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Rensselaer Polytechnic's Strength of Materials Class Lecture 1 Slideshow
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Wk1 – Lecture 1 Dana R. Swalla PhD, PE
Lecture 1: Normal stress/strain
1
• Intro to Mechanics of Materials• Normal Stress• Normal Strain/Deformation• Units• Homework and Problem solving format• Example problems• Homework assignment
Wk1 – Lecture 1 Dana R. Swalla PhD, PE 2
Intro• Mechanics of Materials requires:
– Equilibrium– Constitutive Laws– Compatibility
• Examples of solid bodies we will study– Bar with axial load
– Shafts in torsion
– Beams in bending
– Columns in compression
Wk1 – Lecture 1 Dana R. Swalla PhD, PE 3
Normal Stress• Definition: Force per unit area, or intensity of the forces distributed over a given section.
• Sign Convention: Tension (+) Compression (-) • Units:
Area
Force
Ref 2
• F vs P vs P’ (‘force’ vs ‘load’):
• Centric vs eccentric loading:
• Effect of distribution:2
3
23
10
10_1
in
lbfpsi
lbfkip
m
NkPa
Wk1 – Lecture 1 Dana R. Swalla PhD, PE 4
Definition of Normal Strain
•Strain vs Deformation: Strain is the deformation of the member per unit length and is a dimensionless quantity. However, the original units are often kept (m/m, in/in, etc).
•Effect of Geometry:
Ref 1Constant cross section
Variable cross section
L
dx
d
xx
lim0
A load, 2P, is required to produce the same deformation in a rod of the same length, but with an area, 2A
Note, however, that the stress and strain are the same.
Wk1 – Lecture 1 Dana R. Swalla PhD, PE 5
Homework Format, posting, etc
• See LMS
Wk1 – Lecture 1 Dana R. Swalla PhD, PE 6
Example 1:
Ref 2
Wk1 – Lecture 1 Dana R. Swalla PhD, PE 7
Example 2:
Ref 2
Wk2 – Lecture 3 Dana R. Swalla, PhD, PE 8
References
Ref 1
Ref 2
Ref 3
Ref 4