CIVL 311
Stress Transformations Plane Stress
F
n
= 0:
n = x cos 2 + y sin 2 + 2 xy sin cos
n =
F = 0:
t
(
y =
+ y)
2
nt =
x =
x
(
y)
x
2
(
x
+ y)
2
(
xy =
x
+ y)
2
(
x
(
+
y)
2
cos 2 + xy sin 2
sin 2 + xy cos 2
+
(
x
y)
2
(
y)
2
x
x
y)
2
cos
Strain Rotational Transformation About a Principal Axis
(Note: Works for plane strain and plane stress, too)
" # = " x cos 2 # + " y sin 2 # + $ xy sin# cos#
"x%
(" x + " y ) + (" x & " y ) cos 2# + $ xy sin 2#
=
"y% =
2
(" x + " y )
$ x %y %
=&
2
!
&
2
(
CIVL 311 Strength of Materials
Review for Midterm Exam 3
General Information: The exam may contain a variety of problem types (true/false, multiple choice,
short answer, numerical, etc.) but most of the point credit will derive from numerical problems.
Nu
CIVL 311 Strength of Materials
Review for Midterm Exam 2
General Information: The exam may contain a variety of problem types (true/false, multiple choice,
short answer, numerical, etc.) but most of the point credit will derive from numerical problems.
Nu
CIVL 311 Strength of Materials
Review for Midterm Exam 1
General Information: The exam may contain a variety of problem types (true/false, multiple
choice, short answer, numerical, etc.) but most of the point credit will derive from numerical
problems. Nu
CIVL 311
Test 1 Review
Multi-Faceted Design
Select a wall thickness for the centrically-loaded tension member, as shown. (Not drawn to
scale).
Given:
Cross-section is to be a hollow square with constant wall thickness, t.
E = 29,000 ksi
allow = 12 ksi
CIVL 311 AXISYMMETRIC TORSION MEMBERS
ELASTOPLASTIC BEHAVIOR
Equation Supplement
Note: The equations shown below are valid for either solid or hollow members,
unless stated otherwise.
CASE I: Initial yielding (linear-elastic)
#yJ
Ty = c
"y =
T yL
JG
CASE
CIVL 311 Elasto-Plastic Torsion
c m ax
=
c m ax
=
(axisymmetric, small deformations)
(same conditions as above, plus homogeneous, linear-elastic)
Dene:
T y = to r q u e p r o d u cin g in ital y ield in g
T p = f u l l y p l a st i c t o r q u e
=
G
y
T
y
Coordinate Roational Transformation
Given a point with coordinates (x,y) in an original, convenient coordinate system.
Determine the coordinates (x',y') of the same point in a rotated coordinate system.
Y
Y'
y'
y
X'
x'
x
x = y sin + x cos
y = y cos x sin
CIVL 311 Moment-Area Method
Beam Segment
A
B
Elastic Curve
" AB
" BA
! AB
! BA
M/EI Diagram
AM
C
EI
0
xA
xB
"A B = "B A = A M
EI
!A B = A M x A
EI
!B A = A M x B
EI
M
EI