On a Paradoxical Phenomenon Related to Beams on Elastic Foundation: Could External Compliant Leads Reduce the Strength of a Surface-Mounted Device?

1988 ◽  
Vol 55 (4) ◽  
pp. 818-821 ◽  
Author(s):  
E. Suhir
Keyword(s):  
Integrated Circuits ◽  
Mechanical Behavior ◽  
Elastic Foundation ◽  
Flexural Rigidity ◽  
Bending Moment ◽  
Stress Relief ◽  
Governing Parameter ◽  
Paradoxical Situation ◽  
Beams On Elastic Foundation ◽  
Device Technology

Compliant external electrical leads are often utilized as strain buffers in surface-mounted device technology to provide the necessary stress relief for the device, when the substrate is subjected to bending. A paradoxical situation was observed, however, during testing of compliant leaded hybrid integrated circuits (HIC): In some tests the bending moment, applied to the printed wire board (PWB) and causing HIC fracture, turned out smaller (not greater), when leads of greater compliance were installed. We show that such a paradoxical situation is due to the redistribution of lead reactions at certain combinations of HIC length, HIC and PWB flexural rigidity, and spring constant of the elastic attachment. Our analysis has indicated, that only sufficiently compliant leads can essentially reduce the stresses, while leads of moderate compliance can result in even greater stresses in the HIC than stiff leads. We suggest an easy-to-calculate governing parameter, which characterizes the mechanical behavior of HIC/PWB and similar assemblies with compliant attachments.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

scholarly journals An Investigation into the Effect of Cracking on the Response of Drilled and Postgrouted Concrete Pipe Pile under Lateral Loading

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Zhijun Yang ◽  
Qing Fang ◽  
Bu Lv ◽  
Can Mei ◽  
Xudong Fu
Keyword(s):  
Flexural Rigidity ◽  
Bending Moment ◽  
Test Results ◽  
Lateral Loads ◽  
Analysis Method ◽  
Pile Head ◽  
Laterally Loaded Piles ◽  
Pipe Pile ◽  
Concrete Pipe ◽  
Laterally Loaded

The cracks are likely to initiate on a lateral loaded pile and would cause greater deflection at the pile head. However, there is a lack of thorough investigation into the effect of cracking on the response of the lateral loaded pile. In this article, a full-scale field test was carried out to investigate the behavior of Drilled and Postgrouted Concrete Pipe Pile under lateral loads. A novel analysis method for the lateral loaded pile, which can take the cracking effects into consideration, was proposed, and the validity was verified by the test results. With the proposed method, the cracking effects on flexural rigidity, displacement, rotation, and bending moment of the pile were studied. In brief, cracking effect would dramatically reduce the flexural rigidity of the pile, remarkable increase the displacement and rotation of the pile top, and slightly decrease bending moment of the pile. Unambiguously, the results show that the proposed method can excellently predict the response of laterally loaded piles under cracking effects.

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