E106 Lecture Problem 215

1
E106 Lecture Problem - 215

• Nikhil Sonde
• 2/21/07

2
The Problem

• 215. A 3/8-inch diameter piece of chalk with a
  failure strength of 29 psi (yes, psi)
• fails in a three-point bending test at a load
  of 0.200 lb. What is the length of the piece of
  chalk?

3
Background

• 3 point bending/flexural test

4
Why the 3-point test?

• Tensile stress test cannot be used for ceramics
• Difficult to make specimens with required
  geometry
• Brittle ceramics are hard to grip without
  breaking
• Ceramics fail after only about 0.1 strain, so to
  avoid bending stresses, the specimens must be
  perfectly aligned
• Ceramics are much stronger in compression than in
  tension

5
Solution
M maximum bending moment c distance from
center of specimen to outer fibers I
moment of inertia of cross-section
29 psi
0.2 lb
0.1875 in
3.00 in
Insert 7.18 again
6
Questions?