ON THE STRENGTH OF SHIP BOTTOM PLATING

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78-04861A000400030014-1
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 9
• Document Creation Date: December 20, 2016
• Document Release Date: June 6, 2006
• Sequence Number: 14
• Publication Date: August 1, 1955
• Content Type: REPORT

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25X1
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 Approved For Release 2007/10/23: CIA-RDP78-04861A000400030014-1
ON THE STRENGTH OF SHIP BOTTOM PLATING
J. M. Kiitchieff
Sch1 ffstechnik, 2 ( 1954) 19-21, 84
( From German)
NOTATION
a Frame spacing
b Breadth of ship
Thickness of plate
E Modulus of elasticity
Poisson's ratio
Hydrostatic pressure
D ?rA J -Rigidity of plate
12 U
W, P.)0 Deflection of plate, or maximum deflection
fl Fixed end moment of i cm. wide plate strip
n An Integer
U'0 Tensile stress
k2 - ?b {7f 2 CZ2 h~
Y_i ll
Q? Maximum bending stress
"max Greatest absolute value of combined stress
U Increase In frame spacing due to longitudinal bending of ship
A Cross sectional area of longitudinal members excluding bottom plating
C, Co Distance of C. (I from bottom of keel for cross sectional area of longitudinal
members without and?with bottom plating
I, Io corresponding Inertia moments
1' = Inc, WQ = IC/CO Corresponding resisting moments
Bending moment for longitudinal bending of ship.
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It The botton plating is divided by frames and longitudinals Into panels. Within such a
panelp each plate is loaded in bending by the hydrostatic pressure and simultaneously stressed in
tension or compression by longitudinal bending of the (ship) hull. The bending deflection of
such a plate Is sufficiently large to require its influence on the bending moment to be Considered.
The basic assumption of Kirchhoff's theory of the rigid plate [1-4]* is, therefore, not fulfilled,
and the application of this theory may lead to erroneous results.
In shim' bottoms of usual construction, the panels are rectangles, of which one
side (spacing of longitudinal girders) is so long that the bent plate nay be regarded as a
cylindrical envelope, the generating lines of which are parallel to such long side (longitudinal).
This enables the as yet unsolved problem of the bending of thin plates to be equated 'to the much
simpler problem of the bending of a plate strip parallel to the short edge of the plate (Figure 1).
The validity of this procedure is indirectly confirmed by the results of the Kirchhoff
theory, according to which, for a rectangular plate fixed at the edge, the maximum bending moment
even for an aspect ratio of 1, differs only by 0.1% from that for a plate of infinite length.
2. The differential equation of the elastic curve of a uniformly-loaded strip is
d2 w
Ddx2 = qx(a - x) - mo ...... (1)
from which, in known manner, for the freely supported plate:
1 q a4 x X 2 X 31
w 24 D . a C -2 [ a j + la
wo
and for a plate fixed at the edges:
1 q a4 x
= 24. D (a
5 q a4
1 q a4
w0 a
D
I,-
.. ?.e. (3)
...... (4)
...... (5)
These closed expressions [5] are not very suitable for further analysis, and are
expanded In trigonometrical series [6]; obtaining then, for the freely-supported plate:
co
4
. 7D n5 sin n 77 a
n co
w _ g 1 f
a
87f4 D ~n4 ill-coc2n,rx
n=1
...... (6)
...... (7)
Retaining, in equations (6) and (7), only the first terms of the expansions, we?get
values of Woo differing only by 0.5% and 1.5% from (3) and (5).
If in addition to normal loading the plate strip is also uniformly stressed in axial
tension, the differential equation of the elastic curve will be:
d2 1d
Dam qx (a - x) -%+oO hw
and, as above, for the freely supported plates:
aD
= 4 ga4r.' -x
W
i D (n2 + A2) sin n 7r
N1
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00.
