bioe119-fall98-final-Keaveny-exam

bioe119-fall98-final-Keaveny-exam - ME 176 Final Exam, Fall...

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ME 176 Final Exam, Fall 1998 Name: __________________________________________ Page 1 of 11 Tuesday, December 15, 5:00–8:00 PM, 1998. Answer all questions for a maximum of 100 points. Please write all answers in the space provided. If you need more space, there is an additional page at the end. Indicate your answer as clearly as possible for each question. Write your name at the top of each page as indicated. Read each question very carefully! ____________________________________________________________________________________ 1. (15 points total) Dynamic Planar (2D) Analysis of the Skeleton Gravity is the most common force used to offer resistance in physical therapy. An exercise mass m ex is placed on a patient’s foot for quadriceps strengthening (Figure 1). This mass behaves as a concentrated mass acting at a distance L from the knee joint center o . The patient, sitting on a chair, is asked to extend their shank off the floor. At some instant, the shank is at an angle q to the vertical, as shown, and can be assumed to be rotating about the fixed knee center o with angular velocity w and angular acceleration a . Assume that: 1) the mass of the shank and foot (not including the exercise mass) is m leg with a center of mass at a distance L 1 from the knee center and a mass moment of inertia I leg about this point; 2) the ankle joint is rigid; 3) the only other loads acting on the shank are the joint resultant force and moment ( F res-k and M res-k respectively) at the knee joint; and 4) this is a two-dimensional planar rigid body problem. (i) [7 points] Draw a free body diagram, including all accelerations, of the knee/foot/mass system. Figure 1 (ii) [8 points] Write out the equation of rotational motion about the knee joint center. Express all inertial parameters explicitly in terms of I leg, m ex and m leg .
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ME 176 Final Exam, Fall 1998 Name: __________________________________________ Page 2 of 11 2. (25 points total) Shear Lag Theory, Load Sharing, and Load Transfer (i) [10 points] For shear-lag theory applied to two concentric cylinders loaded axially: (a) draw the free-body diagrams of the relevant differential elements of the structure (b) write out the equations for the kinematic assumptions (c) write out the equations for the constitutive assumptions (d) write out the boundary conditions
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ME 176 Final Exam, Fall 1998 Name: __________________________________________ Page 3 of 11 (ii) [5 points] From these equations, derive the overall governing differential equation: d 2 g dx 2 p (1 + d ) D G t E 1 A 1 g = 0 where g is the shear strain in the interface material, x is the distance along the interface, d is the ratio of the axial stiffnesses (E 1 A 1 /E 2 A 2
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This note was uploaded on 09/16/2009 for the course BIO ENG 119 taught by Professor Keaveny during the Spring '09 term at University of California, Berkeley.

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bioe119-fall98-final-Keaveny-exam - ME 176 Final Exam, Fall...

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