ME 562 Homework Set 4 Solutions
1.
Due May 17, 2011
7
d 0.105" , D 0.80" , Pmax 25 lb , Pmin 0 , Nd 10 cycles .
From (141),
c D / d 7.619
Sut Bd a 184,600(0.105)0.1625 266.1 ksi
From Table 14.8 for steel under released loading at 10,000,000 cycles
f 10
ME 562 Homework Set 4
Due May 17, 2011
1. An existing helicalcoil compression spring is wound from unpeened music wire
with a diameter of d 0.105" . The mean diameter of the spring is D 0.80" as
shown. The applied load fluctuates between 0 and 25 lb. A d
dm .
( c f~&4%6%
El
A
Problem L . The figure shows a brake with only one shoe, being applied by a 1.5 kN force. Four seconds
after force F is applied, the drum comes to a stop. During this time the drum makes 110 revolutions. Use
the short shoe approxim
Contact Examples
Example 1
Rollers supported by a steel base
( E = 30 106 psi, = 0.30 ) are
used to allow a top plate to
translate in two directions while
carrying a pile of material with a
density of = 0.10 lb/in 3 . The
rollers are either steel or brass
Estimating Fatigue Cycles
Fatigue failure is often addressed by
considering two different regions, low cycle
( N 103 cycles) and high cycle ( N 103
cycles). Some materials may have a definite
bilinearity in their SN curve at 103 cycles,
and others may n
Linear Elastic Fracture Mechanics
y
Determining the state of stress near the tip of a
crack can be complicated. Depending on the
loading conditions, different modes of fracture
can be identified. These modes are known as :
y
x
xy
xz
yz
z
Mode I, Mode II,
Load Sharing Examples
Example 1
Assume a similar situation to that in example 1, except that the two pillars at the
end of the beam are to be replaced with a single steel pillar. The top 2 of the pillar
has a diameter of 0.125, and the diameter of the rem
Modified Goodman Diagram
This presentation is designed to give the flavor of what was involved in fatigue analysis for high cycle fatigue
using a modified Goodman diagram before current approaches were used. In developing the following
relationships we wi
Multiaxial Fatigue
Different approaches to identifying the equivalent completely reversed normal stress for multiaxial fatigue
are explored. The basic relationship to be determined is the equivalent completely reversed stress, which is
given as
eq CR
e
Press Fit Examples
Example 1
A 3indiameter steel shaft ( E 30 106 psi , =0.3 ) is
pressed into a steel hub with an outside diameter of 6 in.
and an inside diameter of 3 in. Knowing that the
contacting pressure is 7000 psi and the coefficient of
friction
Recitation 4
Load Sharing and Redundant Assemblies, Stress Concentrations, Static Failure Theories
Load Sharing Example 1
identical fixedfixed beams ( EI 10 107 psi ) are attached to springs as
shown. The length of each beam is L 5 ft and the springs hav
=
a d"
B = / y &XI psi
J
=
 o /LZ<
.
(d
def I P C ~
yw
=
FK

=
5.$4
Y Y $
ProMem3. A helical compression spring made of oil tempered carbon steel, is subjected to a load which
varies fiom 400 N to 1000 N. T l~e pring index is 6 and the design factor of
ME 562 Homework Set 5
Spring 2007
Due May 8, 2007
Problem 1 . Using the structural method of assuming all rivets to carry a proportional share of the load,
compute the tensile stress in the main plate at row 3 of the quadrupleriveted butt connection show
Name
5
,
I~jbh~
M E 562 EXAM I1
O PEN BOOK (Closed Notes)
Thursday May 1 7,2007
Instructions: (1) Write your name in the upper right hand comer of this sheet. (2) Complete the exam,
using your book, but without notes or homework. Read all the vroblems ver
ME 562 Homework Set 1 (Review Problems)
Spring Quarter 2007
Due April 3 2007
Problem 1. A hollow shaft must carry a torque of 3,400,000 Nmm at a shearing stress of 55 MPa. The
inside diameter is to be 0.65 of the outside diameter. Find the value of the o
ME562 Homework Set 2
Due April 10, 2007
Problem 1. The shaft AD is supported in bearings at A and D and has pulleys attached at B and C. The
pulley at B is 40in. diameter and weighs 300 lb. while at C is 32in. diameter and weighs 180 lb. Make the
horizo
ME 562 Homework
Due Tuesday April 17, 2007
Problem 1. The shaft shown below is made of stainless steel (E = 26 x 106 psi). Determine asaft diameter
to insure that the first critical speed be no less than 3600 rpm.
Problem 2. Problem 820 Text
Problem 3. A
ME562 Homework Set 4
Due April 24, 2007
Problem 1. The lead screw of a lathe has Acme threads of 50 mm outside diameter and a pitch of 8 mm. The screw
must exert an axial pressure of 2500 N in order to drive the tool carriage. The thrust is carried on a c
ME 562 Homework Set 5
Spring 2007
Due May 8, 2007
Problem 1. Using the structural method of assuming all rivets to carry a proportional share of the load,
compute the tensile stress in the main plate at row 3 of the quadrupleriveted butt connection shown
ME 562 Homework Set 6
Spring 2007
Due May 15, 2007
Problem 1. Prob. 149 Text
Problem 2. A helical spring of rate 10 N/mm is mounted on top of another spring of rate 7 N/mm. Find
the force required to give a total deflection of 50 mm.
Problem 3. A helical
ME 562 Homework Set 7
Spring 2007
Due May 29, 2007
Problem 1. Problem 16.1 Text
Problem 2. The figure shows a brake with only one shoe, being applied by a 1.5 kN force. Four seconds
after force F is applied, the drum comes to a stop. During this time the
Practice Problems: Spring 2006
1. A steel shaft of constant diameter is simply supported at the ends. The distance between supports is 20
in. and a mass weighing 50 lb is located 4 in. to the right of the left bearing. The shaft must operate at 1800
rpm a
ME 562 Homework Set 1 Solutions
Spring 2007
Problem 1. A hollow shaft must carry a torque of 3,400,000 Nrnm at a shearing stress of 55 MPa. The
inside diameter is to be 0.65 of the outside diameter. Find the value of the outside diameter.
Solution:
d i =
ME562 Homework Set 2
Due April 1 0,2007
Problem 1. The shaft AD is supported in bearings at A and D and has pulleys attached at B and C. The
pulley at B is 40in, diameter and weighs 300 lb. while at C is 32in. diameter and weighs 180 lb. Make the
horizo
ME 562 Homework
Due Tuesday April 17,2007
Problem 1. The shaft shown below is made of stainless steel (E = 26 x lo6psi). Determine $af)diameter
to insure that the first critical speed be no less than 3600 rpm.
Problem 3. A key is sometimes used as a shear
ME562 Homework Set 4
Due April 24,2007
Problem 1 . The lead screw of a lathe has Acme threads of 50 mm outside diameter and a pitch of 8 mm. The screw
must exert an axial pressure of 2500 N in order to drive the tool carriage. The thrust is carried on a c
Stress Concentration and Failure Examples
Example 1
A structural component is subjected to an axial
force, a bending moment , and a torque as shown.
Knowing that d 1.25" , a design factor of safety of
nd 2.5 is desired, and that S y 125 ksi ,
determine th