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    It was shown that the influential zone of vertical deformation of soil around pile groups and the influential thickness of compressive stratum under pile tips were approximately equal to the width of pile-cap and pile length respectively under the design load.
    研究表明:群桩基础边界大小由群桩基础变形特性控制,成桥阶段时大型哑铃型承台群桩基础周围外侧土体竖向变形影响范围和桩端土体压缩层影响深度,分别为一倍承台宽度和一倍桩长;
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    The results indicate that the MDTMD(Ⅰ-1) provides better effectiveness and robustness than both DTMD and multiple tuned mass dampers(MTMD)(including the arbitrary integer based MDTMD and odd number based MTMD) with equal total mass.
    数值结果表明MDTMD(I-1)比DTMD和基于任意整数多重调谐质量阻尼器(MTMD)和基于奇数MTMD具有更好的有效性和鲁棒性。
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    The results show that under the condition of that the outflow equals to 110 mL/min,the water which has been disinfected by the triiodine resin is secure for drinking when the disinfected time is equal to or exceed 12.05 s,and the bacteriological indexes and turbidity of which are in accord with the sanitary standard of drinking water for armed forced in wartime,and the concentration of residual iodine is less than 0.7 mg/L,which is harmless to human body.
    结果表明:在出水流量为110 mL/min的条件下,当接触时间为12.05 s时,消毒后出水的细菌学指标可达到军队战时饮用水卫生标准,出水余碘浓度始终低于0.7 mg/L,对人体无害。
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    In order to calculate PMV(Predicted Mean Vote) and PPD(Predicted Percentage of Dissatisfied) under air conditioning in summer,under the conditions of relative humidity 20 % and air velocity 0.1 m/s~0.5 m/s,indoor air temperature(equal to mean radiant temperature) 22 ℃~30 ℃,PMV is nomographed when people are seated,standing,and light activity.
    为了计算夏季空调时的PMV-PPD,分别在居室者静坐、站立或轻作业时,在相对湿度为20%、气流速度为0.1 m/s~0.5m/s,室内空气温度(=平均辐射温度)为22℃~30℃的条件下,与PMV的关系进行图解化。
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    Maximum seismic displacement of SDOF system with viscous damper based on the equal cyclic energy criteria
    基于能量准则的SDOF阻尼减震结构最大地震位移
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  equal
It is well-known that the ring of invariants associated to a non-modular representation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation.
      
The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
      
We also give conditions for the two algebras to be equal, relating equality to good filtrations and saturated subgroups.
      
We present two generalizations of the orthogonal basis of Malvar and Coifman-Meyer: biorthogonal and equal parity bases.
      
An important property of this matrix is that the maximum and minimum eigenvalues are equal (in some sense) to the upper and lower frame bounds.
      
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It is pointed out in this paper that the following apparent discrepancies exist in Coulomb's Theory: (1) In any problem in mechanics, a force to be definite must have all the three factors involved under consideration. In Coulomb's Theory, however, the point of application of the soil reaction on the plane of sliding is somehow neglected, thus enabling the arbitrary designation of the obliquity of the earth pressure on the wall to be equal to the friction angle between the wall surface and soil. As a matter...

