engr-36_lab-24_fa07_lec-notes.ppt 1 bruce mayer, pe engineering-36: engineering mechanics - statics...

ENGR-36_Lab-24_Fa07_Lec-Notes.ppt1

Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 36

Lab-24 Lab-24 Chp10Chp10

FlexiblFlexiblee

CablesCables



Chain Catenary Equil.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



Excel Plot To Locate Excel Plot To Locate Root RegionsRoot Regions

Catenary Chain Problem

6

7

8

9

10

11

12

13

14

15

16

17

18

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

c (m)

Ter

m1,

Ter

m2

(m)

term 1 (m)

Term 2 (m)

file = Prob_Cat-Chain_0707.xls

0.3773 5.906



Excel Numerical Anal.Excel Numerical Anal.c term 1 Term 2 c term 1

(m) (m) (m) (m) (m)

0 2.00E+14 16 0.361 17.262017870.03 2.69603E+13 16 0.362 17.177535780.06 3115400.392 16 0.363 17.094054010.09 18065.83367 16 0.364 17.011556770.12 1497.694293 16 0.365 16.930028590.15 353.5972065 16 0.366 16.849454290.18 139.6814446 16 0.367 16.769819020.21 73.68836658 16 0.368 16.691108170.24 46.43634608 16 0.369 16.613307460.27 32.87723276 16 0.37 16.53640286

0.3 25.21776021 16 0.371 16.460380620.33 20.48053104 16 0.372 16.385227250.36 17.34751638 16 0.373 16.310929520.39 15.16710031 16 0.374 16.237474450.42 13.58831543 16 0.375 16.164849310.45 12.40878376 16 0.376 16.093041620.48 11.50515385 16 0.377 16.022039110.51 10.79871147 16 0.378 15.951829770.54 10.23725378 16 0.379 15.882401790.57 9.785007218 16 0.38 15.8137436

0.6 9.416756729 160.63 9.11428979 16 0.3771 16.014982680.66 8.864167338 16 0.3772 16.007934170.69 8.656283865 16 0.3773 16.000893570.72 8.482912235 16 0.3774 15.993860860.75 8.338054909 16 0.3775 15.986836040.78 8.216993857 160.81 8.115972316 160.84 8.031965877 16 5.9 15.989076780.87 7.962515213 16 5.901 15.99104134

0.9 7.90560211 16 5.902 15.993005920.93 7.859556383 16 5.903 15.994970510.96 7.822985128 16 5.904 15.996935110.99 7.794718367 16 5.905 15.998899721.02 7.773766849 16 5.906 16.000864351.05 7.759288982 16 5.907 16.002828991.08 7.750564687 16 5.908 16.00479364



MATLAB PlotMATLAB Plot

0 1 2 3 4 5 6 7-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

c

Ch

ain

Ca

t(c

)

ChainBalance Catenary



MatLab Code – Part-1MatLab 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 analysisChainCat = @(z) (z/2).*(2*sinh(1./z) + cosh(1./z)) - 4;% use 501 pts unsing LinSpace, must avoid Division by ZEROcmin = 0.3; cmax = 7; n = 500;c = linspace(cmin,cmax,n);%% Make a Horizontal LineHL = zeros(1,n);%% Calc the values, u(c) using ChaingCatu = ChainCat(c);%% Plot u = ChainCat(c) vs cplot(c, u, c, HL), xlabel('c'), ylabel('ChainCat(c)'),... title('ChainBalance Catenary'), grid%% Use fzero to find roots preciselyc1 = 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 outputdisp('Values for a using fzero Command')disp('a1 in meters = ')disp(a1)disp('a2 in meters = ')disp(a2)



MatLab Code – Part-2MatLab Code – Part-2% also solve symbolicallysyms csymcnum = 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 analysisy = (x/2).*(2*sinh(1./x) + cosh(1./x)) - 4;

engr-36_lab-24_fa07_lec-notes.ppt 1 bruce mayer, pe engineering-36: engineering mechanics - statics...

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