An Exact Theory For Computing Internal Force Envelopes Of Skeletal Structures Under Moving Loads

Internal force envelopes of skeletal structures under moving loads are important to structure designs of bridges, floor continuous beans and plant crane beams. However, in the former classical structure mechanics, there is no well solution for envelops. In large-scale engineering problems, it is difficult to obtain accurate and reliable answer of the envelope.Towards computing internal force envelopes of skeletal structures under moving loads, the thesis introduces conceptions of the influence surfaces and surfaces of internal forces, and sets up the functions with two variables defining the relationship between the structural internal forces and the place of the moving loads. It changes all mechanical conditions needed into a complete mathematical information, and makes research ideas clear and simple.Based on analyzing surfaces of internal forces, the thesis presents properties of influence surfaces, internal force surfaces and internal force envelopes, presents a way of computing exact discrete value, and analytic expression of shear envelopes. In engineering, the extreme value and the internal force sub-function points are an important to design control, and in envelopes it's the same. If we draw an envelop by the way of connecting discrete points, some sharp points and extreme points may disappear, and the shape of the envelop may be inaccurate. Analytical expressions of shear envelopes can be solved, and the control points will be obtained naturally. But it needs further consideration for control points of moment envelopes.Based on the conception of internal force surfaces, the thesis shows a new way to understand the absolute maximum moment, the extreme points and the sharp points of moment envelopes. For the absolute maximum moment, based on the absolute maximum moment theorem in the thesis, we can compute it by searching dividing lines of internal force surfaces. For the extreme points, we can find it by computing the absolute maximum moment in a small range. For sharp points, by judging the sub-regional of the two cross-sections, we can know the existence of the sharp point between them, and then find the sharp point by dividing the range numerically. Based on the understanding above, the thesis gives the accurate calculation methods and provides some guidance of the algorithm design, so that the program can be as efficiently as possible.The concepts and ideas in the thesis are extendable for further study of internal force envelopes, such as considerations of shear deformation, variable cross-section bar, various forms of moving loads, and else.