It is pointed out in this paper that the following apparent discrepancies exist in Coulomb's Theory: (1) In any problem in mechanics, a force to be definite must have all the three factors involved under consideration. In Coulomb's Theory, however, the point of application of the soil reaction on the plane of sliding is somehow neglected, thus enabling the arbitrary designation of the obliquity of the earth pressure on the wall to be equal to the friction angle between the wall surface and soil. As a matter of principle, the point of application should never be slighted while the obliquity of the earth pressure could only have a value that is compatible with the conditions for equilibrium. (2) If the point of application of the soil reaction is taken into account in the problem, the sliding wedge would only tend to slide either on the plane of sliding or on the surface of wall but not on both at the same time, thus frustrating the very conceptidn of sliding wedge upon which Coulomb's Theory is founded. (3) The above discrepancies arise from the fact that the shape of the surface of sliding should be curvilinear in order to make the wedge tend to slide as desired, while Coulomb, however, adopted a plane surface instead. (4) Coulomb, in finding the plane of sliding, made use of the maximum earth pressure on the wall (for active pressure), which refers to the different magnitudes of pressure corresponding to different assumed inclinations of the plane of sliding. But from the relation between the yield of wall and amount of pressure, this maximum value is really the minimum pressure on the wall, which it is the purpose of the theory to find. In engineering books, however, this terminology of maximum pressure has caused considerable confusion, with the result that what is really the minimum pressure is carelessly taken as the maximum design load for the wall. How can a minimum load be used in a design?This paper also attempts to clarify some contended points in Rankine's Theory: (1) It is claimed by Prof. Terzaghi that Rankine's Theory is only a fallacy because of the yield of wall and that of the soil mass on its bed. This charge is unjust as it can be compared with Coulomb's Theory in the same respect. (2) Some books declare that Rankine's Theory is good only for walls with vertical back, but it is proved in this paper that this is not so. (3) It is also generally believed that Rankine's Theory is applicable only to wall surfaces with no friction. This is likewise taken by this paper as unfounded and illustration is given whereby, in this regard, Rankine's Theory is even better than Coulomb's, because it contains no contradiction, as does Coulomb's.

本文從力學觀點對庫隆理論提出下列問題:(1)在解算力學問題時,每個力有三個因素都該同時考慮,但庫隆對土楔滑動面上土反力的施力點竟置之不理,因而才能對擋土墙上土壓力的傾斜角作一硬性假定,使它等於墙和土間的摩阻角,然而施力點是不能不管的,因而土壓力的傾斜角是不能離開平衡條件而被隨意指定的。(2)如果考慮了土反力的施力點,則土楔祇能在滑動面上,或在墙面上,有滑動的趨勢,而不能同時在兩個面上都有滑動的趨勢,因而庫隆的基本概念“滑動土楔”就站不住了。(3)問題關鍵在滑動面的形狀;如要使土楔在滑動面和墙面上同時有滑動趨勢,則滑動面必須是曲形面,然而庫隆採用了平直形的滑動面。(4)庫隆的土楔滑動面是從墙上最大的土壓力求出的(指主動壓力),這裏所謂“最大”是指適應各個滑動面的各個土壓力而言,但對適應墙在側傾時土壓力應有的變化來說,這個最大土壓力却正是墙上極限壓力的最小值。一般工程書籍,以為這土壓力既名為最大,就拿它來用作設計擋土墙的荷載,荷載如何能用最小的極限值呢?本文對朗金理論中的下列問題作了一些解釋:(1)朗金理論在擋土墙的位移問題上所受的限制,是和庫隆理論一樣的,竇薩基教授曾就此問題認為朗金理論是幻想,似乎是無根據的。...

本文從力學觀點對庫隆理論提出下列問題:(1)在解算力學問題時,每個力有三個因素都該同時考慮,但庫隆對土楔滑動面上土反力的施力點竟置之不理,因而才能對擋土墙上土壓力的傾斜角作一硬性假定,使它等於墙和土間的摩阻角,然而施力點是不能不管的,因而土壓力的傾斜角是不能離開平衡條件而被隨意指定的。(2)如果考慮了土反力的施力點,則土楔祇能在滑動面上,或在墙面上,有滑動的趨勢,而不能同時在兩個面上都有滑動的趨勢,因而庫隆的基本概念“滑動土楔”就站不住了。(3)問題關鍵在滑動面的形狀;如要使土楔在滑動面和墙面上同時有滑動趨勢,則滑動面必須是曲形面,然而庫隆採用了平直形的滑動面。(4)庫隆的土楔滑動面是從墙上最大的土壓力求出的(指主動壓力),這裏所謂“最大”是指適應各個滑動面的各個土壓力而言,但對適應墙在側傾時土壓力應有的變化來說,這個最大土壓力却正是墙上極限壓力的最小值。一般工程書籍,以為這土壓力既名為最大,就拿它來用作設計擋土墙的荷載,荷載如何能用最小的極限值呢?本文對朗金理論中的下列問題作了一些解釋:(1)朗金理論在擋土墙的位移問題上所受的限制,是和庫隆理論一樣的,竇薩基教授曾就此問題認為朗金理論是幻想,似乎是無根據的。(2)有些工程書中認為朗金理論是專為垂直的墙?

