Don't worry if you don't understand everything on these pages. Sometimes I am not sure that I completely understand all of these concepts. There are 5 parts in this section:

**Definitions**- basic definitions applicable to structure**Stress**- What are the stresses (forces) that are acting on your structure?**Columns and the Law of Squares**- the math of columns.**Bracing**- different types of braces and their application

- Most structures have vertical pieces designed to support weight (columns) and less than vertical pieces (braces) designed to resist forces acting on the columns and to add stability to the structure.
- A shorter column holds more weight that a longer column of equal size, shape and material.
- Adding horizontal braces to a column effectively "cuts" the column into shorter pieces that will hold more weight.
- Diagonal braces resist twisting in a structure.

These definitions are probably not technically correct from an engineers standpoint but they are working definitions for these tutorials.

**Structure**- This is what you are building to hold weight.

**Column**- A full height vertical piece of the structure that has the primary purpose of supporting weight. Since columns primary purpose is to hold weight it is important that the bottoms of the columns contact the ground and the tops of the columns contact the surfaces they are supporting.

**Brace**- A piece of the structure that is designed to resist pressure (or stress) on the structure. Braces typically run between columns and are less than vertical.

**Member**- A general term used to refer to a Column or a Brace.

**Critical Length**- The length where wood (or any material) no longer bends but crushes. As a wood column gets shorter and shorter it becomes harder and harder to make it bend by putting weight on the top of the column. At some point the wood will not bend no matter how much weight you put on it - it will simply crush.

**Buckling load**- amount of weight required to cause a structure to fail.

**Stress (Force)**- Stress is what your team managers feel when it is 2 weeks to tournament and your script isn't done, your props aren't complete and you haven't finished a structure.

Actually, stress is a force or pressure when one member of part of a member presses on, pulls on or pushes against another member or part of a member. It can also be the pressure that tends to compress or twist another member or part of a member.

Typically, columns are always in compression. The columns are put in compression as the pressure board and weights are added on top of the structure. Braces can either be in compression or tension depending on the structure design. Braces are used to resist compression in columns.

Shear is difficult to explain. The technical definition of shear is the internal stress in a beam that is a result of non-axial loading. (Yeah.....I am sure you got that). Imagine holding your hands together upright in a prayer position and then sliding one of them down. (Thanks to Ernie Change for the definition and the visual demonstration). This is shear. Shear can occur at different places in the structure depending on the design. Most teams that solved the challenge DIsigning Bridges had to deal with shear in the bridges they constructed.

Another force that acts on a structure is a rotational force (or twisting). Technically it is called torsion or torque. This rotational force is a result of forces being transferred from the vertical load (i.e. the weights being placed) to a slightly horizontal load. Many teams structures fail because they do not adequately control the tendency of the structure to twist or rotate.

Click the link on the right for a short video of a structure twisting to failure. We took this video during the Triplicity challenge. We modified our structure tester so we could test the smaller individual pieces of the three part structure. I was using a strip of paper wrapped around the columns to resist twisting. As you watch the video you will see a bend form in the paper which affected its ability to resist the twisting forces and the structure twists down. Notice that the columns did not crush. This structure failed because it was not braced sufficiently to stop the rotational forces acting on it. | VIDEO (1.4MB MPG file) |

The types of stresses or forces that act on your structure (be they compression, tension, shear) fall into two general categories. "Static" forces and "dynamic or live" forces. Static forces are forces that do not move. Once a weight is placed on a structure it is a "static" force or load because it is not moving. If you were to climb on top of the pressure board and do a dance this would be a live load because you are moving. The initial placement of a weight on a structure places a dynamic load on the structure because it is in motion.

When designing a structure, the team should concentrate on carrying the static loads placed on the structure while keeping in mind that they must also deal with a certain amount of dynamic or live load during weight placement.

Most structure challenges involve testing a static load on the structure by placing weights. The only dynamic load placed on the structure is the dynamic load created by weight placement.

Years ago my brother's team competed in a couple of structure challenges that required placing dynamic loads on the structure by: 1) applying a twist to the structure as certain increments of weight placement were reached and 2) by rolling pool balls down ramps into the sides of the structure at certain weight placement increments. I have never competed in this type challenge so have no experience in dealing with these types of forces.

