of thermal expansion.<br />

Elastic elongation of a parabolic cable is approximately<br />

2<br />

� 2�<br />

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

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

H � horizontal component of tension in cable<br />

Hl 16 ƒ<br />

�L � 1 � (5.221)<br />

ARE 3 l<br />

If the corresponding change in sag is small, so that the effect on H is negligible,<br />

this change may be computed from<br />

15 Hl 1 � 16ƒ /3l<br />

16 AREƒ 5 � 24ƒ /l<br />

2 2 2<br />

�ƒ � 2 2<br />

(5.222)<br />

For the general case of vertical dead load on a cable, the initial shape of the<br />

cable is given by<br />

MD HD y � (5.223)<br />

D<br />

where M D � dead-load bending moment that would be produced by the load in a<br />

simple beam<br />

H D � horizontal component of tension due to dead load<br />

For the general case of vertical live load on the cable, the final shape of the cable<br />

is given by<br />

M � M<br />

D L<br />

yD � � � (5.224)<br />

H � H<br />

D L

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