The method of complementary I_0/I diagram for simplifying the computations of non-uniform beam constants is presented in this paper. The so-called "complementary I_0/I diagram" is the remaining I_0/I diagram of the haunched or de-haunched (or tapered) parts at the two ends of a beam after the I_0/I diagram of a non-uniform beam has been subtracted from the I_0/I = 1 diagram of a uniform beam.In the method of I_0/I diagram presented previously by the second author, the various momental areas have to be computed...

The method of complementary I_0/I diagram for simplifying the computations of non-uniform beam constants is presented in this paper. The so-called "complementary I_0/I diagram" is the remaining I_0/I diagram of the haunched or de-haunched (or tapered) parts at the two ends of a beam after the I_0/I diagram of a non-uniform beam has been subtracted from the I_0/I = 1 diagram of a uniform beam.In the method of I_0/I diagram presented previously by the second author, the various momental areas have to be computed for the entire length of a beam; in the method of complementary I_0/I diagram, the various momental areas need be computed for the lengths of the non-uniform sections at the two ends of the beam only. Hence the latter method is somewhat simpler than the former and may be considered as its improvement.The angle-change constants are the fundamental constants of a nonuniform beam, and only the coefficients of the angle-change constants need be computed. As any non-uniform beam may be considered as a uniform beam haunched or de-haunched or tapered at its one or both ends, the various anglechange coefficients φ may be computed separately in three distinct parts, viz., of a uniform beam, and φ~a and φ~b of the haunches at its two ends a and b, and then summed up as shown by the following general equation:φ=φ~a-φ~b (A) The values φ~a and φ~b are positive for haunched beams and negative for dehaunched or tapered beams, and either of them is zero for the end which is neither haunched nor de-haunched. To simplify the computations of the values of φ~a and φ~b, the complementary I_0/I diagram at each end of a beam is substituted by a cubic parabola passing through its two ends and the two intermediate points of the abscissas equal to 0.3 and 0.7 of its length. Then the value of φ~a or φ~b is computed with an error of usually less than 1% by the following formula:φ~a or φ~b = K_(0y0)+K_(3y3)+K_(7y7), (B) wherein y0, y3 and y7 are respectively the ordinates at the abscissa equal to 0, 0.3, and 0.7 of the length of the diagram, and the three corresponding values K_0, K_3 and K_7 are to be found from the previously computed tables.A set of the tables of K-values for calculating the values of φ~a and φ~b of the shape angle-changes and the load angle-changes under various loading conditions may be easily computed, which evidently has the following advantages: (1) As indicated by formulas (A) and (B), the computations of φ~a, φ~b and φ with K-values known are very simple; (2) the approximation of the results obtained is very close; (3) A single set of such K-value of the tables is applicable to non-uniform beams of any shape, any make-up, and any crosssection; and (4) as the K-values are by far easier to compute than any other constants, a comprehensive set of the tables of K-values with close intervals and including many loading conditions may be easily computed.Besides, by means of formulas (A), existing tables of constants such as A. Strassner's for beams haunched at one end only may be utilized to compute the shape and load constants for asymmetrical beams with entirely different haunches at both ends.Finally, five simple but typical examples are worked out first by the approximate method and then checked by some precise method in order to show that the approximation is usually extremely close.

