HOMEWORK SOLUTIONS
Week 9: Due Friday 10 November
1. The cantilever beam in Figure 1(a) is of length L = 5 feet and is loaded by an end force P.
The beam cross-section is shown in Figure 1(b). Find th
HOMEWORK SOLUTIONS
Week 11: Due Friday 1 December
1. Figure 1 shows the stresses acting on an element of material. Find the three principal stresses
1 , 2 , 3 and the absolute maximum shear stress max
HOMEWORK SOLUTIONS
Week 10: Due Friday 17 November
1. When drilling a hole in a steel bar, a 1/ 16th inch diameter drill bit experiences an axial force
of 30 lb and a torque of 2 lb in. Find all the c
HOMEWORK SOLUTIONS
Week 6: Due Friday 20 October
1. The initially square element with sides of length l deforms to ABCD as shown in Figure 1.
Determine the shear strain 73y.
A)?
B(0.02,1.02) c
HOMEWORK SOLUTIONS
Week 12: Due Monday 11 December
1. A rectangular block of polycarbonate plastic is confined in a rigid die as shown in Figure
1. A pressure p is applied to the upper surface as show
THE UNIVERSITY OF MICHIGAN
ME 558 Discrete Design Optimization
Problem Set #7
Topics: Heuristics
Problem 1 Show select(P ) returns string si P = cfw_s1 , s2 , . . . , sn with probability
f it[si ]
n
THE UNIVERSITY OF MICHIGAN
ME 558 Discrete Design Optimization
Problem Set #6
Topics: Shortest path algorithms, MST algorithms.
Problem 1 Consider a simplied version of the robot path design in Engine
THE UNIVERSITY OF MICHIGAN
ME 558 Discrete Design Optimization
Problem Set #5
Topics: BFS and DFS, shortest path algorithms.
Problem 1 Simulate by hand Graph-Search(G, s) on the directed graph in Figu
c
Copyright 19992000
by K. Saitou
1
THE UNIVERSITY OF MICHIGAN
ME 558 Discrete Design Optimization
Problem Set #2
Topics: Discrete models, math fundamentals.
Problem 1 Show that for any nite set S, a
THE UNIVERSITY OF MICHIGAN
ME 558 Discrete Design Optimization
Problem Set #3
Topics: Gomorys cutting plane algorithm
Problem 1 Consider an ILP problem (note: this is a maximization problem)
maximize
THE UNIVERSITY OF MICHIGAN
ME 558 Discrete Design Optimization
Problem Set #4
Topics: B&B.
Problem 1 Find the solution of the following ILP problem using the branch-and-bound method coupled
with the g
THE UNIVERSITY OF MICHIGAN
c
Copyright 19992000
by K.
Saitou
ME
558 Discrete Design Optimization
1
Problem Set #1
Topics: Discrete models, math fundamentals.
Problem 1 Write the coil compression sprin
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 8
Strain - Life Approach
3/17/17
2
Concept of the Local Strain Life Approach
Straincontrolled
fatigue
specimen
Crack nucleation
and small c
Homework #2 - Solution
2-1. Calculate KI for a rectangular bar containing an edge crack loaded in three point
bending.
P = 35.0 KN; W = 50.8 mm; B = 25 mm; a/W = 0.2; S = 203 mm
P/2
P/2
S
a
P
W
2-2. C
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 6
Rainflow Cycle Counting
D
2/22/17
Rainflow Cycle Counting
Identification of rainflow cycles as basic damaging
events
Hysteresis Loops
LOA
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 7
Todays Topics
Modification of S-N Curve
n
n
n
n
3/8/17
Surface Finish Factor
Size Effector
Stress-Based Fatigue Analysis and Design
n
Fat
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 5
Importance of Fatigue in Engineering
Design
2/15/17
2
Importance of Fatigue in Engineering
Design
About 90 percent of mechanical failures
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 4
Todays Topics
Chapter 3: Elastic-Plastic Fracture Mechanics
n
Apply to materials that exhibit time-independent nonlinear behavior
(plasti
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 2
Todays Topics
Instability and R-Curve
Stress Analysis of Cracks
n
n
n
n
n
n
n
n
1/18/17
Failure Modes
Stress Intensity Factor
Relationshi
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 3
2.8 Crack Tip Plasticity
Linear elastic stress analysis of sharp cracks predicts infinite
stresses at the crack tip. However, in real mat
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 1
Course Description
A comprehensive review of fracture and fatigue
processes in engineering material with emphasis
on mechanics instead of
FATIGUE FROM VARIABLE
AMPLITUDE LOADING
Ali Fatemi - University of Toledo
All Rights Reserved
Chapter 9 Variable Amplitude Loading
1
FATIGUE FROM
VARIABLE AMPLITUDE LOADING
SPECTRUM LOADS AND CUMULAT
MATERIAL BEHAVIOUR
All real bodies are deformable, meaning that their size and shape generally
change when loads are applied to them. If a problem is statically indeterminate,
the deformation of the c
TORSION OF CYLINDRICAL BARS
We consider the case where a cylindrical bar (it may be solid or hollow) is
loaded by a twisting moment or torque T , as shown in Figure 1. For the cylindrical
bar, it is c
AXIAL LOADING (DETERMINATE PROBLEMS)
From Hookes law, an elastic bar in uniaxial tension will experience a tensile
strain
x
x =
,
(1)
E
where x is the tensile stress and E is Youngs modulus. We assume
ME 211003 INTRODUCTION TO SOLID MECHANICS
Midterm Examination I Practice Examination
Attempt all questions
MULTIPLE CHOICE QUESTIONS
1. (1 point) The force in Figure 1 acts at the point B and has magn
ECCENTRIC LOADING
In developing the bending formula
M
E
= = ,
I
y
R
(1)
we assumed that the beam was transmitting a bending moment M, but that the
axial force F was zero. In fact, the axial force tran
ME 382 Winter 2017
Homework 5
(Due Friday, February 17, 2017)
1.
Explain the following observations:
(i) Nickel can be strengthened by adding small hard particles of thoria.
(ii) At room temperature,
Due in class Thursday 01/26 (section 1 Capecelatro) Wednesday 01/25 (section 2 Johnsen)
Problem set #2 ME 320 Winter 2017
Problem 1: FM 2.48
Problem 2: FM 2.66
Problem 3: FM 2.78
1
Problem 4: FM 3.15