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Q3 Calculate the minimum and maximum torsional shear stresses in the cortical bone that occur during bone fracture of a typical tibial bone. For simplification, assume pure torsional loading conditions, with zero loads in other planes.

Q3 Calculate the minimum and maximum torsional shear stresses in the cortical bone that occur during bone fracture of a typical tibial bone. For simplification, assume pure torsional loading conditions, with zero loads in other planes.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Table 1: Mechanical behavior of human cadaver tibial bones during pure torsional loads applied with the proximal tibia fixed and the torque applied to the distal tibia until there is bone fracture. Medial condyle Tibial tuberosity- Medial malleolus -Lateral condyle Head of fibula Ti-6Al-4V grade 5 Stainless Steel 316L Region of bone resection -Lateral malleolus L = 365 mm Annealed Annealed Torque at ultimate failure (bone fracture) Displacement (twist angle) at ultimate failure Torsional Stiffness Table 2: Mechanical properties of candidate materials for the rod. Material Process Yield Strength (MPa) 880 220-270 Do = 23 mm Elastic Modulus (GPa) 115 190 d₁ = 14 mm Figure 1: Representative tibia bone showing the resection region (blue arrows) and median length (L). A circular cross section of distal tibia taken at the level of resection) showing the median inner (di) and outer (Do) diameters of the cortical bone. A tibia bone after resection with the proposed metal solid rod (black line) inserted into the distal tibia and ready for attachment of the prosthetic foot. Intramedullary Canal Ultimate Tensile Strength (MPa) 950 600-800 Cortical Bone 40 Nm-216 Nm 5° -12° 10 Nm/° - 55 Nm/° Ultimate Shear Strength (MPa) 550 400 1/2L
Transcribed Image Text:Table 1: Mechanical behavior of human cadaver tibial bones during pure torsional loads applied with the proximal tibia fixed and the torque applied to the distal tibia until there is bone fracture. Medial condyle Tibial tuberosity- Medial malleolus -Lateral condyle Head of fibula Ti-6Al-4V grade 5 Stainless Steel 316L Region of bone resection -Lateral malleolus L = 365 mm Annealed Annealed Torque at ultimate failure (bone fracture) Displacement (twist angle) at ultimate failure Torsional Stiffness Table 2: Mechanical properties of candidate materials for the rod. Material Process Yield Strength (MPa) 880 220-270 Do = 23 mm Elastic Modulus (GPa) 115 190 d₁ = 14 mm Figure 1: Representative tibia bone showing the resection region (blue arrows) and median length (L). A circular cross section of distal tibia taken at the level of resection) showing the median inner (di) and outer (Do) diameters of the cortical bone. A tibia bone after resection with the proposed metal solid rod (black line) inserted into the distal tibia and ready for attachment of the prosthetic foot. Intramedullary Canal Ultimate Tensile Strength (MPa) 950 600-800 Cortical Bone 40 Nm-216 Nm 5° -12° 10 Nm/° - 55 Nm/° Ultimate Shear Strength (MPa) 550 400 1/2L
You are working on a design team at a small orthopaedic firm. Your team is starting to work on a lower limb (foot-ankle) prosthesis for individuals who have undergone foot amputation (bone resection at the distal tibia). You remember hearing about "osseointegration" in an exciting orthopaedic engineering class you attended at Clemson, so you plan to attach the foot prosthesis using a solid metal rod inserted into the distal tibia. You think stainless steel or titanium alloy might be a useful rod material. You decide to begin this problem by identifying typical tibial bone anatomy and mechanical behavior (as provided in the tables and image below). You assume the tibial bone can be modeled as a hollow cylinder of cortical bone, as represented in the image. You anticipate the length of the rod will be 1/2 the length of the tibia. Q3 Calculate the minimum and maximum torsional shear stresses in the cortical bone that occur during bone fracture of a typical tibial bone. For simplification, assume pure torsional loading conditions, with zero loads in other planes.
Transcribed Image Text:You are working on a design team at a small orthopaedic firm. Your team is starting to work on a lower limb (foot-ankle) prosthesis for individuals who have undergone foot amputation (bone resection at the distal tibia). You remember hearing about "osseointegration" in an exciting orthopaedic engineering class you attended at Clemson, so you plan to attach the foot prosthesis using a solid metal rod inserted into the distal tibia. You think stainless steel or titanium alloy might be a useful rod material. You decide to begin this problem by identifying typical tibial bone anatomy and mechanical behavior (as provided in the tables and image below). You assume the tibial bone can be modeled as a hollow cylinder of cortical bone, as represented in the image. You anticipate the length of the rod will be 1/2 the length of the tibia. Q3 Calculate the minimum and maximum torsional shear stresses in the cortical bone that occur during bone fracture of a typical tibial bone. For simplification, assume pure torsional loading conditions, with zero loads in other planes.
Expert Solution
Step 1

Given data:

Outer Radius  =  Do = 23 mm = 0.023 m

Inner Radius  = Di = 14 mm = 0.014 m

Torque at ultimate failure = 40 to 216 Nm

Twist angle at ultimate failure = 5° to 12°

Torsional stiffness = 10 Nm/° to 55 Nm/°

 

We have to calculate the minimum and maximum torsional shear stresses in the cortical bone that occur during bone fracture.

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