ME 180 ACU Mechanical Engineering Determine Angles Matlab Questions Solve all eight problems listed in the following document: Homework Assignment 04 Chap

ME 180 ACU Mechanical Engineering Determine Angles Matlab Questions Solve all eight problems listed in the following document:

Homework Assignment 04 Chapter 6.pdf

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Follow the instructions at the top of the document specifying the proper use of Mohr’s circle. Any Mohr’s circle solution submitted in this course (homework, lab, or exam) must follow these guidelines. To complete the assignment, turn in Problems 1, 3, 6, & 8. Solve Problems 1, 3, & 6 with hand-drawn Mohr’s circles and solutions (NOT MATLAB). Scan your NEAT, WELL ORGANIZED solutions to PDF for submission. Box any answers for easy grader identification. Solve Problem 8 using MATLAB (your code should generate a Mohr’s circle and output all answers using “fprint”). Publish your code to PDF, combine all four problems (1, 3, 6, & 8) in to one PDF file, then upload.

MATLAB code (m-file and published PDF file) for problem 6.3, Dowling 5th edition, is found here:

MohrsCircleProb6_3RevSum20.pdf

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MohrsCircleProb6_3RevSum20.m

You can use the m-file as a template to solve Problem 8, but, of course, you’ll have to add code to determine stress components from given strain values to enter Mohr’s circle. Or, if you’re feeling ambitious, you can write code to generate a Mohr’s strain circle, then calculate principal stresses from the determined principal strains. ME180 Chapter 6 Problem 6.3 5th ed.
Patrick Homen CLASS EXAMPLE PROBLEM
Problem 6.3 Dowling 5th ed.
A state of stress that occurs on the free surface of a solid body is
sigx = 50, sigy = 100, and tauxy = -60 MPa.
(a) Evaluate the two principal normal stresses and the one principal
shear stress that can be found by coordinate system rotations in
the x-y plane, and give the coordinate system rotations.
(b) Determine the maximum normal stress and the maximum shear stress
at this point.
clear
clc
% PLANE STRESS: sigx, sigy, tauxy nonzero; sigz, tauxz, tauyz = 0.
% Enter given stress element components:
sigx = 50; % MPa
sigy = 100; % MPa
tauxy = -60; % MPa
% PLANE STRESS: sigx, sigy, tauxy nonzero; sigz, tauxz, tauyz = 0.
% stress components given above
% Calculate center of Mohr’s circle:
OC = (sigx+sigy)/2;
% Calculate radius of Mohr’s circle:
Rad = (((sigx-OC)^2) + tauxy^2)^0.5;
% Calculate principal normal stresses:
sig1 = OC+Rad;
sig2 = OC-Rad;
% Max shear in 1-2 plane (tau3) = R, report later.
% Calc and report max shear later in program to report after
principals.
% DRAW MOHR’S CIRCLE:
% Draw sigma and tau axes for Mohr’s circle:
% Limits of sigma axis 10% beyond principal normals:
% Ensure crosses origin,left end always negative (considers case when
% both principal normal stresses are positive):
sigleft = min(sig2*1.1,(-1)*(0.1)*sig2);
% Ensure crosses origin, right end always positive (considers case
when
% both principal normal stresses are negative):
sigright = max(sig1*1.1, (-1)*(0.1)*sig1);
% Need zeros for both axes to cross at origin:
zero = zeros(1,2);
% For sigma axis:
% “x” coordinates of sigma axis:
sigLR=[sigleft sigright];
% “y” coordinates of sigma axis = “zero” = [0 0]:
% Draw sigma axis by plotting ends:
1
ME180 Chapter 6 Problem 6.3 5th ed.
figure(1);
plot(sigLR,zero,’b–‘);
hold on
grid on
title(‘Mohr”s Stress Circle’)
xlabel(‘sigma, MPa’)
ylabel(‘tau, MPa’)
% Limits of tau axis:
tautop = Rad*1.1;
taubot = Rad*(-1.1);
% “y” coordinates of tau axis:
tauTB=[tautop taubot];
% Use “zeros” for “x” coordinates of tau axis
% Draw tau axis by plotting top and bottom end points
plot(zero,tauTB,’b–‘);
% Establish limits of plot, set range of axes:
% Will draw Mohr’s circle within boundaries of plot by setting axis
limits:
axis([sigleft-0.2*Rad sigright+0.2*Rad taubot-0.2*Rad tautop
+0.2*Rad]);
% Plot X-face, symbol = “X” in black:
% Note use of “Dowling Method” to ensure (+) shear plots down by
% multiplying the shear tauxy by (-1):
plot(sigx,(-1)*tauxy,’k*’);
% Plot Y-face, symbol = “V” in black:
plot(sigy,tauxy,’k*’);
% Ensure Mohr’s circle displays as a circle:
axis equal
% Plot center point, symbol = “+” in black:
OCx = OC;
OCy = 0;
plot(OCx,OCy,’k+’);
% Draw diameter through circle from x-face to y-face:
xcoords = [sigx sigy];
ycoords = [(-1)*tauxy tauxy];
plot(xcoords,ycoords,’b’); % “b” sets blue diameter.
% Plot principal stresses, mark with “diamonds”:
sig12 = [sig1 sig2];
plot(sig12,zero,’k*’);
% Plot principal shears, mark with “circles”:
OCxs = OCx * ones(1,2);
taus = [Rad (-1)*Rad];
plot(OCxs,taus,’k*’);
% Calculate theta, degrees:
% “if” statement covers case when sigx = sigy (denominator=0):
if sigx > OC | sigx < OC; theta = (atand(abs(tauxy)/abs(sigx-OC)))/2; else theta = 45; end % Plot Mohr's circle with dashes on perimeter of circle: % Generate points (90) to plot circle: % Initialize vector of sigma values: circlex = []; 2 ME180 Chapter 6 Problem 6.3 5th ed. % Initialize vector of tau values: circley = []; % Use while loop to generate vectors with 90 values: i = 1; while i = sigy & tauxy > 0;
fprintf(“The 1-Principal axis
from the x-axisn”, theta)
elseif sigx >= sigy & tauxy < 0; fprintf("The 1-Principal axis x-axisn", theta) elseif sigx < sigy & tauxy > 0;
fprintf(“The 1-Principal axis
from the x-axisn”, 90-theta)
elseif sigx < sigy & tauxy < 0; fprintf("The 1-Principal axis x-axisn", 90-theta) end fprintf("n"); is %5.2f degrees counterclockwise is %5.2f degrees clockwise from the is %5.2f degrees counterclockwise is %5.2f degrees clockwise from the % Report max shear in 1-2 plane (tau3) which = Rad: fprintf('The Principal Shear in the 1-2 plane (tau3) = %5.2f MPa n',Rad); % Determine and report max shear in ANY plane: % Max shear in ANY plane (taumax) depends on signs of principal normal % stresses: 3 ME180 Chapter 6 Problem 6.3 5th ed. % Use "if" statements for all cases: if sig1 > 0 & sig2 > 0;
taumax = sig1/2;
fprintf(‘The Max Shear is in the 1-3 plane (tau2) = %5.2f MPan’,
taumax);
elseif (sig1>0&sig2==0)|(sig1>0&sig2
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