Computer Prep Math Project 8

Technical Math II Lab2: Truss Trigonometry Lab 2: Truss Trigonometry

Name Name

Name Name This lab is based on assignments originally written by Kevin Mirus, a former math instructor at Madison Area Technical College, now head of the STEM Center. Imagine that you’ve been hired by a roof truss company. The company is going all CNC for its production, which means programming a computer with dimensions for trusses to be cut and assembled. Your boss wants you to take the truss shown below, and come up with formulas that describe the dimensions of each piece that make up the truss. The two angled pieces in the truss have midlines that run from the center of the top chord to the center of the outside of the roof rafters. The formulas should be in terms of the span of the truss (dimension L on the diagram), the pitch of the roof p (for example, p = 1/3 for a 4-12 pitch roof), and the width W of the boards used. On the next few pages, you will have to derive your formulas for each piece. If you require more space for your derivations and results attach your work on additional sheets. Each part of the lab is worth 10 points.

Part I: (2 points) Write the formula for the angle in terms of the pitch p.

Write the formula for the overall height H of the truss in terms of L, , and W.

As a check on your formulas, if L = 20.0 ft, W = 12.0 in and p = 1/2, then you should get and  = 26.57, H = 6.00 ft. Page 2 Technical Math II Lab2: Truss Trigonometry Part II: (4 points) Write the formulas in terms of L, , and W for the labeled dimensions and angles of the rafter shown below. As a check on your formulas, if L = 20.0 ft, W = 12.0 in and p = 1/2, then you should get 1 = 26.565, 2 = 153.435, 3 = 63.435, 4 = 116.565, s1 = 26.833 in, s2 = 13.416 in, L1 = 134.164 in and L2 = 104.164 in . Additional values for checking are shown in the attached sample spread sheets of Part V. Page 3 Technical Math II Lab2: Truss Trigonometry Part III: (4 points) Write the formulas in terms of L, , and W for the labeled dimensions and angles of the center post shown below. As a check on your formulas, if L = 20.0 ft, W = 12.0 in and p = 1/2, then you should get 5 = 126.870, 6 = 26.565, s3 = 6.708 in, L3 = 46.584 in and L7 = 43.584 in . Additional values for checking are shown in the attached sample spread sheets of Part V. Page 4 Technical Math II Lab2: Truss Trigonometry Part IV: (10 points) Write the formulas in terms of L, , and W for the labeled dimensions of the angle piece below. As a check on your formulas, if L = 20.0 ft, W = 12.0 in and p = 1/2, then you should get

7 = 126.870, 8 = 116.565, 9 = 153.435, and 10 = 53.130, s4 = 15.000 in, s5 = 9.708 in, s6 = 7.416 in, L4 = 37.874 in, L5 = 44.582 in and L6 = 51.215 in . Additional values for checking are shown in the attached sample spread sheets of Part V.

This is probably the most difficult part of the calculations. The following hint may help you get started. Consider the right triangle ABC with angle ABC = 90. Bisect AC at point M and form segment MB. From M drop a perpendicular to AB at point D. Now consider triangles ADM and BDM. Page 5 Technical Math II Lab2: Truss Trigonometry Page 6 Technical Math II Lab2: Truss Trigonometry Part V: (30 points) Now suppose your boss wants a table showing all the calculations for every combination of spans from 10 feet to 20 feet in two foot increments, and pitches from 1/6 to 6/6 in 1/6 increments for members made of 2 by 4's (i.e., W = 3.5 inches). The top of the spread sheet should display a descriptive title, the names of the group members, and a schematic of the full truss. The four graphic images (truss.gif, rafter.gif, centerpiece.gif, and anglepiece.gif) are available on the website http://matcmadison.edu/alehnen/TechmathII/TechMathIILabs.html. For each of the three truss members considered in Parts II through IV display the following: 1. A graphic of the piece. 2. A summary of your analysis which shows a typed text version of the formula you derived for each dimension or angle associated with the piece.

3. A table which shows under separate column headings the input data (L and p), the angle  in both radians and degrees and all other calculated measurements associated with the piece. There should be row of values for each value of L and p requested. All calculated dimensions should be displayed in inches with two decimal places. All calculated angles except  should be displayed in degree measure with three decimal places. The Excel trigonometric functions, SIN(), COS() and TAN() assume that the input angle is in radians. The Excel tan-1 function has the name ATAN(). It outputs the angle in radians. The Excel function PI(), no argument specified, gives the value of Pi. Use the Landscape option and the scaling adjust under Page Setup so that the results of all columns can be seen on a single sheet of paper. Attach a complete printout of your spreadsheet as part of your lab report. Sample parts of the spreadsheet are shown on the following pages. Page 7 Technical Math II Lab2: Truss Trigonometry Page 8 Technical Math II Lab2: Truss Trigonometry Page 9 Technical Math II Lab2: Truss Trigonometry