1 qa? 1 1-cos2n7rX
$ 7r4 D n2 (n2 + 4 X2) a
n=1
q a2,7--
1
J2
P j = T12 / 1 n2 + j k2
Putting X = g t 7r X in the earlier equation (7):
00
00
7r X 2 k7-"' 1 _
coth -- _ + -
2 ;-K 7rz , n2 + h ~2
The difference between the length of the bent strip and the frame spacing:
1 + 19dx_a
and equation (10) can be written in closed form:
Qa2 x 7rk
MO =71~2r-? 00th 2-1~
....,. (9)
..... (10)
..... (10')
Comparing equations (8) and (9) with (6) and (7) and restricting crosideration to the
first terms of the expansions, we get from (8) for the freely supported plate:
W = -^ -Q- sin 7T -X
1 +.X2 a
and from (9) for the plate fixed at the edges:
X
.1w~r1-2coa27r
?.?.. (11)
..... (12)
It will be seen that positive axial forces (tension) reduce the bending deflection in
the ratio of 1:(1 + )2) and 1:(1 + 4X2) respectively. Negative axial forces (compression,
X2 < 0), on the other hand, increase the amount of deflection, the values )2 = - 1 and 4 X2 = - 1
representing the bulging of a freely supported ( Figure 2) and a rigidly held (Figure 3) plate
respectively,. under axial compression.
3. It has hitherto been assumed that the end cross-sections of the strip are free to move
in the X-direction, and that the intensity of the axial forces Is known. We shall now examine
the case when these motions or displacements are known.
can be written, neglecting the higher-order terms:
..... (13)
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2
lJ cc -a - M cbc
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Introducing equation (12), this difference becomes, for a fixed strip:
1 - 27TW x 1 lrtd 2
-~ ( sing 2 1r - CbC = ? ...... (14)
81(1+4X2) a_f a a ~2(1+~2)]
fo
elongation of the strip, viz.:-
1 -12 ha 1 - a D
E.h = E.h a2
...... (15)
If, however, the frame spacing is increased by the longitudinal bending of the strip, by
an amount 14 then, the elongation must be equated to the sum:
U + 1 17 W0 2
a l(1+4 2)]
...... (16)
If the bottom plating is removed in one frame space over the 4wle breadth of the ship
(Figure 4), and replaced by uniformly distributed forces (intensity oo h), then
u (1a oobh + CO +
(1 - ?2) ~ ~2 D (A + q + j
-?2)X2ah1+bh lA+}] _
am. 1 77 Wo
(1-~)E I+ a [2 (1+hX2)
4 [i+bh1+11 3G?2) Ch12r +
+ 3G?2) f E IP- C a ] 2 (1 + I X2) 2 ...... (17)
or substituting for W. the value according to equation (5), the equation:.
from rich h X2 can be determined.
Wo
b h
c - co - c
A+bh
Io-I = bhc2- (c-c2o)(A+ bh) - bhc2
I(A+bh)+Abhc2
_ CA
7'
= W[1+bh(A+
Cj]
we can write equation (17) In the following form:
x2 3(1 ?2) a 2N 3(1-)h q2 as 1
7 E .._ h Wo 4086 Wo C E 1 h 7 (1 + 4 X2) 2
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If Jl2 > 0, 1.e. if the plating is stressed in tension (in the wave hollow), the second term
on the right side of the equation, corresponding to the tension due to hydrostatic pressure
is usually small compared with the first term. It is thus possible to write (at any rate,
in first approximation):
X2 3 (1 - ?2) Al
.....,
(19)
4E h.~wo
...... (W)
The second approximation can then be calculated directly, by substituting the value of (19)
in the right hand side of equation (18); which, however, will very seldom be necessary.
if X2 < 0 (on the wave crest), the last multiplier on the right?hand side of
equation (18) > 1, but < 16/9, as will presently be shown, The second term on the right side
thus remains small, also in this case, and the calculation can also, in this case, be performed
in the manner shown above.
In considering the bending of the plate strip it has hitherto been assumed that its end
cross-sections are fixed, which follows from the symmetry of the loading (Figure 5).
This should not be assumed, however, for the case of bulging; the plate must then
rather be regarded as freely supported; . I.e.
)t2>-1, and (1+hk2)-2