There is an inverse square relationship between the length of a column and the amount of weight that it can carry. If you cut a column in half, one of the shorter pieces will carry four times as much weight as the original column. This is calculated as follows: Take the ½ (you cut the column in half) and invert it to get 2. Then square the 2 (2 x 2) to get 4. If you take a column and cut it into thirds, one of the shorter pieces will carry nine times as much weight. (Invert 1/3 to get 3 and then square the 3 to get 9). A column that is one forth (1/4) the length of another column will carries 16 times as much weight. You can only carry this so far. You can’t make a material stronger than it is. These examples assume that the only thing that changes is the length of the columns. If the column material changes in any way then the examples do not work.

An easier way to look at this may be to think of it this way. If I cut a column into 2 equal sections, the shorter section will hold four times as much weight (2 squared or 2 x 2). If I cut a column into 3 equal sections, the short section will hold nine times as much weight (3 squared or 3x3).

Here is a simple experiment to demonstrate this.

- Take a piece of 1/8" x 1/8" x 36" long balsa wood
**(do not use larger pieces and use only balsa wood)**. - Lay the stick of balsa on a gram scale. The scale will register some weight for the wood. With the balsa stick still on the scale, tare the scale (zero it). This removes the weight of the stick from the scale reading.
- Holding the balsa stick perpendicular to the scale place a finger on the top of the stick and press down until the wood starts to bend. Record the reading on the scale. The number will fluctuate so just pick a number that is in the middle of the readings.
- Record this reading - you have just calculated the "buckling" load (weight) of this particular 36" stick of wood.
- Cut the 36" stick into two 18" pieces.
- Take one of the 18" pieces and repeat steps 2,3 and 4. You have now calculated the buckling load of this 18" piece of the original 36" column. The buckling load of the 18" piece should be very close to four times the buckling load of the 36" piece.
- Take one of the 18" pieces and cut it to 12" in length. The length is now 1/3 the length of the original 36" piece. Try to predict what the buckling weight of the 12" piece will be by multiplying the buckling weight of the 36" by 9. (1/3 inverted = 3 * 3 squared = 9).
- Repeat steps 2,3 and 4 with the 12" piece and compare to your estimate.
- You can use these experiments to learn more about the properties of wood. Make up a chart and record the weight of each stick of balsa before you cut it and then the weight of each piece as you cut it into 18" and 12" pieces. How close to 1/2 the weight of the 36" stick are the two 18" pieces? How close to 1/3 the weight of the 36" stick are the three 12" pieces?

(Note: 1/8" x 1/8" balsa wood is used in this demonstration because most scales should be able to record all of the readings. Conducting the experiment with larger pieces or heavier woods could be dangerous because the amount of force required to make the pieces bend could be excessive resulting in breaking the wood and having a broken sharp point stick into a hand.)

You may wonder what good this information does, because the height of the structure has to meet the specifications of the challenge. It does not do any good to know that if you build a structure that is one half the required height that it will hold four times as much weight.

This information **is** useful because when designing and building a structure, bracing a column makes it act like two shorter columns. So, if you properly brace a 9” column in the middle you now have effectively created two 4.5" columns which can support four times as much weight.

There are two basic types of braces

- Horizontal Braces - Braces that run horizontal between columns
- Diagonal Bracing - Braces that run at an angle between columns

It is possibly an over simplification but horizontal bracing is generally used to resist compression forces in the column and diagonal bracing is generally used to add stability to the structure by resisting twisting.

The goal of designing a structure is to find the optimum mix of

- Column material, size and shape
- Brace material, size, shape and spacing

Ideally, columns should be braced at their critical length. The critical length of a column is the length at which the column will no longer buckle (or bend) no matter how much weight is placed on it. A column at its critical length will fail by crushing. One way to determine if you have braced a structure correctly is to watch the structure as it is tested. If you see the columns buckling (or bending) right before the structure fails then you have not properly braced the structure for the particular columns you have chosen. Well built structures should not "explode" but should simply crush.

There is one other thing you should keep in mind about bracing a structure. Imagine that a 6" column section will support 25 pounds. The Law of squares tells us that a 3" section of the same column will support 100 pounds (invert 1/2 to get 2 - square 2 to get 4 and multiply 4 x 25=100). How much weight will the column support if you stack the 3" piece on top of the 6" piece thus creating a 9" column.

If you said it will support 125 pounds then you guessed wrong. A column is only as strong as its weakest section so this column would only support 25 pounds since the 6" section of column would fail at 25 pounds.