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

1. Engineering 36 Lab-24 Chp10FlexibleCables Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

9. Chain Catenary Equil. • Given Geometry, 8m Chain @ 3.72 kg/m, Frictionless Pulley at Pt-B, Pin at Pt-A • Find values of a for Equilibrium

12. Excel Plot To Locate Root Regions

13. Excel Numerical Anal.

16. MATLAB Plot

17. MatLab Code – Part-1 % B. Mayer 01Aug08 * ENGR36 % Prob Catenary Chain: plot Transcendtal Function and find Zeros % file = E36_CatChain_Plot.m % use with function file CatZeros.m % clear % Define function based on engineering analysis ChainCat = @(z) (z/2).*(2*sinh(1./z) + cosh(1./z)) - 4; % use 501 pts unsing LinSpace, must avoid Division by ZERO cmin = 0.3; cmax = 7; n = 500; c = linspace(cmin,cmax,n); % % Make a Horizontal Line HL = zeros(1,n); % % Calc the values, u(c) using ChaingCat u = ChainCat(c); % % Plot u = ChainCat(c) vs c plot(c, u, c, HL), xlabel('c'), ylabel('ChainCat(c)'),... title('ChainBalance Catenary'), grid % % Use fzero to find roots precisely c1 = fzero('CatZeros', .3) c2 = fzero('CatZeros', 6) % % now recall a = c*cosh(1/c) a1 = c1*cosh(1/c1); a2 = c2*cosh(1/c2); % % Display output disp('Values for a using fzero Command') disp('a1 in meters = ') disp(a1) disp('a2 in meters = ') disp(a2)

18. MatLab Code – Part-2 % also solve symbolically syms csym cnum = solve('csym*sinh(1/csym) + (csym/2)*cosh(1/csym)= 4') % % Note that the Symbollic Solver does NOT return the smaller root % disp('Value for a using Symbolic solve Command') anum = cnum*cosh(1/cnum) function y = CatZeros(x) % B. Mayer 05Dec06 * ENGR36 % Prob 7.133: plot Transcendtal Function and find Zeros % use with file = E36_Prob7_133_Plot.m % Define function based on engineering analysis y = (x/2).*(2*sinh(1./x) + cosh(1./x)) - 4;