結構動力方程式的論文

Journal of Structural Engineering, ASCE
June 18, 2015, June 22, 2015
Title
　　Dynamic Equation
Abstract
　　The dynamic equation is proposed to replace the structural dynamics.
Keyword: Structural Dynamics

I.　　Dynamic Equation

　　In the structural engineering, the structural dynamics is not accurate enough for the structural design, and the damping should be not the velocity item in the original dynamic equation, Eq. (1) (Lin 1999). When the structure accepts the earthquake force, the structure generates the heat to maintain the conservation of mass. In such kind of situation, the damping is like the mass, but it is not the other thing. In the structural dynamics, the damping is considered as the acceleration item, and the proposed dynamic equation is as the equation, Eq. (2). In the most books, the general solution of Eq. (2) has been solved by the scholars, and this is the proposed dynamic equation. Besides, the vibration problem can be decrypted by the Eq. (3), and the general solution of Eq. (3) has been solved by the scholars.

	Eq. (1)
	Eq. (2)
	Eq. (3)

Reference

Y. S. Lin (1999) Basis of Structural Dynamics, Winsoon Book Store

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阻尼是結構質量的一部分，經轉換為熱消失於結構物。
阻尼力是結構動力方程式的加速度項，經抵抗地震力消耗結構質量轉換為熱。

數學難題：ｃｍｈｕａｎｇ ｃｏｎｊｅｃｔｕｒｅ

Journal of Computational and Applied Mathematics
June 16, 2015
Title
　　cmhuang conjecture
Abstract
　　The cmhuang conjecture has been proposed by Ching-Min Huang, but the mathematical proof must be proposed by the interested person. In the deflection problem of the USD or LRFD method, the cmhuang conjecture can be applied in the engineering calculation. However, if the mathematical proof is not proposed by anybody, the cmhuang conjecture should not be applied in the ASD method.
Keywords: cmhuang conjecture, ASD, Structural Reliability

I.　　cmhuang conjecture

　　As everyone knows, the cmhuang problem (C. M. Huang 2016) is the important problem for the ASD method (AISC 1989), but Ching-Min Huang intends to adopt the D, L, E, and X loadings to proposed the ASD formulas.


References

C. M. Huang (2016) "Reconstruction of Structural Reliability," Doctoral Dissertation in Mathematics, Registered Number: 2010370005, Institute of Disaster Prevention and Mitigation Engineering, Department of Civil Engineering, Tsinghua University, Beijing 100084, P.R.C., Supervisor: C. Dong, Ph.D. Aircraft, Oct. 3, 2016
American Institute of Steel Construction (1989) AISC Manual of Steel Construction: Allowable Stress Design, 9th Edition, American Institute of Steel Construction

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人工塑鉸的論文

Journal of Structural Engineering, ASCE
June 14, 2015
Title
　　Assumed Plastic Hinge Positions of Beam Members
Abstract
　　The engineer can define the assumed plastic hinge of beam members more accurate.
Keywords: Beam, Plastic Hinge

I.　　Assumed Plastic Hinge Positions of Beam Members

　　In the partial structural cases, the beam behavior must consider the uniform loading, but the actual beam behavior of the building structures is the isosceles triangle. According to the beam behavior, the moment diagram shows the structural loading is the isosceles triangle, and the theoretical moment equations can be found in the LSD Manual (CSSE 2003). As the numerical analysis results, the isosceles triangle loading has the result, x=0.223149101094592L, and the uniform loading has the result, x=0.211324865405187L. However, the small beam may be adopted in the structural design, and the midpoint loading has the result, x=0.25L. Actually, the midpoint loading is a part of the isosceles triangle loading, and the assumed plastic hinge may move the original position. The assumed plastic hinge position can be calculated by interpolation method, and the different loadings and the differences of the x positions can be calculated by the engineer.

　　According to the real case, the beam can find the position, x=0.224573841022353L, with the small beam, and the beam can find the position, x=0.224573841022353L, without the small beam. When the engineer intends moving the assumed plastic hinge from the ends of the beam, he can be more accurate to define the assumed plastic hinges for the both sides. The suggested assumed plastic hinge is 0.222~0.227L with the small beam, and the suggested assumed plastic hinge is 0.220~0.225L without the small beam. Besides, the engineer also may adopt the software to measure the distance, and the software method is the easiest way to find the assumed plastic hinge. As everyone knows, the steel beam and RC beam can adopt the assumed plastic hinge technology, and the structural design may have the higher safety for the people.


Reference

Chinese Society of Structural Engineers (2003) Steel Structural Design Manual, Tech Book Publisher

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國小數學問題（某數）	國中數學問題（一元二次方程式）	高中職數學問題（Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ）