MATLAB Report ERC015

MATLAB Report - Coursework

Student Name:

Student ID:

Course Code: ERC015

Module Leader:

Due Date:

Table of Contents

Table of Contents. 2

MATLAB Report (1) 3

MATLAB Report (2) 4

Matlab Function. 4

Command Window.. 6

MATLAB Report (1)

Problem 3: Braking Performance

% Problem 3: Braking Performance

% This script calculates stopping distances of a race car under braking.

% The stopping distance is given by the equation: d = v^2 / (2a)

clear; clc; close all;

% 1. Define variables

% Initial speeds from 50 to 300 km/h in steps of 10 km/h

speeds_kmph =50:10:300;

speeds_mps =speeds_kmph * (1000/3600); % Conversion to m/s

?celeration values in m/s?2;

decelerations = [4,6,8,10]; % Different braking decelerations

% 2. Compute v?2; for all speed values

v_squared = speeds_mps.^2;

% 3. Calculate stopping distances for all combinationsa

% Initialize matrix: rows=speeds, columns=decelerations

stopping_distances = zeros(length(speeds_mps), length(decelerations));

for i = 1:length(decelerations)

a =decelerations(i);

stopping_distances(:, i) = v_squared ./ (2*a);

end

% 4. Extract stopping distances for specific speeds at a = 6 and 10 m/s?2;

target_speeds = [80,160,240]; % km/h

target_indices = find(ismember(speeds_kmph, target_speeds));

a6_index = find(decelerations==6);

a10_index = find(decelerations==10);

% Extract the corresponding stopping distances

stopping_selected_6 = stopping_distances(target_indices, a6_index)

stopping_selected_10 = stopping_distances(target_indices, a10_index)

% 5. Modify stopping distance at 200 km/h with a = 8 m/s?2;

% Increase it by 8%

index_200 = find(speeds_kmph == 200);

a8_index = find(decelerations == 8);

stopping_distances(index_200, a8_index) = ...

stopping_distances(index_200, a8_index) * 1.08;

% 6. Save the data in a .mat file

save('braking_data.mat', 'speeds_kmph', 'speeds_mps', 'decelerations', ...

'stopping_distances', 'stopping_selected_6', 'stopping_selected_10');

% 7. Plot stopping distance vs speed for each deceleration

figure;

hold on;

% Create a different marker for each deceleration

markers = {'o','s','d','^'};

colors = lines(length(decelerations));

for i = 1:length(decelerations)

plot(speeds_kmph, stopping_distances(:, i), ...

'LineWidth', 1.5, ...

'Marker', markers{i}, ...

'Color', colors(i,:), ...

'DisplayName', sprintf('a = %d m/s?2;', decelerations(i)));

end

grid on;

?d labels and legend

xlabel('Speed (km/h)');

ylabel('Stopping Distance (m)');

title('Stopping Distance vs. Speed for Various Decelerations');

legend('Location', 'northwest');

hold off;

MATLAB Report (2)

Matlab Function

function beam_analysis(L, P, w, E, I, c, sigmaY)

?AM_ANALYSIS Performs structural analysis of a cantilever beam

% beam_analysis(L, P, w, E, I, c, sigmaY) analyzes a cantilever beam

% with:

% L = Length of beam (m)

% P = Concentrated load at free end (N)

% w = Uniformly distributed load (N/m)

% E = Young's modulus (N/m?2;)

% I = Second moment of area (m?)

% c = Distance from neutral axis (m)

% sigmaY = Yield strength (N/m?2;)

% 1. Initialize variables and create position vector

n_points = 1000; % Number of points for analysis

x = linspace(0, L, n_points)'; % Position vector along beam

% 2. Preallocate arrays for results

M_x = zeros(n_points, 1); ?nding moment

sigma_x = zeros(n_points, 1); ?nding stress

delta_x = zeros(n_points, 1); ?flection

% 3. Calculate beam response at each point

for i = 1:n_points

?nding moment calculation

M_x(i) = -P*(L - x(i)) - (w/2)*(L - x(i))^2;

?nding stress calculation

sigma_x(i) = -(M_x(i)*c)/I;

?flection calculation

delta_x(i) = (P/(6*E*I))*(x(i)^3 - 3*L*x(i)^2) ...

- (w/(24*E*I))*(x(i)^4 - 4*L*x(i)^3 + 6*L^2*x(i)^2);

end

% 4. Check for failure (stress exceeds yield strength)

failure_points = find(abs(sigma_x) > sigmaY);

if ~isempty(failure_points)

warning(['Beam failure detected at ', num2str(length(failure_points)), ...

' points! Stress exceeds yield strength.']);

end

% 5. Create plots

% Common plot settings

line_width = 1.5;

% Figure 1: Bending Moment Diagram

figure;

plot(x, M_x, 'b', 'LineWidth', line_width);

title('Bending Moment Distribution');

xlabel('Position along beam (m)');

ylabel('Bending Moment (Nm)');

grid on;

% Figure 2: Bending Stress Distribution

figure;

hold on;

% Plot safe region as thick red line

safe_region = abs(sigma_x) <= sigmaY;

plot(x(safe_region), sigma_x(safe_region), 'r-', 'LineWidth', 3, 'DisplayName', 'Safe Region');

% Plot unsafe region as thick black dotted line (appearing as connected dots)

unsafe_region = ~safe_region;

plot(x(unsafe_region), sigma_x(unsafe_region), 'k.', 'MarkerSize', 12, 'DisplayName', 'Unsafe Region');

hold off;

% Customize plot appearance

title('Bending Stress Distribution', 'FontSize', 12, 'FontWeight', 'bold');

xlabel('Position along beam (m)', 'FontSize', 10);

ylabel('Bending Stress (Pa)', 'FontSize', 10);

% Set both axes to start from 0

xlim([0 L]);

ylim([0 max(abs(sigma_x))*1.1]);

% Configure legend and grid

legend('Location', 'northeast', 'FontSize', 9);

grid on;

box on;

% Figure 3: Deflection Curve

figure;

plot(x, delta_x, 'g', 'LineWidth', line_width);

title('Deflection of the Beam');

xlabel('Position along beam (m)');

ylabel('Deflection (m)');

grid on;

% 6. Parameter suggestions if failure occurs

if ~isempty(failure_points)

fprintf('nSuggested parameter modifications to prevent failure:n');

?lculate required scaling factor to stay within yield

max_stress = max(abs(sigma_x));

scaling_factor = max_stress / sigmaY;

% Option 1: Reduce loads

fprintf(' - Reduce P by %.1f%% and w by %.1f%%n', ...

(scaling_factor-1)*100, (scaling_factor-1)*100);

% Option 2: Increase beam properties

fprintf(' - Increase I by %.1f%%n', (scaling_factor-1)*100);

fprintf(' - Or increase c by %.1f%%n', (1-1/scaling_factor)*100);

% Option 3: Use stronger material

fprintf(' - Use material with E > %.2f GPan', E*scaling_factor/1e9);

end

end

Command Window

L = 5; P = 10000; w = 2000; E = 200e9;

I = 0.00000833; c = 0.05; sigmaY = 250e6;

beam_analysis(L, P, w, E, I, c, sigmaY);