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

Engineering 25 Problem 10-25Catenary Tutorial Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

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

Catenary Length (2) • Next, relate horizontal distance, x, to cable-length s • Then • Recall Trig ID:

Using Trig ID in ds Equation Catenary Length (3) • Now find Length, L, between pts a & b by integrating ds

Now Eliminate θ Catenary Length (4) • From Differential Diagram note: • Sub Out tanθ in the definite Integral for L:

Finally Catenary Length (5) • Now in the Case of Prob10-25 • But it’s a bit Tedious so Let’s have MATLAB do it • An Analytical Soln for L is possible as

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 Catenary Length (6) • Find numerical value for L between 0 & 50 using double command

MATLAB Code

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