Lecture 9 Announcements HW#5 due TODAY!!!!!  HW#6 due Wednesday, 2/7 HW#7 due MONDAY, 2/12 (you have 3 extra days) HW#8 due Wednesday 2/14 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Contact Stresses (handout from Mohsenin book) Hertz Problem of Contact Stresses Importance: “In ag products the Hertz method can be used to determine the contact forces and displacements of individual units” 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Assumptions: Material is homogeneous Loads applied are static Hooke’s law holds Contacting stresses vanish at the opposite ends Radii of curvature of contacting solid are very large compared to radius of contact surface Contact surface is smooth 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Maximum contact stress occurs at the center of the surface of contact a and b are the major and minor semiaxes of the elliptic contact area For ag. Products, consider bottom 2 figures in Figure 6.1 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity In the case of 2 contact spheres: 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity To determine the elastic modulus, E… for steel flat plate: for steel spherical indentor: 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Stacked particles (grain, seeds, dirt clods) Figure 5.1 Dropped particles Grain bin and handling damage Figure 5.3 – Table 5.13: example of product testing. Broken or damage material: determined using sieves. Bruised fruit: determined by visual inspection, spectral reflectance, Magness-Taylor pressure tester. 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

BAE2022/BAE4400 Physical Properties of Biological Materials HW#8 Assignment Problem 1: An hydrostatic bulk compression test on a sample of oranges indicates an average bulk modulus of 375 psi. Testing of specimens from the same group of oranges shows a compression modulus E of 425 psi. Some of the whole oranges are subjected to a parallel plate test. The average orange diameter is 2.375 inches and the axial deformation for the whole oranges was 0.025 inches for a force of 4 lbs. Estimate the modulus of elasticity for the whole oranges using the Hertz formula for contact stresses. Problem 2: A 10 lb. crate of apples is placed on top of an open box of strawberries (single layer). A previous test of a similar box of strawberries indicated a compression modulus of 325 psi. The average diameter of a strawberry is 1.125 inches. The axial deformation at 10 lb is 0.0375 inches. Estimate the modulus of elasticity for the strawberries using the Hertz formula. (Bulk modulus = 250 psi) Problem 3: When soybeans are loaded using an auger into a grain bin at 13.1 meters (10° C), what percent of whole soybeans on the bottom of the grain bin can be expected to be damaged? Problem 4: 3000 bu. of winter wheat at 11.1% mc (wet basis) is loaded into the top of a 31.4 meter silo with a concrete bottom. How many bushels of the wheat will remain undamaged? 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials