ME 309 – Project #1 For this project you may work with a partner or individually. A data file is provided (project_data.xlsx) that contains the digitized coordinates of the outer and inner contours of a cross section of bone as shown below. Your task is

ME 309 – Project #1

For this project you may work with a partner or individually. A data file is provided (project_data.xlsx) that contains the digitized coordinates of the outer and inner contours of a cross section of bone as shown below. Your task is to compute the area moments of inertia, IXX, IYY for the section enclosed by the inner and outer contours with respect to the origin of the XY coordinate system. The scale is in mm. The steps and formulas are provided. Use subroutines and functions to help with organization. Test each module thoroughly. Present all your results including your name(s) in a single sheet.

Steps:

1. Compute the centroid of the outer contour to establish the origin of the coordinate system

2. Using an appropriate interpolation function calculate new points on the inner and outer contours at common one degree increments (360 points).

3. Triangulate adjacent points on each contour to form two discrete triangles as shown below

4. Compute the location of the centroid, C (with respect to the global coordinate system X,Y) and moments of inertia, Ill, Imm for each triangle with respect to its centroid using the formulas provided. Choose (1,2 so that axis 1-1 is parallel to the x-axis of the global coordinate system.

1

5. Compute I11, I22 using (1,2 (Note: Axis 1-1 is parallel to Axis X-X)

6. Compute the triangle inertia with respect to the global coordinate axes using the parallel axis theorem

7. Compute the total inertia, IXX, IYY by summing X and Y components of the triangle inertias.

Xo(i), Yo(i)

Xo(i+1), Yo(i+1)

Xi(i+1), Yi(i+1)

Xi(i), Yi(i)

2

2

1

1

m

m

l

l

d

yl

ym

b

C

(1,2

a

1

1

2

2

X

Y

dy

dx