# 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 Koch 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 (Jennings, 2015)

## 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.

An extremely important tool in an engineer’s skillset is the use of simulation tools. Many times, complex designs require quick analysis that cannot be done by calculation or prototyping, so simulation comes in handy and as it saves both time and money. Specifically Finite Element Analysis (FEA) splits a component up into small components (called a mesh) and solves them all simultaneously in order to get a complete look at the product at hand. This simulation only works for isotropic materials, meaning that the materials properties (tensile strengths, modulus, etc.) are the same for all sides of the material. This may not be true for certain materials. While members of the group are designing and building a boom, others will discuss a simulated boom in order to understand the effect of the forced displacement, and use that information to improve the initial design.

# 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 the design.

• 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 meters horizontally from the front edge of the anchorage
• The boom must be anchored in two minutes or less
• The boom may not touch anything but the anchorage
• The basic weight ratio (3) for the competition uses the weight supported divided by the boom weight

• (3)

• The winning design will be determined by the weighted design ratio (4), which uses the weight ratio, anchor time, and boom length

(4)

# Design Considerations

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

# 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
• Kevlar string

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

# Procedure

## Note for Hybrid Session

In-person are expected to complete the competition part of the procedure, indicated by the label (In-Person). Remote students are expected to complete the virtual boom analysis part of the procedure, indicated by the label (Remote). Any procedure labeled (Hybrid) is expected to be completed through a joint collaboration between remote and in-person students.

## 1. Boom Design and Construction (Hyrbrid)

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 or on the EG1003 website. Label the design clearly and discuss the pros and cons of the design with your teammates.
3. Once teams have design ideas completed, teams will be combined to make sure there are an adequate amount of in-person students.
4. While in-person students lay out the boom design with real life parts in step 5, virtual students will analyze a sample boom simulation on Fusion 360 to gain a better understanding of the forces that will affect the boom. This is highlighted in the section below.
5. 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.
6. After the virtual students have completed the Virtual Boom Analysis procedure, and in-person students have completed step 5 of this procedure, ask a TA to begin load testing for your in-person boom.
7. A TA will weigh the boom and record the weight in the competition spreadsheet for the section.

## 2. Virtual Boom Analysis (Remote)

The steps below will go through how to analyze and understand the boom simulation, and find the corresponding design ratio for it. The boom simulation was made using the parts with the same shape of the in-person boom parts, and an assumed material with the approximate inputted properties of wood was used (Research isotropic vs orthotropic materials). The data needed for the design ratio will be found and translated and the forces along the boom will be analyzed to improve the in-person boom design.

1. The example of the boom model can be found in a ZIP folder here. The latest version of Fusion 360 must be downloaded for the parts to appear properly.
2. Unzip the parts to a space on the computer.
3. In Fusion 360, open the Data Panel (icon with 9 boxes at the top left) and click Upload. Select the unzipped part files to upload them to Fusion 360’s cloud memory. Fusion 360 can only import files uploaded to its cloud.
4. Ensure that the Design workspace is open in Fusion 360. This is indicated at the top left.
5. The Theoretical Boom file can be inserted into a new Fusion 360 file by simply dragging and dropping them from the Data Panel into the space. Alternatively, right click the components and select Insert into Current Design.
6. Save the blank file by going to File > Save as.

### Mass of the Boom

1. Go to the Browser on the left-hand side of the workspace. Use the small, white arrows on the left of the part names to open their folders. Open the Bodies folder of the part, right click the body of interest, and select Properties (Figure 9).
2. In the Properties dialog that appears, record the mass of the body.
3. Repeat these steps for all the bodies in the boom design and add the masses to obtain the total mass of the boom. Record the total mass of the boom in your Lab Notes.
Figure 9: Obtain Mass of Bodies

### Length of the Boom

1. In the toolbar, go to Inspect > Measure.
2. In a side view of the boom, select a point at the front of the anchor and then another point at the tip of the boom.
3. In the Measure dialog, check the XYZ Delta box.
4. From the Measure dialog, record the length in meters in your Lab Notes.
Figure 10: Sample Boom Length Measurement

### Understanding the Results

1. After completing the model of the boom in Fusion 360 and the initial analysis, switch the workspace from Design to Simulation at the top left of the screen. In the New Study dialog that appears, select Static Stress > Create Study. Note: If you get an interference warning it can be ignored since seeing the contacts allows better visualization of the boom’s deflection.
2. The results will now be calculated and obtained. In the Browser tab, right click Results > Solve. In the Solve dialog, click Solve 1 Study. Wait for the simulation to complete.
3. After the simulation has been solved, the workspace will show a deflected boom similar to the one shown below in Figure 11.
Figure 11: Sample Boom Deflection
4. The scale on the right will be reading Safety Factor with a scale from 0-15. Make sure the minimum safety factor is above 1. The safety factor is the yield strength of the material divided by the maximum stress calculated at a point. If this is under 1, this is the simulation showing a broken part.
5. Simulation contacts describe the interaction between parts in an assembly.

### Finding the Reaction Force

1. The reaction force will be determined. In the Results toolbar, go to Inspect > Reactions and click the bottom face of the boom anchor as the Entity. By Newton's Second Law, the static displaced structure should have a reaction force on the fixed face equal to an imaginary weight placed when the beam was deflected. There is a force on the bottom face of the boom anchor that is a resultant of the 20 cm displacement at the end of the boom. This is the reaction force.
2. From the Reactions dialog, record the axial force (should be the largest) on the same axis that the displacement was directed on (Figure 12). It should be the largest of the three axial forces.
Figure 12: Reactions
3. Using the Reaction Force found, calculate the weight ratio (5) as well as the weighted design ratio (4) for the given virtual boom. This is done by following the math below derived from Newton’s Second Law. Assume Anchor time as 30 seconds.

(5)

## 3. Competition (In-Person)

Note: Attaching the boom to the anchorage is a critical phase of the competition. Anchoring will be timed. Making sure there is 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 two minutes.

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 there are no more hands touching the boom. The TA will give the anchoring time. This value will be used to compute the boom's design ratio
2. A TA will measure 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) 0.2 m vertically. The load supported will be weighed on the lab scale and recorded in the competition spreadsheet for the section (Figure 10)

A TA has prepared an Excel file with the section's results. It can be accessed in the Lab Documents section of the EG1003 website. This chart must be included in the PowerPoint presentation and in the Data/Observations section of the lab report. The lab work is now complete. Please clean up the workstation. Return all unused materials to a TA. Refer to the Assignment section for the instructions to prepare the lab report.

# Assignment

## Individual Lab Report

Follow the lab report guidelines laid out in the EG1003 Writing Style Guide in the Technical Writing section of the manual. The following points should be addressed in the appropriate section of the lab report.

• Describe the rules of the competition in the Introduction. What consequences did the rules have for any design decisions? Use the appropriate equations in the answer.
• What factors were considered in designing the boom? Was any of the background information used?
• What was the basic weight ratio and weighted design ratio for the design?
• Describe how the components chosen functioned in the design, and describe its height/length/shape
• Discuss design improvements. How can the design be optimized (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 the spreadsheet with every boom's results. Describe the results and talk about other designs in the class
• Discuss what part of the lab you completed for your group and why it was important to the overall experiment.

Remember: Lab notes must be taken. Experimental details are easily forgotten unless written down. EG1003 Lab Notes paper can be downloaded and printed from the EG1003 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 EG1003 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 EG1003 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 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?

# 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