Spaghetti Bridge Design Project

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1 Spaghetti Bridge Design Project EI 2018 Contents 1 Project Overview Introduction Theory and Online Simulator The Method of Joints Virtual Bridge Design Spaghetti Bridge Day Competition Bridge Specifications Bridge Construction Rules Penalties Tiebreakers Project Overview Each group is to design and build a bridge made from spaghetti and epoxy. The objective is to construct a bridge that will carry the heaviest load while still meeting specifications. Bridges will be loaded until they fail during the Spaghetti Bridge Day Competition on the last day of class. 2 Introduction A truss is a structure that is composed of straight members connected at their ends by hinged connections to form a stable configuration. One example is shown in Figure 1. When loads are applied to a truss only at the joints, forces are transmitted only in the direction of each of its members so the members experience tension or compression forces, but not bending forces. Trusses have a high strength to weight ratio and consequently are used in many structures from bridges to roof supports to space stations. One benefit of truss structures is that, with a few simplifying assumptions, it is possible to calculate the force in each member using the Method of Joints as described in Section 3.1. Members that experience large forces can be strengthened so that each part of the bridge is just as strong as it needs to be. This is one reason that truss designs are relatively lightweight and low-cost. 3 Theory and Online Simulator 3.1 The Method of Joints The locations where members meet are called nodes or joints, and we assume the joint is composed of a frictionless pin that allows rotation. When the truss is static (not moving), 1

Figure 1: This railroad bridge is one example of a truss structure. then all the bridge components must be in equilibrium and the forces must sum to zero.

2 Figure 1: This railroad bridge is one example of a truss structure. then all the bridge components must be in equilibrium and the forces must sum to zero. The Method of Joints is one approach to solving for the force in each member of a truss, such as the one shown in Figure 2. Figure 2: This is an example of a truss, modeled after the bridge in Figure 1. First, the reaction forces at the pinned and rolling supports are calculated by considering the truss as a whole and requiring that x-direction forces, y-direction forces, and moments about one point all sum to zero. In Figure 2, the nodes marked A and E are the ones with the pinned and rolling supports, respectively. The next step is to consider each node individually and require that x-direction forces and y-direction forces sum to zero. Members in tension pull away from the node and members in compression push into the node. Figure 3 shows the Method of Joints solution for the Figure 2 truss. Each support provides a 5 kn vertical force to balance the 10 kn load applied at the bottom center node. The members along the bottom of the bridge are in tension, and the members along the top are in compression. Note that some members are currently carrying no load and can be removed along with the node where the connection makes a right angle (try this yourself using the online simulator described in Section 3.2). 2

Figure 3: This is the Method of Joints solution for the truss in Figure 2. See Figure 4 for a description of the software used to generate this solution.

3 Figure 3: This is the Method of Joints solution for the truss in Figure 2. See Figure 4 for a description of the software used to generate this solution. Assumptions inherent to the Method of Joints: 1. Truss members are connected at the ends by frictionless pins. 2. The truss is loaded only at the joints. 3. Truss members are in tension or compression but not bending. 4. The truss is stable and statically determinate (next section). 5. We ignore the weight of the truss itself. Criterion for a statically determinate truss: This method works only for statically determinate, stable trusses. A necessary (but not sufficient) criterion for a determinate, stable structure with one pinned support and one rolling support is M + 3 = 2N, (1) where M is the number of members and N is the number of nodes. The left-hand side of Equation 1 represents the number of unknowns. The unknowns are as follows: the force in each member, the x- and y-forces for the pinned support, and the force from the rolling support (M + 3). The right-hand side of Equation 1 represents the number of equations. The x-direction forces and y-direction forces must sum to zero at each node, so we have two equations at each node for a total number of equations equal to 2N. If there are more equations than unknowns, then a solution may not exist. If there are more unknowns than equations, then we do not have enough information to find a unique solution. 3.2 Virtual Bridge Design One tool you have at your disposal is a computer program that implements the Method of Joints described in Section 3.1. A screenshot of the program is shown in Figure 4. The program is available online at 3

Trusses are created by attaching members to nodes. First, node locations are specified. Then, the nodes are linked by members to create a structure.

