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This page contains frequently asked questions related to *[shell elements|kb:shell]*. {on-this-page} h1. General h2. What are the practical limits on the maximum thickness of shell elements relative to the shell dimension? When using the thick plate formulation, both the bending and the shear deformations are accurately (within the assumptions of the formulation) accounted for. I have attached verification example 2-012 in which 0.1 in x 0.1 in shell elements with 0.5 in thickness are used and the solution obtained from SAP2000 exactly matches independent solution. As a general rule, one would expect that thick-plate effects would become important when the span to thickness ratio is about 20:1 to 10:1, and the adequacy of the formulation would be good for a ratio of down to about 5:1 or 4:1. Note that this is the span of deformation we are talking about here. As the elements are meshed, the elements may actually be thicker than the plan dimension, and that is OK. The important thing to consider is the ration of the span of deformation to thickness. However, please note that all shell elements are approximate and a special case of three-dimensional elasticity. Depending on your specific needs, shell elements may be appropriate, but for some other types of analyses (such as assessment of local behavior) you may obtain more accurate response by using solid elements. You can always set up simple test problems to check the difference between different modeling approaches. h2. Could you explain the difference between thick shell and thin shell elements? The two thickness formulations for area section, available in SAP2000, determine whether or not transverse shearing deformations are included in the plate-bending behavior of a plate or shell element: * The thick-plate (Mindlin/Reissner) formulation includes the effects of transverse shear deformation * The thin-plate (Kirchhoff) formulation neglects transverse shearing deformation Shearing deformations tend to be important when the thickness is greater than about one-tenth to one-fifth of the span. They can also be quite significant in the vicinity of bending-stress concentrations, such as near sudden changes in thickness or support conditions, and near holes or re-entrant corners. Even for thin-plate bending problems where shearing deformations are truly negligible, the thick-plate formulation tends to be more accurate, although somewhat stiffer, than the thin-plate formulation. However, the accuracy of the thick-plate formulation is more sensitive to large aspect ratios and mesh distortion than is the thin-plate formulation. It is generally recommended that you use the thick-plate formulation unless you are using a distorted mesh and you know that shearing deformations will be small, or unless you are trying to match a theoretical thin-plate solution. The thickness formulation has no effect upon membrane behavior, only upon plate-bending behavior. As a general rule, the contribution of shear deformations becomes important when the span to thickness ratio is about 20:1 to 10:1, and the adequacy of the formulation would be good for a ratio of down to about 5:1 or 4:1. Note that this is the span of deformation. As the elements are meshed, the elements may actually be thicker than the plan dimension, and that is OK. The important thing to consider is the ration of the span of deformation to thickness. h2. I have area object with more than 4 vertices and I have not specified any meshing. However the analysis model shows mesh. How was this mesh created? It no auto-meshing has been assigned to an area object that has been drawn using more than 4 nodes, the program will use general meshing tool to mesh such areas. h2. What is the difference between "Uniform (Shell)" and "Uniform to Frame (Shell)" loads {verify} When using the "Uniform (Shell)" option, the uniform loads are applied directly to the shell elements and are transferred to the structure via the joints of the shell element. When using the "Uniform to Frames (Shell)" option, the uniform loads are applied directly to the frame elements defined along the edges of the shell under consideration. You can define one way or two way load distribution. Please note that you can review how the "Uniform" to Frames loads are distributed to the frame elements in your model by using "Display > Show Load Assigns > Area" menu command. h2. How can I model simply supported slab using shell elements? Please see the [Modeling simply supported shells|tutorials:Modeling simply supported shells] tutorial. h2. How can I post-process area output (the area is used to model bridge diaphragm) to get meaningful design forces? You could obtain diaphragm design forces from joint forces of the shells used to model the diaphragms. These shell joint forces would need to be transformed to the location of interest. Please note that the program uses this procedure to obtain section cut forces; using section cuts to obtain the design forces would, therefore, be another alternative. h2. How are stresses for the shell elements calculated? Can I compare the calculated stresses directly to the allowable stress of shell material? Yes, the shell stresses obtained from SAP2000 can be directly compared to the allowable stress of the material. You can display the shell stresses by right-button click on the shell elements when the stresses are displayed or by reviewing the