Young’s Modulus of a Chicken Bone

Introduction

The strength of bone depends on the stresses to which it is subjected.  While we have not done a biomechanical analysis of a leg and thigh bone of a chicken, we can suggest that the two may be subjected to different stresses and may therefore have different properties.  This laboratory is designed to examine the elastic modulus of the chicken leg and thigh bone.

Null Hypothesis

The null hypothesis for this laboratory is:

The Young's modulus of a chicken leg bone (scientific term “ossius drumstickus”) is the same as that for a chicken thigh bone.

The alternative hypothesis is:

The Young’s modulus of a chicken leg bone differs from that of a chicken thigh bone.

Experimental Setup

Again, you will assemble your own experimental system.

You can support the bone so that it looks like a simply supported beam, as depicted in Figure 2.

is the load applied to the middle of the beam (bone), and  is the distance between the supports (not the length of the bone).  The load pushes the beam downward by a small amount , according to the following formula:

The equation can be solved for  as a function of  and .

Thus, by measuring both load and deflection you can back E out of the equation.

Transducer Calibration

You will need to calibrate your displacement detector, based on some known displacement.  The concept for the displacement transducer is shown in Figure 3.  A photoresistor with a piece of electrical tape across one half  is attached to the bone, and the laser is directed at the edge of the tape.  As the bone moves downward, the light from the laser strikes more of the photoresistor, causing a decrease in resistance that is monotonically related to the deflection.

You need to ensure that you know how much load was applied to your bone.  Calibrated weights would serve this purpose well.  An alternative is to use water as a standard.  You know the density of water (1 g/cm3 in the metric scale, or, in the English system “a pint’s a pound the world around”).  Thus, if you can measure a volume of water, you know the mass. Of course, density will vary somewhat with temperature, but is the variation significant for the purpose of this laboratory?

You will want to measure deflection for a number (N) of applied loads.

The I Parameter

The equation for deflection as a function of load includes the parameter I, which depends on the geometry of the beam (bone).  You should make the assumption that the bone is a hollow tube, with a cross-section as shown to the right.  You will need to know the thickness of the wall and the bone outer or inner diameter.

Data analysis

1.     Determine the calibration of your sensor (concentration as a function of voltage).

2.     Determine the applied loads for each of the N measurements.

3.     From your sensor and its calibration, determine the deflection for each applied load.

4.     Plot deflection as a function of applied load.

5.     Use the equation from your statics book to determine the elastic modulus, given the data you collected for each of the N pairs of deflection and load.

6.     When you have obtained the elastic modulus (the average of the N trials), you can use this to compare theory (the equation for deflection as a function of load) to the data you collected.

7.     Discuss reasons for any differences (theory vs experiment).

1.     Perform Student’s T-tests to test the hypothesis.  Provide a p-value.  Are the results significant?

BIEN 435

Louisiana Tech University

Last Updated February 27, 2005

Steven A. Jones