ＰＤ結構設計

Structural Safety
July 25, 2015
Title
　　Probability-based Design for the Structural Design
Abstract
　　In the probability-based design, the structural size, material strength, and structural load have the different variability of the uncertain probability, and the three probability functions can be applied into the structural design to define the failure probability. In the mathematical calculation, the failure probability can be calculated by the multi-variable integration approach (C. M. Huang 2015), and the value should be transferred into the β value to control the scope as the structural design.
Keywords: Probability-based Design, Structural Design

Reference

C. M. Huang (2015) "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, Jul. 12, 2015

結構可靠度在結構設計的理論解釋

Structural Safety
July 24, 2015
Title
　　Theoretical Explanation of Structural Reliability for the Structural Design
Abstract
　　The theoretical explanation is proposed to descript the Structural Design of Structural Reliability.
Keywords: Structural Reliability, Structural Design

I.　　Theoretical Explanation of Structural Reliability for the Structural Design

　　After the Reconstruction of Structural Reliability (C. M. Huang 2015) is proposed by C. M. Huang, the structural design must be changed to fit the design method of the structural reliability. In the structural reliability, the dead load does not have the variability, but the live load has the variability with the 20% uncertain probability. However, whatever the structural load is the dead load or live load, the fundamental error scope has the 30% uncertain probability.

　　In the earthquake and wind forces, they are defined as the accidental loads without any uncertain probability, and they are directly adopted by the engineering codes or engineer. In the Earthquake Theory of Water Wave, the vertical acceleration is defined as the 3/8 lateral acceleration, and the vertical acceleration can be 0.15m/s² in the medium earthquake, 0.4m/s². Actually, the medium earthquake is the standard condition for the excess of the dead load, and the stronger earthquake may be controlled by the earthquake or wind equation.

　　In the structural size, the error value is very similar to the normal distribution, and the sectional and length errors have several levels. The size errors include ±1.5cm, ±0.75cm, ±0.5cm, ±0.25cm, ±0.15cm, ±0.05cm in the sectional error, and the size errors include ±3.0cm, ±1.5cm, ±1.0cm, ±0.5cm, ±0.3cm, ±0.1cm in the length error. In the thin structure, the size error is ±0.1cm in the sectional error, and the size error is ±0.01cm in the thickness error.

　　In the structural design, the elastic design of materials is adopted as the design standard, and the yield ratio have the higher value to raise the plastic deformation. Besides, the material strength of the structural experiment is very similar to the Type I distribution in statistics, and the scope of the yield stress can be defined as the minimum (-4%), standard, and maximum values (+16%).

　　According to the structural experiment of the yield stress, the yield stress, Fy, is defined by the 0.2% strain of the experimental material, and the elastic modulus, E, can be calculated by the equation, E=Fy/0.002. The Poisson ratio, ν, is known to calculate the shear modulus, G, and the relationship of G and E can defined by the following equation (Gere & Timoshenko 1972). In the design method of structural reliability, the E and G adopt the theoretical values to calculate the structural strength, and the two values have the minimum, standard, and maximum values.


　　In the metal materials, the residual stress must be considered to reduce the yield stress, and the adopted yield stress does not include the residual stress. In the concrete structures, the concrete strength should follow the minimum, standard, and maximum values to execute, and the residual stress of the rebar must be considered to reduce the yield stress in the structural design.