本文叙述一种I_0/I余圖法,以簡化变梁常数的計算。所謂I_0/I余圖,即自等截面梁的I_0/I=1圖減去变梁的I_0/I圖后所剩余的兩端梁腋的I_0/I圖。 於本文第二著者前此所建議的I_0/I圖法中,必須計算变梁全長的I_0/I圖的各次矩图面积,於I_0/I余圖法中,則只須計算变梁兩端梁腋的I_0/I余圖的各項积分值。故后法显此前法为簡單,亦可视作系前法的进一步的改善。 角变常数为变梁的基本常数,而所須計算者只是各項角变常数的系数φ,簡称为“角变系数”。任一形式的变梁均可视作一端或兩端的加腋梁或減腋梁。採用I_0/I余圖法,則变梁的各項角变系数φ的計算可分开为等截面梁的φ及其a与b兩端梁腋的φ~a与φ~b三部分而后綜合之,以公式表之,即於加腋梁φ~a与φ~b为正号;於減腋梁φ~a与φ~b为負号,於无梁腋之端則其φ~a或φ~b之值为霉。 計算梁腋的φa或φ~b值时,可用一根三次拋物線以代替I_0/I余圖而計算其各項积分的近似值。由是可得其中y_0,y_3及y_7为a或b端I_0/I余圖的三个豎距。如按变梁的形角变系数及其在各种荷載下的载角变系数將各項K值列成表格,則此項表格显有下列优点:(一)应用步驟簡單,...

本文叙述一种I_0/I余圖法,以簡化变梁常数的計算。所謂I_0/I余圖,即自等截面梁的I_0/I=1圖減去变梁的I_0/I圖后所剩余的兩端梁腋的I_0/I圖。 於本文第二著者前此所建議的I_0/I圖法中,必須計算变梁全長的I_0/I圖的各次矩图面积,於I_0/I余圖法中,則只須計算变梁兩端梁腋的I_0/I余圖的各項积分值。故后法显此前法为簡單,亦可视作系前法的进一步的改善。 角变常数为变梁的基本常数,而所須計算者只是各項角变常数的系数φ,簡称为“角变系数”。任一形式的变梁均可视作一端或兩端的加腋梁或減腋梁。採用I_0/I余圖法,則变梁的各項角变系数φ的計算可分开为等截面梁的φ及其a与b兩端梁腋的φ~a与φ~b三部分而后綜合之,以公式表之,即於加腋梁φ~a与φ~b为正号;於減腋梁φ~a与φ~b为負号,於无梁腋之端則其φ~a或φ~b之值为霉。 計算梁腋的φa或φ~b值时,可用一根三次拋物線以代替I_0/I余圖而計算其各項积分的近似值。由是可得其中y_0,y_3及y_7为a或b端I_0/I余圖的三个豎距。如按变梁的形角变系数及其在各种荷載下的载角变系数將各項K值列成表格,則此項表格显有下列优点:(一)应用步驟簡單,只有几个簡單的乘法与加減法;(二)所得結果的近似程度頗高,差誤一般不超过1%;(三)应用范圍广泛,只一套K值表可用於任何截面及?

This paper describe the analysis of stresses in a building of three spins and thre storeys. For the want of a better hame, we shall call the product of the sum of the shears at the either ends of eads tier of columns and their length the shear moment for that tier or storey. Evidently the sum of moments at ends of all the columns belonging tothe same storey must equal to the shear moment of the same storey. To begin with we assume that the shear moment in each storey separately equals l. Let us take the...

This paper describe the analysis of stresses in a building of three spins and thre storeys. For the want of a better hame, we shall call the product of the sum of the shears at the either ends of eads tier of columns and their length the shear moment for that tier or storey. Evidently the sum of moments at ends of all the columns belonging tothe same storey must equal to the shear moment of the same storey. To begin with we assume that the shear moment in each storey separately equals l. Let us take the nth. storey first. A unit shear moment in this storey will induce certain fixed-end moments in the columas, which will be then distributed among the joints at end of the columns belonging to this storey_2 leaving the moments at any other joint alone. Since the block distribution coefficients and carrying over factors to the second joints used for this distribution are calculated for the whole truss, the moments in a number of joints are still unbalanced, at the same time new moments appear at ends of columns of the (n+1) th and(n—l) th. storeys, so that new shear moments are acquired also by these two storeys. On the other hand the shear moment in the nth. storey is no longer equals to 1, but some new value a. this will not matter, the important thing is that we have determined definitely the ratios between this uew shear moment value a and the moments at the ends of the columns belonging to these three storeys and the shear moments in storeys below and above, In order to bring the value of the shear moment in the nth. storey back to l, we divide all these end moments and shear moments by a, the result is a set of new values, which will be called, for convenience, the influence values due to shear moment in the nth. storev.Wben the building truss is being analysed, we multiply the influence values of different storeys by a set of suitable numbers, and put the results in successive rows in a table. The multiplying should be so chosen that the sums of shear moments for saeh storey should equal approximately their actual values. The end moments are then balanced by block distribution. After this distribution the shear moment for each storey will differ from their actual values appreciably7 the difference wiil be then made up by repetition of the above process as'often as required. For the truss under consideration7 the calculations are repeated only once, then the maximum error in values of shear moments is already so low (only 0.075%), a second repetition of the process is quite unnecessary.

