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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

Engineering 25. Tutorial: Catenary Cables. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. Partial Catenary. The cable has a mass of 0.5 kg/m and is 25 m long. Determine the vertical and horizontal components of force it exerts on the top of the tower.

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

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  1. Engineering 25 Tutorial: CatenaryCables Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. Partial Catenary • The cable has a mass of 0.5 kg/m and is 25 m long. • Determine the vertical and horizontal components of force it exerts on the top of the tower.

  3. Eqns Used

  4. MATLAB Code % Bruce Mayer, PE % ENGR36 * 22Jul2 % ENGR36_Tutorial_Partial_Catenary_H13e_P7_119_1207.m % K1 = tand(30) K2 = asinh(K1) S0 = @(z) (z/K2)*(sinh(K2*(z+15)/z)-K1) - 25 xB = fzero(S0, 10) xA = xB+15 u = 0.5*9.81 TO = u*xB/K2 TA = TO*cosh(u*xA/TO) QA = atand(sinh(u*xA/TO)) WA = TO*tand(QA)

  5. MATLAB Results xB = 8.2804 xA = 23.2804 u = 4.9050 TO = 73.9396 TA = 181.0961 QA = 65.9026 WA = 165.3141

  6. Chain Lift Problem • The man picks up the 52-ft chain and holds it just high enough so it is completely off the ground. The chain has points of attachment A and B that are 50 ft apart. If the chain has a weight of 3 lb/ft, and the man weighs 150 lb, determine the force he exerts on the ground. Also, how high h must he lift the chain? Hint: The slopes at A and B are zero.

  7. Eqns Used

  8. MATLAB Code % Bruce Mayer, PE % ENGR36 * 22Jul2 % ENGR36_Tutorial_Chain_Lift_Catenary_H13e_P7_124_1207.m % Zf1 = @(q) (q/3)*sinh(75/q) - 26 TO = fzero(Zf1, 150) h = (TO/3)*(cosh(75/TO) - 1) Q = atand(78/TO) Th = 3*h + TO Tup = Th*sind(Q)

  9. MATLAB Results Zf1 = @(q)(q/3)*sinh(75/q)-26 TO = 154.0033 h = 6.2088 Q = 26.8614 Th = 172.6297 Tup = 78

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