4 Trusses are created by attaching members to nodes. First, node locations are specified. Then, the nodes are linked by members to create a structure. Once the structure is established, two of the nodes must be assigned as support nodes. One must be a pinned node, i.e., one that can provide support in both the x- and y-directions. The other must be a rolling node, i.e., one that can provide support in only one direction. Finally, one or more nodes can be assigned to bear loads by adding forces. If you want to erase the entire design, you can refresh the webpage. Once the truss structure is built, solving the truss will determine the forces in each member and support. If you have too many or too few members or supports, then a solution does not exist and you will see an error message at the bottom of the screen. Nodes, members, support nodes, and loads can be added or removed at any time. The Method of Joints works by creating and solving a matrix equation. To see the matrix equation and solution, look for the button labeled Show matrix eqn. The force in each member is shown just before the equal sign and is labeled as M#.#, where the numbers represent the node numbers. To see the number for each node, look for the button labeled Node labels on/off. Forces provided by the supports are labeled S#x or S#y for the x- and y-directions (the # is the node number). Create the truss Compression member Node Solve the truss Forces on each member are shown in boxes. red = compression blue = tension Pinned support Horizontal rolling support Force (load) Tension member Figure 4: This online computer program can be used to solve trusses using the Method of Joints. It is available at 4 Spaghetti Bridge Day Competition The final day of Engineering Innovation is the Spaghetti Bridge Day Competition. Student teams will compete to see whose bridge holds the greatest net load. This section details the rules for the competition. 4

5 4.1 Bridge Specifications 1. The bridge is to be built from regular spaghetti and 5-minute epoxy. One exception is that the decking may be made of angel hair pasta. Each team will also be given a wooden loading platform to build into the bridge. 2. The bridge shall be free-standing and must span two level surfaces which are 50 cm apart. 3. The support for the bridge shall be from the top of the level surfaces. The edges of the level surfaces cannot be used in any way for support. 4. The bridge must include a decking of spaghetti to provide a suitable road surface at least 5cm wide across the full span of the bridge. Three conditions must be met: (a) Gaps in the bridge deck are not to exceed 2 mm. (b) A block of wood (5 cm x 5cm x 10 cm) representing a car must be able to move along the length of the decking unobstructed from end to end. The bridge does not need to support the weight of this car; you may support the car s weight as it passes through the bridge. (c) The deck of the bridge must not be more than 5 cm above or below the ends of the bridge at any point along its length. Any violation of these decking requirements will result in a penalty. 5. You must incorporate a loading platform consisting of an eye-bolt secured to a piece of plywood (0.7 cm x 5 cm x 10 cm). This platform is to be attached at the center of the bridge such that the bottom of the eye-bolt is no more than 5 cm from the top of the bridge decking. All loads will be suspended from this eye-bolt, and there must be a clear space directly below it to allow loads to be attached. Loads will be attached using an S-hook, and, if necessary, a 10 mm diameter metal rod extension. If, during loading, the bridge twists in such a way as to cause the bridge to touch the rod at any point other than the eye-bolt, thus lending additional support, the bridge will be disqualified. 6. If the maximum vertical depth of the bridge, from the highest point in its structure to the lowest point, exceeds 25 cm, then a penalty will be applied. 7. If the maximum weight of the bridge including the loading platform exceeds 250 grams, then a penalty will be applied. 4.2 Bridge Construction Rules You may use dowel rods or other materials during construction, but they must be removed prior to the competition. No dremel rotary tools or other power tools are allowed during construction, since dremel tools produce pasta/epoxy dust that is unhealthy to inhale and power tools present safety concerns. You may use sandpaper to remove excess epoxy. Cutting tools like utility knives and saw blades may be used, subject to supervision and safety protocol for your space. 4.3 Penalties 1. The penalty for improper decking (P deck ) is as follows: P deck = 2 kg. (2) 5

6 Figure 5: The rules are summarized in this diagram. 2. The penalty for an overweight bridge (P weight ) is as follows: g P weight = ( bridge weight ). (3) 3. The penalty for a bridge that is too tall (P height ) is as follows: 2 25 cm P height = ( bridge height ). (4) The total load that the bridge supports is called the supported load. The total load that your team will get credit for, after penalties, is called the net load and is calculated as net load = supported load P weight P height P deck. (5) If the decking meets all requirements, then P deck = 0. If the bridge weight is less than 250 g, then P weight = 1. If the bridge height is less than 25 cm, then P height = 1. Any bridge that holds a net load greater than or equal to 3 kg will receive full credit for this assignment. 4.4 Tiebreakers In the event that two or more bridges support the same net load, the following tiebreakers can be used: 1. The bridge without penalties wins. 2. The bridge with the greatest supported load (before penalties) wins. 3. The bridge with the lowest weight wins. 4. The bridge with the shortest height wins. Apply in the order listed until one bridge is designated the winner. 6

Statics Chapter 6 Structural Analysis Eng. Iqbal Marie Hibbeler, Engineering Mechanics: Statics,13e, Prentice Hall

Statics Chapter 6 Structural Analysis Eng. Iqbal Marie iqbal@hu.edu.jo Hibbeler, Engineering Mechanics: Statics,13e, Prentice Hall 6.1 Simple Trusses 6.1 Simple Trusses truss structure composed of straight,