ME350
CHAPTER 1: STRESS
(PART-I)
Associate Prof. Hussein Zein
Mechanical Engineering Department
College of Engineering
Qassim University
Course Schedule:
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CHAPTER 1: STRESS
CHAPTER OBJECTIVES:
 Review important principles of statics.
 Use the principles to determine internal
resultant loadings (internal reaction forces)
in a body.
 Introduce concepts of normal and shear
stress.
 Discuss applications of analysis and design of
members subjected to an axial load or direct
shear load.
Why do we study Mechanics of Materials?
Anyone concerned with the strength and physical performance
of natural/man-made structures should study Mechanics of
Materials.
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Introduction to Mechanics of Materials
Definition: Mechanics of materials is a branch of
applied mechanics that deals with the behaviour of
solid bodies subjected to various types of loading.
Compression
Tension (stretched)
Bending
Torsion (twisted)
Shearing
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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
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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!

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SUPPORT TYPES AND REACTIONS (2D):
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SUPPORT TYPES AND REACTIONS (2D):
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Pin connections
allow rotation.
Reactions at pins
are forces and
NOT MOMENTS.
Degrees of
Freedom?
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STATIC EQUILIBRIUM


Vectors:
SF = 0
Coplanar (2D) force systems:
SFx = 0
SFy = 0
SMz = 0
SM = 0
Perpendicular
to the plane
containing the
forces
• Draw a FBD to account for
ALL loads acting on the body.
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Example FBD:
Draw a FBD of member ABC, which is
supported by a smooth collar at A, roller at
B, and link CD.
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GROUP PROBLEM SOLVING (continued)
C
A
B
F.B.D
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EXAMPLE: FIND THE VERTICAL REACTIONS AT
A AND B FOR THE SHAFT SHOWN BELOW.
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FBD
(800 N/m)(0.150 m) = 120 N
225 N
A
B
Ay
By
F.B.D
Comment on dashed line around the distributed load.
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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 
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STATICS: YOU NEED TO BE ABLE TO…
 Draw
free-body diagrams,
 Know support types and their corresponding
external 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
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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.

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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.

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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.
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COMPONENTS OF RESULTANT
• Components are
found perpendicular
& parallel to the
section plane.
• Internal reactions are
used to determine
stresses.
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COPLANAR FORCE SYSTEM
Start with internal system
of forces as shown below
to get proper signs for V,
N and M.
V
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Summary of Typical Strength of Material Problem:
1. Draw FBD.
2. Calculate unknown external reaction forces first (at
supports).
3. Calculate internal forces at point of interest by cutting
member if necessary.
4. Calculate area properties (inertia, centroid, area, etc.).
5. Calculate stress!!
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F.B.D
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Bending Moment, Shear force, and Normal Force
Sign convention for bending moment (M):
Negative Bending
Positive Bending
Sign convention for Shear force (V) :
Positive Shear
Negative Shear
Sign convention for Normal force (N) :
Positive Normal
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Negative Normal
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F.B.D
F.B.D
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EXAMPLE: 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.
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F.B.D
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Example (Classwork):
Determine the resultant internal loadings acting on the cross
section at G of the beam shown in fig. 1-6a. Each joint is pin
connected.
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(Classwork):
F.B.D
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QUESTIONS?
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