Problem 6-38 of "Mechanics of Materials", by Hibbeler, 8th. edition,
in US system of customary units (Lb, in).
The problem is to draw the diagrams for shearing force and
bending moment for a beam, which is the wing of an aircraft,
while it is static on the ground. The forces applied on the structure
are a concentrated weight of 3000 Lb corresponding to an engine,
the weight carried by the landing gear is 15000 Lb, and the
weight of the structure itself (this may include the fuel inside
the wings), which is a distributed uniformly varying load.
The values of shear force and bending moment have to be
calculated at point A, which is the attachment point of the
wing to the fuselage of the aircraft.
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% Universidad Autonoma de Ciudad Juarez, Mexico
disp(' ')
disp('Problem 6-38, Hibbeler, "Mechanics of Materials", 8th. ed.')
disp(' ')
% the reaction from the ground through the landing gear,
% and the distributed load of the structure itself.
% First portion of the beam, 0 < x < 96, inch
V(index) = -125 * x(index)^2 / (8*12^2);
M(index) = V(index) * x(index)/3;
M(index) = M(index)-3000*(x(index)-96)...
+6.25* (x(index)-96)^3 / (30*12^2);
end
M(index) = M(index) + 15000*(x(index)-120);
end
grid
xlabel('x, inch')
ylabel('Shear force, Lb')
title('Shear force diagram')
axis tight
plot(x,M, 'r', 'linewidth', 2.5)
grid
xlabel('x, inch')
ylabel('Bending moment, Lb-in')
title('Bending Moment diagram')
axis tight
disp(V(N))
disp(' ')
disp('_______________________________________')
format short