Beam Analysis Design a matlab function to calculate internal

Beam Analysis: Design a matlab function to calculate internal stresses for maximum and minimum bending moments and plot their distribution on the cross section.

Solution

% This Matlab code can be used for simply supported beam with single point % load or uniformly distributed to find the % * Support reaction % * Maximum Bending Moment % * Shear force diagram % * Bending Moment daigram clc; clear; close all disp(\'Simply Supported Beam\'); % Data input section disp(\' \'); L = input(\'Length of beam in meter = \'); disp(\' \');disp(\'Type 1 for point load, Type 2 for udl\') Type = input(\'Load case = \'); if Type == 1 disp(\' \'); W = input(\'Load applied in kN = \'); disp(\' \'); a = input(\'Location of Load from left end of the beam in meter = \'); c = L-a; R1 = W*(L-a)/L; % Left Support Reaction. R2 = W*a/L; % Right Support Reaction. else disp(\' \'); W = input(\'Uniformly distributed load in kN/m = \'); disp(\' \'); b = input(\'Length of udl in meter = \'); disp(\' \'); cg = input(\'C.G of udl from left end of the beam in meter = \'); a = (cg-b/2); c = L-a-b; R1 = W*b*(b+2*c)/(2*L); % Left Support Reaction. R2 = W*b*(b+2*a)/(2*L); % Right Support Reaction. end % Discretization of x axis. n = 1000; % Number of discretization of x axis. delta_x = L/n; % Increment for discretization of x axis. x = (0:delta_x:L)\'; % Generate column array for x-axis. V = zeros(size(x, 1), 1); % Shear force function of x. M = zeros(size(x, 1), 1); % Bending moment function of x. % Data processing section if Type == 1 for ii = 1:n+1 % First portion of the beam, 0 < x < b V(ii) = R1; M(ii) = R1*x(ii); % Second portion of the beam, b < x < L if x(ii) >= a V(ii) = R1-W; M(ii) = R1*x(ii)-W*(x(ii)-a); end end x1 = a; Mmax = W*a*(L-a)/L; else for ii = 1:n+1 % First portion of the beam, 0 < x < a if x(ii) < a V(ii) = R1; M(ii) = R1*x(ii); elseif a <= x(ii) && x(ii)< a+b % Second portion of the beam, a < x < a+b V(ii) = R1-W*(x(ii)-a); M(ii) = R1*x(ii)-W*((x(ii)-a)^2)/2; elseif x(ii) >= (a+b) % Second portion of the beam, a+b < x < L V(ii) = -R2; M(ii) = R2*(L-x(ii)); end end x1 = a+b*(b+2*c)/(2*L); Mmax = W*b*(b+2*c)*(4*a*L+2*b*c+b^2)/(8*L^2); end disp(\' \');disp ([\'Left support Reaction\' \' = \' num2str(R1) \' \' \'kN\']) disp(\' \');disp ([\'Left support Reaction\' \' = \' num2str(R2) \' \' \'kN\']) disp(\' \');disp ([\'Maximum bending moment\' \' = \' num2str(Mmax) \' \' \'kNm\']) figure subplot(2,1,1); plot(x, V, \'r\',\'linewidth\',1.5); % Grafica de las fuerzas cortantes. grid line([x(1) x(end)],[0 0],\'Color\',\'k\'); line([0 0],[0 V(1)],\'Color\',\'r\',\'linewidth\',1.5); line([x(end) x(end)],[0 V(end)],\'Color\',\'r\',\'linewidth\',1.5); title(\'Shear Force Diagram\',\'fontsize\',16) text(a/2,V(1),num2str(V(1)),\'HorizontalAlignment\',\'center\',\'FontWeight\',\'bold\',\'fontsize\',16) text((L-c/2),V(end),num2str(V(end)),\'HorizontalAlignment\',\'center\',\'FontWeight\',\'bold\',\'fontsize\',16) axis off subplot(2,1,2); plot(x, M, \'r\',\'linewidth\',1.5); % Grafica de momentos flectores; grid line([x(1) x(end)],[0 0],\'Color\',\'k\'); line([x1 x1],[0 Mmax],\'LineStyle\',\'--\',\'Color\',\'b\'); title(\'Bending Moment Diagram\',\'fontsize\',16) text(x1+1/L,Mmax/2,num2str(roundn(Mmax,-2)),\'HorizontalAlignment\',\'center\',\'FontWeight\',\'bold\',\'fontsize\',16) text(x1,0,[num2str(roundn(x1,-2)) \' m\'],\'HorizontalAlignment\',\'center\',\'FontWeight\',\'bold\',\'fontsize\',16) axis off