Lecture 18
Textbook Sections:
5. Analysis and Design of Beams for Bending
5.1 SHEAR AND BENDING MOMENT DIAGRAMS
CE 533 - Mech. of Materials
1
Introduction
Goal - Analysis and design of beams
Beams - structural members supporting loads at
various points
Lecture 02
Textbook Sections:
1.2 Stresses in the Members of a Structure
1.2B Shearing Stress
1.2C Bearing Stress in Connections
1.2D Application to the Analysis and Design of Simple
Structures
1.2E Method of Problem Solution (Read)
CE 533 - Mech. of Mate
Lecture 07
Textbook Sections:
2. Stress & Strain: Axial Loading
2.4 POISSONS RATIO
2.5 MULTIAXIAL LOADING: GENERALIZED HOOKES LAW
2.6 DILATATION
CE 533 - Mech. of Materials
1
Poissons Ratio
For a slender bar subjected to axial
(i.e., uni-axial) loading:
Lecture 08
Textbook Sections:
2. Stress & Strain: Axial Loading
2.7 SHEARING STRAIN
2.8 DEFORMATIONS UNDER AXIAL LOADING
2.9 St VENANT PRINCIPLE
CE 533 - Mech. of Materials
1
Review: States of Stress
Uniaxial
Multiaxial
General
CE 533 - Mech. of Materials
Lecture 20
Textbook Sections:
5. Analysis and Design of Beams for Bending
5.3 DESIGN OF PRISMATIC BEAMS FOR BENDING
CE 533 - Mech. of Materials
1
Design of Prismatic Beams for Bending
The largest normal stress is found at the surface where the
maximum be
Lecture 03
Textbook Sections:
1.3 Stress on an Oblique Plane under Axial Loading
1.4 Stress under General Loading Conditions;
Components Of Stress
CE 533 - Mech. of Materials
1
Stress on an Oblique Plane
Pass a section through the
member forming an angle
Lecture 05
Textbook Sections:
2. Stress & Strain: Axial Loading
2.1 An Introduction to Stress and Strain
CE 533 - Mech. of Materials
1
Stress & Strain: Axial Loading
Suitability of a structure or machine may depend on the deformations in
the structure as
Lecture 01
Textbook Sections:
1.1 Review of Statics
1.2 Stresses in the Members of a Structure
1.2A Axial Stress
CE 533 - Mech. of Materials
Slide #1
Chapter 1: Introduction - Concept of Stress
The main objective of the study of the mechanics
of material
CE533 - Mechanics of Materials
Exam #4 12/3/10
Professor Peterman
Name: SOLUTIONS
ID #:
"On my Honor, as a Student I have neither given nor received
unauthorized aid on this exam"
Signed:
Remember to include units and directions with all answers as approp
r
Problem I (35 points). A cantileverbeamis
madeofwood (E : 1.8x 106psi,I:72 #; anO
subjectedto the loadings shown. Using the
Moment-Area Method, determine:
p) the slope at end C
b) the deflection at end C
85 lb/in
30 kip-in
A
cl
20in-f
40 in
S harrR-
Be;
CE533 - Mechanics of Materials
Exam #2 3/3/17
Professor Peterman
Name:
ID #:
"On my Honor, as a Student I have neither given nor received
unauthorized aid on this exam"
Signed:
Problem 1: _
(35 Points)
Problem 2: _
(30 Points)
Problem 3: _
(35 Points)
Tot
CE533 - Mechanics of Materials
Exam #3 4/7/17
Professor Peterman
Name:
ID #:
"On my Honor, as a Student I have neither given nor received
unauthorized aid on this exam"
Signed:
General Instructions:
1.
2.
3.
4.
Present your work as clearly as possible.