stresses in a tabular format via "Display > Show Tables > ANALYSIS RESULTS > Element Output > Area Output > Table: Element Stresses - Area Shells". The stresses are calculated as a product of stress-strain constitutive matrix and strain vector which is obtained from joint displacements. The procedure is not based on a simple formula, but rather on several techniques described in the following references cited in the [CSI Analysis Reference Manual|kb:manual]: * A. Ibrahimbegovic and E. L. Wilson: "A Unified Formulation for Triangular and Quadrilateral Flat Shell Finite Elements with Six Nodal Degrees of Freedom," Communications in Applied Numerical Methods, Vol. 7, pp. 1--9, 1991 * R. L. Taylor and J. C. Simo: "Bending and Membrane Elements for Analysis of Thick and Thin Shells," Proceedings of the NUMEETA 1985 Conference, Swansea, Wales, 1985 The above references are available in the open literature. A comprehensive description can also be found in Prof. E. L. Wilson’s book available from CSI at [http://orders.csiberkeley.com/ProductDetails.asp?ProductCode=ELWDOC-3D]. See page [Shell element formulation DRAFT] for additional details. h2. How does the program apply stiffness modifiers for shell elements? When [stiffness modifiers|kb:stiffness modifier] are applied, the corresponding terms in the [stiffness matrix] of the shell element will get modified. You could also look at this as reducing (or increasing) the [Young's|kb:Young's modulus] or shear moduli of the material for the given directions. The stiffness matrix for the entire structure is then assembled and the equilibrium equations are solved to find the unknown displacements. The displacements are then used to calculate the internal forces and stresses. h1. Layered Shell Element h2. Can you explain the coupling of membrane and plate behavior for nonsymmetrical layering? *Extended Question:* The CSI Analysis Reference Manual states: "Unless the layering is fully symmetrical in the thickness direction, membrane and plate behavior will be coupled". If the element is defined such that planes remain plane in the thickness direction, then even for a symmetric definition of membrane layers, the layers would contribute to the out of plane bending stiffness and see stresses when there is rotations in the plate element. Am I missing something here? *Answer:* You are correct that the membrane layers contribute to bending. The statement here regards whether or not transverse loading generates membrane forces/deformation, and likewise whether or not in-plane loading generates bending. The coupling effect could be demonstrated by applying uniform temperature load to the shell element. For symmetrical layering, the temperature load will cause only in plane deformations. For nonsymmetrical layering, out-of-plane deformations will be generated. This is similar to bi-metal strip, illustrated in this Wikipedia article: [http://en.wikipedia.org/wiki/Bi-metallic_strip] h2. Could you please explain how the material orientation is related to the element orientation? *Extended Question:* It is not clear how the material orientation and the S11, S22, and S12 orientation are defined for the elements. Are the 1, 2, and 3 directions the same as the local axes for the shell element, that can be seen as red, white, and blue colors on the screen? In the "Nonlinear Shear Wall" movie, for longitudinal bar elements, a material angle of 90 degrees is used and then the nonlinearity is defined in the S11 direction, which is the horizontal direction for the element. This suggests that internally, the program is rotating the local axis for that layer by 90 degrees relative to the element local axis. Is that the right interpretation? Would it have the same effect to have the material at zero degrees, but define the nonlinearity in the S22 direction? On the other hand, if the angle is just referring to material orientation, should not the nonlinearity be defined in the S22 direction which is the nonlinear direction? *Answer:* As shown in our the figures below (the first one was taken from our manual, while the second one was taken from the video), the material orientation in a given layer is defined relative to the material local coordinate system by specifying a material angle. Using material angle of 90 degrees and specifying the nonlinearity in S11 direction has the same effect as using material angle of 0 degrees and specifying the nonlinearity in S22 direction. For uniaxial materials like rebar, whose behavior is only defined in the material 1 direction, you must use the former specification. For fiber-wrapped composites, you may want to specify material behavior at other some angle, say 45 degrees, to the element local axes. Note that loading and the output forces/stresses will always be in the element axes, even though you may specify material properties in the material coordinates. !Shell_section_material_angle.png! !Shell_section_layer_definition.png! {hidden-content} Related incidents: * [27953: Explanation of shell forces and stresses convention|$4161679] {hidden-content} {hidden-content} Related emails: * {email:date=1/27/2011|from=am|to=qn|subject=Good explanation of thin, thick and layered shell element formulation|comment=|id=6881428} {hidden-content}page is devoted to frequently asked questions (FAQ) related to shells. |
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Formulation
What is the difference between thick and thin shells?
