Thin Arc Clamped in Plane Bending

This test lets you validate the combined case. The aim is to compare a static case (where several forces are applied) and a combination of static cases (the set of forces of each static case is therefore equivalent to the one of the first configuration).

Reference:

• AFNOR technique, SFM Paris, Guide de validation des progiciels de calcul de structures, SSLL 06/89, p30, 1990.

• Results of the first configuration (all forces applied are located in one static case)

Specifications

Geometry Specifications

r = 3 m = 90°
Hollow circular section:  rext = 0.01 m  rint = 0.008 m

Analysis Specifications

Young Modulus (material): E = 200 GPa
Mesh Specifications: Linear beam elements Mesh size: 50 mm
Restraints: Clamp on A
Loads: At point B: Distributed force defined in the first static case: F1x = 10 N Distributed force defined in the second static case: F2y = 5 N Moment defined on the third static case: Mz = 8 N.m For the combined case, the three static cases have the same coefficient: 1

Results

Analytical Solution

• At point B:

  
   

  Sensors	Values
  Translation displacements uB (mm)	379.1
  Translation displacements vB (mm)	241.7
  Rotation displacements zB (rad)	0.1654

  Computed Results

• Case computed with only one static case, gathering all applied forces:

  Sensors	Values
  uB (mm)	378.97885
  vB (mm)	241.73313
  zB (rad)	0.165

• Case computed with the combined case:

To Perform the Test:

The thin_arc_combined.CATAnalysis document presents a complete analysis of this case.

The thin_arc_total.CATAnalysis document presents a complete analysis of this case.

To compute the case, proceed as follow:

1. Open one of the CATAnalysis document.

2. Compute the case in the Generative Structural Analysis workbench.

3. Create local sensors (Displacement vectors and Rotation vector).