b2 b av r2 bi The trapezoidal cross sectional area of the cu

b2 b. av r2 bi The trapezoidal cross sectional area of the curved beam shown can be kept constant for any value of b by fixing bav and h. Write a MATLAB code that plots the magnitudes of the maximum tensile and compressive bending stresses as bi varies from 0 to 6 inch. Use the following data: h4 in, ba 3 in, M 1500 lb.ft and r8 in

Solution

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clear all
clc
% Given parameters:
bavg = 3;          % Average width of the trap. c/s
h    = 4;            % height of the trap. c/s
M    = 1500*12; % Moment in lb.in not lb.ft
                        % +ve moment since its action straightens the bar
r1   = 8;             % radius of the inner edge from the center of curvature

b1_var = 0:0.1:6; % Side b1 varying from 0 to 6 inches

%%% For loop calculating stresses for varying b1 from 0 to 6 inches:
for i = 1:size(b1_var,2)
  
% Other Geometric parameters:
b1   = b1_var(i); % Assigning b1 values from 0 to 6 inches
b2   = 2*bavg-b1; % calculatig b2 from b1 and bavg
r2   = r1+h;          % radius of the inner edge from the center of curvature
A    = bavg*h;       % Ares of c/s of the trapezium

%%% Calculation of the neutral axis (r):
r = A/(b2-b1+(((b1*r2-b2*r1)/h)*log(r2/r1))); % Neutral axis distance from the center of curvature

%%% Calculation of the centroidal axis (rc):
rc = r1+ (h/3)*((b1+2*b2)/(b1+b2));    % Centroidal axis distance from the center of curvature

%%% Maximum tensile and bending compressive stresses:

% Distance of the Neutral axis to the inner and outer fibers(Ci & Co):
% Sign convention -> +ve towards the Center of curvature
Ci = r-r1;
Co = r-r2;

% Distance between the Centroidal axis and the Neutral axis (e):
e = rc-r;
% Maximum tensile stress on the innermost fiber (Sigmai):
Sigmai(i) = M*Ci/(A*e*r1);
% Maximum Compressive Stress on the outermost fiber(Sigmao):
Sigmao(i) = M*Co/(A*e*r2);
end

%%% Plots:

% Max. bending tensile stress vs width b1 of the c/s

figure,plot(0:0.1:6,Sigmai);
xlabel(\'b1 (in.)\')
ylabel(\'Max. bending tensile stress (lb/in^2)\')
title(\'Max. bending tensile stress vs width b1 of the c/s\')

% Max. bending compressive stress vs width b1 of the c/s
figure,plot(0:0.1:6,Sigmao);
xlabel(\'b1 (in.)\')
ylabel(\'Max. bending compressive stress (lb/in^2)\')
title(\'Max. bending compressive stress vs width b1 of the c/s\')