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PPB 25403 Strength of Materials
Lecture 1: Stress Analysis
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Mechanics of Materials: An Introduction
What?
Why?
Applications?
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Introduction
Mechanics of materials is a study of the relationshipbetween the external loads on a body and the intensityof the internal loads within the body.
This subject also involves the deformations and stability
of a body when subjected to external forces.
Applications:
Complete picture of mechanical behaviour such as
forces, motion Safe design in all type of structures i.e building, bridges,
airplanes, ships, motors, machines.
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Learning Outcomes
Stress
Review of Free Body Diagram
Equilibrium of a Deformable Body
Stress Concept
Normal and Shear Stresses
Factor of Safety
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Equilibrium of a Deformable Body
External Forces1.Surface Forces
- caused by direct
contact of otherbodys surface
2.Body Forces- other body exerts a force
without contact
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Equilibrium of a Deformable Body
ReactionsSurface forces developed at the
supports/points of contact between bodies.
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Equilibrium of a Deformable Body
Equations of EquilibriumEquilibrium of a body requires a balance
of forcesand a balance of moments
For a body with x, y, zcoordinate systemwith origin O,
Best way to account for these forces isto draw the bodys free-body diagram(FBD).
0M0FO
0,0,0
0,0,0
zyx
zyx
MMM
FFF
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Equilibrium of a Deformable Body
Internal Resultant LoadingsObjective of FBD is to determine the resultant
force and moment acting within a body.
In general, there are 4 different types ofresultant loadings:
a) Normal force, N
b) Shear force, Vc) Torsional moment or torque, T
d) Bending moment, M
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Stress
Distributionof internal loading is important inmechanics of materials.
We will consider the material to be continuous.
This intensityof internal force at a point iscalled stress.
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Stress
Normal Stress
Force per unit area acting normal toA
Shear Stress
Force per unit area acting tangent toA
A
FzA
z0
lim
A
F
A
F
y
Azy
x
Azx
0
0
lim
lim
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Average Normal Stress in an Axially Loaded Bar
When a cross-sectional areabar is subjectedto axial force through the centroid, it is onlysubjected to normal stress.
Stress is assumed to be averaged over the area.
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Average Normal Stress in an Axially Loaded Bar
Average Normal Stress DistributionWhen a bar is subjected to a
constant deformation,
Equilibrium 2 normal stress components
that are equal in magnitudebut opposite in direction.
A
P
AP
dAdFA
= average normal stressP = resultant normal forceA = cross sectional area of bar
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Example 1
The bar has a constant width of 35 mm and a thickness of 10 mm. Determine the
maximum average normal stress in the bar when it is subjected to the loadingshown.
Solution:By inspection, different sections have different internal forces.
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Solution:
By inspection, the largest loading is in region BC,
kN30BCP
Since the cross-sectional area of the bar is constant,
the largest average normal stress is
(Ans)MPa7.8501.0035.0
10303
A
PBCBC
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Average Shear Stress
The average shear stressdistributedover each sectioned area that develops ashear force.
2 different types of shear:
A
Vavg
= average shear stressP = internal resultant shear forceA = area at that section
a) Single Shear b) Double Shear
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Allowable Stress
Many unknown factors that influence theactual stress in a member.
A factor of safetyis needed to obtained
allowable load.The factor of safety(F.S.) is a ratio of the
failure load divided by the allowable load
allow
fail
allow
fail
allow
fail
SF
SF
FFSF
.
.
.
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What we have learned today
Free Body Diagram
Equilibrium of a Deformable Body
Stress Concept
Normal and Shear Stresses
Factor of Safety