Page 43 - Failure Analysis Case Studies II
P. 43
29
7. Wood, R. H., Engineering Plasticity, Cambridge University Press, 1968.
8. Jones, N., Report 71-20, contract GK-20189X, 1971.
9. Hodge, P. G., Limil Analysis of Rotationally Symmetric Plales and Shells. Prentice-Hall, 1963.
IO. Wood, R. H., Plastic and Ehtir I)e.sign of Slabs and Plates. Ronald Press, 1961.
11. Johnson, R. P.. Structural Concrete. McGraw-Hill, 1967.
APPENDIX
Estimafe of Iowest nalura1frequenc.v offirewalf segment
An upper bound to the lowest natural frequency w of a plate with all edges clamped, uniform mass per unit area m and
uniform plate flexural rigidity D, can be estimated by Rayleigh's method from
where w(x, y) is a arbitrary deflection function which satisfies the kinematic boundary conditions, and both integrals are
over the area of the plate. We consider a triangular plate whose vertices are (0, 0) (a, 0) and (0, h), and take
which satisfies the boundary conditions for a clamped plate. The calculation is assisted by the integral
which is a special case of a standard integral quoted by Gradshteyn and Ryzhik 151. After some algebra:
