Graphing in Mathcad

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Draw a FBD of the beam for x = 2 m. Class Problem: A stunt motorcycle driver rides a wheelie across a bridge. The combined weight of the rider and the motorcycle is 2.45 kN (about 550 lbs). Draw a FBD of the beam for x = 2 m. Determine the reactions at A and C for x = 2 m. Derive an equation for the reactions at A and C as a function of x. Enter the equation from (c) into Mathcad, and plot Ay and Cy versus x on the same plot. Assumptions: The tire will have frictional forces with the road that could lead to a non‐zero value for Ax. Ignore these forces when computing reactions. Ignore dynamic effects (bumps, bouncing, change in motorcycle angle, etc. ). Solution: 𝑦 𝑊=2.45𝑘𝑁 x=2m 5m 𝐴 𝑥 𝑥 𝐴 𝑦 𝐶 𝑦

b. Determine the reactions at A and C for x=2m 𝐹 𝑥 = 𝐴 𝑥 =0 𝑦 𝐴 𝑥 𝐴 𝑦 𝐶 𝑦 𝑊=2.45𝑘𝑁 b. Determine the reactions at A and C for x=2m 𝐹 𝑥 = 𝐴 𝑥 =0 𝑀 𝐴 =−2.45𝑘𝑁∙2𝑚+ 𝐶 𝑦 ∙5𝑚=0 + c. Derive the reactions for A and C as a function of x. Starting with Cy , replace the distance of “2m” with the variable “x.” 𝐶 𝑦 = 2.45𝑘𝑁∙2𝑚 5𝑚 =0.98𝑘𝑁 𝐶 𝑦 = 2.45𝑘𝑁∙2𝑚 5𝑚 ⟹ 𝐶 𝑦 (𝑥)= 2.45𝑘𝑁∙𝑥 5𝑚 𝐹 𝑦 = 𝐴 𝑦 + 𝐶 𝑦 −2.45𝑘𝑁=0 𝐴 𝑦 +0.98𝑘𝑁−2.45𝑘𝑁=0 Now, solve for Ay in terms of x, utilizing the equation for Cy as determined above. 𝐴 𝑦 =1.47𝑘𝑁 𝐴 𝑦 + 𝐶 𝑦 −2.45𝑘𝑁=0 𝐴 𝑦 =2.45𝑘𝑁− 𝐶 𝑦 ⇒ 𝐴 𝑦 (𝑥)=2.45𝑘𝑁− 2.45𝑘𝑁∙𝑥 5𝑚 𝐴 𝑦 (𝑥)=2.45𝑘𝑁−0.49∙𝑥

d. Enter the equation from (c) into Mathcad, and plot Ay and Cy versus x on the same plot. In preparation to put the equations derived in part c into Mathcad, it is good practice to parameterize the equations. To parameterize, means to assign a variable to all knowns. You can define these variables at the beginning of your Mathcad worksheet. Now if any of these known values change you only have to make adjustments to the beginning of the sheet and the Mathcad recalculates all of the answers accordingly. Parameterized variables: 𝑊=2.45𝑘𝑁 𝑙=5𝑚 If we define these variables at the beginning of our Mathcad worksheet, we can use these forms of the equations for C(x) and Ay(x). From part c. 𝐶 𝑦 𝑥 = 2.45𝑘𝑁∙𝑥 5𝑚 ⟹ 𝐶 𝑦 (𝑥)= 𝑊∙𝑥 𝑙 𝐴 𝑦 𝑥 =2.45𝑘𝑁− 2.45𝑘𝑁∙𝑥 5𝑚 ⟹ 𝐴 𝑦 (𝑥)=𝑊− 𝑊∙𝑥 𝑙

Second value in the list d. Enter the equation from (c) into Mathcad, and plot Ay and Cy versus x on the same plot. Notice these X and x are different. X is defined to equal 2m, but x is used as the function variable. Mathcad is case sensitive. You can use that to your advantage. Step 1: Early in the spreadsheet define the parameterized variables. Enter the parameterized form of the equations. Be sure to write the functions as Ay(x) and Cy(x). Use a colon to assign the left hand side to the right hand side, which will display as := on your screen. Step 2: Set the first, second and last values of the variable x. The increment in x will be set to the second value minus the first value; that is, the increment will be 0.2 below (0.2 = 0.2 – 0). Key Stroke: x : 0m , 0.2m 5m (notice how the structure appears once you type the comma) Second value in the list Starting value Ending value

Step 3: Go to the “Plots” tab and click “Insert Plot” and choose “XY Plot” Step 4: Enter the appropriate independent and dependent variables. The independent variables are the x values. The dependent variables are the Ay and Cy ; we will plot two lines on one graph. Step 5: Add the second plot on the graph by pressing <shift> <enter>. Notice how the graph starts at 0m and ends at 5m.

Step 6: Customize the plot through formatting. Move the y-axis to a more intuitive location by clicking on the label and dragging it to a different location. Change line colors. Add markers. Adjust line thickness.