Perform a bending analysis of a laminate tube or beam.
Select the Bending tab from the Tube/Beam Analysis window to perform the bending analysis. All algorithms used in this form are taken from Roark's Formulas for Stress and Strain (Ref. 11.1, pp. 100-104), and the limitations and assumptions listed therein apply here. Once the Laminate and Tube Geometry have been defined, complete the following seven steps in the Bending tab (see image below):
- Boundary Conditions and Loading - The analysis boundary conditions are selected from a drop-down menu. Four distinct boundary conditions are available (Simple-Simple, Free-Fixed, Fixed-Fixed, Simple-Fixed), all of which are subjected to three distinct loading conditions (Point, Uniform Distributed, and Triangular Distributed). When you select an option, the graphic for that option will be displayed in the window above the drop-down. The dimensions and loading required to define the analysis are depicted in the drawing.
- Stiffness Calculation Method - Of particular interest on this form are the "Stiffness Calculation Method" options. The two options apply to closed cross-sections only (rectangle, circle, and ellipse).
- The "Ply-By-Ply Tube" option forces all bending analyses to be calculated on a ply-by-ply basis through the thickness of the laminate. That is, the stiffness contribution for each ply is modeled separately.
- The "Laminate Tube" option uses the structural (or smeared) properties of the entire laminate in bending calculations. Whenever you analyze a closed section beam using the "Laminate Tube" option, turn the "Coupling" option under the Laminate tab to zero. This is critical to generating accurate results.
- L - Length - Specify the overall length of the beam.
- W - Load - Specify the point load applied to the beam. Required input for point load type only.
- x - Location - Specify the location on the beam at which the point load "W" is applied. Required input for point load type only.
- w - Load/Unit Length - Specify the distributed load on the beam. For triangular loads, the load per unit length input "w" is the value of the distributed load at beam location "b" divided by the entire beam length.
- Calculate - Once the input has been completed, click Calculate to compute the bending solution. The output box on the right side of the window shows the results of the defined analysis. Depending upon the Boundary Conditions and Loading Type selected, the output will vary:
- EI: This is the overall cross sectional stiffness of the beam.
- Reaction: Vertical forces or loads reacting to the vertical input load. Positive (+) is an upward reaction.
- Rotation: For simply supported or free end conditions, the beam will rotate at end points ("a" - left side of beam and "b" - right side of beam). Positive (+) rotation is counter-clockwise.
- Moment: Reaction moments at "a" and "b". Positive (+) moment is counter-clockwise.
- MomentMax: Maximum moment induced in the cross-section. The location of this moment is also displayed.
- (+)/(-) MomentMax: For Fixed-Fixed or Simple-Fixed boundary conditions, the beam will exhibit a maximum (+) and (-) set of moments. This is the maximum moment induced in the cross-section.
- StressMax: Maximum stress induced by the MomentMax in the outermost fiber of the cross-section.
- (+)/(-) StressMax: For Fixed-Fixed or Simple-Fixed boundary conditions, the beam will exhibit a maximum (+) and (-) set of stresses. This is the maximum stress induced by the (+)/(-) MomentMax in the outermost fiber of the cross-section.
- StressOps: Maximum stress on the "opposite" side of the beam from the StressMax. This is important in a composite beam because even though the stress magnitude opposite the maximum stress may be less, beam failure may initiate here due to the lower allowable in tension or compression.
- (+) or (-) StressOps: See explanation under (+)/(-) StressMax and StressOps above.
- DeflectMax: Maximum vertical deflection of the beam under the applied loads. The location of this maximum deflection is displayed.
- Deflection: Vertical deflection of the beam under the applied load at the point of load application. This is not necessarily the maximum deflection. The location of the deflection is displayed.
Resulting beam stresses can now be compared to the allowable stresses for the laminate calculated under First Ply Failure Survey or Progressive Failure options under the "Laminate" module.