# Example 4.1
IPS
d = 1.25 in
a = pi() * d^2 / 4
f = 2.05e4 lbf
sig = f / a; ksi


# Example 4.2
MKS(N, N m)
f = 8 kN / 2
d = 10 mm
a = pi() * d^2 / 4; mm^2
sig = f / a; MPa

# Example 4.3
f = 8 kN / 2
d = 10 mm
a = pi() * d^2 / 4; mm^2
sig = f / a; MPa
E = 210 GPa
nu = 0.3
len = 325 mm
eps = sig / E
del_len = eps * len
del_d = -nu * d * del_len / len; nm

# Example 4.4
IPS
f1 = 3500 lbf
nu = 0.3
d = 0.5 in
a = pi() * d^2 / 4
sig1 = f1 / a; ksi
E = 30.6 Mpsi
eps1 = sig1 / E
len = 12 in
del_len = eps1 * len
del_d = -nu * d * del_len / len
k = E * a / len

f2 = 1000 lbf
sig2 = f2 / a; ksi
eps2 = sig2 / E
del_len2 = eps2 * len

# Example 4.5
d = 8 mm
f = 385 N
a = pi() * d^2 / 4
tau = f / a; MPa

# Example 4.6
IPS
d = (3 / 8) in
f = 350 lb / 2
a = pi() * d^2 / 4
tau = f / a; ksi

# Example 4.7
E = 207 GPa
rho = 76e3 N / m^3
E / rho

# Example 4.8
IPS
f = 1500 lbf
rf = 2.5 in
BEGIN
v = 1000 lbf # initial guess
rv = 0.5 in
sumM = -f * rf + v * rv
END
solve(sumM, v)

a = (1.75 in)  * (0.25 in)
tau = v / a; psi
sy = 60 ksi / 2
FOS = sy / tau

# Homework Problems:

TBD