FE Exam Formulas Ch. 6 Flashcards
Purpose and Variables of…
Stress on a Cross Section
sigma=stress on the cross section
P=loading
A=cross-sectional area
Purpose and Variables of…
Strain
delta=elastic longitudinal deformation
L=length of member
Purpose and Variables of…
Strain
epsilon=engineering strain
deltaL=change in member length
L0=original length of member
Purpose and Variables of…
Hooke’s Law/Stress Related to Elastic Modulus
sigma=stress
E=elastic modulus
epsilon=engineering strain
Purpose and Variables of…
Shear Strain
gamma=shear strain
tau=shear stress
G=shear modulus
Purpose and Variables of…
Poisson’s Ratio
G=shear modulus
E=modulus of elasticity
v=Poisson’s ratio=lateralstrain/longitudinalstrain
Purpose and Variables of…
Normal Stress due to Bending
sigmax=normal stress
M=moment at the section
I=moment of inertia of the cross section
y=distance from the neutral axis to the fiber location above or below the neutral axis
Purpose and Variables of…
Maximum Normal Stress due to Bending
sigmax=maximum normal stress
M=moment at the section
c=distance from the neutral axis to the outermost fiber of a symmetrical beam section
Purpose and Variables of…
Normal Stress using Elastic Section Modulus
sigmax=normal stress
M=moment at the section
s=elastic section modulus
Purpose and Variables of…
Elastic Section Modulus of Beam
s=elastic section modulus
I=moment of intertia of the cross section
c=distance from the neutral axis to the outermost fiber of a symmetrical beam section
Purpose and Variables of…
Transverse Shear Stress
tauxy=transverse shear stress
V=shear force
Q=A’y’=first moment of area above or below the point where shear stress is to be determined
A’=area above the layer on which the desired transverse shear stress acts
y’=distance from neutral axis to area centroid
b=width or thickness of the cross section
I=moment of intertia of the cross section
Purpose and Variables of…
Transverse Shear Flow
q=transverse shear flow
V=shear force
Q=A’y’=first moment of area above or below the point where shear stress is to be determined
A’=area above the layer on which the desired transverse shear stress acts
y’=distance from neutral axis to area centroid
I=moment of intertia of the cross section
Purpose and Variables of…
Percent of Elongation
deltaL=change in length
L0=initial length
Purpose and Variables of…
Percent of Reduction
Ai=initial area
Af=final area
Purpose of…
Total Energy
Purpose and Variables of…
Strain Energy per Unit Volume
u=strain energy
U=total energy
A=unit area
L=unit length
sigma=stress
E=modulus of elasticity
Purpose and Variables of…
Modulus of Elasticity
E=modulus of elasticity
epsilon=engineering strain
P=loading
A=area
delta=elastic longitudinal deformation
L=length
Purpose and Variables of…
Deformation Caused by a Change in Temperature
deltat=Deformation Caused by a Change in Temperature
alpha=thermal coefficient of expansion
L=length
T=final temperature
T0=initial temperature
Purpose and Variables of…
Torsional Stress
tau=torsional stress
T=torque
r=radius
J=polar moment of inertia
Purpose and Variables of…
Angle of Twist
phi=total angle (radians) of twist
T=torque
L=length of shaft
G=shear modulus
J=polar moment of inertia
Purpose and Variables of…
Circumferential Stress
sigmat=circumferential stress
Pi=internal pressure
r=radius
t=thickness
sigmaa=axial stress
Purpose and Variables of…
Circumferential Stress
sigmat=circumferential stress
Pi=internal pressure
r0=radius final
ri=radus initial
sigmar=radial stress
Purpose and Variables of…
Circumferential Stress
sigmat=circumferential stress
Po=external pressure
r0=radius final
ri=radus initial
sigmar=radial stress
Purpose and Variables of…
Maximum Deflection
vmax=maximum deflection
w=distributed force
L=length of beam
E=modulus of elasticity (Table 1)
I=moment of intertia
Purpose and Variables of…
Maximum Slope of Beam
theta=slope of beam
w=distributed force
L=length of beam
E=modulus of elasticity (Table 1)
I=moment of intertia
Purpose and Variables of…
Deflection of Beam
delta=deflection
w=distributed force
x=point of interest
E=modulus of elasticity (Table 1)
I=moment of intertia
L=length of beam
Purpose and Variables of…
Distortion Energy Theory
Sy=yield strength
sigma=stress
Purpose and Variables of…
Coulomb Mohr Theory
sigma=stress
Sut=tensile ultimate strength
Suc=compressive ultimate strength
Purpose and Variables of…
Maximum and Minimum Normal Stress (Principal Stresses)
sigmaa=maximum stress
sigmab=minimum stress
sigma=stress
tauxy=shear acting in x and y direction
