Fundamental Equations of Laminated Beams, Plates and Shells

2015 ◽  
pp. 1-35 ◽  
Author(s):  
Guoyong Jin ◽  
Tiangui Ye ◽  
Zhu Su
Keyword(s):  
Laminated Beams ◽  
Plates And Shells ◽  
Fundamental Equations

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

Study on the strength of glued laminated timber beams with round holes: difference in structural performance between homogeneous-grade and heterogeneous-grade timber

2021 ◽  
Vol 67 (1) ◽  
Author(s):  
Shigefumi Okamoto ◽  
Nobuhiko Akiyama ◽  
Yasuhiro Araki ◽  
Kenji Aoki ◽  
Masahiro Inayama
Keyword(s):  
Scots Pine ◽  
Maximum Shear Stress ◽  
Material Strength ◽  
Laminated Beams ◽  
Strength Grade ◽  
Glued Laminated Timber ◽  
The Difference ◽  
Materials Used ◽  
Beam Height ◽  
Timber Beams

AbstractVarious design codes and design proposals have been proposed for glued laminated timber beams with round holes, assuming that the entire beam is composed of homogeneous-grade timber. However, in Japan, glued laminated timber composed of homogeneous-grade timber is rarely used for beams. In this study, the difference in the load-bearing capacity of glued laminated beams composed of homogeneous-grade timber and heterogeneous-grade timber with round holes when fractured by cracking was investigated experimentally and analytically. The materials used in the tests were glued laminated beams composed of homogeneous-grade Scots pine timber with a strength grade of E105-F345 and heterogeneous-grade Scots pine timber with a strength grade of E105-F300. Experiments confirmed that although the glued laminated beams composed of heterogeneous-grade timber have a lower material strength in the lamina with holes, its resistance to fracturing due to cracks associated with the holes is almost the same as that of the glued laminated beams composed of homogeneous-grade timber. The stresses acting on the holes in the laminated timber with holes of less than half the beam height were lower in the glued laminated beams composed of heterogeneous-grade timber than in the glued laminated beams composed of homogeneous-grade timber. The ratio of the stresses was found to be approximately equal to the ratio of the maximum bending stress or the maximum shear stress acting on the inner layer lamina, as determined by Bernoulli–Euler theory.

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