Analytical calculation of the deflection of the lattice truss
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, gene...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | https://doi.org/10.1051/matecconf/201819303015 |
| _version_ | 1818347741402628096 |
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| author | Kirsanov Mikhail Tinkov Dmitriy |
| author_facet | Kirsanov Mikhail Tinkov Dmitriy |
| author_sort | Kirsanov Mikhail |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T17:38:59Z |
| format | Article |
| id | doaj.art-9958a0be58c745d0a760b5eba5ebd2c3 |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-12-13T17:38:59Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-9958a0be58c745d0a760b5eba5ebd2c32022-12-21T23:36:50ZengEDP SciencesMATEC Web of Conferences2261-236X2018-01-011930301510.1051/matecconf/201819303015matecconf_esci2018_03015Analytical calculation of the deflection of the lattice trussKirsanov MikhailTinkov DmitriyAn 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.https://doi.org/10.1051/matecconf/201819303015 |
| spellingShingle | Kirsanov Mikhail Tinkov Dmitriy Analytical calculation of the deflection of the lattice truss MATEC Web of Conferences |
| title | Analytical calculation of the deflection of the lattice truss |
| title_full | Analytical calculation of the deflection of the lattice truss |
| title_fullStr | Analytical calculation of the deflection of the lattice truss |
| title_full_unstemmed | Analytical calculation of the deflection of the lattice truss |
| title_short | Analytical calculation of the deflection of the lattice truss |
| title_sort | analytical calculation of the deflection of the lattice truss |
| url | https://doi.org/10.1051/matecconf/201819303015 |
| work_keys_str_mv | AT kirsanovmikhail analyticalcalculationofthedeflectionofthelatticetruss AT tinkovdmitriy analyticalcalculationofthedeflectionofthelatticetruss |