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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

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

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