Engineering 25
Chp4
Tutorial:
Prob 4.35
Solution
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
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
Engineering/Math/Physics 25: Computational Methods
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Develop Solution on BD
Engineering/Math/Physics 25: Computational Methods
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
When in Doubt → Plot
 Plot TAB & TAC vs LAC
P4.35 - 2-Cable Supported Load
3
TAB
TAC
Max-T
Tension: TAB & TAC (Kip)
2.5
TAB Limits
2
1.5
1
0.5
0
3
3.5
4
4.05 ft
4.5
 Locate LACmin
5
LAC (ft)
Engineering/Math/Physics 25: Computational Methods
4
5.5
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
6.5
When in Doubt → Plot
 Zoom-In on Answer
P4.35 - 2-Cable Supported Load
2.2
TAB
TAC
Max-T
2.1
Tension: TAB & TAC (Kip)
TAB Limits
2
1.9
1.8
1.7
1.6
1.5
3.5
4.025 ft
3.6
3.7
3.8
3.9
4
4.1
LAC (ft)
4.2
4.3
4.4
 Locate LACmin more Precisely
Engineering/Math/Physics 25: Computational Methods
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
4.5
Engineering/Math/Physics 25: Computational Methods
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Engineering/Math/Physics 25: Computational Methods
7
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Engineering/Math/Physics 25: Computational Methods
8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Engineering/Math/Physics 25: Computational Methods
9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Engineering/Math/Physics 25: Computational Methods
10
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
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
Engineering/Math/Physics 25: Computational Methods
11
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
% 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
Bruce Mayer, PE
Engineering/Math/Physics 25: Computational Methods
12
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
TriAngle Template
Engineering/Math/Physics 25: Computational Methods
13
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt