Problem #1 (35 pts)
After fracture of the tibia, a callus forms around the fracture site, consisting of a mixture of woven bone and
cartilage. Over time, the callus is replaced with normal, organized bone tissue (called lamellar bone) that is
much stronge

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Due July 12, 2016
Problem Set 3: Linear Elasticity and Viscoelasticity
Problem #1: During normal motion, the medial collateral ligament (MCL) is subjected to a tensile axial load of
60 N. Assume the MCL is a prismatic bar with length 10

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Due July 5, 2016
Problem Set 2: Stress, Strain, Mechanical Properties of Materials, and Linear Elasticity
Problem #1: The lining of blood vessels, called the endothelium, is made up of cells called endothelial cells.
These cells are con

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Due August 16, 2016
Problem Set 8: Stresses in Beams
Problem #1: During a football game, a player is tackled in the open field and suffers an intense lateral load to
his tibia. The situation can be described by the following simple beam

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Due July 5, 2016
Problem Set 2: Stress, Strain, Mechanical Properties of Materials, and Linear Elasticity
Problem #1: The lining of blood vessels, called the endothelium, is made up of cells called endothelial cells.
These cells are con

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Due March 3, 2015
Problem Set 8: Normal and Shear Stresses in Beams
Problem #1: During a football game, a player is tackled in the open field and suffers an intense lateral load to
his tibia. The situation can be described by the follow

Modeling Exercise II
a) Diagrams
Figure 1- Cross Section of Axon, blue
Figure 2 Side view of a Microtubule
circle represents a single
Figure 3 - Side view of a microtubule microtubule
20 microtubules make up an axon
with forces illustrated
Figure 4
of a
M

BMES 345 Practice Problem Solutions
1. Introduction to Stress and Strain
2. Mechanical Properties of Tissues and Biomaterials
3. Linear Elasticity
Problem #1: Consider the forearm in 90o flexion and holding a ball, as shown.
The mass of the forearm is 1.1

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Due January 27, 2015
Problem Set 3: Viscoelasticity and Axial Loading
Problem #1: Consider the creep response of a viscoelastic biological tissue under a compressive stress of 2
MPa:
0.040
0.035
0.030
Strain
0.025
0.020
0.015
0.010
0.00

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Due January 20, 2015
Problem Set 2: Stress, Strain, Mechanical Properties of Materials, and Linear Elasticity
Problem #1: The lining of blood vessels, called the endothelium, is made up of cells called endothelial cells.
These cells are

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Due in-class February 12, 2015
Modeling Exercise 2: Modeling Non-Uniform Axial Loading of a Microtubule
One of the important functions of microtubules is to serve as a highway for transport of vesicles and
organelles, in conjunction wit

Solutions for Problem Set 2
Problem #1: The lining of blood vessels, called the endothelium, is made up of cells called endothelial cells.
These cells are constantly subjected to shear forces generated by the fluid flow in the circulatory system.
Consider

Solutions to Problem Set 6
Problem #1: An osteosarcoma (bone tumor) is removed from a patients tibia, leaving a large defect in the
patients bone. The surgeons use an experimental bioactive ceramic scaffold to replace the defect, press
fitting it into the

Solutions for Problem Set 5
Problem #1: A number of polymer biomaterials have been considered for orthopedic applications, but the
strength of these polymers is often a concern. To address, researchers and engineers have reinforced these
polymers with fib

Solutions to Problem Set 3
Problem #1: During normal motion, the medial collateral ligament (MCL) is subjected to a tensile axial load of
60 N. Assume the MCL is a prismatic bar with length 10 cm, cross-sectional area 11 mm2, an elastic modulus
E = 275 MP

Solutions to Problem Set 7
Problem #1: Draw the shear force and bending moment diagrams for this simple beam subjected to a
concentrated load and a couple.
Reaction loads:
Shear force and bending moment:
Segment 1: 0 < x < L/3
;
Segment 2: L/3

Solutions to Problem Set 4
Problem #1: Consider the portion of the cervical spine known as C3-C6, consisting of four cervical vertebrae
and three interposing intervertebral discs:
Assume you can model each vertebral body and intervertebral disc as prismat

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Due August 9, 2016
Problem Set 7: Beams and Bending
Problem #1: Draw the shear force and bending moment diagrams for this simple beam subjected to a
concentrated load and a couple.
Problem #2: An atomic force microscope (AFM) is a highl

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Due June 28, 2016
Problem Set 1: Stress and Strain
Problem #1: Consider the cross-sections of the humeri from an adult tennis player (adapted from Jones et al.,
Journal of Bone and Joint Surgery 1977), assuming the cross-sections are an

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Due August 2, 2016
Problem Set 6: Torsion and Pressure Vessels
Problem #1: An osteosarcoma (bone tumor) is removed from a patients tibia, leaving a large defect in the
patients bone. The surgeons use an experimental bioactive ceramic sc

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Problem Set 9: Stresses in Beams, Deflection of Beams, and Plane Stress
Problem #1: Consider this hypothetical (and, to be honest, patently absurd) five point bending test of a chicken
leg bone:
a) Determine the reaction loads (forces a

Solutions for Problem Set 8
Problem #1: During a football game, a player is tackled in the open field and suffers an intense lateral load to
his tibia. The situation can be described by the following simple beam:
Assume that the tibia has an outer diamete

Solutions for Problem Set 9
Problem #1: Consider this hypothetical (and patently absurd) five point bending test of a chicken leg bone:
a) Determine the reaction loads (forces and moments) at the support points A and B.
First draw the free body diagram of

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Student ID#:
Due in-class January 22, 2015
Modeling Exercise 1: Building Blocks of a Model Microtubule
Microtubules are a major component of the cytoskeleton of cells, and are particularly prominent in transport of
vesicles and organelles, the struc

Modeling Exercise III
1. The authors assume that the kinocilia are homogenous, cylindrical rods and they were modeled as
isotropic cantilevered beams with the elastic properties using the EulerBernoulli and Timoshenko
beam model.
2. The Euler- Bernoulli t

BMES 345 Practice Problems
1. Introduction to Stress and Strain
2. Mechanical Properties of Tissues and Biomaterials
3. Linear Elasticity
Problem #1: Consider the forearm in 90o flexion and holding a ball, as shown.
The mass of the forearm is 1.1 kg, and

Solutions for BMES 345 Exam #1
Problem #1 (30 points)
Consider the following pairs of tensile stress-strain curves:
a) (5 points) (Figure A) Which material is more brittle? 1
b) (5 points) (Figure B) Which material is tougher? 1
c) (5 points) (Figure C) W

Solutions for Problem Set 2
Problem #1: The lining of blood vessels, called the endothelium, is made up of cells called endothelial cells.
These cells are constantly subjected to shear forces generated by the fluid flow in the circulatory system.
Consider

Solutions to Assignment #6
Reading: Please read the review article entitled Evaluation of left ventricular torsion by cardiovascular
magnetic resonance (Young and Cowan, Journal of Cardiovascular Magnetic Resonance 2012), and answer
the following question

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Due February 3, 2015
Problem Set 4: Axial Loading
Problem #1: Consider the portion of the cervical spine known as C3-C6, consisting of four cervical vertebrae
and three interposing intervertebral discs:
Assume you can model each vertebr