Engineering 25
Problems
2.24
Solutions
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-25: Computational Methods
1
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
P2.24 Cable Support
 Consider a Pin-and-Cable
Supported Beam
5m
400N
≈ 90 lbs
3m
 The Cable Anchor Pt-D is
VARIABLE For the Constant
Parameters shown
Engineering-25: Computational Methods
2
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
P2.24 Cable Support
 Since the VERTICAL
Anchor-Pt for Lc is also
Variable, the
Horizontal
Anchor-pt, D,
can be MOVED
 Using the Methods of
ENGR36 We find the CableTension function, T(D)
T
Lb L cW
D L D
Engineering-25: Computational Methods
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2
b
2
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
P2.24  Problem
 a. Use Element-by-Element
operations and the MATLAB
min command to
• Find the Anchor-Position, D,
The MINIMIZES T
• Calc this minimum Value of T
 b. Check T vs. D Sensitivity
by plotting T vs. D.
• By How Much can D change if
T is allowed to rise to 1.1*Tmin
(110% of Tmin)
Engineering-25: Computational Methods
4
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
¿¿Class Question??
 Given
5m
400N
≈ 90 lbs
3m
 What is the MAXIMUM
POSSIBLE Value of D
(regardless of T)?
Engineering-25: Computational Methods
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Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
¿¿Class Question??
 HOW Many Values of
D Satisfy the given
Criteria:
• What is D when T is allowed to
rise to 1.1*Tmin (110% of
Tmin)
5m
400N
≈ 90 lbs
3m
Engineering-25: Computational Methods
6
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
2.24 Game Plan
 Part a) Solve analytically
using min as instructed
 Part b) Solve
• Approximately using the Graph
• Anallytically using the find
command
Engineering-25: Computational Methods
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Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
2.24 Graphical Soln
 The T vs D graph (fully labeled)
ENGR25 * P2-24
1550
1500
DshortSide
DlongSide
Tupper Limit
T (N)
1450
T
1400
1350
(Tmin, Dmin)
2.12m, 1333N
1300
1.4
1.6
1.8
≈1.62
Engineering-25: Computational Methods
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2
2.2
D (m)
2.4
2.6
≈2.54
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
2.8
2.24 Analytical Soln
minT =
1.3333e+003
k =
355
minD =
2.1240
showing min T and Dmin location on Graph.
Hit ANY KEY to continue
upper =
1.4667e+003
use the crosssing-pt on the plot to estimate Du for Tu, then hit ANY
KEY to continue
The Horizontal Line is the limit the Cable-Tension Limit, Tupper
Use FIND to locate DShortSide associated wtih Tupper
Dupper =
1.6210
When Tlimit increases by 10%,then the Support position, D, can be
DEcreased by this %
-23.6817
DlongSide =
2.5252
When Tlimit increases by 10%,then the Support position, D, can be
INcreased by this %
18.8898
To see OVERALL sensitivity HIT ANY key
Engineering-25: Computational Methods
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Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
Overall Sensitivity
 Any D between 1m-2.8m
yields relatively low Tension
4
4.5
ENGR25 * P2-24
x 10
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
Engineering-25: Computational Methods
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1.5
D (m)
2
2.5
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
3
MATLAB Code-a
% Bruce Mayer, PE
% EGNR25 10Sep11
% P2_24_Cable_Supported_Beam_Tutorial_1109.m
% Part a
%* The UNchanging ParaMeters
W = 400; Lb = 3; Lc = 5; % in units of N, m, m
%* The INdependent Variable
D = [0:0.006:Lb]; % in m
% Calc the Cable tension, f(D)
T = Lb*Lc*W./(D.*sqrt(Lb^2-D.^2)); % in N
%
% Use min Command to find minimum T and its associated index, k
[minT, k] = min(T)
minD = D(k)
%
% Part b
disp('showing min T and Dmin location on Graph.
Hit ANY KEY to
continue')
%
Dplot = [1.5:0.0022:2.6];
upper = 1.1*minT % Use to make a horizontal line at the upper tension
Tplot = Lb*Lc*W./(Dplot.*sqrt(Lb^2-Dplot.^2));
plot(Dplot,Tplot, [1.5,2.6],[upper,upper], minD, minT,'-.r*',
'linewidth', 3),grid
xlabel('D (m)'); ylabel('T (N)'); title('ENGR25 * P2-24');
gtext({'T',; '(Tmin, Dmin)'; 'Tupper Limit'; 'DshortSide';
'DlongSide'})
%
disp('use the crosssing-pt on the plot to estimate Du for Tu, then hit
ANY KEY to continue')
disp('The Horizontal Line is the limit the Cable-Tension Limit,
Tupper')%
pause
%
disp (' ')
disp('Use FIND to locate DShortSide associated wtih Tupper')
disp(' ‘)
Engineering-25: Computational Methods
11
Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt
MATLAB Code-b
%
% Need to determine the LAST values of D that satisfies: Tplot>=Tupper
%
disp(' ')
Tupper = 1.1*minT;
Kupper = find(Tplot<Tupper); % finds indicies of all Tplot's that meet
criteria
Dupper = Dplot(Kupper(1)) % The LAST Value of the Kupper's gives
shorest D
%
% Sensitity analysis
Dshortpct = 100*(Dupper - minD)/minD';
disp(' ')
disp('When Tlimit increases by 10%,then the Support position, D, can
be DEcreased by this %')
disp(Dshortpct)
%
% Find Dlong
Dlong = linspace(minD, 2.9, 500);
Tlong = Lb*Lc*W./(Dlong.*sqrt(Lb^2-Dlong.^2));
klong = find(Tlong>=Tupper); % finds indicies of all Tlong's that
meet criteria
DlongSide = Dlong(klong(1)) % element-1 is the shortest D on the long
side
Dlongpct = 100*(DlongSide - minD)/minD';
disp(' ')
disp('When Tlimit increases by 10%,then the Support position, D, can
be INcreased by this %')
disp(Dlongpct)
%
%
disp('To see OVERALL sensitivity HIT ANY key')
pause
Dsens = [0.05:0.003:2.95];
Tsens = Lb*Lc*W./(Dsens.*sqrt(Lb^2-Dsens.^2));
plot(Dsens,Tsens, 'linewidth', 3),grid
xlabel('D (m)'); ylabel('T (N)'); title('ENGR25 * P2-24');
Engineering-25: Computational Methods
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Bruce Mayer, PE
ENGR-25_Prob_9_3_Solution.ppt