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 to Assignment #1
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 annular (i.e., the humerus is a
hollow circul

Practice Problems Key
Problem #1: Consider the forearm in 90o flexion and holding a ball, as shown.
The mass of the forearm is 1.1 kg, and the diameter of the biceps tendon is 3 mm.
A. Determine the stress in the biceps tendon as a function of the weight

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

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

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 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

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Worked with:
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

Name:
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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

Name:
Worked with:
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

Name:
Worked with:
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

Name:
Worked with:
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

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

Name:
Worked with:
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

862
The Journal of Experimental Biology 214, 862-870
2011. Published by The Company of Biologists Ltd
doi:10.1242/jeb.051151
RESEARCH ARTICLE
Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft
stiffness and base rotational

Due via BbLearn on Friday, July 8 @ 11:59 pm ET
Modeling Exercise 1: Constitutive Models of the Anterior Cruciate Ligament
In class, we have reviewed the mechanical properties of materials and discussed constitutive equations for
ideal materials, focusing

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

Name:
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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

Name:
Worked with:
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

Name:
Worked with:
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

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

Name:
Worked with:
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

Name:
Worked with:
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

Problem #1: Torsional loading of agarose gels seeded with chondrocytes (cells from articular cartilage)
is one strategy to stimulate tissue growth and engineer cartilage in vitro. Typical cell-seeded agarose
gels are circular discs, 8 mm in diameter and 1

Practice Problems
o
Problem #1: Consider the forearm in 90 flexion and holding a ball, as shown.
The mass of the forearm is 1.1 kg, and the diameter of the biceps tendon is 3 mm.
A. Determine the stress in the biceps tendon as a function of the weight of

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