How Do You Calculate Displacement for an Irregular Cantilever Beam?

[timmy996]

Hello,

I am trying to figure out how to calculate displacement for an irregular cantilever beam, i.e. one that is not the normal straight-beam that you would see in a textbook.

Please see the attached image. If the left end is fixed, and I want to calculate the displacement of point A due to an applied force at that point, how would I go about it?

Are you still able to use M_x = EI * d^2y/dx^2 and solve for displacement by integrating? I am not exactly sure how the geometry of the weird bended shape comes into play. Thanks.

- T

 

[skeleton]

The cantilever beam has three segments:
1) Horizontal segment with moment inertia I_1
2) Diagonal segment at middle with moment inertia I_2
3) Diagonal segment at end with moment inertia I_3

Note: I_2 is determined relative to global Y axis (not local Y axis). Thus, I_2>I_1 as illustrated. I_3 is not required for calculations; only its horizontal length is needed.

The beam has four points
A) At support
B) Right of segment 1
C) Right of segment 2
D) Right of segment 3

Procedure:
a) Calculate flexure and deflection over segment 2
b) Calculate flexure and deflection over segment 1
c) Add deflection 1 and 2 to give total deflection at point C
d) Determine curvature at point C
e) Determine tangent of segment 3, and thus deflection of segment 4
f) Add deflection of point step (c) to setup (e) to yield total deflection at (4)