2.24 Given reasonable values of the material parameters for bone, estimate the axial stress in your femur due to standing, walking, and running. Toward this end, estimate the increase in the applied load (in terms of body weight and in comparison to the load due to standing) due to walking and running. Once done, note that even though we did not discuss it, bone exhibits viscoelastic, not just elastic, behavior under certain conditions. In particular, the Young's modulus increases with increases in strain rate. It has been estimated, for example, that Ec, where is the extensional strain rate and c and d are material parameters. If E= 16 GPa at = 0.001 s-¹ (slow walking) and d~0.06, find the value of c. Next, compute the value of E for vigorous activity, with 0.01 s¹, and discuss how this would effect your first estimate for stress in your femur.

2.24 Given reasonable values of the material parameters for bone, estimate the axial stress in your femur due to standing, walking, and running. Toward this end, estimate the increase in the applied load (in terms of body weight and in comparison to the load due to standing) due to walking and running. Once done, note that even though we did not discuss it, bone exhibits viscoelastic, not just elastic, behavior under certain conditions. In particular, the Young's modulus increases with increases in strain rate. It has been estimated, for example, that Ec, where is the extensional strain rate and c and d are material parameters. If E= 16 GPa at = 0.001 s-¹ (slow walking) and d~0.06, find the value of c. Next, compute the value of E for vigorous activity, with 0.01 s¹, and discuss how this would effect your first estimate for stress in your femur.

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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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

### Problem 2.24

Given reasonable values of the material parameters for bone, estimate the axial stress in your femur due to standing, walking, and running. Toward this end, estimate the increase in the applied load (in terms of body weight and in comparison to the load due to standing) due to walking and running.

Once done, note that even though we did not discuss it, bone exhibits viscoelastic, not just elastic, behavior under certain conditions. In particular, the Young’s modulus increases with increases in strain rate. It has been estimated, for example, that

\[ E \sim c \dot{\varepsilon}^d \]

where \( \dot{\varepsilon} \) is the extensional strain rate and \( c \) and \( d \) are material parameters. If \( E = 16 \) GPa at \( \dot{\varepsilon} = 0.001 \) s\(^{-1}\) (slow walking) and \( d \approx 0.06 \), find the value of \( c \).

Next, compute the value of \( E \) for vigorous activity, with \( \dot{\varepsilon} \approx 0.01 \) s\(^{-1}\), and discuss how this would affect your first estimate for stress in your femur.

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