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This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) 192 Other structural applications of steel 5.3.2 Special features 5.3.2.1 Elementary cable mathematics Load–extension relationship Extension e TL = AE where T = load in cable L = length of cable A = cross-sectional area E = Young’s modulus. Typical values for materials are given in Table 5.1. The E value for wire rope applies after the construction stretch has been pulled out of wire rope by load cycling to 50% of the ultimate tensile strength. In wire rope the construction stretch can be as much as 0.5%. This is of the same order of magnitude as the elastic stretch in the cable at maximum working load. Circular arc loaded radially (Fig. 5.24) Tension T = PR where P = load/unit length radial to cable R = radius of cable. Radius of circular arc, R (Fig. 5.25) Radius R S 2 d = + 8d2 Table 5.1 Material properties Material E Ultimate (kN/mm 2 ) tensile strength (N/mm 2 ) Solid steel 210.0 400–2000 Strand 150.0 2000 Wire rope 112.0 2000 Polyester fibres 7.5 910 Aramid fibres 112.0 2800
This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) where S = span d = dip. Catenary loaded vertically (Fig. 5.26) Horizontal force H WS = 8d Vertical force 2 2 Maximum tension T = ( H + V ) where S = span d = dip W = vertical load/unit length. These formulae permit initial estimates of forces in cables to be made. For full and accurate analysis it is necessary to use a non-linear computer analysis which takes into account the change of curvature caused by stretch. For well-curved cables the 1 V 2 WS = 2 P load/rn Fig. 5.24 Circular arc loaded radially S 2 Fig. 5.25 Radius of circular arc 2 radius R S 2 Cable structures 193
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