ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 1 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 25 Problem Catenary Tutorial

ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 2 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Catenary Length Catenary Length  Consider a cable uniformly loaded by the cable itself, e.g., a cable hanging under its own weight.  We would like to find the Curve-Length of the cable, s, as function of x alone Use Differential Analysis

ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 3 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Catenary Length (2)  Next, relate horizontal distance, x, to cable-length s  Then  Recall Trig ID:

ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 4 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Catenary Length (3)  Using Trig ID in ds Equation  Now find Length, L, between pts a & b by integrating ds

ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 5 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Catenary Length (4)  Now Eliminate θ  From Differential Diagram note:  Sub Out tanθ in the definite Integral for L:

ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 6 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Catenary Length (5)  Finally  Now in the Case of Prob10-25  An Analytical Soln for L is possible as  But it’s a bit Tedious so Let’s have MATLAB do it

ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 7 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods Catenary Length (6)  MATLAB SOLUTION PLAN syms for x, a, b Set y = 10*cosh[(x-20)/10] Take dydx = diff (y) Find L = int(sqrt(1+dydx ^2),a,b) Set a = 0, b =50 Find numerical value for L between 0 & 50 using double command

ENGR-25_Prob_10-25_Catenary_Solution.ppt.ppt 8 Bruce Mayer, PE ENGR/MTH/PHYS25: Computational Methods MATLAB Code