Whitney Brown Wentworth Institute of Technology

Engineering Statics Mech 251-01

Abstract

The requirements of the Statics Truss experiment was to build a truss out of twenty-five popsicle sticks that was to be 12 inches long and 3 inches high. The objectives were to build a structure that would withstand the load of a hydraulic press, and produce an adequate efficiency, determined by the load divided by the weight of the structure. The objectives of the experiment were accomplished and the efficiency was calculated to be 6763.29 lbs. The Load withstood by the structure was determined to be 527 lbs. and the weight was measured to be .0779 lbs. The results of the experiment were more sufficient than expected, however the source of error proved to be what was predicted. Recommendations for a future experiment of these requirements and objectives would be to place the load on the strongest members of the structure, instead of distributing it across the center of the truss. This method proved accurate in improving results through experiments conducted by members of the class.

Introduction

A truss is a structure that consists of members joined together at their endpoints. When designing and analyzing a truss structure that is to be subjected to a given load the forces that each member and joint of the structure will undergo under the application of the load, must first be determined. Each truss member acts as a two force member and therefore the forces at the ends of the member must be directed along the axis of the member.1 If the force tends to pull away from the ends of the member it is a tensile force (T), meaning it undergoes tension. If the force tends to push into the member it is compressive force (C), meaning it undergoes compression. Compression members must be made thicker than tension members because of the buckling of column effect that occurs when a member is in compression.2 When analyzing the forces on the truss as an entire system the forces experienced by each individual member are considered to be internal with respect to the entire system, therefore a separate method must be used to determine the forces applied to each member.

1 Hibbeler, R.C. Engineering Mechanics, Statics, Tenth Edition. Pearson Prentice Hall 2004. Pg. 259 2 Ibid Pg. 259

There are two methods that can be used in order to analyze each member of the truss. The first is the method of joints. Instead of considering the entire system under an equilibrium analysis, the method of joints considers the equilibrium of one joint of the truss at a time, making the forces on each member connected to that joint become external forces. The second method of analyzing the forces on each member is the method of sections. The method of sections is used to determine the loadings acting within a body, and is based on the principle that if a body if in equilibrium then any part of the body is also in equilibrium.3 A section of the body is analyzed therefore causing the internal forces on each member to become external for that particular section. The equilibrium equations are then used to determine the forces in each member of the section.

Data & Results

The results of the experiment were more sufficient than expected, however the source of error was proven to be what was predicted. When designing and constructing the truss, it was clear that the outside vertical beams and the connecting middle vertical members would undergo compression. Therefore the outside beams and top joints A and B were built thick and strong to withstand most of the load. It was apparent at the end of the design process that the two connecting beams would not withstand the compressive force that they would undergo. Each middle member was one popsicle stick thick as compared to the three popsicle sticks of the outside beams. Therefore when the load was applied the middle members experience the buckling or column effect that occurs when a member is in compression. This source of error is displayed by the red arrows in Fig. 1. The compression in the middle members as well as the compression in the beams also created a compressive force on joints A and B, which eventually snapped the joints right off of the beams, as displayed by the red indicators at joints A and B. The beams however, due to their rigidness were unaffected by the load. The middle members could not withstand the compression that the beams could, therefore the truss failed at the joint in which the two met, joints A and B. The bottom members of the truss as well as the four joints along the bottom members, like the two side beams were also unaffected by the load due to the strength in both the beams and the joints. The blue arrows in Fig. 1 indicate the force felt on the middle bottom beam by the outside supports, due to the strength and rigidness that the joints had. The truss was determined to have held 527 lbs. before the two middle members buckled. Its weight was measured to be .0779, making its efficiency 6763.29, which compared well with the results of the class.

3 Ibid Pg. 273

Conclusion

This experiment of the design and analysis of a truss supported the importance of an analysis on each member of a structure before its construction. If one member was not taken into account or the analysis was incorrect the structure could fail instantly. Therefore the method of joints or the method of sections is crucial in the design of structures such as trusses. After the experiment it was clear what types of designs work well, and which dont. It was also apparent that the types of materials used, in many cases, affected the results. In this case glue and cutting utensils were the only varying materials, but in many cases they played an important role in the success of the design. During the class a student experimented with placing the load on the right side of the structure instead on placing it across the center of the top beam. This enabled most of the load to be distributed through the strongest beam instead of across the top. If the experiment was to be repeated a recommendation to apply the load to the side of the design, might allow for some alleviation of the compression on the middle members, therefore lessening the greatest source of error that occurred.