# Objective

The experimental objective of this lab is to design and assemble a boom. This is a competition lab, and the booms will be judged by a design ratio that uses boom weight, boom length, weight held, and anchor time. The highest design ratio will win the competition.

# Overview

A boom is used to lift and move heavy objects that are often heavier than the boom itself.

A common example of a boom is a cantilever bridge, which uses two booms extending from a common base (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 Koch Queensboro Bridge

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

Figure 4 shows a bascule bridge, more commonly known as a drawbridge. This bridge uses a big, flat boom.

Figure 4: Bascule Bridge

Cranes are another 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 lb load. It is attached to the ground by anchor bolts driven through a 400,000 lb concrete pad poured a few weeks before the crane is erected (Howstuffworks.com, 2003).

Figure 5: A Tower Crane (Jennings, 2015)

## Stress and Strain

Distributing the load being lifted over the length of the boom is the main challenge 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. The design of a boom must consider the properties of the materials used to build the boom.

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. The mechanical properties and deformation of solids are explained by stress and strain. According to Serway and Beichner in “Physics for Scientists and Engineers,” stress is the external force acting on an object per 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. 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.

(1)

The resulting strain (2) is calculated by dividing the change in length of the material by the original length. This equation finds the strain for a rod of a material. In (2), ΔL is the change in length and L0 is the rod's original length.

(2)

There are three basic types of stresses; tensile (pulling or stretching), compressive (squeezing or squashing), and shear (bending or cleaving). Consider a straight metal beam. If a tensile stress is applied to both ends of the beam, the length of the beam will increase, while the cross-sectional area of the beam perpendicular to the force applied will decrease. Under compressive stress, the opposite will occur. If the beam is subjected to shear stress, it will bend towards the direction of the applied force, and both the length and cross-sectional area of the beam will become distorted. Figure 7 depicts a graphic representation of the three common forms of stress.

Figure 7: Example of a Boom Under Three Common Modes of Stress

Strain is proportional to stress for material dependent values of strain. If the material is known, it is possible to derive strain from measured stress, and vice-versa, up to a certain level of stress. This proportionality constant is referred to as the elastic modulus, or Young’s modulus. The moduli of different materials is an important factor to consider when designing or building any form of structure that will be under stress.

## Stress-Strain Curve

A graph of stress-strain shows the relationship between the stress and strain of a material under load. Figure 8 shows the stress-strain curve of a common metallic building material. In the elastic region, the material will regain its original shape once the stress is removed. The elastic region in Figure 8 is fairly linear. The slope of this linear portion of the stress-strain curve is the elastic modulus.

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). In the plastic region, the material loses its elasticity and is permanently deformed. A linear approximation with the elastic modulus is no longer accurate.

The ultimate tensile strength is the maximum stress a material can undergo. The fracture stress is the point at which the material breaks. Fracture stress is lower than the ultimate tensile strength of a material because the material has reached that level of stress and has already begun to fail. The cross-sectional area is constantly decreasing until the material finally breaks.

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

# Competition Rules

The following rules must be followed to qualify for the competition. Violation of any of these rules will result in the disqualification of the design.

• The boom must be anchored to the white plastic anchorage provided at the front of the lab
• The boom must extend at least 1.5 m horizontally from the front edge of the anchorage
• The boom must be anchored in 2 min or less
• The boom may not touch anything but the anchorage
• The boom’s performance will be assessed by its anchor time, boom weight, boom length, and the weight it can support before deflecting 0.20 m vertically

The basic weight ratio (3) for the competition uses the weight supported in grams divided by the boom weight in grams. This ratio SHOULD be greater than 1, but it is not required to compete.

(3)

The winning design will be determined by the weighted design ratio (4), which uses the weight ratio, anchor time in seconds, and boom length in meters. Each component ratio should be greater than 1.

(4)

# Design Considerations

• How can the boom be built and/or reinforced to prevent as much deflection as possible?
• Which aspects of the competition ratio can minimize the design ratio?

# Materials and Equipment

• Two thick dowels (1.1 cm × 122 cm)
• Two thin dowels (0.8 cm × 122 cm)
• Six bamboo skewers (30.5 cm)
• 3D printed dowel connectors
• Cellophane tape
• String

Note: A saw is available to cut the dowels. Ask a TA for assistance, as only TAs may use the saw.

# Procedure

## Part 1. Boom Design and Construction

1. Assess the materials and consider the design options, keeping in mind the competition specifications. Preliminary sketches must be completed during this process.
2. Sketch the basic design in pencil using the lab notes paper provided by a TA. Label the design clearly and have a TA sign and date it.
3. Construct the boom based on the completed sketch and the available materials. A TA will provide the materials allowed for the design. If the design is modified during the construction phase, make sure to note the changes and describe the reasons for them.
4. Since anchor space is limited, each boom is only allowed to use an anchor for 10 min at a time. The TAs will keep track of the time, and booms will rotate every 10 min to ensure that every boom has access to an anchor. During the downtime, continue working on the boom to make the best use of the next anchoring opportunity.

## Part 2. Competition

Note: Attaching the boom to the anchorage is a critical phase of the competition. Anchoring will be timed. Making a plan to anchor the boom quickly will improve its standing in the competition. Practice anchoring before the trial begins. The boom will be disqualified if anchoring the boom takes more than 2 min.

1. When the TA says "Go," attach the boom to the anchorage and shout "Done" when the boom is anchored. The TA will only stop the timer once all hands are off the boom. The TA will give the anchoring time that will be used to compute the boom's design ratio.
2. A TA will measure the horizontal length of the boom and record the length in the competition spreadsheet for the section.
3. A TA will attach a basket to the end of the boom and add weights until the boom deflects (bends) 0.20 m vertically. The load will be weighed on the lab scale and recorded in the competition spreadsheet for the section.
4. A TA will weigh the boom and record the weight in the competition spreadsheet for the section.
5. The design ratio for the boom design will be used to decide the winner of the competition.

A TA will prepare an Excel file with the section's results and upload it to the the Lab Documents section of the EG1004 website.

# Assignment

## Individual Lab Report

Follow the lab report guidelines laid out in the EG1004 Writing Style Guide in the Technical Writing section of the manual. Use the outline below to write this report.

• What factors were considered in designing the boom? Discuss the background information that was used
• Describe the competition rules, the ratio, and materials in the Introduction. What impact did the rules, the materials and ratio have on any design decisions?
• Describe the function of each component used in the design
• Describe the advantages and disadvantages of the boom design
• Discuss potential design improvements. How can the design be optimized (i.e. improve the design ratio) using the experience gained from this lab?
• Which elements of the boom were stressed by the load? Did the load deflect to the side, and if so, did that contribute to the boom failing? Describe the load’s direction and how the load contributed to the failure?
• Include the Excel spreadsheet with all the boom designs in the class. Discuss other designs in the class
• Contribution Statement

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 EG1004 Lab Presentation Format in the Technical Presentations section of the manual. When preparing the presentation, consider the following points.

• How can the boom design be improved?
• Other than the examples given in this lab, what are other boom examples in the real world?
• Which elements of the boom (e.g., wooden dowels, 3D printed dowel connectors, string, etc.,) were stressed by the load, in what directions, and could potentially lead to the failure?

# References

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

Jennings, James. 2015. “Up, UP in a Crane: What Life is Like as a Tower Crane Operator.” Philadelphia. Accessed 14 January 2020 from www.phillymag.com

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