Download Solution to Problem 4.35: Minimum LAC Value for a 2-Cable Supported Load and more Slides Computational Methods in PDF only on Docsity! Chp4 Tutorial: Prob 4.35 Solution Docsity.com Problem 4.35 • The Situation – Cable Supported Weight = 6ft 3ft = = 2000 lbs = 2 kip Find Minimum Value for LAC subject to Constraint • TAB & TAC Both ≤2000 lbs Docsity.com When in Doubt → Plot • Zoom-In on Answer • Locate LACmin more Precisely 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 LAC (ft) Te ns io n: T A B & T A C (K ip ) P4.35 - 2-Cable Supported Load TAB TAC Max-T TAB Limits ≈4.025 ft Docsity.com ZO Ce wt is 2S Bruce Mayer, PE
{ 2 paert | a a Engineering instiuctor
Chabot College
25665 Hesperian Blvd
Hayward, CA 94545
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The Command Session >> run Prob4_35_Loaded_Cables Minimum value for LAC in ft = 4.0260 TAB at LACminimum in kip => 1.9993 TAC at LACminimum in kip => 1.7878 Support Angle at LACminimum in ° => 36.8932 index of LACmin => 139 Docsity.com % Bruce Mayer, PE % ENGR225 * 20Feb12 % Prob 4.35 * file Prob4_35_Loaded_Cables_1202.m % % Plot L_AC for 0° to 90° using 500pts by LinSpace LAC0 = 3; LAC90 = 6.71; % length in Feet; n = 500; % number of plotted points LAC = linspace(LAC0, LAC90, n); % in ft % % the Fixed Parameters LAB = 3; % in feet D = 6; % in feet W = 2; % wt in kip (kilo-lbs) % % Calc angle vectors theta = acos((D^2 + LAB^2 - LAC.^2)/(2*D*LAB)); phi = asin(LAB.*sin(theta)./LAC); % % Calc TAB & TAC plotting Vectors for k = 1: length(LAC) % Define for THIS VALUE of k the Matrix Mult terms A = [-cos(theta(k)), cos(phi(k)); sin(theta(k)), sin(phi(k))]; P = [0; W]; % For THIS VALUE of k Solve for 2-unknowns in 2-eqns using BackDivision T = A\P; % Assign temporary tension solns to permanent vectors TAB(k) = T(1); TAC(k) = T(2); end % % Plot the tension % make Horizontal line vectors at 2000 lbs (2 Kip) Xln = [LAC(1), LAC(length(LAC))]; Yln = [2, 2]; % in Kip plot(LAC, TAB, 'g--', LAC, TAC,'b:', Xln, Yln, 'r-', 'LineWidth', 3),... xlabel('LAC (ft)'), ylabel('Tension: TAB & TAC (Kip)'),... title('P4.35 - 2-Cable Supported Load '), grid,... legend('TAB', 'TAC', 'Max-T'), axis([3 6.7 0 3]) % axis([3 6.7 0 3]) ** axis([3.5 4.5 1.5 2.2]) % % Find LACmin and Corresponding Tensions % use FOR Loop to test every Case, Collect Mins in Bucket % that depends on LAC % Initialize colletion buckets LACmin = 7; % ft TABmin = 3; % kip TACmin = 3; % kip Mmin = n + 9; % make larger than the no. items in LAC-vector for m = 1:length(LAC) Test_No = m; if (TAB(m)<=2)&(TAC(m)<=2) % OK to here; now test if current LAC < LACmin % m_ok = m if LAC(m) < LACmin % if OK here => replace OLD LACmin with current LAC LACmin = LAC(m); TABmin = TAB(m); TACmin = TAC(m); Mmin = m; end end Docsity.com