MCHT 213 – Section 1 and 2
Strength of Materials
Section 1 – 12:00 – 1:15 pm Tue/Thur
Section 2 – 1:25 – 2:40 pm Tue/Thur
Office (230 REDC): T/R: 3:30 – 4:30 p.m.,
W: 4:00 – 5:00 p.m.
Instructor: Bob Michael, P.E.
Perfect
Compliment!!
PS Instructor:
Robert J. Michael, PE
Office:
Phone:
Email:
Burke 230
(814) 898-6192
rxm61@psu.edu
Practicing
Engineer:
• Design – NVH
Products
• Structural Analysis
• FEA
• Vibration Analysis
2
Today…
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Introduction
Syllabus
Homework
Course Objectives
Statics review (Key Statics book Ch 5
and 6)
• Internal reactions
SEE Syllabus – Key Points:
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Grade Distribution
Grade Scale
HW Guidelines
Attendance Policy
Makeup Policy
Academic Integrity
Support Services – SEEK TUTORING –
REDC 240 – schedule on board
• COURSE OBJECTIVES
Schedule – reading and HW assignments:
Key to Success??
Reading assignment for class
on 8/23
Homework problems to solve after
F = partial
class on 8/23 due 1 week after
assigned, or due on 8/30
solutions!!
Course
Title
Page
Name & Date
Chapter &
problem no.
Sketch of
situation
What you are
to find
Always include
UNITS
FBD’s as
necessary
No more than TWO
problems per page
LATE HOMEWORK
NOT ACCEPTED
Engineering
Calculation
Paper
Box or underline
answers
Homework
Engineering Mechanics
Rigid Body
Mechanics
Deformable Body
Mechanics
Fluid
Mechanics
Statics
MCHT 111
Strength of
Materials
MCHT 213
Dynamics
MET 206
(also SoM Lab
MCHT 214)
ALSO, Advanced SoM (320) and FEA courses
Mechanics of Materials
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External Loads produce Internal Loads
Internal Loads cause a body to deform
Internal Loads cause stress
How much does body deform?
How much stress?
Is it Safe at this stress?
How big should it be so stress is low
enough?
Course Outcomes 1
• Solve axially loaded members for stresses and
deflections in statically determinate or
indeterminate cases including thermal stresses.
• Solve torsionally loaded shafts for stresses and
deflections in statically determinate or
indeterminate cases.
• Solve beams under bending for stresses.
• Solve transversely loaded beams for internal shear
forces and bending moments. Develop shear and
moment diagrams.
Course Outcomes 2
• Solve beam deflection problems using integration,
and superposition.
• Solve for the stresses in beams with combined
axial and transverse loads.
• Solve for stresses in general cases of combined
loading and check for yielding using simple yield
criteria.
• Solve for transformed stresses, principal stresses
and construct and interpret Mohr's circle for
stresses.
• Solve axially loaded slender beams for buckling
under a variety of boundary conditions.
Begin Chapter 1:
Statics Review: External Loads
Small contact area;
treat as a point
FR is
resultant of
w(s) = area
under curve,
acts at
centroid
Acting on
narrow area
One body
acting on
another
One body
acting on
another w/o
contact
External Loads:
• External loads can be Reaction Loads
or Applied Loads!
• Must solve for all unknown external
loads (reaction loads) so that internal
loads can be solved for!
• Internal loads produce stress, strain,
deformation – SofM concepts!
Support Types and Reactions (2D):
Support Types and Reactions (2D):
Pin connections
allow rotation.
Reactions at pins
are forces and
NOT MOMENTS.
Degrees of
Freedom
Static Equilibrium
• Vectors:
SF = 0
SM = 0
• Coplanar (2D) force systems:
SFx = 0
SFy = 0
SMo = 0
• Draw a FBD to account for
ALL loads acting on the body.
Perpendicular
to the plane
containing the
forces
Example FBD:
Draw a FBD of member ABC, which is supported
by a smooth collar at A, roller at B, and link CD.
GROUP PROBLEM SOLVING (continued)
FBD
Example: Find the vertical reactions at A and B
for the shaft shown.
