T y R d ERS

Rxy Ryz

1 d2y du

Now ā€” = ā€”- and, for small deflections, ā€” = tan0 = 9 (radians). R dxl dx

1 _d2y _ dd Rxy dx2 dx and de sx = uā€” (= radial strain) dx

Consider now the diagram Fig. 7.2 in which the radii of the concentric circles through C\ and D, on the unloaded plate increase to \(x + dx) + (9 + d9)u] and [x + u9], respectively, when the plate is loaded.

Looded plate

Looded plate

Circumferential strain at Dj

2 nx u9

Substituting eqns. (7.3) and (7.4) in eqns. (7.1) and (7.2) yields i.e.


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