英语翻译The structure is statically indeterminate to the second degree,so that two redundant forces have to be removed.Several choices are possible,e.g.,the moment and the vertical reaction at C,or the vertical reactions at A and B.For the purpos

英语翻译The structure is statically indeterminate to the second degree,so that two redundant forces have to be removed.Several choices are possible,e.g.,the moment and the vertical reaction at C,or the vertical reactions at A and B.For the purpos
英语翻译
The structure is statically indeterminate to the second degree,so that two redundant forces have to be removed.Several choices are possible,e.g.,the moment and the vertical reaction at C,or the vertical reactions at A and B.For the purposes of this example,we shall remove the vertical reaction at B and the moment at C.the released structure is then a simple bean AC with redundant forces and direction as shown in fig.14-1b.the location and direction of the various redundant and displacements is referred to as a coordinate system.
The positive directions of the redundant F1 and F2 are chosen arbitrarily but the positive directions of the displacements at the same location must always accord with those of the redundant.The arrows in Fig.14-1 b indicate the chosen positive directions in the present case and,since the arrows indicate forces as well as displacements; it is convenient in a general case to label the coordinates by numerals 1,2,3…,n.
Following this system,Fig.14-1c shows the displacements at B and C as and respectively.In fact,as shown in Fig.14-a,the actual displacements at those points are zero,so that and represent the inconsistencies in deformation.
The magnitude of and can be calculated from the behavior of the simply supported beam of Fig.14-c.For the present purposes,we can use the data of Appendix B.Thus
And
The negative signs show that the displacements are in directions opposite to the positive directions chosen in Fig.14-1b.
The displacements due to unit values of the redundant are show in Fig.14-d and e.These displacements are as follows (again from Appendix B):
The general coefficient represents the displacement at the coordinate i due to a unit redundant at the coordinate j.
The geometry-relations express the fact that the final vertical translation at B and the rotation at C vanish.The final displacements are the result of the superposition of the effect of the external loading and of the redundant on the released structure.Thus the geometry-relations can be expressed as

英语翻译The structure is statically indeterminate to the second degree,so that two redundant forces have to be removed.Several choices are possible,e.g.,the moment and the vertical reaction at C,or the vertical reactions at A and B.For the purpos
这个结构是拉压超静定到第二学位,所以这两个多余的部队已经被移除.有几个选项,例如:那一刻起,他和垂直反应或垂直的反应,在与本例,我们应将垂直的反应在B和C的时刻.然后释放出一个简单的结构和多余的力量和豆子AC的方向.14-1b如图.这个位置和方向的各种冗余和位移被看作是一个坐标系统.
积极的方向的冗余和任意选择积极的方向,但在同一地点的位移必须符合那些多余的.在Fig.14-1的箭头b表示选择积极的方向在本案,因为箭显示力量以及位移;它是在一般情况下的便利,由数字标签坐标1、2、3…,n.
以下这个系统、图显示了.14-1c位移和B和C的分别.事实上,如图Fig.14-a,实际的位移那些分数是零,那么,代表着对变形.
的大小,可以计算出行为的Fig.14-c简支梁的.现在,我们可以使用数据的附录b
,
负面的迹象表明,位移在积极方向相反方向的选择.14-1b图.
由于单元的位移值显示在图是多余的.14-d和e.这些位移如下(再从附录B).
一般的系数的位移的坐标代表我由于一个单位的冗余状态.协调
这个geometry-relations表达的事实是,最终在B和垂直翻译轮值C消失.最后位移叠加的结果的影响,在外载荷和冗余的释放的结构.因此geometry-relations可以表示为一个