Analytical Dependence of Deflection of the Lattice Truss on the Number of Panels

Lecture Notes in Civil Engineering 2020
Mikhail Kirsanov, Dmitrijs Serdjuks, Karīna Buka-Vaivade

The case of load in the middle of the span is considered. An algorithm is given for deriving the analytical dependence of the deflection of a truss on the number of panels. It is shown that for a certain combination of panel numbers over the height of the truss and along the length of the span, the determinant of the system of equations of node equilibrium turns to zero that corresponds to the kinematic variability of the structure. It is noted that numerical calculation can obscure this feature due to inaccuracy of calculations. To obtain an exact formula, the computer mathematics system Maple is used. The coefficients of the final formula are obtained from the solution of linear homogeneous recurrent equations found from the analysis of the sequence of solutions for trusses with different number of panels. An example of a scheme of possible velocities of nodes of a variable truss is given. The formula for the deflection of the truss for the number of panels for which the truss is unchanged is derived by induction.

Keywords
Deflection, Frame, Induction, Kinematic variability, Maple, Truss
DOI
10.1007/978-3-030-42351-3_3
Hyperlink
https://link.springer.com/chapter/10.1007/978-3-030-42351-3_3

Kirsanov, M., Serdjuks, D., Buka-Vaivade, K. Analytical Dependence of Deflection of the Lattice Truss on the Number of Panels. In: Proceedings of EECE 2019. Lecture Notes in Civil Engineering. Vol.70. Cham: Springer, 2020. pp.25-35. ISBN 978-3-030-42350-6. e-ISBN 978-3-030-42351-3. ISSN 2366-2557. Available from: doi:10.1007/978-3-030-42351-3_3

Publication language
English (en)