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.

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.

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.

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.

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.

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.

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.

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.