ENGR-2530
Strength of Materials
Section 4
Lecture 1
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Lecture Outline
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Class Format and Logistics
Statics Review
Free Body Diagram
Static Equilibrium
Internal forces
Concept of stress
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Contact Info
Instructor: Dr. Omar El-Shafee
Office: JEC 4004, Email: elshao2@rpi.edu
Office hours: Monday, Thursday 2-3pm (Webex)
TA: Fairooj Ta-seen
Email: taseef@rpi.edu
Office hours: Wednesday 2-6 pm (Webex Teams)
Thursday 11 am-12 pm (Webex)
Syllabus posted on LMS
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Office Hours
• Wednesday Problem sessions held in webex
teams.
• Office hours are held in instructor/TA
personal space listed on syallbus.
• Exam format TBA.
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Course Format
• Lectures
• In class activities
• 2 mid term exams: 45% *
*Highest exam will be worth 25%
• 1 final exam: 30%
• Assigned problems:
– HW: 20%
– ICA: 5%
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Class Logistics
• No electronic devices allowed.
• Cell Phones Turned off or Silent.
• Must Bring Calculator (Can’t use cellphone
calculator), pencil, ruler, Compass (to be used
later on this semester).
• During in class problems you can discuss with
your colleagues or ask me or TA.
• Wednesdays (4-6pm) are blocked for exams,
other weeks for problems sessions.
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Indeterminacy
• A statically determinate structure:
All member forces and external reactions can
be determined by using equations of
equilibrium.
• An indeterminate structure :
Has more unknown member forces
reactions than equations of equilibrium.
number of unknowns, in excess of
available equations of equations, is
degree of indeterminacy.
and
The
the
the
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Static analysis problem steps
• Identify the requirements from the problem
statement.
• Draw Free body Diagram(s).
• Apply Scalar Equations of Equilibrium
(2 for particle Equilibrium, 3 for rigid body
Equilibrium).
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Free-Body Diagram
• To apply equilibrium equations to a body, a carefully
prepared drawing that shows the “body of interest”
separated from all interacting bodies is needed. This
drawing is called a free-body diagram.
• The forces exerted by all other bodies must be
determined and shown on the diagram.
FCD
W
Procedure for Drawing Free-Body Diagrams:
Major Steps
• Select body (or combination of bodies) to be isolated and
analyzed.
• Sketch the body, extracting it from any supports or
connections (i.e., separate the body from all interacting
bodies). Do NOT draw FBD on top of original drawing.
• Draw all forces that are exerted on the isolated body by
contacting bodies or attracting bodies that were removed
during the isolation process. Show these exposed forces on
the free-body diagram using vectors drawn in their correct
locations and orientations.
• Draw a set of coordinate axes on or near the free-body
diagram. Also, show any dimensions needed for fully
defining the body and forces acting on it.
Static Analysis Example
• The structure is
designed to support a 30
kN load.
• Calculate:
Reaction forces at the
supports
Force in each structural
member
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FREE-BODY DIAGRAM (FBD)
2 Force Members
4 Unknowns
3 Equations:
What Should We Do???
FOCUSING ON JOINT B
Joint B must satisfy static equilibrium:

 FB  0
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 30 kN  0
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4
F


F

F
0
 x
AB
BC
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 Fy FBC
FBC  50 kN
FAB  40 kN
EQUILIBRIUM
Now we are able to calculate
reaction forces at A and C 
Ax  40 kN
Ay  0
C x   40 kN
C y  30 kN
NORMAL STRESS OF AXIAL LOADING
Axial load: Internal forces normal to section perpendicular to
member axis
F
  lim
A0 A
P

A
Assume Uniform
Stress Distribution
Very Simply: The force per unit area on a given section is
called the stress on that section ( σ )
Example
750
mm
450
mm
30
mm
60
kN
20
mm
20
kN
Two solid cylindrical rods AB
and BC are welded together at
B and loaded as shown. Find
the average normal stress at
the midsection of
(a) rod AB, (b) rod BC.
Solution
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Example
Solution
FBD of member ABC
FBD of member DEF
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HW1
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Electronic HW. “Connect”
Due Friday (9/10) 2pm.
Submit Hardcopy of calculations on LMS.
NO Late Submission Allowed.
For now you can solve Problems 1,2 and 3.
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