Simple Form Truss—Individual Kit
Introduction
The ability to make strong, rigid structures has been important ever since the first buildings were constructed many thousands of years ago. In modern times, structural strength is even more important with the construction of complex bridges and skyscrapers. All these structures have the same physical property in common—they are all in static equilibrium. This laboratory activity introduces the concept of static equilibrium. Your task, as an engineer, will be to hang a “sign” over a sidewalk for the lowest material cost.
Concepts
- Trusses and boom supports
- Torque
- Second- and third-class lever arms
- Static equilibrium of a rigid body
Background
Static equilibrium occurs when all the forces acting on a structure are in perfect balance. That is, there is no linear or rotational movement. If a building or bridge is not in static equilibrium, the unbalanced forces, the most significant being from the force due to gravity, will eventually cause the structure to fall. The ability to maintain static equilibrium becomes more difficult when an object must be supported from above instead of below. Long suspension bridges are generally supported by wire cables that attach to the tops of the supporting bases (see Figure 1). Overhanging signs and cranes are similar to suspension bridges and rely heavily on strong cables, a supporting lever, also called a boom or truss, and cable attachments. In order to save costs, engineers attempt to limit the amount of material used to support a structure, while still maintaining a high level of strength so that the structure stays in static equilibrium for many years to come.
{12670_Background_Figure_1}
A simple truss is a supporting structure consisting of a lever arm (boom) and a supporting cable. A simple truss can act as either a Class II lever or a Class III lever, depending on where the supporting cable is in relation to the supported load (see Figure 2). The fulcrum of the truss is the pivot point where it is connected to the supporting wall.
{12670_Background_Figure_2}
Experiment Overview
Laboratory Objective Guidelines The boom used to hang the sign must be attached to the wall of the building at a specific location. The sign should be hung as far away from the building as possible in order to maximize its visibility and marketing potential. Also, in order to keep the costs of the project down and still maintain building code, the “cable” material used can only support half the weight of the sign. If the “cable” attempts to support more than half the weight of the sign (250 g; 2.45 N), the “cable” will snap. In order to accomplish this task, experiment with the position of the sign on the boom, the angle of the boom and the position of the supporting rope. Hint: Hang the mass and attach the string at 10 cm, 25 cm and 40‑cm on the meter stick, and use boom angles of 30°, 45° and 60°.
- Sign mass: 500 g
- Boom attachment height on wall: 20 cm
- Maximum supporting weight of cable: 250 g
- Cost of supporting cable: $5/cm
Materials
Binding clips, 2 C-clamp, 3" (optional, but recommended) Hooked mass, 500-g Meter stick, half, with support stand clamp (Simple Form Truss) Protractor Ruler or metric stick Scissors Spring scale, 1000-g String Support clamp with bracket Support stand
Prelab Questions
- Use simple right-hand triangle geometry to determine the length of string (l) needed to support a 40-cm-long boom when the string is held at a 30° angle and the boom is held parallel with respect to the ground. Assume the string is attached to the wall directly above the pivot point of the boom. Hint: Use right-angle triangle geometry (see Figures 3 and 4).
{12670_PreLab_Figure_3}
- Using your solution to Prelab Question 1 as a guide, calculate the string lengths for the different string positions, and string angles given in the data table. Assume the string “attachment point” is directly above the pivot point of the boom. Record these values in the data table.
Safety Precautions
The materials in this lab are considered safe. Please follow normal laboratory safety guidelines.
Procedure
- Obtain the Simple Form Truss, two binding clips, support stand, 500-g hooked mass, string, scissors, protractor, ruler and 1000-g spring scale.
- Use scissors to cut two pieces of string—one approximately 50 cm and the other approximately 15 cm.
- Tie one end of the 50-cm string to the spring-scale handle.
- The setup for the Simple Form Truss is shown in Figures 5 and 6.
{12670_Procedure_Figure_5}
Note 1: The spring-scale scale should face the measurer. Note 2: Tie the 15-cm string around the binder clip to form a loop that is just large enough to allow the string to slide along the meter stick (see Figure 7). The hooked mass will hang from the string and the binder clip will prevent the string from slipping. The spring-scale binder clip should be clipped on the bottom edge of the meter stick. This will prevent the clips from being pulled off the meter stick.
{12670_Procedure_Figure_7}
Note 3: (Optional) Clamp the support stand to the tabletop using a C-clamp. Note 4: Figure 6 shows how to use the mass binder clip when the mass and string are attached at the same position on the meter stick. Only one binder clip is used for this setup.
- Lab partner responsibilities:
Lab partner 1: Hold the base of the support stand with one hand and pull on the string with your other hand to lift the boom so it is parallel to the ground as well as keep the string at the proper angle. (If a C-clamp is used, the support stand should be secure and it will not be necessary to hold it down with one hand.) Lab partner 2: Measure and record the angle of the string with the protractor and the force measurement from the spring scale.
- Follow steps 7–10 to collect spring-scale force data for each particular test given in the data table. When the mass and string are connected at the same position, set up the boom as shown in Figure 6. All other tests will be set up similar to Figure 5. Hang the mass from the string, making sure the mass clip is secured to the meter stick and does not slip. Both clips should be centered around the appropriate mark on the meter stick (see Figure 8).
{12670_Procedure_Figure_8}
- With the ring stand firmly held down with one hand, slowly pull on the string toward the ring stand rod in order to raise the boom until it is parallel to the ground. Pull the string in the same plane as the boom in order to prevent the boom from spinning around the support stand rod. Note: It may be easier to raise the boom with one hand first and then pull on the spring scale until there is enough tension to support the boom.
- Slowly raise or lower the string angle, while maintaining the parallel boom, until the string is at the appropriate angle according to the value in the data table. Use a protractor to measure the approximate angle of the string (see Figure 9). The angle should be within ±3° of the value in the data table for the specific test. All angles should be measured with respect to the horizontal.
{12670_Procedure_Figure_9}
- When the boom and string are at the proper angles, measure and record the force indicated on the spring scale. Note: Depending on the mass used, some tests may result in a force greater than 1000 g. If this occurs, record >1000 g in the data table.
- When all the data has been collected for a particular mass position and string angles, slowly lower the mass to the tabletop.
- Repeat steps 6–10 for each test in the data table, using the appropriate clip positions, and string angle for each test. Measure and record the force on the spring scale when the string angle is at the appropriate value (within ±3°). Note: It is easier to move the mass clip and looped string when the mass is removed from the string.
- Consult your instructor for appropriate storage procedures.
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