The derivation of an analytical method to examine the stress field near the end of a simply supported, laminated beam is presented. Specific effort has been directed to accurately calculate the transverse-shear and normal stress by incorporating the exact displacement relations derived, by Kozik (1970). The method accommodates any combination of material lay-up and any type of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion most accurately characterizing the physical supports. The solution and application of the method is presented in Part II of this paper.

Issue Section:
Research Papers
Topics:
Anisotropy, Displacement, Shear (Mechanics), Stress
1.
Benthem
J. P.
,
1963
, “
A Laplace Transform Method for the Solution of Semi-Infinite and Finite Strip Problems in Stress Analysis
,”
Quarterly Journal of Mechanics and Applied Mathematics
, Vol.
16
, pp.
413
–
429
.
2.
Horvay
G.
, and
Born
J. S.
,
1957
, “
Some Mixed Boundary-Value Problems of the Semi-Infinite Strip
,”
ASME Journal of Applied Mechanics
, Vol.
24
, pp.
261
–
268
.
3.
Johnson
M. W.
, and
Little
R. W.
,
1965
, “
The Semi-Infinite Elastic Strip
,”
Quarterly of Applied Mathematics
, Vol.
22
, pp.
335
–
344
.
4.
Khandoker, S. I., 1988, “Improved Analysis of Laminated Heterogeneous Beams and Associated Formulation of a New Finite Element Method,” Ph.D. dissertation, Texas A&M University, College Station, TX.
5.
Kozik
T. J.
,
1970
, “
Linear Exact Transverse Displacement Variation
,”
AIAA Journal
, Vol.
8
, No.
2
, pp.
366
–
370
.
6.
Mathieu, E., 1890, The´orie de l’Elasticite´ des Corps Solides, Second Edition, Gauthier—Villars, Paris, France, pp. 140–178.
7.
Noor
A. K.
, and
Burton
W. S.
,
1989
, “
Assessment of Shear Deformation Theories for Multilayered Composite Plates
,”
Applied Mechanics Review
, Vol.
42
, No.
1
, pp.
1
–
13
.
8.
Ochoa, C., and Kozik, T. J., 1987, “Transverse Shear and Normal Stresses in Laminated Plates,” Design and Analysis of Composite Materials Vessels, ASME PVP-Vol. 121, PD-Vol. 11, pp. 117–119, Pressure Vessels and Piping Conference, San Diego, CA.
9.
Ochoa, O. O., 1980, “Transverse Shear and Normal Stresses in Laminated Beams,” Ph.D. dissertation, Texas A&M University, College Station, TX.
10.
Ochoa, O. O., and Kozik, T. J., 1987, “Transverse Shear and Normal Stresses in Laminated Beams,” Design and Analysis of Composite Materials Vessels, ASME PVP-Vol. 121, PD-Vol. 11, pp. 1–8, Pressure Vessels and Piping Conference, San Diego, CA.
11.
Pagano
N. J.
, and
Pipes
R. B.
,
1971
, “
The Influence of Stacking Sequence on Laminate Strength
,”
Journal of Composite Materials
, Vol.
5
, pp.
50
–
57
.
12.
Pagano
N. J.
, and
Pipes
R. B.
,
1973
, “
Some Observations on the Interlaminar Strength of Composite Laminate
,”
International Journal of Mechanical Science
, Vol.
15
, pp.
679
–
688
.
13.
Pagano
N. J.
,
1974
, “
On the Calculation of Interlaminar Normal Stress in Composite Laminate
,”
Journal of Composite Materials
, Vol.
8
, pp.
65
–
81
.
14.
Picket
G.
,
1944
, “
Application of the Fourier Methods to the Solution of Certain Boundary Problems in the Theory of Elasticity
,”
ASME Journal of Applied Mechanics
, Vol.
11
, pp.
176
–
182
.
15.
Pipes
R. B.
, and
Pagano
N. J.
,
1970
, “
Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension
,”
Journal of Composite Materials
, Vol.
5
, pp.
50
–
57
.
16.
Reddy
J. N.
,
1989
, “
On Refined Computational Models of Composite Laminates
,”
International Journal of Numerical Methods
, Vol.
27
, pp.
1
–
22
.
17.
Reissner
E.
,
1945
, “
The Effect of Transverse Shear Deformation on the Bending of Elastic Plates
,”
ASME Journal of Applied Mechanics
, Vol.
12
, pp.
69
–
77
.
18.
Reissner
E.
,
1972
, “
A Consistant Treatment of Transverse Shear Deformations in Laminated Anisotropic Plates
,”
AIAA Journal
, Vol.
10
, No.
5
, pp.
716
–
718
.
19.
Reissner
E.
,
1979
, “
Note on the Effect of Transverse Shear Deformation in Laminated Anisotropic Plates
,”
Computational Methods in Applied Mechanical Engineering
, Vol.
20
, No.
3
, pp.
203
–
209
.
20.
Reissner
E.
,
1985
, “
Reflections on the Theory of Elastic Plates
,”
Applied Mechanics Review
, Vol.
38
, No.
11
, pp.
1453
–
1464
.
21.
Whitney
J. M.
, and
Sun
C. T.
,
1973
, “
A Higher Order Theory for Extensional Motion of Laminated Composites
,”
Journal of Sound and Vibration
, Vol.
30
, pp.
85
–
97
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.