bioe119-Spring1994-mt1-Keaveny-exam

bioe119-Spring1994-mt1-Keaveny-exam - 7########

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Unformatted text preview: 7######## ##################6N#######W#######T##################4##[##4##[##4[####4[####4[# ###4i#f##4####4####4####4####4####5#####5##Z##5_#x##4####5# ##5####6$#*##6N####4[########6$####6 ####6$####6$####6N####6$####6$####6$####6$####6$####6$####ME 176 Mid-Term Exam, March 25, 1994Write answers in the space provided. Write on back side if extra space is needed. You have a total of 45 minutes to answer all questions (12:151:00 pm). Closed book, closed notes. Use of a calculator is allowed. Please write your name on the top of each page.1. [20 points] Skeletal Loads. A. [6 points] On a single graph, plot typical ground reaction forces acting on the foot in the vertical and fore-aft directions for the stance phase of gait. Label the axes with typical values, normalizing the axes (Force: x Body-weight; time: percent gait cycle). For the fore-aft component, make a posteriorly-directed force negative. B. [12 points] Write out the equations of motion (SF = ma; SM = Ia) for the isolated shank (knee-ankle segment) that is in contact with the ground as shown in Figure 1. Using the sign convention as shown in Figure 1, write your equations such that all inertial terms are on the right hand side of the equation. Do not assume circular motion about point o. For the moment equation, take moments about the knee joint (point o), and express your answer using only inertial and acceleration terms with respect to the center of mass (as is typically done in clinical gait analyses). Ignore the mass and geometry of the foot, i.e. assume that the ground reaction forces act at the ankle joint. SFx equation: SFy equation: SMo equation: C. [2 points] If the resultant moment about the knee joint is generated by the joint contact force and the simultaneous action of two muscle forces, write out one extra equation that can be used to solve the otherwise indeterminate system: 2. [20 points] Musculoskeletal Materials. Which of the following statements are correct (circle correct statements)?a) cortical bone is composed primarily of lamellar bone while trabecular bone is composed primarily of woven bone; b) the tensile and compressive strengths of cortical bone are equal for transverse loading;c) cortical bone is an anisotropic material;d) cyclic loading of cortical bone can cause its modulus to decrease;e) the modulus of cortical bone is highly dependent on anatomic site;f) the modulus of trabecular bone is lower than that of cortical bone, but the torsional strengths are equal;g) the compressive strength of trabecular bone always increases with increasing apparent density but its tensile strength is always independent of apparent density;h) trabecular bone modulus increases with increasing loading rate, but its strength is independent of the loading rate;i) the strength of the femoral diaphysis depends only on the strength of the bone tissue within the diaphysis;j) falling to the side of the hip increases the risk of a hip fracture compared to falling backwards;k) the risk-factor for a fracture of the vertebral body depends only on the strength of the vertebral body;l) increasing the collagen content increases the static (equilibrium) compressive modulus of cartilage;m) cartilage permeability decreases with increasing applied strain;n) the tensile modulus of tendon is approximately 1000 MPa;o) osteoblasts are the main bone producing cells while osteocytes are the main bone resorbing cells; p) the tensile and compressive moduli of trabecular bone are equal;q) for loading that simulates a fall to the side of the hip, old femora are approximately two times weaker than young femora;r) cortical and trabecular bone creep in a qualitatively similar way to creep of metals;s) the tensile strength of cortical bone decreases at a rate of approximately 5% per decade;t) assuming human femoral cortical bone is a transversely isotropic material, 7 elastic constants are necessary to describe fully its elastic behavior. 3. [35 points] Trabecular Bone Mechanics. A. [25 points] Assume that the honeycomb shown in Figure 3 fails by plastic yielding of the oblique cell walls. Derive the following expression for the moment Mp required to cause full yielding of the oblique cell walls (for in-plane, vertical loading of the honeycomb). Your analysis should account for the strength asymmetry of the cell wall material. [Note: (x2 y2) = (x-y)(x+y)]. #where # ; # is the compressive yield strength of the cell wall material; # is the tensile yield strength of the cell wall material; and a is the distance from the neutral axis to the centroidal axis of the beam. B. [5 points] Will the value of r affect the strength asymmetry of the whole specimen (for the assumed failure mode in this problem)?C. [5 points] What is the ratio of the specimen strength for strength symmetry of the cell wall material [r=1.0] to the specimen strength for strength asymmetry of the cell wall material [r=0.7]? 4. [25 points] Stresses in Long Bones.The diaphyses of long bones are hollow and composed primarily of cortical bone material because this structural combination may be more efficient physiologically than that of a solid bone composed primarily of trabecular bone material. To gain some insight into this issue, consider two hypothetical circular, cylindrical diaphyses of the same length (L) subjected to the same bending moment (M). One diaphysis is hollow (outer diameter Doh; inner diameter Dih), and is composed of uniform cortical bone with an apparent density rcort. The other diaphysis is solid (outer diameter Dos), and is composed of uniform trabecular bone with an apparent density rtrab = b rcort (b<1). Assume that the body adapts such that the risk-factor R (applied stress / yield strength = s/sy) at the periosteal surface of the diaphysis is equal for each model. For this situation, derive the following expression: # where g = Dih/Doh.Additional assumptions/hints:The stresses in the bone can be calculated using simple beam theory.The yield strength of the bone material is linearly proportional to its apparent density #(sy = a r, where a is some constant).See next page for bonus question. 4. 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