References

C. M. Huang (2015) "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, Jul. 12, 2015
J. M. Gere & S. P. Timoshenko (1972) Mechanics of Materials, D. Van Nostrand Company

水波紋地震力理論

Journal of Structural Engineering, ASCE
July 24, 2015
Title
　　Earthquake Theory of Water Wave
Abstract
　　When a stone is dropped into the water to observe the water wave, the vertical water wave must be less than the 3/8 lateral water wave. In the seismic design, the vertical acceleration can be defined as the 3/8 lateral acceleration, and the acceleration relationship is called the Earthquake Theory of Water Wave.
Keyword: Earthquake Theory of Water Wave

建築橋樑ＩＩ

　　我有４６ｍ跨度的ＲＨ型鋼橋樑做法，就是在建築橋樑的兩端採用１８ｍ的ＲＨ型鋼，端部對ＲＨ型鋼上、下翼版做握持式固定端２ｍ，所以建築橋樑各突出１６ｍ的懸臂樑長度。其中一端以２ｍ重疊做鉸接固定端，另一端以２ｍ重疊做滾接滑動式接合，亦即２支１８ｍ懸臂樑擺著１支１８ｍ簡支樑，其建築橋樑總跨度為４６ｍ。以單跨簡支樑設置橋墩支撐，倘若架空二層樓的高度１０ｍ，矩形橋墩厚度不小於１﹒６ｍ。經考慮箱型柱為整支１８ｍ不做對接，其建築結構高度應該不逾越２０ｍ，建築橋樑端點周圍箱型柱不小於１﹒５ｍ。建築橋樑涉及大跨度銜接，因而放樣測量精度要求甚高。ＲＨ型鋼以耐候鋼為主，並須以油漆或熱浸鍍鋅做防鏽處理。

臺灣板車運送型鋼或鋼筋，涉及交通道路的迴轉半徑，其最大運載的長度為１８ｍ。

建築橋樑大理石地磚橋面板、女兒牆１﹒２ｍ、橋面路燈間隔１０ｍ、洩水孔
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建築橋樑左跨簡支樑　　　建築橋樑中跨簡支樑　　　建築橋樑右跨簡支樑
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建築橋樑左跨懸臂樑　　　　　　　　　　　　建築橋樑右跨懸臂樑

結構勁度係數Ｑ

Journal of Structural Engineering, ASCE
July 24, 2015
Title
　　Structural Stiffness Coefficient
Abstract
　　In UBC-1994 (UBC 1994), the toughness capacity of structural system, R, was defined by several values, but these values did not have any theory to descript the structural behavior. in seismic design, the structural stiffness coefficient, Q, is proposed to define the structural behavior in the earthquake, and the Q is measured by the seismic experiments to define the various earthquake force for every floor. Of course, the period time, T, should be the effect factor of Q, and the lateral earthquake force can be defined by the equation, V=ZKCW, where Z is the acceleration coefficient, K is the function of Q and T parameters, C is the response-spectrum coefficient, and W is the structural weight.
Keyword: Structural Stiffness Coefficient

Reference

UBC (1994) Uniform Building Code, International Conference of Building Officials

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結構耐震設計理論

建築橋樑

　　臺灣到處興建非必要的橋樑，然而建築得任選二點興建橋樑，將此類橋樑稱為「建築橋樑」。橋樑的結構設計目標，為預拌混凝土車和坦克車，然而建築橋樑以自重和滿載人群為條件，不涉及影響線的移動載重分析。我肯定桁架結構和懸索結構，此乃適合用於建築橋樑的結構。建築橋樑採用簡支樑，亦可採用三跨連續樑涉及橋墩。倘若以步道形式做建築設計，端點應該保有３～５ｃｍ的縫隙，或不低於層間位移角０﹒００５，採取分離式結構分析做結構設計，以避免有影響建築結構的問題。馬來西亞的雙塔大樓，或成大醫院的跨道路橋樑，都是建築橋樑的參考案例。

　　桁架結構有零桿，其意義指無活載重Ｌ，然而仍然有靜載重Ｄ，並經Ｄ＋Ｌ用於計算地震力Ｅ，因而零件有Ｄ和Ｅ的結構載重。在結構變形交點非呈直線下，零桿亦可能有部份活載重Ｌ。在橫風向風力作用下，零桿必然有風力Ｘ的數值。因此，以結構可靠度做結構計算，乃知零桿的３個結構載重公式，都是不為零的結構載重數據。