Answer: For response, please see the Thin vs. Thick shells article.
How are shell stresses calculated, and can these stresses be compared to the allowable stress of shell material?
Answer: Yes, the shell stresses obtained using SAP2000 may be compared directly to the allowable stress of the shell material, as this is the essence of Allowable Stress Design (ASD). Shell stresses may be reviewed in tabular format through Display > Show Tables > Analysis Results > Element Output > Area Output > Table: Element Stresses - Area Shells.
Stresses are calculated as the product of the stress-strain constitutive matrix and the strain vector obtained from joint displacements. The techniques and formulations involved are adopted from the following publications:
- Ibrahimbegovic, A., Wilson, E. (1991). A Unified Formulation for Triangular and Quadrilateral Flat Shell Finite Elements with Six Nodal Degrees of Freedom . Communications in Applied Numerical Methods, 7(1), 1-9.
- Taylor, R., Simo, J. (1985). Bending and Membrane Elements for Analysis of Thick and Thin Shells. Proceedings of the NUMEETA 1985 Conference, Swansea, Wales.
A comprehensive description can also be found in Dr. Wilson’s textbook:
- Wilson, E. L. (2004). Static and Dynamic Analysis of Structures (4th ed.). Berkeley, CA: Computers and Structures, Inc.
How does the software apply stiffness modifiers to shell objects?
Answer: When stiffness modifiers are applied, the corresponding terms of the shell stiffness matrix are modified. This is comparable to modifying, for a given direction, the Young's Modulus or the shear moduli of the material. The structural stiffness matrix is then assembled, and global equilibrium equations are solved to generate deflections. These displacements and rotations then relate to strain fields which produce internal member forces and stresses.
Modeling
How is a simply supported slab modeled using shell objects?
Answer: For response, please see the Modeling simply supported shells tutorial.
What are the practical limits on the maximum thickness of shell objects relative to shell dimension?
Answer: During shell formulation, the ratio of plan dimension to thickness concerns the deformation span between inflection points, and not the actual plan dimension of the shell. Shell thickness may even be greater than the actual plan dimensions so long as the projection of curvature under plate-bending behavior meets the deformation-span to thickness ratios which follow:
Thick-plate effects become significant when the deformation-span to thickness ratio is between approximately 20:1 and 10:1. The formulation itself is adequate for ratio down to 5:1 or 4:1.
Verification example 2-012 is attached. This example models a 0.1in x 0.1in shell object with 0.5in thickness. The solution obtained using SAP2000 matches that from the independent solution, validating the formulation and demonstrating the accuracy of shell behavior.
Please note that shell formulation is an approximate and special case of three-dimensional elasticity. Shell objects may be appropriate for some applications, while solid objects may be more suitable for others, such as with the assessment of localized behavior. Simple test problems may always be run to check the differences between modeling approaches.
How has my area object been meshed before any meshing is specified?
Extended Question: I have an area object with more than four vertices for which meshing is not specified. However, this object is meshed in the analysis model. How was this mesh created?
Answer: CSI Software uses a general meshing tool to mesh objects with more than four nodes when no auto-meshing has been assigned.
