find tension, shear and moment on a pinned parabolic arch with vertical loading in matlab

main.m
spanLength = ...; % length of the arch span (in meters)
archHeight = ...; % height of the arch (in meters)
loading = ...; % vertical loading on the arch (in newtons)
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main.m
% Since the arch is symmetrical, we only need to calculate half of the arch
x = linspace(0, spanLength/2, 100); % divide the half-span into 100 sections
y = archHeight * (1 - (x / (spanLength/2)).^2); % equation of the parabolic arch
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main.m
distributedLoad = loading / archHeight; % distributed load per unit length
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main.m
reactionForce = distributedLoad * spanLength / 2; % reaction force at the pinned ends
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main.m
% Calculate the tension
tension = sqrt((diff(y) / diff(x)).^2 + 1) * distributedLoad;

% Calculate the shear
shear = -(diff(tension) / diff(x));

% Calculate the moment
moment = -(diff(shear) / diff(x));
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main.m
plot(x(2:end), tension);
title('Tension')
xlabel('Position along the span')
ylabel('Tension')

figure
plot(x(2:end), shear);
title('Shear')
xlabel('Position along the span')
ylabel('Shear')

figure
plot(x(2:end), moment);
title('Moment')
xlabel('Position along the span')
ylabel('Moment')
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