Abstract
An algorithm is given for deriving the dependence of the deflection of a planar statically determinate beam truss on the number of panels, dimensions and load. Three load cases are considered: uniform load on the lower belt, upper belt and vertical force in the middle of the span. By induction, generalizing a series of solutions for trusses with a consecutively increasing number of panels, the desired formula is obtained for the deflection and horizontal displacement of the mobile support of the truss. All transformations are performed in the system of symbolic mathematics Maple. For a sequence of coefficients of the desired formula, using the special Maple operators, homogeneous recurrent equations are constructed and solved. The coefficients found are in the form of polynomials in the number of panels. The asymptotic property of the solution is found. On the graphs of the dependence of the deflection on the number of panels and on the height, extreme points are found. The solution can be used to test the calculations obtained numerically.
Highlights
In design practice, all calculations for the strength, stability and endurance of rod structures are performed numerically [1,2,3,4,5]
Analytical calculations of building structures are quite rare, and the formulas on which they are based generally have a narrow field of application
Known methods of determining the forces in rods and the displacement of nodes are applied in any program of symbolic mathematics (Maple, Mathematica, Derive, Reduce, etc.)
Summary
All calculations for the strength, stability and endurance of rod structures are performed numerically [1,2,3,4,5]. The calculation of a particular truss with dimensions and loads, designated as variable parameters, is quite simple For this purpose, known methods of determining the forces in rods and the displacement of nodes are applied in any program of symbolic mathematics (Maple, Mathematica, Derive, Reduce, etc.). It is much more difficult to obtain the dependence of forces or displacements on the number of panels or rods of a truss if a calculated design has a periodic structure with a certain type of periodicity cell. A method is used to induct generalizations of a number of solutions for trusses with a consecutively increasing number of panels The inductive method in the problem of the deflection of a truss taking account of the creep of the material was solved in [18]
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