Assignment 3

Please write answers to the following questions:

1. A specimen for a tension test has a total length of 12 inches, and a "gauge section" (the uniform part of the "dogbone") of 8 inches.  The cross section of the gauge section is 1.00 in X 0.25 in.  Two strain gauges are mounted on the sample at the midpoint, one on each (opposite) side.  When the sample is put in the upper jaws, the bottom of the sample does not line up with the lower jaws.  It is necessary to push the end of the sample by 0.50 inches to allow it to fit in the bottom jaws.

(a) Estimate how this misalignment will affect your strain readings assuming that the specimen is made of aluminum; (b) bamboo.
(c) Explain why you think that the ISO standard (Part 1, section 12.4.5) specifies the use of two strain guages on opposite sides.

2.  In specifying the appropriate dimensions of a bamboo beam for a bending test, Section 10.4 of the ISO Standard, Part 1, reads "In order to obtain a failure in bending, the free span shall be at least 30D, in which D is the outer diameter [of the culm]".  This is restated in Section 10.4 of Part 2.  Give an explanation for this recommendation based on a simple mechanical analysis of a beam under 4-point bending.  Hint: draw the shear and moment diagrams of two beams under 4-point bending, a short one and a long one.  What is the difference in testing a short beam vs. a long beam?

Comment: the standard 30D is based on the research of Vaessen & Janssen (1997), which is reference [4] in Part 2.  It is NOT expected that you read and re-derive this result.  Rather, the point of the exercise is to use some basic ideas from Mechanics of Materials to at least see that the length of the sample has a potential on the kind of failure that will occur.