Plane Truss Subjected to Force, Thermal and Kinematic Actions
Objective: Determination of the stress-strain state of a truss subjected to force, thermal and kinematic actions.
Initial data file: SSLL12_v11.3.spr
Problem formulation: The two-span truss is loaded by two concentrated forces FE and FF in the nodes of the top chord, uniformly heated across all cross-sections of its elements by the value of ΔT and subjected to the displacement of its supports by the values of vA, vB and vC. Determine the longitudinal force N in the support diagonal BD and vertical displacement v (Z) in the point D of its joint with the bottom chord and the lattice members.
References: M. Laredo, Resistence des materiaux, Paris, Dunod, 1970, p.579.
Initial data:
| Lattice members A1: | |
| EF = 2.961·108 Н | - axial stiffness; |
Elements of the top and bottom chords, support diagonals and support vertical A2: |
|
| EF = 5.922·108 N | - axial stiffness; |
Elements modeling the constraints in the support nodes in the directions vA, vB and vC (null elements): |
|
| EF = 1010 N | - axial stiffness; |
Boundary conditions: |
|
| θ = 30º | - angle of the support area in the node C; |
Properties of the material: |
|
| α = 10-5 1/ºC | - linear expansion coefficient |
Loads and actions: |
|
| FE = 1.5·105 N | |
| FF = 1.0·105 N | |
| ΔT = 150 ºC | |
| vA = 0.020 m | |
| vB = 0.030 m | |
| vC = 0.015 m. | |
Finite element model: Design model – plane hinged bar system. Lattice members: A1 – 8 elements of type 1, elements of the top and bottom chords, support diagonals and support vertical A2 – 9 elements of type 1; elements modeling the constraints in the support nodes in the directions vA, vB and vC – 3 elements of type 154. Boundary conditions in the direction uA are provided by imposing the respective rigid constraint. Number of nodes in the design model – 13.
Results in SCAD
Design and deformed models
Values of vertical displacements v (Z) (m)
Values of longitudinal forces N (N)
Comparison of solutions:
|
Parameter |
Theory |
SCAD |
Deviations, % |
|
Vertical displacement vD (Z), m |
-1.6180∙10-2 |
-1.6177∙10-2 |
0.02 |
|
Longitudinal force NBD, N |
43633.0 |
43633.5 |
0.00 |