The basic differential equation of the elastic curve for a simply supported, uniformly loaded beam (Fig. P24.16) is given as EI dx? dy wLx_ wx 2 2 where E = the modulus of elasticity and I = the moment of inertia. The boundary conditions are y(0) = y(L) = 0. Solve for the deflection of the beam using (a) the finite-differ- %3D %3D %3D ence approach (Ax = 0.6 m) and (b) the shooting method. The following parameter values apply: E = 200 GPa, I = 30,000 cm“, w = numerical results to the analytical solution: %3D 15 kN/m, and L = 3 m. Compare your wLx³ y = 12 EI wx4 24 EI wL'x 24 EI
The basic differential equation of the elastic curve for a simply supported, uniformly loaded beam (Fig. P24.16) is given as EI dx? dy wLx_ wx 2 2 where E = the modulus of elasticity and I = the moment of inertia. The boundary conditions are y(0) = y(L) = 0. Solve for the deflection of the beam using (a) the finite-differ- %3D %3D %3D ence approach (Ax = 0.6 m) and (b) the shooting method. The following parameter values apply: E = 200 GPa, I = 30,000 cm“, w = numerical results to the analytical solution: %3D 15 kN/m, and L = 3 m. Compare your wLx³ y = 12 EI wx4 24 EI wL'x 24 EI
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![The basic differential equation of the elastic curve for
a simply supported, uniformly loaded beam (Fig. P24.16) is
given as
d'y
EI
wLx_ wx
2
dx?
2
where E = the modulus of elasticity and I = the moment of
inertia. The boundary conditions are y(0) = y(L) = 0. Solve
for the deflection of the beam using (a) the finite-differ-
%3D
%3D
ence approach (Ax = 0.6 m) and (b) the shooting method.
The following parameter values apply: E
30,000 cm", w = 15 kN/m, and L = 3 m. Compare your
numerical results to the analytical solution:
= 200 GPa, I
%3D
wLx?
wxt
.3
wL'x
y =
12 EI
-
24 EI
24 EI](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a93e557-3c1a-4acf-b162-db01876dde4d%2F042f4631-a07f-4072-b404-a9009ea354ba%2F1c6wl5v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The basic differential equation of the elastic curve for
a simply supported, uniformly loaded beam (Fig. P24.16) is
given as
d'y
EI
wLx_ wx
2
dx?
2
where E = the modulus of elasticity and I = the moment of
inertia. The boundary conditions are y(0) = y(L) = 0. Solve
for the deflection of the beam using (a) the finite-differ-
%3D
%3D
ence approach (Ax = 0.6 m) and (b) the shooting method.
The following parameter values apply: E
30,000 cm", w = 15 kN/m, and L = 3 m. Compare your
numerical results to the analytical solution:
= 200 GPa, I
%3D
wLx?
wxt
.3
wL'x
y =
12 EI
-
24 EI
24 EI
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