<jupyter_start><jupyter_text>Calculations for Bending Resistance of 3/4" SAE J429 Grade 8 Bolt per CSA S16-14 13.5  E.Durham - 11-Jun-2019<jupyter_code>import math
import pint
unit = pint.UnitRegistry(system='mks')

# define synonyms for common units
inch = unit.inch; mm = unit.mm; m = unit.m; MPa = unit.MPa; psi = unit.psi; kN = unit.kN
ksi = unit.ksi; dimensionless = unit.dimensionless; s = unit.second; kg = unit.kg

def u_round(Q, digits=3):
    """
    Takes a Pint.py quantity and returns same rounded to digits, default it 3 digits
    """
    try:
        unit.check(Q.units)
        magnitude = Q.magnitude
        units = Q.units
        return round(magnitude,digits) * units
    except:
        print('ERROR: u_round() first arguement must be a Pint.py quantity')
        return NaN
# Geometric Properties:
d = 19.05*mm
A = 285*mm**2
Z = (d**3)/6

# Mechanical Specifications for SAE J429 Grade 8
F_u = 150000*psi # minimum Tensile Strength
F_u.ito(MPa)
F_y = 130000*psi # minimum Yield Strength
F_y.ito(MPa)
# 13.1 Resistance factors:
phi = 0.9 * dimensionless     # structural steel
phi_u = 0.75 * dimensionless<jupyter_output><empty_output><jupyter_text>13.5 Bending - Laterally supported members  The factored moment resistance, $M_r$, developed by a member subjected to uniaxial bending moments about a principal axis where effectively continuous lateral support is provided to the compression flange, or where the member has no tendency to buckle laterally, shall be taken as follows: a) for Class 1 and Class 2 sections (except that singly symmetric I-sections and T-sections shall not yield under service loads):  $M_r = \phi Z F_y$  $M_r = \phi M_p$   b) for Class 3 sections:  $M_r = \phi S F_y$  $M_r = \phi M_y$<jupyter_code>M_r = phi * Z * F_y
print('M_r =', u_round(M_r.to(kN*m),3))<jupyter_output>M_r = 0.929 kilonewton * meter
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