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Class #2.1Class #2.1Civil Engineering Materials – CIVE 2110Civil Engineering Materials – CIVE 2110
Strength of MaterialsStrength of Materials
Mechanical Properties Mechanical Properties
of Ductile Materialsof Ductile Materials
Fall 2010Fall 2010
Dr. GuptaDr. Gupta
Dr. PickettDr. Pickett
22
Strain Energy Strain Energy
External energy is required to deform specimen.External energy is required to deform specimen.Internal energy is stored in specimenInternal energy is stored in specimen during deformation process.during deformation process.Work = Energy = Force x DisplacementWork = Energy = Force x Displacement Force starts from ZERO, Force starts from ZERO, Strain Energy = Strain Energy = ΔΔU = U = “work done” “work done” ΔΔU =U = due to average force over load process. due to average force over load process.
VE
VolVE
Vol
AreaStressFU
ntDisplacemeForceUEnergyStrain
ZZZZ
ZYXZZZZYXZ
ZZZZ
2
2
1
2
1
2
1
2
12
1
2
12
1
33
Strain Energy Strain Energy
Strain Energy = Strain Energy = ΔΔU = U = “work done” “work done”
ΔΔU =U = due to average force over load process. due to average force over load process.
EV
UuDensityEnergyStrain
EV
UuVolumeunitperEnergyStrain
VE
VolVE
Vol
AreaStressFU
ntDisplacemeForceUEnergyStrain
Z
Z
ZZZZ
ZYXZZZZYXZ
ZZZZ
2
2
2
2
1
2
1
2
1
2
1
2
1
2
12
1
2
12
1
44
Strain Energy – Modulus of ResilienceStrain Energy – Modulus of Resilience
Modulus of Resilience:Modulus of Resilience:
- A measurement of a material’s ability to - A measurement of a material’s ability to
absorb energyabsorb energy
WITHOUT PERMANENT deformation.WITHOUT PERMANENT deformation.
- Area under ELASTIC portion of - Area under ELASTIC portion of
stress-strain diagram.stress-strain diagram.
EusilienceofModulus PL
PLPLr
2
2
1
2
1Re
55
Strain Energy – Modulus of ToughnessStrain Energy – Modulus of Toughness
Modulus of Toughness:Modulus of Toughness:
- A measurement of a material’s ability to - A measurement of a material’s ability to
absorb energy BEFORE FAILURE.absorb energy BEFORE FAILURE.
- Area under ENTIRE stress-strain diagram.- Area under ENTIRE stress-strain diagram.
- Materials with high toughness- Materials with high toughness
will give warning before failure (GOOD)will give warning before failure (GOOD)
AreaPlasticE
uToughnessofModulus PLt _2
1 2
66
Modulus of Toughness - ConcreteModulus of Toughness - ConcreteConcrete - need warning before failureConcrete - need warning before failure
- put in steel reinforcement bars- put in steel reinforcement bars
High Toughness Low ToughnessHigh Toughness Low Toughness
77
Poisson’s RatioPoisson’s RatioPoisson’s Ratio:Poisson’s Ratio:- For material that is:- For material that is:
- Homogenous- Homogenous- Isotropic- Isotropic- in linear elastic range- in linear elastic range
the material VOLUME must remain CONSTANTthe material VOLUME must remain CONSTANT - deformations in the Longitudinal direction- deformations in the Longitudinal direction must be compensated for by deformationsmust be compensated for by deformations in the TWO directions PERPENDICULAR to thein the TWO directions PERPENDICULAR to the Longitudinal direction.Longitudinal direction.
L
rRatiosPoissonalLongitudin
Lateral
''
88
Poisson’s RatioPoisson’s Ratio
Poisson’s Ratio:Poisson’s Ratio:
- Typical values:- Typical values:
steel = 0.27 - 0.32steel = 0.27 - 0.32
aluminum = 0.35aluminum = 0.35
cast iron = 0.28cast iron = 0.28
copper alloys = 0.34 - 0.35copper alloys = 0.34 - 0.35
concrete = 0.15concrete = 0.15
wood = 0.29 – 0.31wood = 0.29 – 0.31
L
rRatiosPoissonalLongitudin
Lateral
''
99
Shear Stress-Strain DiagramsShear Stress-Strain DiagramsAssumptions:Assumptions:- Material is: - Material is:
- loaded in pure shear- loaded in pure shear- homogeneous- homogeneous- isotropic- isotropic- ductile- ductile- in linear elastic range, has- in linear elastic range, has - proportional limit, - proportional limit, - Shear Modulus of Elasticity, G- Shear Modulus of Elasticity, G - Modulus of Rigidity, G- Modulus of Rigidity, G
12'
EGGLawsHooke
PL
PLG
1010
Shear Stress-Strain DiagramsShear Stress-Strain Diagrams
GGSteelSteel = 11x10 = 11x1066 psi psi
GGAluminumAluminum = 4x10 = 4x1066 psi psi
GGCopperCopper = 5.5x10 = 5.5x1066 psi psi
12'
EGGLawsHooke
PL
PLG
1111
CreepCreepCreep = time dependent Creep = time dependent permanent deformationpermanent deformation
Due to – Load Due to – Load - Temperature- Temperature
Creep Strength = highest initial stress that theCreep Strength = highest initial stress that the material can be subjected tomaterial can be subjected to
in order to avoid a specifiedin order to avoid a specified creep strain creep strain over a specified timeover a specified time
1212
FatigueFatigueFatigue = BRITTLE fracture at Fatigue = BRITTLE fracture at
stress < material’s Yield Stressstress < material’s Yield Stress
due to repeated load cyclesdue to repeated load cycles
Cause: Localized stress > average stressCause: Localized stress > average stress
Fatigue Limit = stress below which Fatigue Limit = stress below which
NO failure occurs for s NO failure occurs for s
specified number of cyclesspecified number of cycles
Endurance Limit = Fatigue LimitEndurance Limit = Fatigue Limit
1313
FatigueFatigueFatigue Limit = stress below which Fatigue Limit = stress below which
NO failure occurs for s NO failure occurs for s
specified number of cyclesspecified number of cycles
Endurance Limit = Fatigue LimitEndurance Limit = Fatigue Limit
1414
Shear StrainShear StrainExample:Example:
Problem 3-30Problem 3-30
Hibbeler 7Hibbeler 7thth edition, edition,
pg. 116pg. 116
1515
Shear StrainShear StrainExample:Example:
Problem 3-32Problem 3-32
Hibbeler 7Hibbeler 7thth edition, edition,
pg. 117pg. 117