TEST CASE 9.2 BAR STRUCTURE LOADED WITH A UNIFORMLY DISTRIBUTED LOAD IN THE AXIAL DIRECTION
Reference:
Perelmuter A.V., Kabantsev O.V. Analysis of structures with a changing design scheme, M.: Publishing House of SKAD-SOFT, 2015.
Problem description:
The post, rigidly restrained on one side, consists of 2 sections, which are mounted in turn and loaded with uniformly distributed longitudinal forces f. Determine the internal longitudinal forces N in the rack sections at each stage of assemblage.
Problem sketch:
Type of created problem:
Flat frame (X, Z, UY).
Geometric characteristics:
L = 2 m.
Material properties:
Bending stiffness: EI = 313.32 N·m^{2};
Axial stiffness: EA = 1000 N.
Boundary conditions:
Node 1: X = Z = UY = 0;
Node 3: k_{x} = k_{z} = k_{uy} = 1·10^{18 }N/m – temporary elastic connection (option b).
Loads:
f = 25 N/m.
Model description:
The system is modeled by 2 general finite elements of spatial bar (FE type is 10). Task is solved using two different approaches. The fist problem (option a) is done via classical staging. The second problem (option b) is modeled in the "Assemblage" system.
Calculation results:
Target value |
Classical staging (option a) |
Accounting for the assemblage stages (option b) |
||
1 |
2 |
3 |
||
N_{1}, N |
-100 |
-50 |
-62.5 |
-100 |
N_{2}, N |
-50 |
0 |
-12.5 |
-50 |
N_{3}, N |
0 |
– |
37.5 |
0 |
Internal forces N (option а), N |
Internal forces N at all stages of assemblage (option b), N |