y T The boundary conditions are P ▬▬▬ L The strong form of governing equation for a simply supported beam under a distributed load p, shown in the figure above, is as follows d²v dx² M(x) EI where v is the deflection in y direction, E is Young's modulus, I is the second moment of inertia, M(x) is the internal bending moment and is given by px(L-x) M(x) = 2 I▬▬▬ X V(0)=0 v(L)=0 = 0

y T The boundary conditions are P ▬▬▬ L The strong form of governing equation for a simply supported beam under a distributed load p, shown in the figure above, is as follows d²v dx² M(x) EI where v is the deflection in y direction, E is Young's modulus, I is the second moment of inertia, M(x) is the internal bending moment and is given by px(L-x) M(x) = 2 I▬▬▬ X V(0)=0 v(L)=0 = 0

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

Hint: You should get the final equation as below.
Sta
0
dw dv
dx
-dx
dx
=
P
2EI
L
wx (L - x)dx

y
التاناتي
The boundary conditions are
Р
L
The strong form of governing equation for a simply supported beam under a distributed load
p, shown in the figure above, is as follows
d²v M(x)
dx²
X
0
EI
where v is the deflection in y direction, E is Young's modulus, I is the second moment of
inertia, M(x) is the internal bending moment and is given by
px(L-x)
M(x) =
2
v(0) = 0
v(L)=0

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