Torsion
of a Circular Shaft
pg 357376
What types of loads do we need to
consider?
Spine/backbone
Compression
Fixation device
Tension
Bending
Torsion
Synthes.com
Objectives:
Discuss the effect of applying a torsional load
to a structural member
Ana
A solid steel shaft 14 ft long has a diameter of 6 in for 9 ft of
its length and a diameter of 4 in for the remaining 5 ft. The
shaft is in equilibrium when subjected to the three torques
shown. The modulus of rigidity of the steel is 12,000 ksi.
Determin
Vectors
 
 
Trigonometry/Math
(
)
and direction is defined by right hand rule
Vector in direction n:
Moments/Couples
where r goes from the point of rotation to the force
M=Fd where d is the perpendicular distance between the force and point of rota
Funny pictures of the day
(and the biomechanics behind
it)
Draw the free body diagram of (a) the entire system and (b) the watermelon
The biomechanics becomes 3D
What is the moment applied (a)
at the hand and (b) at the
shoulder from the sword weight?
Dim
Thermal Effects
What happens to the size of a material
when
Heated?
Cooled?
Thermal strain
Coefficient of thermal expansion
: units of strain/degree temp change
=
=
For a homogeneous, isotropic material
Expansion/contraction is same in all d
Example
Determine the deformation of the steel rod
shown under the given loads
Assume that the modulus of elasticity for all
parts is 29x106 psi
Hint: you may make more than one cut at a
time
1
Note: Although the internal forces are shown to occur rig
Anatomy & Terms
Anatomical planes
Three planes are defined
Coronal
Sagittal
Transverse/Axial
1
Anatomy & Terms
Plane of rotation
We will simplify to 2D most of the time
What direction is the primary motion?
2
Anthropometry tells us size,
weight and shape
BE200: Recitation week of 9/23
Solutions
Problem 1
BE200: Recitation week of 9/23
Solutions
The pin and bracket are resisting the forces in all three directions and the moment in the x direction. The
locking mechanism is resisting the moment in the z dire
Problem 1
A 4000lb crate is attached by light, inextensible cables to the truss shown.
a. Trusses are made up of a collection of rigid links also known as twoforce members. What does
this mean about the direction of the forces each link/member exerts on
Problem 1
A 4000lb crate is attached by light, inextensible cables to the truss shown.
a. Trusses are made up of a collection of rigid links also known as twoforce members. What does
this mean about the direction of the forces each link/member exerts on
BE 200: Homework #7
Due: 11/26 by noon
*No late homework accepted due to the extension*
In class or in (not on top of or hanging out of, in) the box outside of Hayden 314.
Note: As the class progresses, your ability to interpret problems should also
progr
Figure 1
F
40 cm
4 bolts
5 cm
4 bolts
3m
5m
Figure 2
Option A
Option B
40 cm
40 cm
5 cm
5 cm
height
2
Figure 3
5N
3 N/cm peak
5mm
3mm
2mm
1mm
1mm
3 N/cm peak
2cm
2cm
2cm
3
Figure 4
5 lb in
25 lb in
40 lb in
d
0.75 in
0.75 in
0.75 in
0.25 in
4
Vectors
 
 
Trigonometry/Math
(
)
and direction is defined by right hand rule
Vector in direction n:
Moments/Couples
where r goes from the point of rotation to the force
M=Fd where d is the perpendicular distance between the force and point of rota
Vectors
 
 
Trigonometry/Math
(
)
and direction is defined by right hand rule
Vector in direction n:
Moments/Couples
where r goes from the point of rotation to the force
M=Fd where d is the perpendicular distance between the force and point of rota
Beam Bending
Deflections
pg. 487506
Beam bending
What have we covered?
Flexural stress
=
Flexural shear stress
I: pg 419,
Appendix A,
parallel axis
theorem
=
=
=
Describe each of these stresses in words
How to they vary in the beam? Length? Cross
sec
Displacement,
Deformation and Strain
What happens when a rigid body is
subjected to a force?
Displacement
d
What happens when a nonrigid body is
subjected to a force?
Deformation:
the change in
size or shape
due to a force
2
Experiment: Two bars,
one
Dr. Dourtes Exam 3 Outline
Making your own is a good study tactic!
This is not meant to be allinclusive!
Beam bending
Flexural/bending normal stresses
o Shortening or elongation of a horizontal plane
o NA, no change in length
Positive bending moment (s
Engineering Drawings
How Design Engineers
Communicate
Left ventricular assist device (LVAD)
Helps the heart pump blood
Someone has to make it
Machinists
2
Engineering drawings
3
Drawing views
4
Dotted lines
A hidden piece of geometry behind the
pi
Welcome to BE200!
Syllabus available on
Canvas
Please review in detail
David Meaney, PhD
(meanee)
Office: 105C Hayden Hall
Email:
dmeaney@seas.upenn.edu
Office Hours: Wed 36pm
LeAnn Dourte, PhD
(doortee)
Office: 314 Hayden Hall
Email: dourte@s
Generating moments
Understanding hip implant
forces



What is the angle of
the joint force to
maintain equilibrium?
What is the role of the
muscle force?
How does orientation
of femur change joint
force?
Analysis
Achilles tendon failure


What is th
BE200: Recitation week of 9/23
Problem 1
As part of your senior design project, you are working with Drs. Weinstein and OMalley at HUP.
One of the locking mechanisms at the base connection in their new robotic surgery equipment
keeps failing and they beli
2
Surgical pliers are used in orthopedic surgery to tighten screws that fasten the rods and pins
to the bone. These may also be used to remove screws during procedures. The hand grip of
these surgical pliers is made to be slip resistant and comfortable in
Lattice Constant = length of a side of a face
BCC Lattice Constant = 4R/3
FCC Lattice Constant = 4R/2
Atomic Packing Factor = volume of atoms in unit cell/ volume of the unit cell
F = AE/L
L=V/A
= nA/VcNa
n = number of atoms in unit cell; A = atomic weig
BE 200 09/16
Phase = physically and chemically homogenous.
Eutectic crystal = different compositions, within crystal not chemically
homogenous.
Metals and crystalline solids
o CoCr alloys
CoCrMo (ASTM F75)
Molybdenum added to produce finer grains