1. Class #1.2 Civil Engineering Materials – CIVE 2110
Strength of Materials
Mechanical Properties
of Materials
Fall 2010
Dr. Gupta
Dr. Pickett

2. Stress and Strain Mechanical Properties of Materials
- used to develop relationships between
Stress and Strain.
- determined Experimentally.

3. Experimental Determination of Mechanical Properties of Materials
Stress and Strain experiments:
A standard specimen of the Material:
- Pulled in Uniaxial Tension.
- Diameter = 0.5 in.
- Gauge Length = 2.0 in. Or
- a strain gauge is placed
parallel to long axis of specimen

4. Stress-Strain DiagramsP
Conventional Stress-Strain Diagram :
Normal Stress calculated using
ORIGINAL cross sectional area, AO.
Called Engineering Stress.
Even though cross section decreases, necks down.
Assumes stress is CONSTANT over cross section.
Normal Strain calculated using
ORIGINAL length, LO.
Assumes strain is CONSTANT over cross section P P

5. Stress-Strain DiagramsP
TRUE Stress-Strain Diagram :
Normal Stress calculated using
ACTUAL cross sectional area, Ai, at any instant.
Called TRUE Stress.
Because cross section decreases, necks down.
Normal Strain calculated using
ACTUAL length, Li , at any instant. P P

6. Stress-Strain Diagram – Ductile Material
Conventional (Engineering)
and TRUE
Stress-Strain diagrams
Differ only in regions of LARGE strain .
σ (KSI)
ε (μ in./in.)

7. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- Label the axes.
- REGIONS:
- Elastic – region where specimen will return to
original size & shape
after loading & unloading
- Plastic - region where specimen will NOT return
to original size &
shape after
loading & unloading
- Yielding – region where
specimen will continue
to elongate with little
or no increase in load
σ (KSI)
ε (μ in./in.)

8. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- REGIONS:
- Strain Hardening – region where specimen will elongate
only with increasing load, and the
cross sectional area will decrease
uniformly over entire specimen gauge length
- Necking - region where
specimen cross sectional
area will decrease in a
localized spot, and
load carrying capacity
will decrease,
uncontrollably
σ (KSI)
ε (μ in./in.)

9. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- POINTS:
- Proportional Limit, σPL – highest stress at which
Stress and Strain
are linearly proportional, via E
- Modulus of Elasticity (Young’s Modulus) –
the slope of the
Stress-Strain curve in the
Linear-Elastic region,
slope up to σPL
(ESTEEL=29x106 psi)
E=Δσ/Δε
σ (KSI)
ε (μ in./in.)

10. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- POINTS:
- Modulus of Elasticity (Young’s Modulus)
the slope of the
Stress-Strain curve in the
Linear-Elastic region,
slope up to the
Proportional Limit
(ESTEEL=29x106 psi)
- Hooke’s Law
E=Δσ/Δε
σ (KSI)
ε (μ in./in.)

11. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- POINTS:
- Modulus of Elasticity
(Young’s Modulus) =
the slope of the
Stress-Strain curve in the
Linear-Elastic region
- alloy content affects
- Proportional Limit
- not Modulus of Elasticity
(ESTEEL=29x106 psi)
E=Δσ/Δε
E=Δσ/Δε
σ (KSI)
ε (μ in./in.)

12. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- POINTS:
- Elastic Limit, σEL – highest stress at which the specimen
will return to original size and shape
after loading and unloading
(Steel, very close to Proportional Limit)
- Yield Point, σY – stress
at which specimen
will have permanent
(plastic) deformation
after loading & unloading,
specimen will elongate
with LITTLE or NO load
increase
(Steel, very close to
Proportional Limit)
E=Δσ/Δε
σ (KSI)
ε (μ in./in.)

13. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- POINTS:
- Ultimate Stress, σU – highest stress on the specimen
- Fracture Stress, σF – stress at which specimen breaks
E=Δσ/Δε
σ (KSI)
ε (μ in./in.)

14. Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- DUCTILE vs. BRITTLE Behavior:
- Ductile behavior – specimen exhibits significant
permanent (plastic) deformation
before failure,
(good, gives warning before failure)
- Brittle behavior –
specimen exhibits
little or no
permanent (plastic)
deformation
(bad, no warning before
failure)
E=Δσ/Δε
σ (KSI)
ε (μ in./in.)

15. Engineering Stress-Strain Diagram – Ductile
Some Ductile materials have
distinct Yield Point and
large yielding region:
- alloys such as;
steel, brass,
- elements such as;
Molybdenum, Zinc
no distinct Yield Point:
- Such as; Aluminum
- need to define a YIELD STRENGTH
- Stress at 0.2% strain
- draw a line from ε = 2000x10-6 = = 0.2%
- parallel to the linear elastic portion of curve
- σYS = stress at intersection of parallel line with curve
E=Δσ/Δε
σ (KSI)
ε (μ in./in.)
ε (μ in./in.)

16. Engineering Stress-Strain Diagram – Brittle
Brittle materials exhibit
LITTLE or NO permanent deformation
BEFORE failure (BAD).
Examples:
- Gray Cast Iron
- Concrete
- Low Tensile Strength
- High Compression Strength
- No failure warning (Tension or Compression)
- BAD
- need to get people
- off bridge
- out of building
E=Δσ/Δε
ε (μ in./in.)
σ (KSI)

17. Brittle - Concrete Concrete - Low Tensile Strength
- High Compression Strength
- No failure warning (Tension or Compression)
- BAD
- need to get people
- off bridge
- out of building

18. Brittle - Concrete Concrete - Low Tensile Strength
- High Compression Strength
- No failure warning (Tension or Compression)
- BAD
- need to get people
- off bridge
- out of building

19. Ductility DUCTILITY can be measured by: - Percent Elongation:
- Percent Reduction of Area:
E=Δσ/Δε
ε (μ in./in.)
σ (KSI)

20. Strain Hardening & Hysteresis
If a specimen is loaded past σEL,
Then unloaded,
Some deformation will be removed,
Some deformation will remain.
The slope of the UNLOADING curve will be
the SAME SLOPE, E, as the LOADING curve.
If specimen is loaded again,
The slope of the re-load curve will be E.
A higher σY will be reached because of
STRAIN HARDENING.
But there will be a smaller plastic region
Remaining,
So DUCTILITY will be less.
E=Δσ/Δε
ε (μ in./in.)
σ (KSI)
Original Yield Point
Yield Point after
Strain Hardening

21. Strain Hardening & Hysteresis
Some energy will be
LOST or USED or DISSIPATED
In the LOAD and UNLOAD processes.
Energy dissipated is a function of the
area inside the LOAD-UNLOAD curves,
called HYSTERESIS loops.
Mechanical hysteresis devices are used to
Reduce EARTHQUAKE forces on structures.

22. Hysteresis Devices

23. Hysteresis Devices

24. Stress -Strain Diagrams
Example:
Problem 3-4
Hibbeler 7th edition,
pg. 102

25. Stress -Strain Diagrams
Example:
Problem 3-4
Hibbeler 7th edition,
pg. 102