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Lab 11 Harish Sridharan CE 311K Lab 11 Fortran Code ! CE311K Introduction to Computer Methods ! Lab11 - Integration Program lab11 implicit none Real Length, alpha Real upper, lower Real F_Tr,F_S13,F_S38,Int_Tr,Int_S13,Int_S38 Real d_Tr,d_S13,d_S38, T_Tr, T_S13, T_S38 Integer i, num, seg(18) ! Open Output File Open (unit=6, file= 'lab11out.dat' , status= 'unknown' ) !input data, define Lenght as 10, alpha as 40 degrees Length=10. alpha=40. alpha=alpha*(3.1415926/180) !conversion of degrees to radians write (6,*) alpha 100 Format (2/, 23x, f4.1, /, 29x, f4.0) Data seg /1,2,3,4,5,7,10,12,15,20,30,50,100,200,300,400,500,1000/ ! Initialization of upper and lower bounds lower = 0.0 upper = Length - lower ! Writing Headers Write (6,200) Write (6,210) Write (6,200) Do i=1,18 ! Calculation of Force and centroid num= seg(i) Call Trapezoidal(lower, upper, num, F_Tr, Int_Tr) Call Simpson13(lower, upper, num, F_S13, Int_S13) Call Simpson38(lower, upper, num, F_S38, Int_S38) d_S38 = Int_S38/F_S38 d_S13 = Int_S13/F_S13 d_Tr = Int_Tr/F_Tr ! Calculation of Tension T_S38 = d_S38*F_S38/(Length* sin (alpha))

T_S13 = d_S13*F_S13/(Length* sin (alpha)) T_Tr = d_Tr*F_Tr/(Length* sin (alpha)) ! Write results into the output file Write (6, 250) seg(i), F_Tr, T_Tr, F_S13, T_S13, F_S38, T_S38 Enddo 200 Format (80( '=' )) 210 Format ( 'Calculated Load and the Tension of the Cable' ,2/,& '# of Segments' ,10x, 'Trapezoidal' ,10x, 'Simpson13' ,12x,& 'Simpson38' ,/,20x,3( 'Force Tension ' )) 250 Format (2x,i4,11x,f9.4,1x,f9.4,2x,f9.4,1x,f9.4,2x,f9.4,1x,f9.4) End !---------------------------------------------------- !lower is lower limit, upper is upper limit ! num is the number of intervals that will be used for the integral ! Int 1 contains the integral of f(x) between lower and upper with num intervals ! Int 2 contains the integral of xf(x) between lower and upper with num intervals Subroutine Simpson38(lower, upper, num, Int1, Int2) implicit none Real lower, upper, Int1, Int2, x, x0, x1, x2, x3, h Real q, xq Integer i, num ! Define functions q(x) = 100*x/(1+x)* exp (-0.5*x) xq(x)= 100*x**2/(1+x)* exp (-0.5*x) ! Initialization ! Define de value of the step h h=(upper-lower)/(3*num) !initialize the values of the integral at zero Int1=0 Int2=0 ! Calculation of Integrals Do i=1, num x0 = lower+3*h*(i-1) x1 = x0 +h x2 = x1 +h x3 = x2 +h Int1= Int1+(3.*h/8)*(q(x0)+3.*q(x1)+3.*q(x2)+q(x3)) Int2= Int2+(3.*h/8)*(xq(x0)+3.*xq(x1)+3.*xq(x2)+xq(x3)) Enddo Return End !------------------------------------------------------ Subroutine Simpson13(lower, upper, num, Int1, Int2) implicit none Real lower, upper, Int1, Int2, x, x0, x1, x2, h Real q, xq Integer i, num ! Define functions q(x) = 100*x/(1+x)* exp (-0.5*x) xq(x)= 100*x**2/(1+x)* exp (-0.5*x) ! Initialization h=(upper-lower)/(2*num) Int1=0 Int2=0

