Consider an extension of Exercise 8.51 in which we wish to explore the stress distribution in a circular disk under an increasing number of boundary loadings. First show that for case:

(a). With four loadings, the center stresses are given by σ_x = σ_y =–4P/πD, τ, _xy = 0, where D is the disk diameter. Next for case.

(b). With eight loadings, show that the center stresses. become σ_x = σ_y =–8P/πD, τ, _xy = 0. Hence conclude that for a general case with N loadings (N = 4, 8, 16,.), the center stresses can be expressed by σ_x = σ_y=–NP/πD, τ, _xy = 0. Thus
as N → ∞, the boundary loading becomes uniformly distributed as shown in case.

(c). And center stresses are then given by σ_x =σ_y=–p, τ, _xy = 0 where p = NP/πD, which can be found from solution (8.4.3).

Equation 8.4.3

Transcribed Image Text:

riri -Rr (P2 -P) + P - R2P 22-2 2-2 Or 0 = de 22 (0 - 0) 1 + ri01 - 20 2-2 2