Introduction

Combine has the capability to convert common solution files with symmetric and antisymmetric loading by reversing the sign of deflections, forces, and stresses to model the response of the symmetric/antisymmetric side of the structure. In this example I will show you how to model antisymmetric loading case for a simple frame and then compare the results with the complete model.

Simple Frame

Modeling

The simple frame model is 10Lx5Wx7.5H platform with W8x10 beams and unsymmetrical plate girder columns (10 top width x 10 height x 5 bottom width x 0.125 thickness). The columns are modeled using unsymmetrical plate girders to illustrate the change in results due to the antisymmetric loading. The orientation of the unsymmetrical plate girders is such that the top flanges are facing away from the center of the structure and the frame is symmetrical about the global X and Y axes.

The load case is 4 lateral loads of 10 kips applied at the top of each column. This loading is antisymmetric about the global Y axis as the loading is directed towards the center of the frame on one side of the structure and away from the center of the structure on the other side.

Results

A code check using the AISC 13th edition was performed on the structure resulting in the following unity check for each member: As you can see, the unity checks are different for each side of the structure due to the antisymmetric loading and the unsymmetrical plate girder sections in the columns.

The deflected shape of the structure shows the double curvature of the beams due to the later load on the structure.

We can use these differences in the each side of the structure to illustrate how the Combine options can be used on a half frame structure to solve both sides of this frame structure.

Half Frame

Modeling

The half frame model was constructed from the simple frame model by deleting half of the structure. The half frame model comprises the right-hand side of the structure.

Antisymmetric boundary conditions for the beams at the interface were created:

Translation in the global Y and Z axes are fixed and rotation about the X axis is fixed.

Two load cases were created to simulate both sides of the simple frame structure and will be used to help verify our solution. Load condition 2 is 2 lateral loads of 10 kips at the top of each column in the global X direction and load condition 3 is in the global -X direction.

Results

Again, a code check using the AISC 13th edition was performed on the structure resulting in the following unity checks for each load condition:

We can also view the deflected shape of the structure for both load conditions:

As you can see, the results for load condition 2 match the right-hand side of the simple frame structure and the results for load condition 3 match the left-hand side of the structure. Of course we needed to create two load conditions to get the solution to both sides of the structure which depending on the size of the structure can be inefficient. Now we will use combine to flip the solution so that we don't have to solve 2 load conditions.

Combine

The combine input file used to generate the mirrored load conditions is quite simple. For this example we will be creating 2 output load conditions which will flip the displacements and stresses for the two load conditions that we created in the half frame model. To create the displacements for the opposite side of the structure I am mirroring the rotations/moments about the global X axis, and the deflections/forces for both the Y and Z axes (100011). Also, because this is an antisymmetric loading case, we will be changing the sign for all stresses.

Here is the combine input file:

CMBOPT 
LCOND 2A LIN 1.0 1.00 1.00 
COMP P 2 1.0 1000111 
LCOND 3A LIN 1.0 1.00 1.00 
COMP P 3 1.0 1000111 
END

A new common solution file is created (cmbcsf.*) which contains the modified displacements, forces, and stresses. We can now run a code check on the mirrored common solution file to see what results we now get.

Here are the AISC 13th edition unity checks for load conditions 2A and 3A:

And the deflected shape of the structure with vertical displacements at each node:

As you can see, the displacements and unity checks have been mirrored so that load condition 2a represents the results for the left-hand side of the structure and load condition 3a represents the results for the right-hand side of the structure. The actual model file has not been modified, although you could create a mirrored copy of the model file as input for the post-processing to view the mirrored results in the correct global coordinate system.

Conclusion

The symmetric/antisymmetric combine features can be a powerful tool to leverage the geometry of the structure to greatly enhance the efficiency of complex modeling problems. While this frame structure may not be complex when compared with other finite element meshes, this simple problem illustrates a workflow that can be extrapolated to more complex models.

I have attached all of the files used for this example as a sample for those who would like to analyze this problem themselves.

stage-communities-bentley2-com.telligenthosting.net/.../Antisymmetric-Loading.zip