! Calculation of Integrals Do i=1, num x0 = lower+2*h*(i-1) x1 = x0+h x2 = x1+h Int1= Int1+(h/3.)*(q(x0)+4.*q(x1)+q(x2)) Int2= Int2+(h/3.)*(xq(x0)+4.*xq(x1)+xq(x2)) Enddo Return End !------------------------------------------------------ Subroutine Trapezoidal(lower, upper, num, Int1, Int2) implicit none Real lower, upper, Int1, Int2, x, x0, x1, h Real q, xq Integer i, num ! Define functions q(x) = 100*x/(1+x)* exp (-0.5*x) xq(x)= 100*x**2/(1+x)* exp (-0.5*x) ! Initialization h=(upper-lower)/num Int1=0 Int2=0 ! Calculation of Integrals Do i=1, num x0 = lower+h*(i-1) x1 = x0+h Int1= Int1+(h/2.)*(q(x0)+q(x1)) Int2= Int2+(h/2.)*(xq(x0)+xq(x1)) Enddo Return End

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Lab 11 MATLAB Code %% Lab 11 Integration % % Author: Hagen Fritz % Date: 09/04/2018 % Department: UT CAEE %% Declaring Symbolic Variables % Declare the symbolic variables q F T d x and M. Remember, you can do this % on a single line but do NOT put commas in between the variable names. If % you did it right, each variable should be highlighted. syms q F T D x M % Create a variable L and set it equal to 10 L=10; % Create a variable ang that will be equal to the angle in degrees (40) ang = 40; % Create the symbolic expressions for q and qx. qx will be almost identical % to q except that it will be multiplied by x. The powerpoint has the % formula for q that you will need. Simply copy this down with the proper % syntax. q = 100*(x/(1+x))*exp(1)^(-0.5*x); qx = x*q; %% Calculation of Variables % Calculate the force using the int() function. You will have four inputs: % the function (q), the variable you are integrating with respect to (x), % the lower bound (0), and the upper bound (L). F = int(q,x, 0,10); % Right now F is still a symbolic expression even though the expression can % be solved to a single solution. Convert F to a double variable by saying % F = double(F); F= double(F); % Calculate the moment using the int() function. In this case, your inputs % will be similar to when you calculated the force except now your function % will be qx. M= int(qx,x, 0,10); % Again convert the symoblic moment equation to a double using double(). M= double(M)

% The centroid is given as the moment divided by the force. You have these % two values so solve for the centroid, d. d= M/F % The equation for tension is given on the powerpoint. Remember to use the % correct function to calculate the sine of the angle. Matlab has two: one % that calculates sine using degrees and another using radians. T= d*F/(L*sind(40)) %% Printing out Variables % Force % Print out the value of the force using fprintf. Remember you need the % format specifier in single quotes. Also be sure to report the UNITS of % force and then end your literal text (portion in the single quotes) with % a \n. This will bring you to the next line. fprintf( 'The Force is equal to: %.2f N \n' , F) % Centroid % Print out the value of the centroid using fprintf and be sure to report % your units. Again, place a \n at the end of your text so you move to the % next line. fprintf( 'The Centroid is equal to: %.2f m \n' , d) % Tension % Print out the value of the Tension using fprintf and be sure to report % your units. fprintf( 'The Tension is equal to: %.2f N \n' , T) %% Assignment % 1. Declare your symbolic variables on line 13 % 2. Create two variables L and ang on lines 17 and 21 respectively % 3. Write out the expressions for q and qx on lines28 and 29, respectively % 4. Use the int() function on q and qx to get the force and moment on % lines 37 and 49 % 5. Use double() to change the force and moment variables from symbolic % variables to double precision (called "casting"); % 6. Calculate the centroid and tension force on lines 58 and 64 % 7. Output the centroid and tension values on lines 80 and 86 %% What to turn in % 1. Copy and paste this matlab code into your master Word Document % 2. Copy and paste your output on the Command Window to your master Word % Document. You should have the force, tension, and centroid. % 3. Submit your Matlab source code (.m file) separately

Lab 11 MATLAB Output

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