# Objective

The experimental objective of this lab is to design and construct a boom following the specifications provided. The boom will be entered in a competition against other booms in the section. The competition will be judged by a ratio that uses boom weight and length, weight held, and anchor time. The highest ratio wins.

# Overview

A boom is used to lift and move heavy objects, often objects that are much heavier than the boom itself. Distributing the weight of the object, or the load, being lifted over the length of the boom is the main problem in boom design. The design must consider the maximum load the boom will be required to lift, how high the load will be lifted, and whether the boom will be moved or remain stationary while loaded.

## Examples of Booms

Certain types of bridges use booms. A cantilever bridge uses two booms extending from a common base. One type of cantilever bridge is a cable-stayed bridge (Figure 1).

Figure 1: A Cable-Stayed (Cantilever) Bridge

The Ed Koch Queensboro Bridge is a double cantilever bridge (Figure 2). It has two bases with two booms extending from each base and the cantilevers placed end to end.

Figure 2: Ed Kock Queensboro Bridge (Double Cantilever)

The Grand Bridge over Newtown Creek is a swing bridge, also known as a rotating bridge (Figure 3). This bridge has two booms mounted on a base that rotates.

Figure 3: Grand Bridge (Swing Bridge)

Figure 4 shows a bascule bridge, more commonly known as a drawbridge, where it is clear that the bridge uses a big, very flat boom.

Figure 4: Bascule Bridge

Not all bridges are booms. Suspension bridges use a deck that is supported by steel cables, not booms. Examples of suspension bridges are the Brooklyn Bridge, Manhattan Bridge, Verrazano-Narrows Bridge, and the George Washington Bridge.

Cranes are the most common example of booms. The crane pictured in Figure 5 is a tower crane. These cranes are a fixture on construction sites around the world. A tower crane can lift a 40,000-pound load. It is attached to the ground by anchor bolts driven through a 400,000-pound concrete pad poured a few weeks before the crane is erected (Howstuffworks.com, 2003).

Figure 5: A Tower Crane

## Stress and Strain

The design of a boom must consider the properties of the materials used to build the boom. The mechanical properties and deformation of solids are explained by stress and strain. When an external force is applied to a material, it changes shape (e.g. changes length and cross-section perpendicular to the length). Understanding how deformation will affect materials is a critical consideration in boom design.

According to Serway and Beichner in “Physics for Scientists and Engineers,” stress is the external force acting on an object per unit cross sectional area. Strain is the measure of deformation resulting from an applied stress (Figure 6).

Figure 6: Material Under Tension

The expression (1) for tensile stress shows the relationship between an applied force and the cross-sectional area.

(1)

In (1), σ is the stress, F is the applied force, and A is the cross-sectional area of the object perpendicular to the force. The resulting strain (2) is calculated by dividing the change in length of the object by the original length.

(2)

In (2), ΔL is the change in length and L0 is the object's original length.

There are three basic types of stresses; tensile (pulling or stretching), compressive (squeezing or squashing), and shear (bending or cleaving). If a rod of material is put under tensile stress, its length increases slightly in the direction of the applied force and its cross-section perpendicular to the force decreases. If the rod is placed under compressive stress, its length in the direction of the force will decrease and its cross-section perpendicular to the force will increase. If the rod is place under shear stress, it will bend in the direction of the applied force and its length and cross-section will be distorted (Figure 7).

Figure 7: Rods of Material Under Stress

Strain is proportional to stress for small values of strain. The proportionality constant depends on the material being deformed and on the type of deformation. The proportionality constant is called the elastic modulus, or Young’s modulus. The moduli for different materials vary considerably and the various moduli for a particular material may also vary significantly. Concrete, for example, is very strong in compression, but less so in tension, and wood breaks quite easily when bent because its natural grain is anisotropic (properties depend on the direction of the material).

## Stress-Strain Curve

A stress-strain curve graphically shows the relationship between the stress and strain of a material under load (Figure 8). In the elastic region, the material will regain its original shape once the stress or load is removed. In the plastic region, the material loses its elasticity and is permanently deformed.

Figure 8: Stress-Strain Curve of a Material Under Tension

The elastic limit for a material is the maximum strain it can sustain before it becomes permanently deformed (i.e. if the stress is decreased, the object no longer returns to its original size and shape). If the stress is greater than the elastic limit, the material will plastically deform and for sufficiently large stress ultimately fail. The ultimate tensile strength is the maximum stress a material can undergo. The fracture stress is the point at which the material breaks under tension. Fracture stress is lower than the ultimate tensile strength because as strain increases, the material becomes thinner and thinner. As this necking down process continues, the load that can be supported decreases and the material breaks.

There are many factors to consider in any design project. When designing and constructing the boom for this competition, remember to consider the materials being used and what might cause those materials to fail under a load.

# Competition Rules

The competition rules must be followed at all times during the competition. Violation of any of these rules will result in the disqualification of your team.

