Linear Static Analysis of a Stayed Steel Chimney

Transcription

1 Linear Static Analysis of a Stayed Steel Chimney

2 Outline 1 Description 2 Finite Element Model 2.1 Units 2.2 Geometry Definition 2.3 Properties 2.4 Boundary Conditions 2.5 Loads Load combinations 2.6 Meshing 3 Analysis 3.1 Analysis Commands 3.2 Results Displacements Axial forces Bending moments Appendix A Additional information Linear Static Analysis of a Stayed Steel Chimney 2/26

3 1 Description This example illustrates the use of rods and beams in three-dimensional space. Therefore we have chosen the problem of a steel chimney (simple cylinder) stayed by four cables on two thirds of the height as shown in Figure 1. It is assumed that the cables are prestressed in such a way that they will not become slack during any loading. Figure 1: Model of the stayed steel chimney Linear Static Analysis of a Stayed Steel Chimney 3/26

4 2 Finite Element Model The three dimensional finite element model consists of beam elements for the chimney and truss elements for the stays. Main menu File New project [Fig. 2] Figure 2: New project Dialog Linear Static Analysis of a Stayed Steel Chimney 4/26

5 2.1 Units We choose millimeter for the unit Length, ton for Mass and Newton for Force. Model Window Reference system Units [Fig. 3] Property Panel [Fig. 4] Figure 3: Model windows Figure 4: Property Panel - Units Linear Static Analysis of a Stayed Steel Chimney 5/26

6 2.2 Geometry Definition Six lines are required to build the model: one for the bottom part of the chimney, one for the top part and one line for each of the support cables. Main Menu Geometry Create Add line [Fig. 5] - [Fig. 10] repeat the operation six times Figure 5: Geometry - Add Line 1 Figure 6: Geometry - Add Line 2 Figure 7: Geometry - Add Line 3 Figure 8: Geometry - Add Line 4 Figure 9: Geometry - Add Line 5 Figure 10: Geometry - Add Line 6 Linear Static Analysis of a Stayed Steel Chimney 6/26

7 Figure 11: View of the model - Lines Linear Static Analysis of a Stayed Steel Chimney 7/26

8 2.3 Properties We assign the element class and the material and geometrical properties to the vertical line segments. Two-noded beam elements are applied and the material is linear elastic. Main Menu Geometry Analysis Property assignments [Fig. 12] Property assignments Add new material [Fig. 13] [Fig. 14] Figure 12: Property assignments Figure 13: Add new material Figure 14: Material properties Linear Static Analysis of a Stayed Steel Chimney 8/26

9 The geometry of the cross-section is specified in Figure 1. Property assignments Add new geometry [Fig. 15] Figure 15: Geometrical properties Linear Static Analysis of a Stayed Steel Chimney 9/26

10 We now define the sloped line segments. Two-noded regular truss elements are applied and the material is linear elastic. The cross-section of the stays is defined by the area. Main Menu Geometry Analysis Property assignments [Fig. 16] Property assignments Add new material [Fig. 17] [Fig. 18] Property assignments Add new geometry [Fig. 19] Figure 16: Property assignments Figure 17: Add new material Figure 18: Material properties Figure 19: Geometrical properties Linear Static Analysis of a Stayed Steel Chimney 10/26

11 2.4 Boundary Conditions We clamp the base of the chimney by fixing the translations and rotations at the bottom end of the vertical line segment [Fig. 20]. Main Menu Geometry Analysis Attach support [Fig. 20] [Fig. 21] Figure 20: Clamping the base Figure 21: View of model - Clamp Linear Static Analysis of a Stayed Steel Chimney 11/26

12 Now the cables are pinned to the ground by fixating the translations at the bottom end of the diagonal line segments [Fig. 22]. Main Menu Geometry Analysis Attach support [Fig. 22] [Fig. 23] Figure 22: Attaching the cables to the ground Figure 23: View of model - All supports Linear Static Analysis of a Stayed Steel Chimney 12/26

13 2.5 Loads Three load cases are defined: a prestress of N/mm 2 is applied to the stays, a uniformly distributed wind load of 10 kn/m is applied along the chimney in the positive X-direction and a uniformly distributed wind load of 10 kn/m is applied along the chimney in the positive Y-direction. Main Menu Geometry Analysis Attach load [Fig. 24] - [Fig. 26] repeat the operation for each load case Figure 24: Prestressing the stays Figure 25: Wind load in the X-direction Figure 26: Wind load in the Y-direction Linear Static Analysis of a Stayed Steel Chimney 13/26

