Normal-pressure tests of circular plates with clamped edges Page: 4 of 17
This report is part of the collection entitled: National Advisory Committee for Aeronautics Collection and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
REPORT NO. 744-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
tained from the Bourdon-tube gage X inounted on the
hand pump.
The loading fixture was proof-tested by subjecting a
pair of 0.06-inch aluninum-alloy plates to a pressure of
600 pounds per square inch. This pressure was suf-
ficient to "dish in" the plates far beyond the elastic
range; nevertheless, there was no sign of slipping at-the
edge and there was only a negligible amount of leakage.
The pressure could be maintained with a small amount
of pumping after the creep due to yielding of the plate
had become small.- - m- ---
4FWiURzn 11.--Plate fixture, pump, and pressure gages.
If slipping is neglected, the principal deviations from
the conditions of an ideally clamped flat plate are prob-
ably due to one of the following effects:
A. The setting up of initial tension (or compression)
in the plate during the damping in the fixture.
B. The. rotation of the clamping rings E and G (fig.
8) as caused by the bending moments set up at the pe-
riphery of the plate due to the normal pressure.
C. The contraction of the diameter of the clamping
rings by the membrane tension present in the plate
under load.
D. Deviations from flatness at no load.
The effect of the first three deviations from ideal
conditions on the center deflection of the plate is dis-
cussed in appendixes A, B, and C and, on the basis of
these discussions, three "deviation indices" are derived
for the relative deviation from ideal behavior. Devia-tions from flatness are discussed for the special case
of initial bowing into a spherical surface in appendix D.
Effect A will cause a decrease in center deflection at
low loads (w,/h<< l) given approximately by equation
(A7) in appendix A:-\O/=1.833(1--),
(la)
where
AAo "-- Ut WQo
w, center deflection with a uniform membrane tension
a, due to clamping
wo,, center deflection for ideal clamping (u,=0)
E Young's modulus of plate material
p Poisson's ratio of late material
a radius of plate
h thickness of plate
Effect A causes a decrease in center deflection of an
elastic circular membrane (that is, circular plate with
large deflections before yielding) given approximately
by equation (A21):(Ib)
k4wA 1m-. a
We, ,] 2 Ethat is, the effect decreases inversely with the square
of the center deflection.
Effect B will cause an increase in center deflection
given approximately by equation (B JO)(Aw. XEhs
Wo--- I --Ax)a(2)
where X is the rotation of clar ping ring due to unit
moment per unit length of clam ping edge.
Effect C will cause an increase in center deflection.
If the plate behaves like an elastic membrane, this in-
crease is given approximately by equation (C014)(3)
(Aw, 1 Jd E
t0,, 3 1-
c rwhere K is the specific contraction of diameter due to
unit radial force per unit length along clamped edge.
Theeffect'D will generally cause a change in center
deflection of the plate as an elastic membrane. It has
no effect on the deflection due to bending which pre-
dominates in the Kirchhoff range (wdo/h < <1). If the
plate is initially bowed into a spherical surface with
center deflection wo, the increase in deflection as an
elastic membrane (w/h > > 1) is given approximately
by (D6)S 2 w 2 w, w,
w 3 w, 3 I/T(4)
Initial bowing into a spherical surface will have a small
effect on the deflection as an elastic membrane, provided
that the initial center deflection is small compared with
the thickness of the plate. It is believed that this con-
dition was satisfied by most of the plates tested. The
estimated initial center deflection is given in the last272
Upcoming Pages
Here’s what’s next.
Search Inside
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
McPherson, Albert E.; Ramberg, Walter & Levy, Samuel. Normal-pressure tests of circular plates with clamped edges, report, October 10, 1941; (https://digital.library.unt.edu/ark:/67531/metadc60003/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.