• Your boom must extend at least 1.5 meters horizontally from the front edge of the anchorage.
• You have 2 minutes to anchor your boom.
• Your boom may not touch anything but the anchorage.
• The basic unweighted ratio for the competition is:
• The winning design will be determined based on the following weighted design ratio:

# Design Considerations

• Which aspects of the competition formula are most advantageous?
• How can the boom be built and/or reinforced to prevent as much deflection as possible?

Note: You and your partner are to design a boom. The boom is to be secured (i.e., anchored) to the white plastic anchorage provided at the front of the lab. The boom must extend at least 1.5 m from the front edge of the anchorage and deflect as little as possible when loaded.

# Materials and Equipment

• 2 Thick Dowels (1.1cm x 122cm)
• 2 Thin Dowels (0.8cm x 122cm)
• 6 Bamboo Skewers (30.5cm)
• 3D Printed Dowel Connectors
• Cellophane Tape
• String

NOTE: A saw is available to cut the dowels. Ask your TA for assistance, as students are not allowed to use the saw.

Figure 9: 3D Printed Dowel Connectors

# Procedure

### Boom Design and Construction

1. Assess your materials and consider your design options, keeping in mind the competition specifications. Make sure you make preliminary sketches during this process.
2. Now sketch your actual basic design in pencil using the graph paper sample provided on the EG website. Label your design clearly and have your TA sign and date it.
3. Construct your boom based on the sketch you just completed and the available materials. Your TA will provide the materials allowed for your design. If you decide to modify your design during the construction phase of your boom, make sure to note the changes and describe your reasons for them.

### Competition

Note: Attaching your boom to the anchorage is a critical phase of the competition. You will be timed. Making sure you have a plan before you start will help you anchor the boom quickly and improve your standing in the competition. You may want to practice before your trial begins. Remember you will be disqualified if anchoring your boom takes more than two minutes.

1. When the TA says "go," attach your boom to the anchorage and shout "done" when your team is finished. The TA will give you your anchoring time. You will use this number to compute your boom's design ratio.
3. Your TA will attach a basket to the end of your boom and add weights until the boom deflects (bends) 0.2 m. The load supported will be weighed on the lab scale and the weight recorded in the competition spreadsheet for your section. See Figure 9.

Your TA has prepared an Excel file with your section's results. Go to the Lab Documents section of the EG Website. This chart must be included in your PowerPoint presentation and in the data section of your lab report. Your lab work is now complete. Please clean up your workstation. Return all unused materials to your TA. Refer to section 3 of Your Assignment for the instructions you need to prepare your lab report.

# Assignment

### Optional BONUS Individual Lab Report

Follow the lab report guidelines laid out in the page called Specifications for Writing Your Lab Reports in the Technical Communication section of this manual. As you write, the following discussion points should be addressed in the appropriate section of your lab report:

• Describe the rules of the competition in your introduction. What consequences did the rules have for your design decisions? Use the appropriate equations in your answer.
• What factors did you consider in designing your boom? Did you use any of the background information?
• What was the weight ratio and design ratio for your design?
• What do you think would be the maximum design ratio for this project? Compare your results with this ideal ratio.
• What important design characteristics should a winning boom include to achieve the highest possible weighted ratio?
• Describe how the components you have chosen function in your design, and describe its overall height/length/shape/etc.
• Discuss design improvements. How would you optimize the design (i.e. improve the ratio) based on experience?
• Which elements of the boom (e.g., wooden dowels, 3D printed dowel connectors, Kevlar string, etc.,) were stressed by the load, in what directions, and contributed to the failure?
• Include spreadsheet with every team's results. Describe the results and talk about other designs in the class.

Remember: Lab notes must be taken. Experimental details are easily forgotten unless written down. EG1004 Lab Notes Paper can be downloaded and printed from the EG1004 Website. Use the lab notes to write the Procedure section of the lab report. At the end of each lab, a TA will scan the lab notes and upload them to the Lab Documents section of the EG1004 Website. One point of extra credit is awarded if the lab notes are attached at the end of the lab report. Keeping careful notes is an essential component of all scientific practice.

### Team PowerPoint Presentation

Follow the presentation guidelines laid out in the page called EG1003 Lab Presentation Format in the Introduction to Technical Presentations section of this manual. When you are preparing your presentation, consider the following points:

• How would you improve your boom design?
• Other than the examples given in this lab, what are other examples of booms?
• Which elements of the boom (e.g., wooden dowels, 3D printed dowel connectors, Kevlar string, etc.,) were stressed by the load, in what directions, and contributed to the failure?

## Footnotes

1 How Stuff Works website. 2003. SHW Media Network. Retrieved July 28th, 2003. http://science.howstuffworks.com/tower-crane3.htm

2 Serway, R., Beichner, R., Physics for Scientists and Engineers with Modern Physics, 5th Edition. Fort Worth, TX: Saunders College Publishing, 2000