II.1 Programming in MATLAB Getting Started Graphing

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ArraysNext, look over the second template shown in Table 2.This program determines the force reactions acting on the barshown in Fig. A2 – 2. The reactions are found by solving a setof three linear algebraic equations. The unknowns in thisproblem are⎛ F ⎞⎜ ⎟x =⎜N A⎟,⎝ N B ⎠where F is the friction force at A, N A is the normal force at A,and N B is the normal force at B. Create the M-file namedtarray.m and type in Table 2. Notice how the program defineselements of vectors and matrices (arrays). Also notice howthese arrays are manipulated using vector algebra. In thisprogram, a set of linear algebraic equations of the form Ax = bis solved by first calculating A -1 and then by calculating thesolution x = A -1 b.Next, save and close tarray.m, go to the commandwindow, typetarrayand hit return. The command window diplays b, A, and thesolution x. You’ll see that F = 31.6987 lb, N A = 68.3013 lb, andN B = 44.8288 lb.4
%% tarray.m%% This m-file is a template for creating arrays. It contains many of the% commands that are commonly used for arrays.%% In this template, a set of linear algebraic equations is solved.%% This template shows:%% - several ways to input a vector% - how to transpose a vector and a matrix% - how to invert a matrix% - how to swap a column in a vector with another column vector% - how to multiply vectors and matrices% - how to perform a for-end loop more efficiently%clearW = 100;L = 2;theta = pi/4;beta = pi/6;b = [W,0,W*L/2*cos(beta)]'% An array is defined by enclosing the elements in% brackets, separating them by commas.% This creates a row vector. The prime following the% right bracket transposes the row vector, making it a% column vector.%% b = [W;0;W*L/2*cos(beta)] % This is another way to define a column vector. Each row% (the rows are one element long) is separated by a% semicolon.A = [0,1,cos(theta);1,0,-sin(theta);0,0,L*cos(theta-beta)] %A matrix is defined by% listing its elements row by row. Each% row is separated by a semicolon.ainv = inv(A);% inv inverts a matrix.% detofA = det(A) % det takes the determinant of a matrix.% Atranspose = A' % a prime after a matrix transposes the matrix.% A(:,2) = [10,10,10]' % Using the colon, the second row of A is replaced with% the column vector [10,10,10]'.x = ainv*b%time1 = [0:1:2*pi]% multiplication/addition of vectors and matrices uses% the same syntax that is used for scalars.% Instead of using a for-end loop. The following syntax%can be used. This instruction creates a row vector of% values starting from 0, stepping in increments of% 1,ending just before 2pi. The loop is created using the% brackets.%time2 = [0:2*pi] % The default increment is 1.%c = cos(time1) % Creates a row vector called c. The array is created% using the parentheses, inside which the array time1% appears.Table 2: Template for Arrays5
Page 3: %% tgraph.m%% This m-file is a temp
Page 7 and 8: function [F,NA] = tfunction(beta,th
Page 9 and 10: Key Commandsclc, clear, edit, what,
Page 11: A2 - 6A stone ornamental bridge bei

II.1 Programming in MATLAB Getting Started Graphing

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