Mechanics of Materials ACCURATE QUESTIONS AND
WELL ELABORATED ANSWERS (CORRECT VERIFIED
SOLUTIONS) CURRENTLY UPDATED VERSION |ALREADY
GRADED A+ (BRAND NEW!!)
When does a material behave elastically?
When the stress is removed, the strain drops to zero (it reforms). When
the strain does not return to zero, plastic deformation has taken
place.
When would a beam fail due to fatigue?
A member may fail at stress levels significantly lower than the
max stress due to repeated loads in the proper locations, if
subjected to load in repetitive cycles.
What is hooke's law?
σ=E*ε, where E is the modulus of elasticity, essentially the ratio of
stress to strain, sigma is the stress, epsilon is the strain.
Deformation equation
σ=PL/AE
,Statically indeterminate strain equation
δ=δ_L+δ_R=0, essentially the
Thermal expansion equation
σ_T=a(dT)L, where a is the constant of thermal expansion. Basically
the strain is equal to the constant of thermal expansion times the
change in temp times the length of the rod.
What is α?
α = temperature expansion coefficient (m/mK, in/in oF)
Stress related to redundant support
σ=P/A=-E*a(dT)
Definition of strain
ε=δ/L (strain is the ratio of the deformation to the original length of the
rod)
What is the deformation due to an applied load?
δ_P=(PL)/(AE)
, Axial strain of a slender bar
ε=σ_x/E, σ_y and σ_z are equal to zero
Conditions for poisson's ratio:
The material must be homogenous and isotropic, essentially it
must be the same throughout and the same when measured from
different directions. In this case, ε_x=ε_y neq 0
What is poisson's ratio?
v=|lateral strain/axial strain| = -ε_y/ε_x.
How is the shearing strain quantified?
tau_xy=G(γ_xy)
What is G?
τ/γ
It is the modulus of rigidity, essentially the ratio of the shearing stress
to
shearing strain, given in the same units as the shear stress (psi/ksi)
since the strain is unitless in radians.
WELL ELABORATED ANSWERS (CORRECT VERIFIED
SOLUTIONS) CURRENTLY UPDATED VERSION |ALREADY
GRADED A+ (BRAND NEW!!)
When does a material behave elastically?
When the stress is removed, the strain drops to zero (it reforms). When
the strain does not return to zero, plastic deformation has taken
place.
When would a beam fail due to fatigue?
A member may fail at stress levels significantly lower than the
max stress due to repeated loads in the proper locations, if
subjected to load in repetitive cycles.
What is hooke's law?
σ=E*ε, where E is the modulus of elasticity, essentially the ratio of
stress to strain, sigma is the stress, epsilon is the strain.
Deformation equation
σ=PL/AE
,Statically indeterminate strain equation
δ=δ_L+δ_R=0, essentially the
Thermal expansion equation
σ_T=a(dT)L, where a is the constant of thermal expansion. Basically
the strain is equal to the constant of thermal expansion times the
change in temp times the length of the rod.
What is α?
α = temperature expansion coefficient (m/mK, in/in oF)
Stress related to redundant support
σ=P/A=-E*a(dT)
Definition of strain
ε=δ/L (strain is the ratio of the deformation to the original length of the
rod)
What is the deformation due to an applied load?
δ_P=(PL)/(AE)
, Axial strain of a slender bar
ε=σ_x/E, σ_y and σ_z are equal to zero
Conditions for poisson's ratio:
The material must be homogenous and isotropic, essentially it
must be the same throughout and the same when measured from
different directions. In this case, ε_x=ε_y neq 0
What is poisson's ratio?
v=|lateral strain/axial strain| = -ε_y/ε_x.
How is the shearing strain quantified?
tau_xy=G(γ_xy)
What is G?
τ/γ
It is the modulus of rigidity, essentially the ratio of the shearing stress
to
shearing strain, given in the same units as the shear stress (psi/ksi)
since the strain is unitless in radians.
