# ENGR 102: Project 1 Beam Analysis and Selection

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**Freshman Engineering, Fall 2015 Statler College of Engineering and Mineral Resources, WVU****ENGR 102: Project 1****Beam Analysis and Selection**__The Project__

Your team is tasked with creating a computer code that will analyze a beam for use as part of a hoist assembly in a fabrication plant. Attached to the center of the beam will be a motorized winch that can pick up 2 tons of load and weighs 360 lbs itself, as illustrated in Figure 1. This beam is simply supported at both ends, the maximum deflection, δmax, for the beam can be found using Equation 1,

60 ft span

360 lb weight

hoist

2 ton capacity

Figure 1. Sketch of the Proposed Beam

𝛿𝑚𝑎𝑥 =𝑃 𝑙3/48 𝐸 𝐼 + 5 𝜔 𝑙4/384 𝐸 𝐼 Equation 1

where P is the point load applied at the center of the beam, 𝑙 is the span of the beam, 𝜔 is the weight per length of the beam, E is the Modulus of Elasticity (a material property, equals 30x106 psi for steel) and I is the Moment of Inertia (a property of the shape). In order to make the mounting of the hoist as simple as possible, the project manager has required some teams to use an I-beam, thus the formula for the Moment of Inertia becomes that shown in Equation 2, based on the flange width, b, section depth, d, web thickness, t, as labeled in Figure 2.

𝐼𝑥𝑐 = 𝑏 𝑑3 − ℎ3(𝑏 − 𝑡)/12 Equation 2

Figure 2. Variable Definitions on the Cross-Sectional Profile of an I-Beam

For some teams the project manager has assigned a box beam, thus the formula for the Moment of

Inertia becomes that shown in Equation 3, based on the beam width, b, beam height, h, and wall

thickness, t, as labeled in Figure 3.

𝐼𝑥𝑐=4 𝑏 ℎ3−(𝑏−2 𝑡)(ℎ−2 𝑡)((ℎ−2 𝑡)2+3 ℎ2)12 Equation 3

Figure 3. Variable Definitions on the Cross-Sectional Profile of a Box-Beam

The owner of the assembly plant is willing to allow up to 1.50 inches of deflection in the beam at the maximum load of the hoist, but also wants to have a low cost for the beam. Using the current price for steel of 0.373 US$ per pound, recommend a beam to the project manager and lead engineer of this design and justify your recommendation.__Requirements__

Your team is to create a MATLAB program that will analyze all of the beams of your team’s respective shape. You are then to interpret the output of your program and recommend one beam to your lead engineer. In order to do this you must complete the following tasks:

Team Charter/Agreement

Gantt Chart (Project Planning/Timeline)

Engineering Log Book

Matlab Program/Code

Poster Presentation

Technical Report__Grading__

MATLAB Code – 40%

Poster Presentation – 20%

Technical Report – 25%

Team Agreement, Gantt Chart and Log Book – 15%**Submission Deadlines**

Team Agreement and Gantt Chart – Tuesday, September 29th (end of class)

Code Submission – Thursday, October 15th

Presentation – Thursday, October 15th

Technical Report – Tuesday, October 22nd

Log Book - Tuesday, October 22nd