Do
Lecture 17
Textbook Sections:
4.7 ECCENTRIC AXIAL LOADING IN A PLANE OF
SYMMETRY
4.8 UNSYMMETRIC BENDING
4.9 GENERAL CASE OF ECCENTRIC AXIAL
LOADING ANALYSIS
CE 533 - Mech. of Materials
1
Centric versus Eccentric Loadings
Centric loading: if the line of
Lecture 13
Textbook Sections:
4. Pure Bending
4.1 SYMMETRIC MEMBERS IN PURE BENDING
4.1A Internal Moment and Stress Relations
4.1B Deformations
CE 533 - Mech. of Materials
1
Pure Bending
Pure Bending: Case of
prismatic members
subjected to equal and
oppos
Lecture 19
Textbook Sections:
5. Analysis and Design of Beams for Bending
5.2 RELATIONSHIPS BETWEEN LOAD, SHEAR, AND
BENDING MOMENT
CE 533 - Mech. of Materials
1
Relations Between Load, Shear, and Moment
Relationship between load and shear:
Fy 0 : V V V
Lecture 04
Textbook Sections:
1.5 Design Considerations
1.5A Determination of the Ultimate Strength of a Material
1.5B Allowable Load and Allowable Stress: Factor of Safety
1.5C Factor of Safety Selection
1.5D Load and Resistance Factor Design
CE 533 - M
Lecture 10
Textbook Sections:
3. Torsion
3.1 STRESSES IN ELASTIC RANGE (continued)
3.2 ANGLE OF TWIST
CE 533 - Mech. of Materials
1
Normal Stresses
Under pure torsion, elements with faces
parallel and perpendicular to the shaft axis
(such as a ) are subj
Lecture 14
Textbook Sections:
4.2 STRESSES AND DEFORMATIONS IN THE
ELASTIC RANGE
CE 533 - Mech. of Materials
1
Stress Due to Bending
From last lecture:
y
c
x m
where m is the maximum absolute value of
the strain when y is largest.
For a linearly elastic
Lecture 11
Textbook Sections:
3. Torsion
3.3 STATICALLY INDETERMINATE SHAFTS
CE 533 - Mech. of Materials
1
Statically Determinate vs. Indeterminate Shafts
CE 533 - Mech. of Materials
2
Statically Indeterminate Shafts
Given the shaft dimensions and the
ap
Lecture 09
Textbook Sections:
3. Torsion
3.1 CIRCULAR SHAFTS IN TORSION
3.1A The Stresses in a Shaft
3.1B Deformations in a Circular Shaft
3.1C Stresses in the Elastic Range
CE 533 - Mech. of Materials
1
Torsional Loads on Circular Shafts
Machinery membe
Lecture 12
Textbook Sections:
3. Torsion
3.4 DESIGN OF TRANSMISSION SHAFTS
CE 533 - Mech. of Materials
1
Design of Transmission Shafts
Principal transmission shaft
performance specifications are:
- Power
- Speed of rotation
Designer must select shaft
ma
Lecture 15
Textbook Sections:
4.2 STRESSES AND DEFORMATIONS IN THE
ELASTIC RANGE (applications Problem)
4.3 DEFORMATIONS IN A TRANSVERSE CROSS
SECTION
CE 533 - Mech. of Materials
1
Deformations in a Transverse Cross
Section
From last lecture
1
M
EI
Altho
Lecture 16
Textbook Sections:
4.4 MEMBERS MADE OF COMPOSITE
MATERIALS
CE 533 - Mech. of Materials
1
Bending of members made of two or more
materials with different moduli of elasticity
Consider a bar consisting of two different materials with E1 and E2
Equations from Exam 1
E
P
A
lateral strain
lat
axial strain
long
p
T (T)L
PL
AE
L
Equations from Exam 2
J
T
J
max
4 4
co ci
2
1
T c
J
y
x
x
M
EI
G
T L
J G
J
My
I
m
4
c
2
Mc M
I
S
Equations from Exam 3
max
V
Aweb
q
dV
w
dx
Mc M
m
I
S
VQ