Handbook of Civil Engineering Calculations

Calculation Procedure:

1. Sketch the loaded cable
   Assume a position of the cable, such as PRSQ (Fig. So). In Fig. 8Z>, locate points P' and
   Q', corresponding to P and Q, respectively, in Fig. 8a.


2. Take moments with respect to an assumed point
   Assume that the maximum tension of 1800 Ib (8006 N) occurs in segment PR (Fig. 8).
   The reaction at P, which is collinear with PR, is therefore 1800 Ib (8006 N). Compote the
   true perpendicular distance m from Q to PR by taking moments with respect to Q. Or
   ^M 6 = 180Om - 500(35) - 750(17) = O; m = 16.8 ft (5.1 m). This dimension establishes
   the true position of PR.


3. Start the graphical solution of the problem
   In Fig. 86, draw a circular arc having Q' as center and a radius of 16.8 ft (5.1 m). Draw a
   line through P' tangent to this arc. Locate R' on this tangent at a horizontal distance of
   15 ft (4.6 m) from P'.


4. Draw the force vectors
   In Fig. Sc, draw vectors ab, be, and cd to represent the 750-lb (3336-N) load, the 500-lb
   (2224-N) load, and the 1800-lb (8006-N) reaction at P, respectively. Complete the trian-
   gle by drawing vector da, which represents the reaction at Q.


5. Check the tension assumption
   Scale da to ascertain whether it is less than 1800 Ib (8006 N) This is found to be so, and
   the assumption that the maximum tension exists in PR is validated.

(b) True position of loaded cable

FIGURE 8

(c) Force diagram

(a) Assumed position of loaded cable