Amphion by Paul Valéry

By Paul Valéry

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2. The functions y>t, ψ5, y>6 are plotted in I Or Ι// 6(Φ = ΟΟ) ^ ^ ^ ^ (OJ>=0) 0-4 — /// 0-2 Ι Ι Ι Ι 1 1 1 1 ENLARGED HORIZONTAL SCALE FIG. 13. 46). (When φ = 0, ψ5 is equal to ψ3 in Fig. 2. L 4 3 8 4 EI ^ L Q 2 BbdG qL 0 ^mai 5 ι. 2bd \ qL t Ί Γ 277 2 qL 8 IJ 2bd c+2t 21 Fig. 13 in terms of Θ for the two extreme cases Li = 0 and L i = o o . A s before, θ can be found from Fig. 11. 8. Beam with Four-point Loading (Antiplane Core and Thick Faces) A n ordinary homogeneous beam with four-point loading is illustrated in Fig.

Furthermore, the maximum direct stress in the faces at any section is: c + 2t t 29 SANDWICH BEAMS D o u b l e differentiation o f e q u a t i o n s ( 2 . 3 0 ) a n d ( 2 . 3 1 ) yields and M2, a n d h e n c e

15a), V = ^-w'2. GW2. 20) yields: -Q1 where A = 2 bd /c. 25) and the substitution Qi = •Dw[" gives *--£HK- &H)+ (2 26) The total shear force is: # ß = ßl + Ö 2 = Substitution for \v2' tial equationt for Q\\ ßl-^/< . 27a) = -a Q, where AG * = mÄx=m- ( 2 2 7 )b In any particular problem in which β is a given function of x, this equation can be solved for Qi. The quantities M±, n>i, q\ may be obtained by integration and differentiation. 26) and the related quantities M 2 , w 2 , q2 again obtained by integration and differentiation.

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