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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 article describes an I_0/I co-map method to simplify the calculation of variable beam constants. The I_0/I co-map is the I_0/I map of the two end beams remaining after subtracting the I_0/I map of the variable beam from the I_0/I=1 map of the equal-section beam. In the I_0/I diagram method suggested by the second author of this paper, the moment map area of the I_0/I map of the full beam must be calculated. In the I_0/I residual graph method, only the variable beam must be calculated. End-beam integral values of I_0/I co-maps. Therefore, the subsequent method shows that the previous method is simple and can be regarded as a further improvement of the predecessor method. The angle change constant is the basic constant of the variable beam, and the only factor to be calculated is the coefficient φ of each angle change constant, which is simply referred to as the “angle change coefficient”. Any type of variable beam can be considered as a twisted or reduced beam at one or both ends. Using the I_0/I co-map method, the calculation of the variable coefficient φ of the variable beam can be divided into three parts: φ of a constant beam and the a and b ends of the beam, and then φ~a and φ~b. The formula is shown in the equation. That is to say, the plus 腋 beams φ~a and φ~b are positive signs; in the subtractive beams φ~a and φ~b are negative signs, and at the end of the beamless 则, they are φ~a or φ. The value of ~b is mildew. When calculating the φa or φ~b values of the beam, a cubic parabola can be used to calculate the approximate value of each integral instead of the I_0/I residual graph. Three vertical distances are available for which y_0, y_3 and y_7 are a or b-side I_0/I co-maps. If the variable K value of the variable beam and its variation factor of the load angle under various loads are used to list the various K values, the table has the following advantages: (1) The application steps are simple and only a few simple Multiplication and addition and subtraction; (b) the degree of similarity of the results obtained is quite high, and the difference is generally not more than 1%; (c) a wide range of applications, only a set of K-value tables can be used for any cross-section and?