LECTURE
Third Edition
RODS: STATICALLY
INDETERMINATE MEMBERS
A. J. Clark School of Engineering Department of Civil and Environmental Engineering
4
Chapter
2.9
by
Dr. Ibrahim A. Assakkaf
SPRING 2003
ENES 220 Mechanics of Materials
Department of Civil and
LECTURE
Third Edition
RODS: AXIAL LOADING AND
DEFORMATION
A. J. Clark School of Engineering Department of Civil and Environmental Engineering
3
Chapter
2.8
by
Dr. Ibrahim A. Assakkaf
SPRING 2003
ENES 220 Mechanics of Materials
Department of Civil and Env
Stress and Strain
MAE314 SolidMechanics
Y.Zhu
Slide 1
Stress and Strain
Introduction to Normal Stress
Stress = Force per unit area
F
=
A
Slide 2
Stress and Strain
Introduction to Normal Stress contd
If the stress varies over the cross-section, we can wri
North Carolina State University
Department of Mechanical and Aerospace Engineering
MAE 314
Solid Mechanics
Fall 2014
Schedule: Mon, Wed 8:05-9:20
Classroom: Engineering Building III 2232
Dr. Kara Peters
Office Hours: 4:00-5:00 PM Tues, Thurs
Office: Engin
LECTURE
Third Edition
INTRODUCTION AND REVIEW:
STATICS & STRESS
A. J. Clark School of Engineering Department of Civil and Environmental Engineering
1
Chapter
1.1- 1.13
by
Dr. Ibrahim A. Assakkaf
SPRING 2003
ENES 220 Mechanics of Materials
Department of C
Normal Stress (1.1-1.2A)
Normal Stress
1
Statics Review
Pins = no moment
Normal Stress
2
Statics Review
Solve for reactions at A & C:
M C 0 Ax 0.6 m 30 kN 0.8 m
Ax 40 kN
Fx 0 Ax C x
C x Ax 40 kN
Fy 0 Ay C y 30 kN 0
Ay C y 30 kN
Ay and Cy can not be
Beams: Pure Bending
(4.1A-4.1B,4.2,4.3)
Beams: Pure Bending
1
Beams in Pure Bending
Prismatic beams subject to equal and opposite couples acting in the
same plane are in pure bending.
Beams: Pure Bending
2
Pure vs. Non-Uniform Bending
Pure bending: She
Torsion: Shear
Stress & Twist (3.1A3.1C,3.2)
Torsion: Shear Stress & Twist
1
Torsion of Circular Shafts
In this chapter, we will examine uniaxial bars subject to torque.
Where does this occur?
Transmission Shaft
Force Couples
Torsion: Shear Stress & Twi
Hookes Law and Modulus of
Elasticity (2.1A-2.12.1E)
Hooke's Law and Modulus of Elasticity
1
Introduction to Normal Strain
Normal strain () is defined as the deformation per unit length of
a member under axial loading.
L
Normal strain is dimensionless bu
Analysis of Beams in
Bending (5.1-5.2)
Analysis of Beams in Bending
1
Bending Moment Along a Beam
In this chapter, we will learn how to find the bending moment M along
the beam.
M is not necessarily constant; sometimes M is a function of x.
We will als
Uniaxial Bar
normal stress
Stress on an oblique plane
F
=
A
shear stress
=
F
A
=
P
cos2
A0
P
sin cos
=
A0
=
F
td
bearing stress
Hookes Law
x
factor of safety
FS =
U
all
y
z
normal strain
=
L
L
xy =
1
x y z
E
E
E
1
= x + y z
E
E
E
1
= x y + z
E
E
E
=
1
Uniaxial Bar
normal stress
normal strain
=
F
A
Hookes Law
=
L
L
1
E
x =
y =
shear stress
elongation of uniaxial bar
F
=
A
z =
PL
=
EA
bearing stress
=
F
td
Stress on an oblique plane
xz
P
cos2
A0
P
=
sin cos
A0
=
factor of safety
FS =
U
all
E
E
x
+
x
1
HW01-MAE314-001 F14
Chapter 1
PROBLEM 1
For the Pratt bridge truss and loading shown determine the
average normal stress in member BE. Knowing that the
cross-sectional area of that member is 7 in2.
SOLUTION
There are two ways to solve this problem. The fi
HW05-MAE314-001 F13
Chapter 6
PROBLEM 1
A column is fabricated by connecting the rolled-steel members
shown by bolts of in diameter spaced longitudinally every
6 in. Determine the average shearing stress in the bolts caused
by a shearing force of 40 kips
HW05-MAE314-001 F13
Chapter 4
PROBLEM 1
Two W5X16 rolled sections are welded together as shown. Knowing that for the steel alloy used,
y=18ksi and u=38ksi using a factor of safety of 2.5 determine the largest couple (moment) that
can be applied about the
HW03-MAE314-001 F13
Chapter 3
PROBLEM 1
The solid spindle AB has a diameter ds and is made of steel with an allowable shear stress of 13ksi,
while sleeve CD. Is made of brass with an allowable shearing stress of 6 ksi. Determine the torque T
for shaft CD
HW11-MAE314-001 F13
Chapter 7
PROBLEM 7.8
For the given state of stress determine a) the principal planes
b) the principal stresses
SOLUTION
We have three different components.
= 5
= 8
= 12
We can use the equation for the principal planes.
2
2(5)
10
HW03-MAE314-001 F13
Chapter 2
PROBLEM 1
Two gage marks are placed exactly 20 in. apart on a in. diameter aluminum rod with E=10.1X106
psi and an ultimate strength of 10ksi. Knowing that the distance between the gage marks is 20.012in
after a load is appli
HW09-MAE314-001 F13
Chapter 9
PROBLEM 1
For the cantilever beam and loading shown, determine a) the
equation of the elastic curve for Portion AB of the beam, b)
the deflection at midspan.c) the slope at B.
SOLUTION
First we need to find the reaction force