Calculation of Load Distribution in Stiffened Cylindrical Shells Page: 33 of 70
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N.A.C.A. Technical emoranduma No. 866
k g9ko- gn-k gn upper sigp /f ora o o O
Form of solution: X ( )k , 2 lower Syn ;f>o or , ( o
92U lower s/n if > 0 or ac> 0
Case In lerrne/o',e bulkheads e/astic, end u//rheads:
elastic . I rgid
D > I g, - sin(kl/)Xsi(n 1-k)y g,= sin(k +f), s;rnA (n*-k)y
(A-B < 1) sin k- .sin n - k)y 2sin k sin-h(n-k l sink (n-k) y
D- g, - (ktl) sinh(n i-k). y g,. (k d) -.inh(nf-k)V
(A -B -) ; k sink in - k)v ; 2 k 5nh (n-k)y+ (k-1)5nh(n-1-k)
D < I gk .inh(kf) sinoh(n -k)y " g,(-sin/(k+f)p sinh((n lf-k)
(A -B> ) p s;on kg S 5h (n-kly f2sink9 sinh(n -k)w+sinh(k-l)psi/(n-l-k)
limili, case ofridSAu/kheads :g, -sirnh(n-k) for/x/ 1 ; g = ri - k for /c/ * f
Table I.- Solutions of elasticity equations for applied characteristic
force group Xo= 1 for shells of finite lengths (end bulkhead
freely deformable).
Case ermediate bulkheads, e/osic, end Bu/kheads:
elastic riqid
A-B < I X = (-+l)e -k cosk+c c s sink, X, = (- )ke" [coskZoSev. sn skj
A-B > Xk, (t 1)k e-kft(fe S ] X,- ( i) e+ [ ik+ k]
s;1. sinh nh
LArn/ng case of rydiu/krhecds (c, 0): X, ( 1) k ekp
Upper sign if x,4 Zxc -- acoa; Lower 59sign if 4wc <2x4-xw
Constants. y - ore cosh(A B)
8x wt x, t+ e +x ,. .
A- xs o rc cos (A -B)
XJc0 c arc cos(A - B
4"- r---r- V 3saLca~Iwx(r*ScY~,. - k- .. p .-'arccoSb(A -B)
s s
, u aco+ / 4 " ore cash/C/
- 2, r - o, , _/
Table II- solutions of elasticity equations for applied characteristic
force group o- 1 for infinitely long shells.32
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Ebner, H. & Köller, H. Calculation of Load Distribution in Stiffened Cylindrical Shells, report, June 1938; (https://digital.library.unt.edu/ark:/67531/metadc63311/m1/33/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.