Advanced Methods of Structural Analysis

5.2 Cable with Neglected Self-Weight 115 Increasing of the thrustHleads to decreasing of the angle ̨ 0 and ̨ 1 ; as a result, th ...

116 5Cables After that, the shape of the cable and internal forces in the cable may be defined easily. The special caseaD0:5llea ...

5.2 Cable with Neglected Self-Weight 117 Constant of integration are obtained from boundary conditions: atxD 0 (supportA) yD 0 a ...

118 5Cables Therefore, the total lengthLof the cable in terms of sag according to (5.13) becomes LD Zl 0 s 1 C  4f l  2  2x l ...

5.2 Cable with Neglected Self-Weight 119 The maximumy-coordinate of the cable in terms of total lengthLand spanlis ymaxD p 3 2 ...

120 5Cables x RA y H N(x) q x q H N(x) Q(x)=RA − qx b a l y x q x RB H RA H A j c x 0 ymax B f y^0 Fig. 5.5 (a) Cable under acti ...

5.2 Cable with Neglected Self-Weight 121 Reaction of supportAequals RA! X MBD 0 WRAlHcC ql^2 2 D 0 !RAD ql 2  Hc l Free-body ...

122 5Cables 5.3 Effect of Arbitrary Load on the Thrust and Sag So far we considered behavior of the cables that are subjected to ...

5.3 Effect of Arbitrary Load on the Thrust and Sag 123 Usually this formula is written in the following form LDlC D 2H^2 ;DD Zl ...

124 5Cables The formulas above allows considering very important problem determining the changeof the parameters of the cable if ...

5.4 Cable with Self-Weight 125 which leads to the required relationship HqCPDHq p 1 C3C3^2 : The sag of the cable fqCPD MCbeam ...

126 5Cables H q N H W N q C W=q 0 s D Free body diagram O x a y Base of catenary s C ds dy A B dx D H W=q 0 s Design diagram N F ...

5.4 Cable with Self-Weight 127 Formula (5.22) for tension at any point can be rewritten as follows N.x/DH r 1 Csinh^2 q 0 H xDHc ...

128 5Cables The sag of the cablefat the axis of symmetry.xD0/in terms of ordinatey.l=2/ of the cable at support is fDy  l 2   ...

5.4 Cable with Self-Weight 129 Slope at pointBis tanmaxDsinh.0:223210/D4:6056! sinmaxDsin.tan^1 4:6056/D0:9772;cosmaxDcos.t ...

130 5Cables Equation of the curve and ordinateyfor support points are y.x/D H q 0 cosh q 0 H xD4:42cosh0:22642x; ymaxD4:42cosh 1 ...

5.4 Cable with Self-Weight 131 Solution.Let a verticaly-axis pass through the lowest pointC. Location of this point is defined b ...

132 5Cables Length of the portionCBisLCB D asinh.xB=a/D 4:48sinh.8:103=4:48/D 13:303m Curve AC. Equation of the curve and slope ...

5.4 Cable with Self-Weight 133 since the lowest pointCis located beyond the curveAB. Let the distance between support points in ...

134 5Cables or in equivalent form sinh D 0 2a D 1 2a q L^20 h^20 (5.33a) CoordinatesxAandxAof the pointsAandBare xADatanh^1  ...