Buckling Lecture 11 ME EN 372 Andrew Ning aning@byu.edu Outline - PDF document

Buckling Lecture 11 ME EN 372 Andrew Ning aning@byu.edu Outline Buckling Theory Example

https://youtu.be/NhQ3lYtzw9Y Buckling Theory

y P L EI d 2 y dx 2 + Py = 0

General Solution: y = A cos( ωx ) + B sin( ωx )

P cr = Cπ 2 EI l 2 C boundary condition 1 fixed-free 4 pinned-pinned 1 fixed-pinned ≈ 2 fixed-fixed 4 A = Cπ 2 E P cr ( l/k ) 2 � where k = I/A

Euler Euler

Johnson Euler � l � 1 / 2 � 2 π 2 CE � = k S y 1 � l � 2 P cr � S y l CE for l 1 � A = S y − k ≤ 2 π k k 1

Example Example Problem