How are masonry shear walls modeled?
Answer: Masonry shear walls are modeled by defining the appropriate material properties or stiffness modifiers. A good resource for masonry properties is the NCMA TEK 14-1A publication.
Why can I not draw an area object between four points?
Answer: If the four points do not lie in a plane, an area object cannot be drawn because the profile is warped. Instead of using four-sided shells, these areas may be drawn using triangles.
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How are shells merged with the sides of frame objects?
Answer: Two modeling options are described as follows:
- Draw special joints along the boundary of the frames, constrain them to the joints of the frame objects, then connect the shells to these special joints.
- Use insertion points to offset the frames from the shells.
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Loading and output
What is the difference between the load assignments Uniform (Shell) and Uniform to Frame (Shell)?
Answer: The difference between these two options is as follows:
- Uniform (Shell) – uniform loading is applied directly to a shell object, then loading transfers to the structure through shell joints which coincide with structural members.
- Uniform to Frame (Shell) – uniform loading is applied directly to the frame objects specified along the edges of a shell. Load distribution may be one way or two way. Distribution of loading may be reviewed through Display > Show Load Assigns > Area.
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VERIFY |
How can I post-process the bridge-diaphragm area-object output to obtain meaningful design forces?
Answer: Diaphragm design forces may be obtained from the joint forces within the shell objects used to model the bridge diaphragms. Through post-processing, joint forces may be transformed into bridge response at the location of interest. Since this basically summarizes the process for generating section-cut forces, it may be more productive to obtain design forces through section cuts.
Layered shell
For unsymmetrical layering, how are membrane and plate behaviors coupled?
Extended Question: The CSI Analysis Reference Manual states that "unless the layering is fully symmetrical in the thickness direction, membrane and plate behavior will be coupled." If the element is defined such that planes remain plane in the thickness direction, then even for a symmetric definition of membrane layers, would not the layers contribute to the out-of-plane bending stiffness and demonstrate stresses with plate behavior?
Answer: This is correct that the membrane layers contribute to bending stiffness. The statement here concerns whether or not transverse loading generates membrane forces and deformation, and likewise, whether or not in-plane loading generates bending behavior. As stated, in-plane deflection will not produce plate bending when a layered shell is symmetric through its thickness.
This coupling effect could be demonstrated by applying a uniform temperature load to the shell object. For symmetrical layering, the temperature load will cause only in-plane deformations. For nonsymmetrical layering, out-of-plane deformations will be generated. As illustrated in the following Wikipedia article, this is similar to bimetallic strip behavior.
How does material orientation relate to object orientation?
Extended Question: How is material orientation and S11, S22, and S12 orientation defined for shell objects? Are the 1, 2, and 3 directions the same as the local axes of the shell? A material angle of 90 degrees is used for longitudinal bar elements in the Nonlinear Shear Wall Watch & Learn video, then nonlinearity is defined in the S11 direction, which is the horizontal direction for the element. Is this correct that the software rotates the local axis, for that layer, by 90 degrees relative to the element local axis? Would it have the same effect to have the material at zero degrees, but define the nonlinearity in the S22 direction? On the other hand, if the angle simply refers to material orientation, should not the nonlinearity be defined in the S22 direction, which is the nonlinear direction?
Answer: As shown in Figure 1, the material orientation of a given layer is defined relative to the local coordinate system. Material angle is measured counterclockwise from local member orientation. Using a 90° material angle with nonlinearity along S11 has the same effect as using a 0° material angle with nonlinearity along S22.
For such uniaxial materials as rebar, where behavior is only defined in the material 1 direction, a 90° material angle with nonlinearity along S11 must be specified. For fiber-wrapped composites, it may be best to specify material behavior along another angle, perhaps at 45° from the member local axes.
Please note that while material properties are specified in material coordinates, loading and output forces and stresses will always be input and reported in terms of member local axes.
Figure 1 - Shell-section material angle
Figure 2 - Shell-section layer definition
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