Influence line for any function Z allows us to calculate Z for any position of a moving load, and that is very important, the most unfavourable position of the moving loads and corresponding value of the relevant function. Unfavourable (or dangerous) position of a moving load is such position, which leads to the maximum (positive…
Influence lines, which describe variation of any function Z (reaction, bending moment, shear, etc.) in the fixed section due to moving concentrated unit load P D 1 may be effectively used for calculation of this function Z due to arbitrary fixed and moving loads. Fixed Loads Three types of fixed loads will be considered: concentrated…
Since the expression for shear depends on whether the load P is located to the left or to the right from the section k, then two positions of the load P need to be considered. The procedure of construction of influence line for shear is presented in tabulated form. In the table we show the…
Simply supported beam subjected to moving unit load P is presented in Fig. 2.4. Construction of influence lines for bending moment and shear force induced at section k are shown below. Bending Moment Mk The bending moment in section k is equal to the algebraic sum of moments of all forces, which are located to…
The following types of beams are considered: simply supported beam, beam with overhang, and cantilever beam. Simply Supported Beam (Fig. 2.1) The beam AB is loaded by moving load P D 1. The moving load is shown by circle and the dotted line indicates the loaded contour for possible positions of the load on the…
Construction of influence lines for one span simply supported and cantilevered beams in case of direct and indirect load applications are considered. All influence lines are constructed using analytical expressions for required factor. Applications of influence lines for fixed and moving loads are discussed. This chapter forms the set of concepts which creates a framework…
A number of independent parameters, which define configuration of a system without deformation of its members is called the degree of freedom. The number of degrees of freedom for any structure may be calculated by the Chebushev’ formula where D, H, and S0 are the number of rigid discs, simple hinges, and constraints of supports, respectively….
Kinematical analysis of a structure can also be done using the static equations. The following criteria for instantaneously changeable systems may be used: (a) Load has finite quantity but the internal forces have infinite values (b) Load is absent and the internal forces are uncertain (type of 0/0) Let us discuss these criteria for structure…
In order to produce a rigid structure in a whole, the rigid discs should be connected in specific way. Let us consider general rules for formation of geometrically unchangeable structures from two and three rigid discs. If a structure is formed from two discs, then their connections may be as follows: 1. Connection by fixed…
Kinematical analysis of a structure is necessary for evaluation of ability of the structure to resist external load. Kinematical analysis is based on the concept of rigid disc, which is an unchangeable (or rigid) part of a structure. Rigid discs may be separate members of a structure, such as straight members, curvilinear, polygonal (Fig. 1.1),…