## 48 Schwedler Domes

An interesting structural form, similar to the ribbed and hooped domes described in Section 4.7 is the Schwedler Dome. In this case, the dome is composed of two force members arranged as the ribs and hoops along with a single diagonal in each of the resulting panels, as shown in Fig. 4.12. Although the structural form looks complex, the structure is determinate and exhibits some interesting characteristics.

The application of the equations of equilibrium available for three dimensional, pinned structures will verify that the Schwedler Dome is a determinate structure. In addition, the application of three special theorems will allow for a significant reduction in the amount of computational effort required for the analysis. These theorems may be stated as:

1. If all members meeting at a joint with the exception of one, lie in a plane, the component normal to the plane of the force in the bar is equal to the component normal to the plane of any load applied to the joint,

2. If all the members framing into a joint, with the exception of one, are in the same plane and there are no external forces at the joint, the force in the member out of the plane is zero, and

3. If all but two members meeting at a joint have zero force, the two remaining members are not collinear, and there is no externally applied force, the two members have zero force.

A one panel high, square base Schwedler Dome is shown in Fig. 4.13. The base is supported with vertical reactions at all four corners and in the plane of the base as shown. The structure will be analyzed for a vertical load applied at A.

At joint B, the members BA, BE, and BF lie in a plane, but BC does not. Since there is no load applied to joint B, the application of Theorem 2 indicates that member BC would have zero force. Proceeding around the top of the structure to joints C and D respectively will show that the force in member CD (at C), and DA (at D) are both zero.

Now Theorem 3 may be applied at joints C and D since in both cases, there are only two members remaining at each joint and there is no external load. This results in the force in members CF, CG, DG, and Dh being zero. The forces in the remaining members may be determined by the application of the method of joints.

Note that the impact of the single concentrated force applied at joint A is restricted to a few select members. If loads are applied to the other joints in the top plane, the structure could easily be analyzed for each force independently with the results superimposed. Regardless of the number of base sides in the dome or the number of panels of height, the three theorems will apply and yield a significantly reduced number of members actually carrying load. Thus, the effort required to fully analyze the Schwedler Dome is also reduced.

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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