Investigations on the Incompletely Developed Plane Diagonal-Tension Field Page: 2 of 26
387-412 p. : ill.View a full description of this report.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
REPORT NO. 697-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
I. THEORIES OF DIAGONAL-TENSION ACTION AND
AUXILIARY THEORIES
THEORY OF THE PURE DIAGONAL-TENSION FIELD
The theory of beams with webs working in pure
diagonal tension was presented by Wagner in reference
1. It assumes that the sheet constituting the web of the
beam has no bending stiffness. Under the action of the
shear stresses, the web will then form a large number of
narrow and shallow folds inclined at an angle a to the
flanges; the stress in the sheet is pure tension in the
direction of the folds. The theory given in reference 1
is so comprehensive that no additional contributions of- f
FIGURE 1.-Diagonal-tension beam.
great importance have been made since it was published.
Mhlention might be made of the study given in reference.
6 dealing with beams having sharply inclined flanges.
The essential principles and results of the theory have
been given in several places, for instance, in references
2, 3, and 4, and are sufficiently well known to aero-
nautical engineers to obviate very detailed discussion
here. It will suffice to recall that the basic case is that
shown in figure 1. If the flanges and the uprights are
heavy, the angle a is 450; the compressive force on each
upright is thenV= d
(1)
Each flange is acted upon by the primary beam force
F=M/lh and by a compressive force2'
(2)
that balances the horizontal component of the diagonal
tension in the sheet. The tensile stress in the web is
27 S
2---2 (3)
U2 htC2
where t is the thickness of the sheet and r is the nominal
shear stress, while 02 is a stress-concentration factor
that depends on the flexibility of the flanges (references
1 and 2). The factor C2 was given by Wagner as a
function of a flexibility parameter designated cd and
defined byoed=0.89d (tI)h
(I-T+ I) I(4)
where Ir and Ic are the moments of inertia of the ten-
sion flange and the compression flange, respectively
(references 1 and 2).The secondary bending moments in the flanges
caused by the vertical component of the diagonal ten-
sion are given by
M=km C,Sd2/h (5)
where kI3,=3J2 over the uprights and kr=%4 midway
between the uprights. The factor C again depends
on the flexibility parameter cd (references 1 and 2).
For convenience, the graph showing C, and 02 is
reproduced here from reference 1 as figure 2.
If each flange is inclined at a moderate angle 6/2 to
the horizontal axis of the beam, the shear S in equations
(1) to (5) is the web shear given by
M
Sw=Se- tan 6 (6)
where SE is the external, or applied, shear.
Beams that differ materially from the basic case, for
instance, beams with inclined uprights or sharply in-
clined flanges or beams with axial load, will not be
discussed in this paper.
PREVIOUS THEORIES OF INCOMPLETE DIAGONAL-TENSION FIELD
Practical experience has shown that the theory of
pure diagonal tension is, in many cases, entirely too
conservative. The principal reason for the disagree-
ment between theory and exp.eriment will be found by
considering the stresses due to shear acting in the web
/.0 - 1 - - - it
C,
C20 2 4 6 8 / 12
ad
FIGURE 2.-Theoretical stress factors for pure diagonal tension (from reference 1).
sheet after buckling; the stresses in the web due to beam
action are neglected in this discussion.
The state of pure shear that exists up to the budding
point in the web is equivalent to tensile and compres-
sive stresses of equal magnitude acting at angles of 450
to the horizontal and the vertical axes. In the pure
diagonal-tension field, the compressive stress is zero
and the tensile stress is twice as much as it would be
in the corresponding state of pure shear. As the shear
force on a beam web increases beyond the budding
point, however, the compressive stress corresponding
to the shear does not vanish suddenly and completely.6 \
6--__7_ ~
388
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.
Kuhn, Paul. Investigations on the Incompletely Developed Plane Diagonal-Tension Field, report, March 28, 1940; (https://digital.library.unt.edu/ark:/67531/metadc66357/m1/2/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.