Build a Beam for 3-Point Bending ID #: 901508820 AME 21241 – Mechanics of Solids
Abstract The experiment performed was to design and build a maximum strength beam using a 10 in. by 40 in. foam board. The rationale behind the design is discussed and schematics are shown. The linear stiffness of the constructed beam was 160 lbf/in. The maximum force and deflection where linear behavior ends was 47.3 lbf and 0.42 in., respectively. The ultimate strength and deflection was 49.1 lbf and 0.71 in., respectively. Failure analysis and discussion of possible design improvements is also provided.
Objective The objective of this laboratory exercise was to design a maximum strength beam, out of foam board, to be subjected to a 3-point bending test. One 10 in. by 40 in. foam board and four glue sticks, as well as the necessary tools, were supplied to build the beam. The beam needed to span a little bit longer than 30 in. to fit onto the testing machine.
Design Rationale Beam analysis provided in the text, “Mechanics of Materials”, by Roy Craig led to the decision to design an I-beam. The knowledge that the applied load was going to act at the center of the beam at the top led to a design that would try to maximize the beam’s resistance at the center. Figure 1 shows the foam board cut diagram. In Figure 1 there were five even cuts 33 in. by 2 in. which were used for the I-beam. One was used for the top, one for the bottom
and 3 as the center of the I-beam. Two cuts 3.5 in. by 2 in. were made and placed at the ends of the bottom so the beam would rest on them in the ATS machine. One 7 in. by 4 in. cut was made and placed at the center of the top of the beam to increase the surface area of the applied load. Twelve 2 in. by 2.25 in. cuts were made and ten were placed as columns to support the inside of the beam. The rest of the material was unused. Figures 2 and 3 show an orthographic projection of the completed foam beam. There were not a lot of tradeoffs due to the constraints. There was unused material and unused glue after the beam was built. Time was the only tradeoff which did not allow for a more detailed analysis to determine the best possible design.
Experimental Testing A 3-point bending stress test was performed with the beam using the ATS testing machine. The constructed beam was placed in the ATS machine so the load would be applied at the top of the center of the beam. A load cell was used to measure the amount of force applied to the beam and a magnetic transducer was used to measure the amount of the beam’s deflection. The test was completed once the ultimate strength was reached and the beam failed.
Results The force and deflection data from the experimental testing was plotted against each other in Figure 4. Several key results can be drawn from this graph. The linear stiffness of the beam was found by calculating the mean slope using several linear data locations. The average linear stiffness was found to be 160 lbf/in. Through inspection of the data from the load cell and magnetic transducer, the maximum force where nonlinear behavior began is 47.2 lbf and the maximum deflection
where nonlinear behavior began is 0.42 in. Also by inspection, the ultimate strength of the foam beam was found to be 49.1 lbf and the deflection at the ultimate strength is 0.71 in.
Discussion The foam beam failed in the weakest locations of the design, which were the spots just after the inner columns on each side. At these locations bending lines formed into the foam and would have eventually cracked. The lines appeared at about the maximum force where the linear behavior ends in Figure 4. The failure mode observed was considered in the design, but the poor load distribution in the beam was not considered. The extra material placed on top of the beam in the center where the load was placed increased the surface area and allowed the load to distribute. In a redesign with the unused material the surface area could be expanded even more to allow for increased load distribution. The material for the four columns at the ends of the beam should have been used more efficiently as they likely had little effect so far from the applied load. Another way to improve the design would be to use the four end columns and the unused material to place columns towards the center of the beam and increase the resistive force where the load is applied. For a complete redesign the foam beam should be built to maximize the height of an I-beam shape. The original design had a center height of only 2 in., which could be changed to 8 in. With such a large area the beam would resist bending much better than in the original design.
References Craig, Roy R., Jr., 2000, “Mechanics of Materials,�2nd ed.
Figures
Figure 1: Foam board cut diagram
Figure 2: End beam view
Figure 3: Top and side beam views
Figure 4: Load vs. Deflection of constructed beam