Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Contents show an example of double integration along with graphs for deflection and slope.
Typology: Lecture notes
1 / 3
This page cannot be seen from the preview
Don't miss anything!
The load is distributed linearly:
2
0 0
w x w x
V x x w x x
3
0 0
w x x w x
M x x
0
The shear force and the bending moment in section x are:
The boundary conditions:
(0) 0
(0) 0
V
M
( ) 0
( ) 0
L
y L
We have found V(x) and M(x); therefore the boundary conditions
at x = 0 are already satisfied.
0
(0) 0
(0) 0
V
M
( ) 0
( ) 0
L
y L
The boundary conditions:
The load is distributed linearly:
The shear force and the bending moment in section x are:
2
0 0
w x w x
V x x w x x
3
0 0
w x x w x
M x x
To find the slope and deflection , we need to use integration:
4
0
1
Since q ( L ) = 0,
4 3
4 4 0 0 0
1 1
w L w L w
C C EI x L x
We have found V(x) and M(x); therefore the boundary conditions
at x = 0 are already satisfied.
5
4 4 4 0 0
2
w w x
EIy x x dx L x dx L x C
The last boundary condition: y ( L ) = 0.
5 4
4 5 0 0 0
2 2 2
w L w w L
