Graphic Statics Tutorial
GENERAL CONSIDERATIONS:
Here are some considerations to bear in mind when working on graphic statics problems:
- The structure must be statically determinate (Recall for a truss that the number of members plus three must equal twice the number of joints, i.e., M+3=2J)
- Begin with loads first, then transfer the members:
- The larger you draw the force polygon, the more accurate you can be on your results
- Accurately drawn, errors can be quite small (1-2%) compared to numerical techniques
- The loads must close on the load line of the force polygon. If not then there is an error.
- To minimize cumulative error, add loads together from a common point of origin rather than accumulating them one after the other.
- It is essential that you use consistent labeling convention as presented in class.
- It takes practice to get used to properly constructing the force polygon and determining the directional sense of forces, but it’s not that hard and once you understand it for one structure, you understand it for any.
- Once the force polygon is drawn, all forces just scale directly from the diagram.
- The longer a force line is, the higher is the force in a member. To optimize a truss, change the geometry to reduce the forces.
- Determine the directional sense of the forces by utilizing the nomenclature for identifying spaces between loads and members. About a joint, member names read in clockwise order…this determines the appropriate name for the member (e.g., 3F versus F3, etc.). Applied to the force polygon, a member name which moves away from a joint in question would be one in tension, one which moves toward the joint would be in compression.
- Watch the precision of your numbers. You can’t be more accurate than the assumptions on your load estimate itself!
EXAMPLES IN AUTOCAD
Here are two example trusses analyzed by the method of graphic statics using AutoCAD. With a very complex design, it may be easier to use AutoCAD to draft the design and then analyze the forces. The trick is that the form diagram will be drawn to scale, as will the force polygon...but they may be vastly different scales. To facilitate the construction of the force polygon, scale the form diagram up or down as required to something close to that of the force polygon...that is if a member of the tuss is say 10' long, and the largest force on the load line is 10K, then scaling up the form diagram by a factor of 1000 will put them in the same relative scale....all that matters is that you accurately transfer the angles of the form diagram to the force polygon, and that the forces on the load diagram are accurately drawn. Finding the final force is then a simple matter of measuring distances between points. The first example was the problem we covered at the end of the last class, the second is exercise 5 from the handouts.
Click on the links to download the individual AutoCAD files:
ON LINE DEMO
Check out this tres-cool demo from a professor at MIT...moving the node and load points will dynamically change the loading diagram. Neat!
TUTORIAL
Due to the copywritten nature of the tutorial materials, it has been moved to the electronic reserve system (ERes) of the Gutman Library web page. You will need to use the password provided in class to access this material (If you forget the password or have trouble accessing ERes, please email me. Note also that you MUST have JavaScript enabled for ERes to operate):