AME 20241: Mechanics of Solids Laboratory 2: Build a Beam for 3-Point Bending

Abstract: This laboratory report contains the design process of a simple foam I-beam. An analysis of the beam is conducted after the application of a 3-point bending from an ATS machine. This beam experienced a linear stiffness of 262 lbf./in. at an ultimate strength of 53.9 lbf. and deflection of 0.351 in. to which it immediately failed. Objective: This laboratory required the design and construction of a beam that spans 30 inches in order to determine the maximum strength and carry load at mid-span. The beam was created exclusively using a 10 by 40 inches piece of foam board of thickness 3/16 inches, 4 hot glue sticks, and Exacto knives. Design Rationale: From the materials mentioned, an I-beam was constructed. The cuts necessary to produce the I-beam are shown in Figured 1.
32 in. 1 in.

5 in.

5 in.

Figure 1: Foam Beam Cut Schematic.

When deciding how to cut foam board, the thought behind it was to target the areas of the beam that would experience the most applied load force. The final design consisted of five 1-inch units hot glued together at three equally spaced sections between two 32-inch long boards. The top and bottom sections 1

were supposed to keep the board from failing at its ends and splitting apart and the middle section was to keep the board from splitting in the middle and dipping inward. The final design is shown in Figure 2.
Top View

Side View

Front View

Figure 2: Finished I-Beam Views

The focuses are at the ends and middle of the beam. Therefore, the I-beam was positioned as seen on the ”Top View” in Figure 2. The purpose was so that a 5-inch buffer would prevent the beam from failing.

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P

R=P/2

R=P/2

V Shear

V

Mmax

Moment

Figure 3: 3-Point Bending Model with Shear and Moment Diagrams There was ample time to think of a design, however the challenge was being confined to the given materials and tools. Figure 3 shows the theory to which was the focus behind the beam design. The figure shows the 3-point bending forces P and R. P is the main force of applied load during testing and R is the reaction force. Experimental Testing: Once the beam was constructed, it underwent the 3-point bending test using the ATS machine. A Magnetic Displacement Transducer was attached to the beam to sense the deflection occurring while testing. The data acquisition board and software recorded the load applied and the deflection of the beam. Since the values are given in voltages, constants are used to obtain the reals values. These values can be seen in Table 1.

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Results: The beam linear stiffness was 262 lbf./in. Figure 4 shows the resulting load-displacement response of the built I-beam. Figure 4 also shows where non-linear behavior begins and the ultimate strength of the beam. All critical values are shown in Table 1.

60

50

Applied Force [lbf.]

40

30

20

Experimental Data

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Ultimate Strenth Non-Linear Behavior Begins Linear Stiffness

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Deflection [in.]

Figure 4: Load-Displacement Response of the Beam

Table 1: Resulting Critical Points Data Applied Load [lbf.] Deflection [in.] Constant Multiples 100 1.894130 Non-Linear Behavior 48.9 0.259 Ultimate Strength 53.9 0.351

Discussion:

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The beam failed around 53.9 lbf. , which is not very good since it has been proven in past years that foam beams could hold over 100 lbf. A major contribution to the early failure of the I-beam would have occurred due to already placed damage before design. There was a crease across the board before designing, cutting, and testing. During testing it was observed that failure began quickly around the injured area of the beam. Also, during the building of the beam only the model in Figure 3 was considered and it was guessed that supporting the ends and middle would be enough to withstand the increasing applied force. There is a rapid and shaky linear stiffness of 262 lbf./in. as shown in Figure 4. Non-linear behavior occurs at 48.9 lbf. and failure soon follows at 53.9 lbf. Although foam is not used in most engineering applications, it can be seen from this laboratory that a lot of consideration goes into the construction of a strong beam. The failure of the the constructed I-beam was weak compared to others that have carried 100 lbf. or more.

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