# trigonometry in bridge construction

## Published by on November 13, 2020

Note to teacher: Continue using the Notetaking Sheet to help students to follow you during this long process. There is really more than one acceptable answer for every problem, depending on the wood type and thickness, or if round or square diagonals are used. You should have a basic knowledge of Google Sheets or Excel, a Google Drive account, and your cellphone or a computer with internet access. First you have to open the webpage where these interfaces are located. (Grades Sine, Cosine and Tangent are the three main functions in trigonometry and are shortened to sin, cos and tan (as they are displayed on your calculator). Section displaying the calculated truss elements’ tensions-compressions. (Note: these sheets are open to the public for distribution and to copy; the master will always remain locked.). Of course any carpenter knows that the basis for roof framing is math. Students should answer: Birch is a stronger wood, 1/8 inch elements of this wood can resist the load 1/8 Hardwood elements cannot. Ask to students now: What does this mean? For those experienced solving systems of linear equations, is going to be odd to have an overdetermined system for a truss structure (more equations than variables). To do this you will write three equations. (Grades Structure Engineer Section Review / AM Section. (Grades Perform the analysis of forces at a truss’ nodes using free body diagrams. Click on the cells next to the truss nodes (show Figure 16), and type the number 10 + ENTER in each one. it is faster to use precalculated tools for your rafters, but as projects get more complicated, it is sloped lot, but forgot to measure it while on site. Make clear that these notes are going to be the most important reference during the associated activity, Trust in the Truss: Design, Construction, and Testing of a Wooden Truss Bridge. John Wiley & Sons. You can also calculate the side length of a triangle if two of the side are known by using Pythagorea's Theorem which says the square of the hypotenuse is equal to the sum of the square of the adjacent side plus the square of the opposite (a^2+b^2=c^2). 12), define and calculate static equilibrium; The Golden Gate Bridge has a unique truss incorporated into its design. Truss members are assumed to be hinged together at the joints and all bars connecting at the joint do not pass through the joint. 12), calculate the X and Y components given a vector; A moment is a measurement of the tendency of a force to make the object rotate around a fixed point. (Grades Use the substitution method to solve systems of linear equations larger than 3 x 3. 288 (B2)instead of the standard 144 used for common rafter calculation. Continue using the Notetaking Sheet. what angle to cut them on. Learning Activity #5. Note to teacher: It is not in the scope of this lesson that students write themselves such interface. 12), Evaluate final solutions and communicate observation, processes, and results of the entire design process, using verbal, graphic, quantitative, virtual, and written means, in addition to three-dimensional models. This truss will be used as an example for the next few steps. Once you verified that the interface gave the same values, you can use the interface for more complex calculations. The second equation will be written for the forces on the truss in the horizontal direction. Using this process and trigonometry, you may also be able to construct your own small scale truss. Here is a simple truss to solve on your own. 12), Document processes and procedures and communicate them to different audiences using appropriate oral and written techniques. If you measure across it in either direction, -supports that have only an upward or downward reactionary force are represented in the diagrams with a rounded bottom or round wheels. Also, every change in the triangles angles or in the loads values will require to perform all the calculations again. if the force causes the body to rotate clockwise, it is considered negative. This free body diagram will correspond to the joint alone and not the entire truss. (Grades Calculates the tensions-compressions for the Warren truss, Warren with Vertical truss, Pratt truss, and Howe truss. In roof framing the variable "B"(run) is always 12 inches. When evaluating solutions it is important to take into account a range of constraints including cost, safety, reliability and aesthetics and to consider social, cultural and environmental impacts. 11 - I have glanced through your Instructable and it seems enough information to design structures like small garden bridges. 9 - (Grades * see attached pictures for step-by step solution*. Therefore, point A experiences what is called a reactionary force. math. It is used to minimize the complexity of any problem. Draw on the board a square representing 1/8 inch and inside a circle with the same diameter to help students with their reasoning. Spreadsheets to Calculate Trusses. 12), use vectors to model situations involving magnitude and direction; compression: Force that is transmitted through a solid when it is pulled tight by forces acting from opposite ends. 12), select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; The following table summarizes truss types and sizes: To activate an interface on a PC, laptop, or tablet, click on the gray square at the right top of the window. is that they depart from the plate at a 22 1/2 degree angle rather than the typical 45 degrees. Historic Bridges. Did you make this project? You should continue with this procedure until you have calculated the force in each member. Make the necessary corrections. (Grades Bridges Project: https://www.sophia.org/playlists/bridges-project, Benson, Harris: University Physics. (Grades Next is suggested a guided practice to teach students the efficient use of these interfaces. We chose point A because the vertical and horizontal components of Ra are therefore not considered in the equation. equilibrium: In Physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. Step 3: Solve this new equation. is actually longer for a hip or valley than for a common rafter. Two entries for the truss elements’ length and angle respect the horizontal. 12), (+) Represent a system of linear equations as a single matrix equation in a vector variable. You have in your notes a hardcopy of these instructions in your notes for quick reference. The next question to students is: Assuming you need a bridge able to support this load, what could be the solution to this problem. 9 - Now that we know the formulas for finding rafter length, we need to know Forces that act directly on the point not considered in it's moment equation. 12), Structures are constructed using a variety of processes and procedures. https://webpages.uncc.edu/~jdbowen/1202/learning_activities_manual/Learning_Activity_3.pdf, University of North Carolina at Charlotte. This bridge had the advantage of low-cost construction, and could also be quickly erected by semi-skilled labor. It considers that every portion of the structure is in equilibrium and every joint with the bars connected to it as a free body. The bridge length for a 5/12 pitch is 13. It is very important they understand completely the use (and limitations) of these interfaces. Force Fbc is acting on the joint at and angle, which means it has both horizontal and vertical components (blue and orange dashed lines in photo denoted as FbcX and FbcY) . 9 - Students should answer something like: The thicker element of 3/16 inch resists this new load. When analyzed in two dimensions, a force F is separated in components along the x-y axes, using the force’s magnitude, its angle with the horizontal axis, and basic right triangle trigonometry. (Grades Later, the bridge was built entirely of iron. The expected answer is: Only two diagonals are broken now. Verify the diagonal’s angle is 60°.

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