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naca-tn-1749

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National Advisory Committee for Aeronautics, Technical Notes - Shear Flows in Multicell Sandwich Sections

naca-tn-1749-shear-flows-in-multicell-sandwich-sections-1

Solutions are developed for shear flows in mnlticell sandwich
sections for various cell-twist distributions. The problems of twisting
and_bending of a cantilever beam.are first considered. More general
cell-twist distributions are then considered, including the arbitrary
distribution. A formmla is also developed for the torsion constant of a
sandwich section.

The relation between load and deflection, for a homogeneous, elastic,
isotropic plate, is expressed by a well- known fourth— order differential
equation. A similar relation between load and deflection for a mnlticell
sandwich plate should be given by a differential-difference equation
since the internal shear flows and cell twists vary in discrete steps.

In order to develop this differential-difference equation for the relation
between load and deflection, it is necessary to know relations between
bending moments, twisting moments, and deflections. It is convenient to
replace the concept of twisting moment by the concept of cellular shear
flows corresponding to the well-known shear flows in a multicell section
according to the St. venant torsion theory. This paper is devoted to the
determination of various relations between cellular shear flows and cell
twists which may exist physically. Solutions are given for the distri-
bution of shear flows required to preserve continuity of the warping
displacements when the rate of twist varies from cell to cell in various
manners. Symmetrical shear-flow distributions provide a resultant torque
on the section but no resultant shear. Antisymmetrical distributions
give neither a resultant shear nor a torque and, hence, are self—
equilibrating A formula is also derived for the torsion constant of a
sandwich section with any number of cells.

A difference equation relating cellular shear flow to cellular twist
(rate of twist) may be derived from the condition that the warping dis-
placement must be a continuous function around any closed path. This is
the condition of continuity for thin-walled. sections. Consider the sand-
wich section shown in figure 1(a) - The nth cell is shown in figure l(b) .
The displaced position of the cell due to loads is shown by/dashed lines.
The angle of twist of the cell is indicated as ¢n‘ The width and height
of the 'cell are indicated by c and h, respectively. The left web, AD,
is web 1: and the right web, BC, is web k+l.

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naca-tn-1749

  • Version
  • 46 Downloads
  • 990.36 KB File Size
  • 1 File Count
  • December 6, 2016 Create Date
  • December 6, 2016 Last Updated
Scroll for Details

National Advisory Committee for Aeronautics, Technical Notes - Shear Flows in Multicell Sandwich Sections

naca-tn-1749-shear-flows-in-multicell-sandwich-sections-1

Solutions are developed for shear flows in mnlticell sandwich
sections for various cell-twist distributions. The problems of twisting
and_bending of a cantilever beam.are first considered. More general
cell-twist distributions are then considered, including the arbitrary
distribution. A formmla is also developed for the torsion constant of a
sandwich section.

The relation between load and deflection, for a homogeneous, elastic,
isotropic plate, is expressed by a well- known fourth— order differential
equation. A similar relation between load and deflection for a mnlticell
sandwich plate should be given by a differential-difference equation
since the internal shear flows and cell twists vary in discrete steps.

In order to develop this differential-difference equation for the relation
between load and deflection, it is necessary to know relations between
bending moments, twisting moments, and deflections. It is convenient to
replace the concept of twisting moment by the concept of cellular shear
flows corresponding to the well-known shear flows in a multicell section
according to the St. venant torsion theory. This paper is devoted to the
determination of various relations between cellular shear flows and cell
twists which may exist physically. Solutions are given for the distri-
bution of shear flows required to preserve continuity of the warping
displacements when the rate of twist varies from cell to cell in various
manners. Symmetrical shear-flow distributions provide a resultant torque
on the section but no resultant shear. Antisymmetrical distributions
give neither a resultant shear nor a torque and, hence, are self—
equilibrating A formula is also derived for the torsion constant of a
sandwich section with any number of cells.

A difference equation relating cellular shear flow to cellular twist
(rate of twist) may be derived from the condition that the warping dis-
placement must be a continuous function around any closed path. This is
the condition of continuity for thin-walled. sections. Consider the sand-
wich section shown in figure 1(a) - The nth cell is shown in figure l(b) .
The displaced position of the cell due to loads is shown by/dashed lines.
The angle of twist of the cell is indicated as ¢n‘ The width and height
of the 'cell are indicated by c and h, respectively. The left web, AD,
is web 1: and the right web, BC, is web k+l.

FileAction
naca-tn-1749 Shear Flows in Multicell Sandwich Sections.pdfDownload 
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2449800 Total Downloads

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NASA-RP-1060 Subsonic Aircraft: Evolution and the Matching of Size to Performance
NASA-RP-1060 Subsonic Aircraft: Evolution and the Matching of Size to Performance
AA-CP-20212-001
AA-CP-20212-001
ADPO10769 Occurrence of Corrosion in Airframes
The purpose of this lecture is to provide an overview ...
MIL-STD-1759 Rivets and Rivet Type Fasteners Preferred for Design
The purpose of this book form standard is to provide ...
MIL-STD-810G Environmental Engineering Considerations and Laboratory Tests
This standard contains materiel acquisition program planning and engineering direction ...