## Lab
Manual for Engrd 202, Virtual Torsion Experiment

(Turkey Tibiotarsus)

### Introduction

In
this module, you will perform data reduction and analysis for
turkey tibiotarsus bones. They are not circular in cross section
and so the analysis for bones is different from the circular samples.
In the analysis, you will approximate the bone as a hollow circular
cross section. You will use the dimensions of the circular cross
section to estimate the stiffness, shear modulus and strength
of the bone.

You will plot the torque vs. twist curve and study it to examine
the behavior of bone under torsional loading. From this plot you
will determine whole bone ultimate torque and stiffness. Based
on these values, you will deduce bone material properties such
as shear strength and shear modulus. You may note that each individual
bone behaves slightly different. Details of the sample geometry,
as defined in slides 6 and 7 of the chalk talk on turkey bone,
are provided along with each data file. For review refer to the
chalk talk on turkey bone. To understand the calculations for
cross sectional area and polar moment of inertia, refer to slide
7 of the chalk talk on turkey bone.

### Procedure

Select
one data set from the wet turkey bone test data and one from the
dry turkey bone test data. The measured dimensions for each bone
sample are listed at the top of the text and Excel data files.
This information is displayed in the Matlab GUI as well. Date
files are named according to the following convention: Material_Type_Repeat.***,
where the stars are in place of the file type extension. For example
turkeybone_Wet_3.xls would be the Excel file containing data for
the test performed on wet turkey sample 3. Plot the torque-twist
curves for the data set; continue your analysis by completing
tables 3 and 4, then proceed to answering the questions below
and to writing your lab report. Step-by-step directions for completing
the data sheets, (tables 3 and 4) are given at the end of the
module.

### Lab Report

Your
lab report should include the completed data sheets, graphs and
a brief discussion of the lab procedure. The report should also
provide answers to the questions below and any other discussion,
observations or comments you wish to include.

### Questions
and data analysis for turkey tibiotarsus:

**1**.
Find the shear modulus, G, and the shear strength, .

**2.** Using your textbooks and other resources, find a different
material (or materials) with similar G values to the wet turkey
bone. Do you think that this material can be used as an artificial
bone?

**3.** Describe in words what the fracture surfaces look like.
Do all the bones break exactly in the same way?

**4.** Suppose you want to breed super turkeys that were twice
the mass of normal turkeys. Do you think the tibiotarsus bone
would be thicker and or bigger in diameter (2 )? If so, by how
much would these increase to double the torsional load carrying
capacity of the wet bone?

**5.** Compare the results you got for the dry turkey bone
to those for the wet turkey bone. How do the ultimate torque Tu
, the bone stiffness, the shear modulus and shear strength differ?

Step by step instructions for completing Tables 3 and 4 for a
given data set and Sample ID

**a)**
Select the data file and open it. You may choose to use a text
file (.txt) or an Excel file (.xls). The Matlab GUI (VL_1_v10.m)
uses the .txt files.

**b)** Enter the sample ID, material and the dimensions of
the test sample on table 3. Use the information given in the header
of the text file or Excel file. If you choose to use the Matlab
program, this information will be displayed on the GUI.

**c)** Calculate the area and polar moment of inertia of the
equivalent circular cross section. Refer to slides 6 and 7 of
the chalk talk on turkey bone for details. Enter these values
in rows 2 and 3 of table 4.

**d)** Plot the torque vs. twist for the sample. For this purpose,
you may choose to use the Matlab GUI. In the Excel files the plots
are provided to you. You may refer to 'Hints for graphing' in
case of any difficulty in plotting the data.

**e)** From the plot, find the ultimate torque Tu. Fill this
value in row 4, table 4.

**f)** Now, plot the torque-twist curve in the linear region.
Find the sample stiffness (equal to the slope of the line). Denote
this value as , the total stiffness (slide 8 of the chalk talk
on turkey bone). Note that you may assume , since the test machine
is almost infinitely stiffer than the bone sample. Enter this
value in row 5, table 4.

**g)** Now using formulas given in slides 9 and 10 of the chalk
talk on turkey bone, calculate the shear modulus and shear strength
for the bone. Enter these values in rows 6 and 7 of table 4.

** **