def Problem6():
""" CORRECT
Analyze a steel shaft with an ultimate
strength of 81 kpsi and fully corrected endurance
limit of 34 kpsi if it undergoes a bending stress
with mean and amplitude stresses of 9 and 10,
respectively, while also undergoing a torsional shear
with mean and amplitude stresses of -10 and 6,
respectively. Assume there are no stress concentrations
or axial loads. Neglect yielding and use the Goodman
failure criterion if needed. Report either the fatigue
factor of safety if it is predicted to have infinite life,
or the number of cycles to failure in thousands of cycles (N/103)."""
Sut = 81 # Kpsi
Se = 34 # Kpsi
sigmaM = 9
sigmaA = 10
TauM = -10
TauA = 6
sigmaM = Fatigue.AlternatingLoadsVonMises(sigmaM, 0, TauM)
sigmaA = Fatigue.AlternatingLoadsVonMises(sigmaA, 0, TauA)
sigmaMax = sigmaA + abs(sigmaM)
nf = Fatigue.Goodman(sigmaA, sigmaM, Se, Sut)
print(nf)
def Problem6(Sut, Sy, Se, Mrev, T, nf):
""" WRONG
Given a uniform diameter shaft made of steel with an
ultimate strength of 76 kpsi, a yield strength of 42 kpsi,
and a fully corrected endurance limit of 22 kpsi, what is
the minimum diameter of the shaft needed to ensure the shaft
will not yield and will have infinite life given a fully
reversed bending moment of 633 in-lbs and a steady torsional
load of 2,346 in-lbs? Use a design factor of 1.4, assume
there are no stress concentrations, and use the Morrow failure
criterion if needed."""
# sigmaA = Fatigue.AlternatingLoadsAmp(sigmaRev, 0)
# sigmaM = Fatigue.AlternatingLoadsMean(sigmaRev, 0)
# tauA = Fatigue.AlternatingLoadsAmp(tau, 0)
# tauM = Fatigue.AlternatingLoadsMean(tau, 0)
# sigmaAp = Fatigue.AlternatingLoadsVonMises(1, 1, 1, sigmaA, 0, tauA)
# sigmaMp = Fatigue.AlternatingLoadsVonMises(1, 1, 1, sigmaM, 0, tauM)
# sigmaMax = sigmaAp + abs(sigmaMp)
# print(sigmaMax)
# ny = Sy/sigmaMax
# print(ny)
A = Fatigue.DEA(1, Mrev, 1, 0)
B = Fatigue.DEB(1, 0, 1, T)
d = Fatigue.DEMorrow(A, B, Se, 122, n=nf, Mode='d')
print(d)
def Problem5(Sut, Se, sigma1, sigma2):
""" CORRECT
Given a steel shaft with an ultimate strength of 100
kpsi and a fully corrected endurance limit of 55 kpsi,
what is the factor of safety against fatigue failure if
it undergoes a normal stress that fluctuates between -50
kpsi and 15 kpsi? Neglect yielding and use the Goodman
failure criterion if needed."""
sigmaA = Fatigue.AlternatingLoadsAmp(sigma1, sigma2)
sigmaM = Fatigue.AlternatingLoadsMean(sigma1, sigma2)
print(sigmaA, sigmaM)
sigmaRev = sigmaA
nf = Se/sigmaRev
print(abs(nf))
def Problem3(Sut, SigmaAr, Se):
""" CORRECT
A steel bar with an ultimate strength of 142 kpsi
is loaded in bending with a completely reversed amplitude
of 39 kpsi. How many cycles (in thousands, or N/10^3)
will the bar withstand until failure? Assume a fully
corrected endurance limit of 28 kpsi is defined at 106 cycles."""
nf = Se/SigmaAr
# print(nf)
f = Fatigue.FatigueStrengthFactor(Sut)
# print(f)
a = Fatigue.CyclesA(f, Sut, Se)
b = Fatigue.CyclesB(f, Sut, Se)
N = Fatigue.Cycles(SigmaAr, f, Sut, Se)
print(N)
def Problem7():
""" WRONG
Given the following image of a shaft, what is the critical
speed of rotation in units of rad/s if the shaft has the
following section lengths and deflections (y) and the centers
of the given sections. Assume the shaft is made of steel and
all dimensions are given in inches. Ignore the weight change
due to the keyway.
L1 = 1.7 in, y1 = 10 x 10-6 in
L2 = 9 in, y2 = 300 x 10-6 in
L3 = 2.1 in, y3 = 150 x 10-6 in
L4 = 2.7 in, y4 = 10 x 10-6 in"""
L1 = 1.7
L2 = 9
L3 = 2.1
L4 = 2.7
lengths = [L1, L2, L3, L4]
dia = [1, 1.25, 1, 7./8.]