FBD
(800 N/m)(0.150 m) = 120 N
225 N
A
B
Ay
By
Comment on dashed line around the distributed load.
See Page 10, Procedure for Analysis for FBD hints.
Equilibrium
Equations
+
SMA  0  .400 m (B y )  120 N (. 275 m)  225 N (. 500 m)
 120 N (. 275 m)  225 N (. 500 m)
By 
 .400 m
B y  363.75N
+

SFy  0  Ay  120 N  363 .75 N  225 N
A y  18 .75 N
A y  18.75N

STATICS: You need to be
able to…
• Draw free-body diagrams,
• Know support types and their corresponding
reactions,
• Write and solve equilibrium equations so that
unknown forces can be solved for,
• Solve for appropriate internal loads by taking
cuts of inspection,
• Determine the centroid of an area,
• Determine the moment of inertia about an
axis through the centroid of an area.
Internal Reactions
• Internal reactions are
necessary to hold body
together under loading.
• Method of sections make a cut through
body to find internal
reactions at the point of
the cut.
FBD After Cut
• Separate the two parts
and draw a FBD of
either side
• Use equations of
equilibrium to relate the
external loading to the
internal reactions.
Resultant Force and Moment
• Point O is taken at the
centroid of the section.
• If the member (body) is
long and slender, like a
rod or beam, the
section is generally
taken perpendicular to
the longitudinal axis.
• Section is called the
cross section.
Components of Resultant
• Components are
found
perpendicular &
parallel to the
section plane.
• Internal reactions
are used to
determine stresses.
Coplanar Force System
Start with internal system
of forces as shown below
to get proper signs for V,
N and M.
Different than
Fig. 1-3(b)
V
Summary of Typical Strength of Material Problem:
1. Calculate unknown reaction forces first.
2. Calculate internal forces at point of interest by cutting
member if necessary.
3. Calculate area properties (inertia, centroid, area, etc.).
4. Calculate stress!!
Examples of 1 and 2 follow
Statics: Example 1 - Pliers
Given: Typical
household pliers as
shown.
Find: Force applied to
wire and force in pin
that connects the two
parts of the pliers.
Do this for homework!
See Solution Link
Side: what is the shear
stress in pin and bending
stress in handle? SofM
Statics: Example 2 – Crane Structure
Given: Crane structure
as shown.
Find: Forces and
FBD’s for cables A-B
and A-E, boom DEF
and post AFC.
Do this for homework!
See Solution Link
Side: what is the normal stress
in cables (average normal
only) and normal stress in
boom and post (combined
loading)? SofM
EXAMPLE
Given: Loads as shown on the truss
Find: The forces in each member
of the truss.
Plan:
1.
2.
3.
4.
Check if there are any zero-force members.
First analyze pin D and then pin A
Note that member BD is zero-force member. FBD = 0
Why, for this problem, do you not have to find the external
reactions before solving the problem?
EXAMPLE (continued)
D 450 lb
45 º
FAD
45 º
FCD
FBD of pin D
+   FX = – 450 + FCD cos 45° – FAD cos 45° = 0
+   FY = – FCD sin 45° – FAD sin 45° = 0
FCD = 318 lb (Tension) or (T)
and FAD = – 318 lb (Compression) or (C)
EXAMPLE (continued)
Analyzing pin A:
FAD
45 º
A
FAB
AY
FBD of pin A
+   FX = FAB + (– 318) cos 45° = 0;
FAB = 225 lb (T)
Could you have analyzed Joint C instead of A?
Statics: Example 3 – Truss Structure
Given: Truss structure
as shown.
Find: Forces in each
member: AB, BC, AD,
EF, BD, BE, CE, CF
Do this for homework!
See Solution Link
Side: what is the normal stress
in each truss member (away
from joints)? SofM
Example 4: The 500 kg engine is suspended from the boom crane as
shown. Determine resultant internal loadings acting on the cross
section of the boom at point E.
Example 5: Find: Reactions at A and C and draw FBD:
Discuss optional “equivalent cantilever”