14 Figure 27: View of model - All loads Linear Static Analysis of a Stayed Steel Chimney 14/26

15 2.5.1 Load combinations Two load combinations are defined: one that is equivalent to load case 3 (wind in the X-direction) and another that is a combination of the prestress in the stays and a wind load in the 45 XY-direction. Main Menu Geometry Loads Open geometry load combination table Figure 28: Geometry load combinations tree Figure 29: Geometry load combinations table Linear Static Analysis of a Stayed Steel Chimney 15/26

16 2.6 Meshing The mesh is defined by dividing the line segments in two parts for the chimney top and four parts for the chimney bottom. The truss elements are not divided; each stay segment is meshed with one truss element. Main Menu Geometry Analysis Set mesh properties [Fig. 30] [Fig. 31] Main Menu Geometry Analysis Generate mesh [Fig. 32] Figure 30: Mesh properties - Top vertical line segment Figure 31: Mesh properties - Bottom vertical line segment Figure 32: Mesh Linear Static Analysis of a Stayed Steel Chimney 16/26

17 To check how the profile of the beam and truss elements compare to the structural dimensions, the 3D graphical view of beams and trusses is generated. Main Menu Mesh Mesh 3D beams and shells Figure 33: View of model - In 3D Linear Static Analysis of a Stayed Steel Chimney 17/26

18 3 Analysis 3.1 Analysis Commands We will perform a structural linear static analysis. Main Menu Analysis New Analysis Analysis window Right click Analysis1 Rename LinSta [Fig. 34] Analysis window Right click LinSta Add command Structural linear static [Fig. 35] [Fig. 36] Main Menu Analysis Run Analysis Figure 34: Analysis window Figure 35: Add command Figure 36: Analysis tree Linear Static Analysis of a Stayed Steel Chimney 18/26

19 3.2 Results The displacements, axial forces and bending moments are generated for both load combinations Displacements Results browser Case Load-combination 1 [Fig. 37] Results browser Output linear static analysis Nodal results Displacements DtX Right click Show contours [Fig. 37] [Fig. 38] Figure 37: Results browser Figure 38: Load combination 1 - Displacements DtX Linear Static Analysis of a Stayed Steel Chimney 19/26

20 Results browser Case Load-combination 2 [Fig. 39] Results browser Output linear static analysis Nodal results Displacements DtX Right click Show contours [Fig. 39] [Fig. 40] Figure 39: Results browser Figure 40: Load combination 2 - Displacements DtX Linear Static Analysis of a Stayed Steel Chimney 20/26

21 3.2.2 Axial forces Results browser Case Load-combination 1 [Fig. 41] Results browser Output linear static analysis Element results Cross-section Forces Nx Right click Show contours [Fig. 41] [Fig. 42] Figure 41: Results browser Figure 42: Load combination 1 - Axial forces Nx Linear Static Analysis of a Stayed Steel Chimney 21/26

22 Results browser Case Load-combination 2 [Fig. 43] Results browser Output linear static analysis Element results Cross-section Forces Nx Right click Show contours [Fig. 43] [Fig. 44] Figure 43: Results browser Figure 44: Load combination 2 - Axial forces Nx Linear Static Analysis of a Stayed Steel Chimney 22/26

23 3.2.3 Bending moments Results browser Case Load-combination 1 [Fig. 45] Results browser Output linear static analysis Element results Cross-section Moments My Right click Show contours [Fig. 45] [Fig. 46] Figure 45: Results browser Figure 46: Load combination 1 - Bending moment My Linear Static Analysis of a Stayed Steel Chimney 23/26

24 Results browser Case Load-combination 2 [Fig. 47] Results browser Output linear static analysis Element results Cross-section Moments My Right click Show contours [Fig. 47] [Fig. 48] Figure 47: Results browser Figure 48: Load combination 2 - Bending moment My Linear Static Analysis of a Stayed Steel Chimney 24/26

25 Appendix A Additional information Folder: Tutorials/StayedSteelChimney Number of elements 10 Keywords: analys: linear static. constr: suppor. elemen: beam class1 l12be l2tru pipe truss. load: elemen force line prestr. materi: elasti isotro. option: direct units. post: binary ndiana. pre: dianai. result: cauchy displa extern force green moment reacti strain stress total. Linear Static Analysis of a Stayed Steel Chimney 25/26

26 DIANA FEA BV Delftechpark 2628 XJ Delft 19a The Netherlands T +31 (0) F +31 (0) DIANA FEA BV Vlamoven 6826 TN Arnhem 34 Netherlands T The +31 (0) F +31 (0)