Architectural Bridge

０﹒８５ｆ’ｃ的意義

　　０﹒８５ｆ’ｃ是以矩形斷面為基礎，去產生等值的矩形應力塊做為混凝土平均壓力值。然而，非矩形斷面的樑柱，０﹒８５ｆ’ｃ在缺角或非均勻斷面的區域，應該對於矩形應力塊做形狀或取值的修正，亦即壓力區不是矩形應力塊或非０﹒８５的數字。

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ACI Structural Journal
July 22, 2015
Title
　　The Meaning of 0.85f'c
Abstract
　　In the concrete structures, the theoretical assumption of 0.85f'c is the rectangle shape for the beam, column, and uniform-thickness plate members, or the 0.85f'c should be change the pressure stress shape or the average value, 0.85 to fit the special-shaped beam, column, and various-thickness plate members.
Keyword: 0.85f'c

ｃｍｈｕａｎｇ ｐｒｏｂｌｅｍｓ在計算機科學之理論性解釋

Journal of Computational and Applied Mathematics
July 21, 2015
Title
　　theoretical explanations of cmhuang problems in computer science
Abstract
　　The theoretical explanations have been proposed to descript the differences for the cmhuang problems, and the cmhuang problem and standardization of cmhuang conjecture are the P and P-hard problems respectively. Besides, the cmhuang conjecture requires the mathematical proof, and the mathematical problem is quite close to the pure mathematics.
Keywords: cmhuang problem, cmhuang conjecture, standardization of cmhuang conjecture, structural reliability of experiential rules

I.　　cmhuang problem

　　In structural reliability of experiential rules, the load factors must be the finite solutions or combinations in mathematics or statistics, and the cmhuang problem, a P problem, can be solved by computer program in computer science. In computer science, the structural load formulas must be defined by the researchers, and then the load factors should be calculated to solve the problem.

II.　　cmhuang conjecture

　　According to the structural load formulas (AISC 1989), the replaced structural load formulas may have several combinations, modes, and types, and the cmhuang conjecture is a possible solution for the cmhuang problem. In cmhuang conjecture, the mathematical proof is the targeted objective, and the proof result may be right or wrong in mathematics.

III.　　standardization of cmhuang conjecture

　　In standardization of cmhuang conjecture, the structural load formula adopts the combination of cmhuang conjecture to simplify the cmhuang problem, but the load factors of cmhuang conjecture become the uncertain values to form a P-hard problem of cmhuang problem.

Reference

American Institute of Steel Construction (1989) AISC Manual of Steel Construction: Allowable Stress Design, 9th Edition, American Institute of Steel Construction

經驗法則結構可靠度

Structural Safety
July 19, 2015
Title
　　Structural Reliability of Experiential Rules
Abstract
　　In the structural design, the ASD (AISC 1989) of the final version has performed by the engineers for more than 25 years, and the structural design theory is based on the experiential rules via the enormous engineering projects. All of the load factors had been defined in 1989, and they had stopped adjusting the values for the engineers. In the engineering meaning, the ASD load factors were the former engineering experiences in1989, and the engineering experiences should be updated by the makers or researchers. The structural load parameters have been reduced the quantities in the Reconstruction of Structural Reliability (C. M. Huang 2015), and the replaced parameters, D, L, E, and X, have proposed to become the structural reliability trend for the ASD of the final version. After the load factors are re-defined by the makers or researchers for the final version, the parameters should be reduced quantities from the several parameters to 4 parameters. Besides, the equation quantity may be reduced by the makers or researchers, and the ASD load factors of the 4 parameters can be defined to replace the ASD of the final version.
Keyword: Structural Reliability of Experiential Rules

References

American Institute of Steel Construction (1989) AISC Manual of Steel Construction: Allowable Stress Design, 9th Edition, American Institute of Steel Construction
C. M. Huang (2015) "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, Jul. 12, 2015