
Reg. 215
TUBE PLATES
Efficiency of Ligament
a) 
When a shell or drum is drilled
for tubes in a line parallel to the axis of the shell
or drum, the efficiency of the ligament between the tube
holes shall be determined as follows : 
(a) When a pitch of the tube holes on every row is equal
(as in Fig.10), the formula is :
p  d 
= efficiency of ligament 
Eqn.(54) 
p 
where
p = pitch of tube holes, inches,
d = diameter of tube holes, inches,
The pitch of the tube holes shall be measured either on
the flat plate before rolling or on the median line after
rolling.
Example : Pitch of the tube holes in the drums
as shown in Fig.10 = 51/4 in. diameter of tube = 31/4".
Diameter of tube holes = 39/32".
p  d 
= 
5.25 
3.281 
= 
0.375, efficiency
of ligament. 
p 
5.25 
(b) When the pitch of tube holes on an one row in unequal
(as in Figs.11 &
12), the formula is :
p nd 
= efficiency of ligament 
Eqn.(55) 
p 
where
p = unit length of ligament, inches,
n = number of tube holes in length p,
d = diameter of tube holes, inches
Example  Spacing shown in Fig.11. Diameter of
tube holes = 39/32".
p  nd 12 
= 
12/ 2 x
3.281 
= 
0.453, efficiency
of ligament. 
p 
12 
Example  Spacing shown in Fig.12 Diameter of
tube hole = 39/32".
p  nd 
= 
29.25
 5 x 3.281 
= 
= 0.439,
efficiency of ligament 
p 
29.25 
(c) The strength of those ligaments between the tube holes
which are subjected to a longitudinal stress shall be
at least onehalf the required strength of those ligaments
which come between the tube holes which are subjected
to a circumferential stress.
(d) (i) When bending stresses due to weight are negligible
and the tube holes are arranged along a diagonal line
with respect to the longitudinal axis, the efficiency,
(z) of corresponding ligaments is given in Fig
14, with the ratio b/a on the abscissa and the ratio
2a  d 
or

d 
used as a
parameter. 
2a 
a 
where
a and b are measured as shown in Figure 13
A & 13 B,
d = diameter of the tube holes.
NOTES :
1. The dimension b should be measured either on the flat
plate before rolling or on the median line after rolling.
2. The data given on Fig.
14 are based on the following
formulae :
Z = 
2 
A + B + Ö
(A  B)^{2} + 4C^{2} 
where,
A = 
cos ø^{2} + 1 
2
( 1 d cosø ) 
a 
B = 
1 
(
1  
d
cos ø 
) (sin^{2 }ø + 1 ) 
2 
a 
( ø = angle of centre line of cylinder to centre line
of diagonal holes)
(ii) The same rule as in paragraph (i) should apply for
the case of drilling holes to a regular sawtooth shown
in Fig.
13C
(iii) In the case of a regular staggered spacing of tube
holes ( see Fig.
13A), the smallest value of the efficiency
z of all the ligaments, longitudinal, circumferential,
and diagonal, is given in Fig.15
by the ratio PC/PL
on the abscissa, and the ratio
PL
 d 
or 
d 
used as a parameter 
PL 
a 
where,
d = diameter of the tube holes;
PC = 2b = twice the distance between circumferential rows
of holes;
PL = 2a = twice the distance between axial rows of holes.
NOTE : The dimension Pc should be measured on the flat
plate before rolling or on the median line after rolling.
The data on Figure
15 are based on the same formulae as
shown in Figure 13
A.
(e) When holes spaced longitudinally along a drum are
not in a straight line, the equivalent longitudinal pitch
for each spacing may be used in the application of the
above rules. The equivalent pitch is obtained by multiplying
the actual longitudinal pitch by the equivalent efficiency
obtained from Fig
14 for each spacing. 



