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Problem 3 3.0r €2.5 Long bones have a thick layer of hard cortical bone, and a porous inner bone marrow layer that is much softer and can be neglected when determining bone strength, so that the bone is modeled as being hollow. The cortical bone has the following mechanical properties: UCS = 195 MPa for compression and UTS = 133 MPa. Transverse direction: UCS = 133 MPa for compression UTS = 51 MPa for tension. Regardless of direction: USS = 69 MPa. In addition, the Young's modulus is 18 GPa in the longitudinal direction and 9.6 in the transverse, while the shear modulus is 3.5 Gpa in any direction. The tibia is the larger bone in the lower leg. The cross-sectional area of cortical bone for four subjects was measured in 1974, between 20% and 80% of the distance from the proximal part (where it connects to the knee). Below 20% and above 80% (near the knee and ankle joints), the cross-section is much larger. Using the data in this figure and the given information about the ultimate stresses of bone, calculate the following: How much compressive axial load would be required to cause the tibia to fail? (You can assume the tibia does not buckle). Also note where and for what reason it fails, and show your logic and work. Hints: 1) You are definitely given information you don't need to use; don't make this harder than it needs to be. 2) There is a range of values for the Area of cortical bone, cm² 2.0 lan 1.5 1.0 0.5 0.0 Post 30% 40% 50% 60% 70% 80% 20% Position along Tibia (0% = proximal, 100% = distal) different subjects, but you can give your answer as an average value, which you can estimate from the figure.

Problem 3 3.0r €2.5 Long bones have a thick layer of hard cortical bone, and a porous inner bone marrow layer that is much softer and can be neglected when determining bone strength, so that the bone is modeled as being hollow. The cortical bone has the following mechanical properties: UCS = 195 MPa for compression and UTS = 133 MPa. Transverse direction: UCS = 133 MPa for compression UTS = 51 MPa for tension. Regardless of direction: USS = 69 MPa. In addition, the Young's modulus is 18 GPa in the longitudinal direction and 9.6 in the transverse, while the shear modulus is 3.5 Gpa in any direction. The tibia is the larger bone in the lower leg. The cross-sectional area of cortical bone for four subjects was measured in 1974, between 20% and 80% of the distance from the proximal part (where it connects to the knee). Below 20% and above 80% (near the knee and ankle joints), the cross-section is much larger. Using the data in this figure and the given information about the ultimate stresses of bone, calculate the following: How much compressive axial load would be required to cause the tibia to fail? (You can assume the tibia does not buckle). Also note where and for what reason it fails, and show your logic and work. Hints: 1) You are definitely given information you don't need to use; don't make this harder than it needs to be. 2) There is a range of values for the Area of cortical bone, cm² 2.0 lan 1.5 1.0 0.5 0.0 Post 30% 40% 50% 60% 70% 80% 20% Position along Tibia (0% = proximal, 100% = distal) different subjects, but you can give your answer as an average value, which you can estimate from the figure.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 3 3.0r €2.5 Long bones have a thick layer of hard cortical bone, and a porous inner bone marrow layer that is much softer and can be neglected when determining bone strength, so that the bone is modeled as being hollow. The cortical bone has the following mechanical properties: UCS = 195 MPa for compression and UTS = 133 MPa. Transverse direction: UCS = 133 MPa for compression UTS = 51 MPa for tension. Regardless of direction: USS = 69 MPa. In addition, the Young's modulus is 18 GPa in the longitudinal direction and 9.6 in the transverse, while the shear modulus is 3.5 Gpa in any direction. The tibia is the larger bone in the lower leg. The cross-sectional area of cortical bone for four subjects was measured in 1974, between 20% and 80% of the distance from the proximal part (where it connects to the knee). Below 20% and above 80% (near the knee and ankle joints), the cross-section is much larger. Using the data in this figure and the given information about the ultimate stresses of bone, calculate the following: How much compressive axial load would be required to cause the tibia to fail? (You can assume the tibia does not buckle). Also note where and for what reason it fails, and show your logic and work. Hints: 1) You are definitely given information you don't need to use; don't make this harder than it needs to be. 2) There is a range of values for the Area of cortical bone, cm² 2.0 lan 1.5 1.0 0.5 0.0 Post 30% 40% 50% 60% 70% 80% 20% Position along Tibia (0% = proximal, 100% = distal) different subjects, but you can give your answer as an average value, which you can estimate from the figure.
Transcribed Image Text:Problem 3 3.0r €2.5 Long bones have a thick layer of hard cortical bone, and a porous inner bone marrow layer that is much softer and can be neglected when determining bone strength, so that the bone is modeled as being hollow. The cortical bone has the following mechanical properties: UCS = 195 MPa for compression and UTS = 133 MPa. Transverse direction: UCS = 133 MPa for compression UTS = 51 MPa for tension. Regardless of direction: USS = 69 MPa. In addition, the Young's modulus is 18 GPa in the longitudinal direction and 9.6 in the transverse, while the shear modulus is 3.5 Gpa in any direction. The tibia is the larger bone in the lower leg. The cross-sectional area of cortical bone for four subjects was measured in 1974, between 20% and 80% of the distance from the proximal part (where it connects to the knee). Below 20% and above 80% (near the knee and ankle joints), the cross-section is much larger. Using the data in this figure and the given information about the ultimate stresses of bone, calculate the following: How much compressive axial load would be required to cause the tibia to fail? (You can assume the tibia does not buckle). Also note where and for what reason it fails, and show your logic and work. Hints: 1) You are definitely given information you don't need to use; don't make this harder than it needs to be. 2) There is a range of values for the Area of cortical bone, cm² 2.0 lan 1.5 1.0 0.5 0.0 Post 30% 40% 50% 60% 70% 80% 20% Position along Tibia (0% = proximal, 100% = distal) different subjects, but you can give your answer as an average value, which you can estimate from the figure.
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