Weights = [32.2*12*0.282*np.pi/4*d**2 for d in dia]
y = [i*10**(-6) for i in [10, 300, 150, 10]]
w = Fatigue.RayleighsLumpedMasses(Weights, y)
print(w)
def Problem7():
""" CORRECT
Given the following image of a shaft,
what is the critical speed of rotation in
units of rad/s if the shaft has the following
section lengths and deflections (y) and the
centers of the given sections. Assume the
shaft is made of steel and all dimensions are
given in inches. Ignore the weight change due
to the keyway. (Do not use average diameter
simplification method.)"""
gamma = 0.282
L = [2.8, 8, 2.5, 4.7]
d = [1, 1.25, 1, 0.875]
y = [i*10**-6 for i in [10, 300, 150, 10]]
A = [np.pi/4*i**2 for i in d]
V = [i * j for i, j in zip(A, L)]
W = [gamma*i*32.2*12 for i in V]
prod = [i * j for i, j in zip(W, y)]
top = 32.2 * 12 * sum(prod)
prodSq = [i * j**2 for i, j in zip(W, y)]
bottom = sum(prodSq)
speed = np.sqrt(top/bottom)
print(speed)
w = Fatigue.RayleighsLumpedMasses(W, y)
print(w)
def Problem7_2(d):
Sut = 175e3
Sy = 160e3
Ma = 600
Mm = 0
Ta = 0
Tm = 400
Seprime = 0.5 * Sut / 1000
Ka = 2 * (Sut / 1000)**(-0.217)
Kb = 0.879 * d**(-0.107)
Se = 55000
Kf = 2.2
Kfs = 1.8
A = Fatigue.DEA(Kf, Ma, Kfs, Ta)
B = Fatigue.DEB(Kf, Mm, Kfs, Tm)
d = Fatigue.DEGoodman(A, B, Se, Sut, n=2.5, Mode='d')
D = d / 0.65
dFinal = 0.75 * D
print(dFinal)
def Problem5():
""" CORRECT
Given a steel shaft with an ultimate strength of 115
kpsi and a fully corrected endurance limit of 50 kpsi,
what is the factor of safety against fatigue failure if
it undergoes a normal stress that fluctuates between 13
kpsi and 49 kpsi? Neglect yielding and use the Goodman
failure criterion if needed."""
Sut = 115 #Kpsi
Se = 50 #Kpsi
sigma1 = 13 #Kpsi
sigma2 = 49 #Kpsi
sigmaA = Fatigue.AlternatingLoadsAmp(sigma1, sigma2)
sigmaM = Fatigue.AlternatingLoadsMean(sigma1, sigma2)
# print(sigmaA, sigmaM)
# sigmaRev = sigmaA
# nf = Se/sigmaRev
# print(abs(nf))
nf = Fatigue.Goodman(sigmaA, sigmaM, Se, Sut)
print(nf)
def Problem3():
"""CORRECT
A steel bar with an ultimate
strength of 109 kpsi is loaded in
bending and failed after 3,890 completely
reversed stress cycles. What is the stress
amplitude that caused the failure? Assume
a fully corrected endurance limit of 33 kpsi
is defined at 106 cycles."""
Sut = 109 # Kpsi
Se = 33 # Kpsi
N = 3890 # Cycles
# From equation 6-11
f = Fatigue.FatigueStrengthFactor(Sut)
a = Fatigue.CyclesA(f, Sut, Se)
b = Fatigue.CyclesB(f, Sut, Se)
Sf = a * N ** b
print(Sf)
def Problem5(d):
""" WRONG
Given a uniform diameter shaft made of
steel with an ultimate strength of 55 kpsi,
a yield strength of 44 kpsi, and a fully corrected
endurance limit of 22 kpsi, what is the minimum
diameter of the shaft needed to ensure the shaft
will not yield and will have infinite life given
a fully reversed bending moment of 621 in-lbs and
a steady torsional load of 1,812 in-lbs? Use a design
factor of 2.0, assume there are no stress concentrations,
and use the Morrow failure criterion if needed."""
Sut = 55000 # psi
Sy = 44000 # psi
Se = 22000 # psi
Mrev = 621 # in-lbs
T = 1812 # in-lbs
sigmaF = Sut + 50000
# Convert to stress
sigma = Stress.BendingRound(Mrev, d/2, d)
Tau = Stress.TorsionalRound(T, d)
sigmaA = sigma
sigmaM = 0
TauA = 0
TauM = Tau
sigmaAp = Fatigue.AlternatingLoadsVonMises(1, 1, 1, sigmaA, 0, TauA)
sigmaMp = Fatigue.AlternatingLoadsVonMises(1, 1, 1, sigmaM, 0, TauM)
sigmaMax = sigmaAp + abs(sigmaMp)
ny = Sy/sigmaMax
print('ny', ny)
# nf = Fatigue.Morrow(sigmaAp, sigmaMp, Se, sigmaF)
# print('nf', nf)
nf = Se/sigmaAp
print('nf', nf)
def Problem7_1():
Kf = 2.2
Kfs = 1.8
Ma = 70
Ta = 45
Mm = 55
Tm = 35
Sut = 700
Sy = 560
Se = 210
A = Fatigue.DEA(Kf, Ma, Kfs, Ta)
B = Fatigue.DEB(Kf, Mm, Kfs, Tm)
d = Fatigue.DEGoodman(A, B, Se, Sut, n=2, Mode='d')
print('Goodman', d)
d2 = Fatigue.DEGerber(A, B, Se, Sut, n=2, Mode='d')
print('Gerber', d2)
d3 = Fatigue.DEMorrow(A, B, Se, Sut + 345, n=2, Mode='d')
print('Morrow', d3)
d4 = Fatigue.DESWT(A, B, Se, Sut, n=2, Mode='d')
print('SWT', d4)