SOLUTION MANUAL
Advanced Mechanics of Materials and Applied Elasticity, 6th edition
by Ansel Ugural, Saul Fenster
SC
O
R
EG
U
ID
ES
, Table of Content
Chapter 1 Analysis of Stress
Chapter 2 Strain and Material Properties
Chapter 3 Problem in Elasticity
Chapter 4 Failure Criteria
SC
Chapter 5 Bending of Beams
Chapter 6 Torsion of Prismatic Bars
Chapter 7 Numerical Methods
O
Chapter 8 Thick-Walled Cylinders and Rotating Disks
R
Chapter 9 Beams on Elastic Foundations
Chapter 10 Applications of Energy Methods
EG
Chapter 11 Stability of Columns
Chapter 12 Plastic Behavior of Materials
U
Chapter 13 Stresses in Plates and Shells
ID
ES
, NOTES TO THE INSTRUCTOR
SC
The Solutions Manual to accompany the text Advanced Mechanics of Materials and
O
Applied Elasticity supplements the study of stress and deformation analyses developed in the
book. The main objective of the manual is to provide efficient solutions for problems dealing
with variously loaded members. This manual can also serve to guide the instructor in the
R
assignments of problems, in grading these problems, and in preparing lecture materials as well
as examination questions. Every effort has been made to have a solutions manual that can cut
through the clutter and is self - explanatory as possible thus reducing the work on the instructor.
EG
It is written and class tested by the author, Ansel Ugural.
As indicated in its preface, the text is designed for the senior and/or first year graduate
level courses in stress analysis. In order to accommodate courses of varying emphasis,
considerably more material has been presented in the book than can be covered effectively in a
single three-credit course. The instructor has the choice of assigning a variety of problems in
U
each chapter. Answers to selected problems are given at the end of the text. A description of the
topics covered is given in the introduction of each chapter throughout the text. It is hoped that
the foregoing materials will help instructor in organizing his or her course to best fit the needs of
ID
his or her students.
Ansel C. Ugural
Holmdel, NJ
ES
iii
, CHAPTER 1
SOLUTION (1.1)
We have
A = 50 75 = 3.75(10−3 ) m2 , = 50o , and x = P A .
Equations (1.11), with = 50o :
x ' = 700(103 ) = x cos2 50o = 0.413 x = 110.18P
SC
or P = 6.35 kN
and
x ' y ' = 560(103 ) = x sin 50o cos 50o = 0.492 x = 131.2P
Solving
P = 4.27 kN = Pall
O
SOLUTION (1.2)
Normal stress is
R
x = PA = 125(103 ) = 50 MPa
0.050.05
( a ) Equations (1.11), with = 20o :
x ' = 50 cos2 20o = 44.15 MPa
EG
x ' y ' = −50 sin 20o cos 20o = −16.08 MPa
y ' = 50 cos2 (20o + 90o ) = 5.849 MPa
5.849 MPa
y’
44.15 MPa
U
16.08 MPa x’
20 o
ID
x
( b ) Equations (1.11), with = 45o :
x ' = 50 cos2 45o = 25 MPa
ES
x ' y ' = −50 sin 45o cos 45o = −25 MPa
y ' = 50 cos2 (45o + 90o ) = 25 MPa
25 MPa
25 MPa
x’
y’
25 MPa
45 o
x
Advanced Mechanics of Materials and Applied Elasticity, 6th edition
by Ansel Ugural, Saul Fenster
SC
O
R
EG
U
ID
ES
, Table of Content
Chapter 1 Analysis of Stress
Chapter 2 Strain and Material Properties
Chapter 3 Problem in Elasticity
Chapter 4 Failure Criteria
SC
Chapter 5 Bending of Beams
Chapter 6 Torsion of Prismatic Bars
Chapter 7 Numerical Methods
O
Chapter 8 Thick-Walled Cylinders and Rotating Disks
R
Chapter 9 Beams on Elastic Foundations
Chapter 10 Applications of Energy Methods
EG
Chapter 11 Stability of Columns
Chapter 12 Plastic Behavior of Materials
U
Chapter 13 Stresses in Plates and Shells
ID
ES
, NOTES TO THE INSTRUCTOR
SC
The Solutions Manual to accompany the text Advanced Mechanics of Materials and
O
Applied Elasticity supplements the study of stress and deformation analyses developed in the
book. The main objective of the manual is to provide efficient solutions for problems dealing
with variously loaded members. This manual can also serve to guide the instructor in the
R
assignments of problems, in grading these problems, and in preparing lecture materials as well
as examination questions. Every effort has been made to have a solutions manual that can cut
through the clutter and is self - explanatory as possible thus reducing the work on the instructor.
EG
It is written and class tested by the author, Ansel Ugural.
As indicated in its preface, the text is designed for the senior and/or first year graduate
level courses in stress analysis. In order to accommodate courses of varying emphasis,
considerably more material has been presented in the book than can be covered effectively in a
single three-credit course. The instructor has the choice of assigning a variety of problems in
U
each chapter. Answers to selected problems are given at the end of the text. A description of the
topics covered is given in the introduction of each chapter throughout the text. It is hoped that
the foregoing materials will help instructor in organizing his or her course to best fit the needs of
ID
his or her students.
Ansel C. Ugural
Holmdel, NJ
ES
iii
, CHAPTER 1
SOLUTION (1.1)
We have
A = 50 75 = 3.75(10−3 ) m2 , = 50o , and x = P A .
Equations (1.11), with = 50o :
x ' = 700(103 ) = x cos2 50o = 0.413 x = 110.18P
SC
or P = 6.35 kN
and
x ' y ' = 560(103 ) = x sin 50o cos 50o = 0.492 x = 131.2P
Solving
P = 4.27 kN = Pall
O
SOLUTION (1.2)
Normal stress is
R
x = PA = 125(103 ) = 50 MPa
0.050.05
( a ) Equations (1.11), with = 20o :
x ' = 50 cos2 20o = 44.15 MPa
EG
x ' y ' = −50 sin 20o cos 20o = −16.08 MPa
y ' = 50 cos2 (20o + 90o ) = 5.849 MPa
5.849 MPa
y’
44.15 MPa
U
16.08 MPa x’
20 o
ID
x
( b ) Equations (1.11), with = 45o :
x ' = 50 cos2 45o = 25 MPa
ES
x ' y ' = −50 sin 45o cos 45o = −25 MPa
y ' = 50 cos2 (45o + 90o ) = 25 MPa
25 MPa
25 MPa
x’
y’
25 MPa
45 o
x
