Introduction to Plate Buckling and Small Deflection Theory — Lesson 1

This lesson covers the concept of buckling in plates, which are two-dimensional members, in contrast to the one-dimensional members like columns discussed in the preceding chapter. The lesson explains the difference between the buckling of plates and columns, highlighting that plates can take further axial load after reaching the critical load, indicating significant post-buckling strength. The lesson also introduces the concept of local and global buckling in plates. The governing differential equation of plate buckling is derived, considering small deflection theory for thin plates. The lesson concludes with the explanation of the assumptions made in deriving the governing differential equation, including no mid-plane strain and no transverse shear deformation.

Video Highlights

00:42 - Discussion on the behavior of plates and columns in terms of deflection and bending moment Discussion on torsional buckling and torsional flexural buckling
07:46 - Discussion on the concept of post-buckling path in plates
15:18 - Explanation of the assumptions for deriving the governing differential equation of the plate buckling
23:17 - Discussion on the concept of no mid-plane strain in small deflection of plates

Key Takeaways

- Buckling in plates is different from columns as plates have significant post-buckling strength.
- Buckling in plates can be local (small plate elements) or global (large flat surfaces).
- The governing differential equation of plate buckling is derived based on small deflection theory for thin plates.
- Assumptions made in the derivation include small deflections compared to plate thickness, small slopes of the deflected middle surface, plane sections remaining plane before and after bending, negligible normal stresses and strains, and the material of the plate being homogeneous and isotropic.