本文計算的是一个三層三间的屋架?衙繉拥淖∽拥淖芗袅退麄兊母叨鹊某朔e喚做这一層的剪力矩,那么这个剪力矩是和同一層的柱子的两端的弯矩的总和值相等的燃俣恳粚拥募袅氐扔?.为便利超見,譬如我們先假定第n層的剪力矩等于1。把这一層的各柱子的兩端的固定端弯炬求得,再把他們在本層的柱子的兩端的各結点分配一下。因为我們用的集体分配系数和隔点傳遞系数是根据整个屋架計算的緣故,有一部分的結点的弯矩是不完全平衡的,同时第n—1和n+1層的柱子的两端出现了新的弯炬,因此这两層也出現了新的剪力矩了。在另一方面,第n層的剪力矩已經不等于1,却等于一个新值α了。但是本層和上下两層的柱子两端的弯矩和上下两層的剪力矩和这个新剪力矩值α的中間是有一定的比例的。为了要本層的剪力矩值仍旧变成1,我們拿α除所有弯矩值和剪力矩值,因此我求得一系列的新值,这些新值就喚做n層的剪力矩的影响值嬎阄菁苁蔽覀兡檬实钡氖党烁鲗拥募袅氐挠跋熘?叫各厨的剪力矩的总和差不多和他們的实在值相等,然后進行分配弯矩。分配之后,各層的剪力矩和他們的实在值必定还有一定的距离或一定的差数。因此我們再用另一批适当的新数值乘各層的剪力矩的影响值,叫各層的剪力矩的总和差不...

本文計算的是一个三層三间的屋架?衙繉拥淖∽拥淖芗袅退麄兊母叨鹊某朔e喚做这一層的剪力矩,那么这个剪力矩是和同一層的柱子的两端的弯矩的总和值相等的燃俣恳粚拥募袅氐扔?.为便利超見,譬如我們先假定第n層的剪力矩等于1。把这一層的各柱子的兩端的固定端弯炬求得,再把他們在本層的柱子的兩端的各結点分配一下。因为我們用的集体分配系数和隔点傳遞系数是根据整个屋架計算的緣故,有一部分的結点的弯矩是不完全平衡的,同时第n—1和n+1層的柱子的两端出现了新的弯炬,因此这两層也出現了新的剪力矩了。在另一方面,第n層的剪力矩已經不等于1,却等于一个新值α了。但是本層和上下两層的柱子两端的弯矩和上下两層的剪力矩和这个新剪力矩值α的中間是有一定的比例的。为了要本層的剪力矩值仍旧变成1,我們拿α除所有弯矩值和剪力矩值,因此我求得一系列的新值,这些新值就喚做n層的剪力矩的影响值嬎阄菁苁蔽覀兡檬实钡氖党烁鲗拥募袅氐挠跋熘?叫各厨的剪力矩的总和差不多和他們的实在值相等,然后進行分配弯矩。分配之后,各層的剪力矩和他們的实在值必定还有一定的距离或一定的差数。因此我們再用另一批适当的新数值乘各層的剪力矩的影响值,叫各層的剪力矩的总和差不多和这些差数相等,然后分配弯矩。这样一遍一遍的算下去等到求得剪力矩和他們的实在值中间没有差数或相差很小才歇手。我們計算这个例題时僅僅算了两遍,最大誤差已經小到0.075%,因此就沒有再算下去了。

 
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