Advanced Methods of Structural Analysis

5.5 Comparison of Parabolic and Catenary Cables 135 Expressions (5.36) allows calculating the tension at supportsAandB NAD1:7834 ...

136 5Cables Ta b l e 5. 2 Comparison of parabolic and catenary cables Parabolic cable Catenary f=l ql 8H .5:10/ H ql  cosh ql 2 ...

5.6 Effect of Axial Stiffness 137 caused by decreasing of the thrust leads to increasing of the sag. If thrustHis fixed, then in ...

138 5Cables The total length of the cable LD 2 f sin ̨ Dl p 1 Ctan^2 ̨Dl r 1 C P^2 4H^2 : (5.37) Now let us introduce the elasti ...

5.6 Effect of Axial Stiffness 139 This equation may be rewritten in equivalent form PD 2 p 2 1  H EA r H^3 EA r 1  H 2EA (5.42 ...

140 5Cables Thus (5.45a)forthrustHmay be presented as HD ql 2 p 6 1 r L 0 .1C"/ l  1 D ql 2 p 6 1 s ˇ  1 C H EA   1 ;ˇD L 0 ...

Problems 141 P 1 =18kN a 2 =22m a 1 =10m l=30m P 2 =15kN A c=3m B a 1 a (^0) a 2 2 1 j Fig. P5.1 5.2.The cable is subjected totw ...

142 5Cables (a)ThrustHis (1) remains the same; (2) twice as much; (3) half as much (b)Maximum axial force is (1) remains the sam ...

Problems 143 (a)Derive equation, which connects parametersq 0 ,l,H,andk (b)Calculate the sag–span ratio for which the maximum te ...

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Chapter 6 Deflections of Elastic Structures This chapter describes some effective methods for computing deflections of deformabl ...

146 6 Deflections of Elastic Structures solution of this problem. At present, methods for computation of the displacements are d ...

6.2 Initial Parameters Method 147 Figure6.1c shows the frame due to action of horizontal forceP. At fixed support Athe linear an ...

148 6 Deflections of Elastic Structures expression for displacement. This expression allows us to calculate slope, bend- ing mom ...

6.2 Initial Parameters Method 149 M.x 2 /DP.x 2 aP/; M.x 3 /DP.x 3 aP/M.x 3 aM/^0 : 4.Integration of differential equation ...

150 6 Deflections of Elastic Structures Combining (6.2) and data in Table6.1allows us to write the general expressions for the l ...

6.2 Initial Parameters Method 151 For positive bending moments atxdue to coupleM,forceP, and uniformly dis- tributed loadq, the ...

152 6 Deflections of Elastic Structures account according to the universal equation (6.3) are reactionRAof the supportA and unif ...

6.2 Initial Parameters Method 153 Fig. 6.4 Design diagram of cantilevered beam and its deflected shape x y Initial parameters: y ...

154 6 Deflections of Elastic Structures As can be seen in this example, the initial parametersy 0 and 0 for the given struc- tu ...