## Matlab Assignment Solution on Torsion Analysis

• 12th Aug, 2022
• 15:18 PM

function Torsion_Analysis()
clear all;
clc;

data=[0.30    1.18
0.26    1.23
0.22    1.15
0.18    1.21
0.14    1.32
0.10    1.48
0.06    1.63
0.02    2.07];
ratio =data(:,1); % dimension (r/d) values
k=data(:,2); % concentration factor values

%%
% Problem 1(a)
%
% k=b*(r/d)^m; or log(k)=mlog(r/d) +log(b)
% [y=mx+c]: equation of a line whose slope is m and y-intercept is c
figure(1)
x=log(ratio); y=log(k);
n=1; ?gree of polynomial
p=polyfit(x,y,n);
x1=linspace(min(x),max(x)); y1=polyval(p,x1);
plot(x,y,'o')
hold on
plot(x1,y1,'b','LineWidth', 1.5)
xlabel 'log(r/d)', ylabel 'log(k)';
hold off
c=0.75;  % y-intercept. Read from the graph
b= exp(c); % since c=log(b)
%
% The line passes through the last point and second last point
fprintf('>> m=%.4f,\t b=%.2f\n',m,b)
%
% Create Table
log_k_predicted= [0.12,0.15,0.18,0.25,0.30,0.38,0.4886,0.7275]; % read from graph
% log_k_predicted=m*x1+log(b);
k_predicted=exp(log_k_predicted)';
varNames={'Experimental_k_data','Predicted_k_values'};
Table=table(k,k_predicted,'VariableNames',varNames);
Tableu=Table(:,:) % Display table with all data
%%
% Problem 1(b)
%
figure(2)
n=4; ?gree of polynomial
p1=polyfit(ratio,k,n);
x2=linspace(min(ratio),max(ratio)); y2=polyval(p1,x2);
plot(ratio,k,'o')
hold on
plot(x2,y2,'b','LineWidth', 1.5)
xlabel 'Dimensions, (r/d)', ylabel 'Concentration factor, k';
hold off

%%
% Problem 1(c)
%
% Create Table
dim=[0.05, 0.10, 0.15, 0.20, 0.25, 0.30]'; % r/d values
k_a=b*(dim.^(m));
k_l=m*dim+c;
varNames={'r_d_ratios','Equation_in_a','Linear_interpolation'};
Table1=table(dim,k_a,k_l,'VariableNames',varNames);
Tableu1=Table1(:,:) % Display table with all data

end