Formulae have been given for the second moment of cross section
I of a unit pleat as the functions of the half angle of a pleat's opening θ, the half width of a unit pleat
l and the thickness of cloth
t, assuming that the surface of the cloth was flat. These formulae could be presented as educational tools to make a comparison of the bending between the canti lever beam of clothing material and a unit pleat.
For the vertical setting of a unit pleat under the condition of tan θ≥_
t/l, the values given by the derived equation
I∧ =
lt (
l2 cos,
2θ+
t2/sin
2θ) /6 were inputed into an Excel program written by VBA. As the half angle θ reached zero, the value of
I∧ diverged to infinity. For a half angle of θ more than about 5° both with
l=2.5 and 4 cm, the value of
I∧ for
t= 0.06 cm was approximately comparable to two times that for
t = 0.03 cm, as expected, since
I∧ had a proportional relation to the thickness t for
t>>
l. In addition, the decreasing tendency of
I∧ for
t= 0.06 cm to that for
t = 0.03 cm were almost the same within the range of θ=15-55° for
l=4 cm.
For the horizontal setting of a unit pleat under the condition of tan θ≥
t/l the values of
I< given by the equation
I<=2
l3t sin
2 θ/3 had a proportional relation to the thickness
t, increased rapidly with
l, and showed the same dependence on the half angle θ.
It has been considered that the divergence of
I∧ arose near θ=0° due to a lack of free opening of a unit pleat for the condition of tan θ≥
t/l. After the deletion of one bent top and two side edges, the equation for vertical setting was written as
I∧,
deleted =
lt (
l2 COS
2 θ
t 2sin
2 θ) /6, yielding a definite value at θ=0°.Furthermore the, difference between this and the former equation for the vertical setting was
lt3 (sin
-2θ-sin
2θ) /6 with the values of 547
lt3 atθ=1°, 21.9lt3 at θ=5° and 5.5lt
3 at θ=10°. With these decreasing tendencies and the adding condition of
t>>
l, the effect of the deletions has not been observed for the not so small angle of θ.
Moreover, for the horizontal setting of this model without one left bend and two edges each at the upper and bottom position, the equation was written as
I<,
deleted = (2
l3& t sin
2 θ + 6
l2 t2 cos θ sin θ +2
lt3 cos
2θ) /3, reaching the equation given by
I<=2
l3t sin
2 θ/3 for
t>>
l.
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