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Problems

Solutions

P2.24 Cable Support

• Consider a Pin-and-Cable

Supported Beam

• The Cable Anchor Pt-D is

VARIABLE For the Constant

Parameters shown

3m

5m

400N

≈ 90 lbs

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)

¿¿Class Question??

• Given
• What is the MAXIMUM

POSSIBLE Value of D

(regardless of T)?

3m

5m

400N

≈ 90 lbs

2.24 Game Plan

• Part a) Solve analytically using

min as instructed

• Part b) Solve
  • Approximately using the Graph
  • Anallytically using the find

command

2.24 Graphical Soln

• The T vs D graph (fully labeled)

D (m)

T (N)

ENGR25 * P2-

T

(Tmin, Dmin)

DshortSide Tupper Limit DlongSide

≈1.62 ≈2.

2.12m, 1333N

Overall Sensitivity

• Any D between 1m-2.8m yields

relatively low Tension

x 10

4

D (m)

ENGR25 * P2-

MATLAB Code-a

% Bruce Mayer, PE % EGNR25 10Sep % 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 = LbLcW./(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 = 1.1minT % Use to make a horizontal line at the upper tension Tplot = LbLcW./(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(' ‘)