Eriksson Wall offers the use of a beam-spring model to perform the analysis of insulated wall panels. The model is based on Dr. Maguire’s research presented in “Generalized beam-spring model for predicting elastic behavior of partially composite concrete sandwich wall panels.’ Note that this paper does not propose a new modeling method, but instead verifies an existing analysis procedure for use with insulated wall panels. The current analysis feature is only valid for uncracked panels. Any paneling cracking will have to be checked by the user.

This procedure uses data obtained from the double shear test, or 5-layer shear test, to model the composite connectors. The double shear test results in a bi-linear curve relating the shear deformation in the connector to the force generated in the connector. The connector producer will provide the bi-linear curve data, strength reduction factors to be applied to the data, and allowable limit states for the connectors.

Finite Element Model

The finite element method is used for the beam spring model. In this model, a beam element is used for each wythe of the member. These elements at the centroid of their corresponding wythe and are connected to each other at each of the horizontal shear connectors. The connectors are assumed to be near infinitely stiff axially (we use a value of 1E8 lb/in) as being stiff forces the wythe to maintain its geometry. The research also has found that the results are not sensitive to changes in axial stiffness. The shear stiffness of the springs comes from the user defined double shear test data.

...

The shear connectors are modeled as a shear spring located at the midway point between the two wythes. The fact that the shear spring is located a distance ‘L’ from each wythe means that any force in the shear spring will also generate a moment in the corresponding wythes. This moment will be each to the force in the spring times L. These springs also have a non-linear spring stiffness. The stiffness of the spring will follow the curve provided by the double shear test. Because of this, the analysis can be iterative if the springs are yielding. When yield happens, the force in the spring yielding is typically redistributed to the neighboring springs as the stiffness typically decreases.

...

The same connector is used to model end blocks in the model. Solid end regions are modeled using near infinitely stiff connectors. By including end blocks, all shear deformation, henceforth referred to as slip, will be restricted and the panel will behave compositely. By including an end block in the model, it is the engineer’s responsibility to ensure that it is properly designed to carry the required forces.

All supports for the beam spring model are placed on the interior wythe. Because of this, all loadings on the exterior wythe must transfer through the connectors to the interior wythe. This means that, for a typical wall panel, the exterior panel’s self-weight, the wind load, and external soil will all be transferred through the shear connectors. All loading is now also placed on the corresponding wythe. The corresponding wythe is determined based on the load’s eccentricity. The final loads will be displayed in the analysis report to show where the loads are applied.

...

Camber

The camber of the wall panel is computed the same way as it is for a traditional wall panel. But instead, the prestressing forces are applied to their individual wythe. These forces transfer through the system and have the capability to bow your panel. For example, if you only prestress a single wythe, the slip caused by axial shortening will cause flexure in your panel. Note that now asymmetric prestressing can cause more than just camber, any slip generated in the panel will cause the shear springs to generate force, and thus internal forces in the wythes. These internal forces are not accounted for at this time in the analysis. For more information on how camber is computed, see the camber page.

Thermal Bow

Thermal bow for a traditional wall panel is accounted for by applying a temperature gradient which varies linearly through the thickness of the panel. In the beam spring model, it assumes that all temperature change happens in the insulation. Therefore, the temperature gradient is now applied as an axial temperature gradient. The total temperature gradient will be split into half, with each half being applied to each wythe. For example, if the exterior wythe is 40 degrees hotter than the interior wythe, the exterior wythe will have a +20 degree gradient and the interior wythe will have a -20 degree gradient. The change in axial length will cause slip in the connectors which will, in turn, cause thermal bow.

...

Expected Outputs

Effective Slip

The slip summary provides a summary of a slip the panel is seeing. Having 0 slip means your panel is behaving compositely. Note that restraining 100% of your slip is not possible and some will always be present, but if one desires more composite behavior in their panel, one should look to restrain the slip in the locations of maximum slip.

Axial Loads

The shear connectors work by transferring force between each wythe. Lateral loads, which previously only produced moment and shear, will not product moment, shear, and axial loads on the wythes. This axial load comes from the shear transfer in the connectors. In general, this axial load will put one of your wythes in tension and the other in compression. Note that depending on the amount of slip being restrained and the stiffness of the connector, this may be a non-negligible amount of force. This force means tension will have to be designed for as a strength check in one of the wythe.