Since Haringx introduced his stability hypothesis for the buckling prediction of helical springs over 60 years ago, discussion is on whether or not the older hypothesis of Engesser should be replaced in structural engineering for stability studies of shear-weak members. The accuracy and applicability of both theories for structures has been subject of study in the past by others, but quantitative information about the accuracy for structural members is not provided. This is the main subject of this paper. The second goal is to explain the experimental evidence that the critical buckling load of a sandwich beam-column surpasses the shear buckling load $GAs$, which is commonly not expected on basis of the Engesser hypothesis. The key difference between the two theories regards the relationship, which is adopted in the deformed state between the shear force in the beam and the compressive load. It is shown for a wide range of the ratio of shear and flexural rigidity to which extent the two theories agree and/or conflict with each other. The Haringx theory predicts critical buckling loads which are exceeding the value $GAs$, which is not possible in the Engesser approach. That sandwich columns have critical buckling loads larger than $GAs$ does, however, not imply the preference of the Haringx hypothesis. This is illustrated by the introduction of the thought experiment of a compressed cable along the central axis of a beam-column in deriving governing differential equations and finding a solution for three different cases of increasing complexity: (i) a compressed member of either flexural or shear deformation, (ii) a compressed member of both flexural and shear deformations, and (iii) a compressed sandwich column. It appears that the Engesser hypothesis leads to a critical buckling load larger than $GAs$ for layered cross section shapes and predicts the sandwich behavior very satisfactory, whereas the Haringx hypothesis then seriously overestimates the critical buckling load. The fact that the latter hypothesis is perfectly confirmed for helical springs (and elastomeric bearings) has no meaning for shear-weak members in structural engineering. Then, the Haringx hypothesis should be avoided. It is strongly recommended to investigate the stability of the structural members on the basis of the Engesser hypothesis.

1.
Haringx
,
J. A.
, 1942, “
On the Buckling and the Lateral Rigidity of Helical Compression Springs, I
,”
0370-0348,
45
, pp.
533
539
.
2.
Haringx
,
J. A.
, 1947, “
On Highly Compressible Helical Springs and Rubber Bars and on Their Application in Vibration Isolation
,” Doctoral thesis, Delft University of Technology, The Netherlands.
3.
Grammel
,
R.
, 1924, “
Die Knickung von Schraubenfedern
,”
Z. Angew. Math. Mech.
0044-2267,
4
, pp.
384
389
.
4.
Biezeno
,
C. B.
, and
Koch
,
J. J.
, 1925, “
Zuschrift an den Herausgeber
,”
Z. Angew. Math. Mech.
0044-2267,
5
, pp.
279
280
.
5.
Biezeno
,
C. B.
, and
Grammel
,
R.
, 1953,
Technische Dynamik
,
Springer-Verlag
,
Berlin
.
6.
Engesser
,
F.
, 1891, “
,”
Zentrale Bauverwaltung
,
11
, pp.
483
486
.
7.
Ziegler
,
H.
, 1982, “
Arguments for and Against Engesser’s Buckling Formulas
,”
Ing.-Arch.
0020-1154,
52
, pp.
105
113
.
8.
Timoshenko
,
S. P.
, and
Gere
,
J. M.
, 1961,
Theory of Elastic Stability
, 2nd ed.,
McGraw-Hill
,
New York
.
9.
Bažant
,
Z. P.
, 2003, “
Shear Buckling of Sandwich, Fiber Composite and Lattice Columns, Bearings, and Helical Springs: Paradox Resolved
,”
ASME J. Appl. Mech.
0021-8936,
70
(
1
), pp.
75
83
.
10.
Bažant
,
Z. P.
, and
Beghini
,
A.
, 2004, “
Sandwich Buckling Formulas and Applicability of Standard Computational Algorithm for Finite Strain
,”
Composites, Part B
1359-8368,
35
, pp.
573
581
.
11.
Bazant
,
Z. P.
, and
Beghini
,
A.
, 2006, “
Stability and Finite Strain of Homogenized Structures Soft in Shear: Sandwich or Fiber Composites, and Layered Bodies
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
1571
1593
.
12.
Attard
,
M. M.
, and
Hunt
,
G. W.
, 2008, “
Column Buckling With Shear Deformations—A Hyperelastic Formulation
,”
Int. J. Solids Struct.
0020-7683,
45
, pp.
4322
4339
.
13.
Attard
,
M. M.
, and
Hunt
,
G. W.
, 2008, “
Sandwich Column Buckling —A Hyperelastic Formulation
,”
Int. J. Solids Struct.
0020-7683,
45
, pp.
5540
5555
.
14.
Fleck
,
N. A.
, and
Sridhar
,
L.
, 2002, “
End Compression of Sandwich Columns
,”
Composites, Part A
1359-835X,
33
, pp.
353
359
.
15.
Sattler
,
K.
, and
Stein
,
P.
, 1974,
Ingenieurbauten 3, Theorie und Praxis
,
Springer-Verlag
,
Wien
.
16.
Allen
,
H. G.
, 1969,
Analysis and Design of Structural Sandwich Panels
,
Pergamon
,
Oxford, UK
, Chap. 8.
17.
Hoff
,
N. J.
, and
Mautner
,
S. E.
, 1948, “
Bending and Buckling of Sandwich Beams
,”
J. Aeronaut. Sci.
0095-9812,
15
, pp.
707
720
.
18.
Attard
,
M. M.
, 2008, “
Sandwich Column Buckling Experiments
,”
Futures in Mechanics of Structures and Materials
, Proceedings of the 20th Australasian Conference on the Mechanics of Structures and Materials, Toowoomba, University of Southern Queensland, Australia, pp.
373
377
.