ENGR36_H13_Tutorial_Catenary_Cables.pptx 1 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 25 Tutorial: Catenary Cables

ENGR36_H13_Tutorial_Catenary_Cables.pptx 2 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics 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.

ENGR36_H13_Tutorial_Catenary_Cables.pptx 3 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Eqns Used

ENGR36_H13_Tutorial_Catenary_Cables.pptx 4 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR36_H13_Tutorial_Catenary_Cables.pptx 5 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR36_H13_Tutorial_Catenary_Cables.pptx 6 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR36_H13_Tutorial_Catenary_Cables.pptx 7 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR36_H13_Tutorial_Catenary_Cables.pptx 8 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics MATLAB Code % Bruce Mayer, PE % ENGR36 * 22Jul2 % ENGR36_Tutorial_Partial_Catenary_H 13e_P7_119_1207.m % K1 = tand(30) K2 = asinh(K1) S0 (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)

ENGR36_H13_Tutorial_Catenary_Cables.pptx 9 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics MATLAB Results xB = xA = u = TO = TA = QA = WA =

ENGR36_H13_Tutorial_Catenary_Cables.pptx 10 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics 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.

ENGR36_H13_Tutorial_Catenary_Cables.pptx 11 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Eqns Used

ENGR36_H13_Tutorial_Catenary_Cables.pptx 12 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR36_H13_Tutorial_Catenary_Cables.pptx 13 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR36_H13_Tutorial_Catenary_Cables.pptx 14 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR36_H13_Tutorial_Catenary_Cables.pptx 15 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics MATLAB Code % Bruce Mayer, PE % ENGR36 * 22Jul2 % ENGR36_Tutorial_Chain_Lift_Catenar y_H13e_P7_124_1207.m % Zf1 (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)

ENGR36_H13_Tutorial_Catenary_Cables.pptx 16 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics MATLAB Results Zf1 TO = h = Q = Th = Tup = 78