Consider the crankshaft
from an inline four-cylinder engine with respective pistons and connecting
rods. The size of the engine components, cylinder 4 pressure profile, and phase
diagram are in accordance with the information given in MP1. The figure shows
output torque coming out of the crankshaft on the right side of the
engine. The crankshaft can be
considered, for simplicity, as a simply supported beam with the supports and
dimensions as shown in Figure 1.

Figure 1: Crankshaft, connecting rods, and pistons for inline
four-cylinder engine (all dimensions in mm).

a) Based on a static-analysis FBD, determine
and plot as a function of crank angle the y component, the z
component, and the
vector sum of
the force transmitted
by the connecting
rod to the
crank for cylinders 3 & 4.
Note that these forces are all transverse to the axis of the crankshaft.

b) Determine the crank angles for cylinders 3
and 4 for which the total transverse force acting on the crankshaft is maximum.
Note that the crank angle is considered to be at zero degrees for the position
of the pistons shown in Figure 1.

c) Calculate
and plot the shear and bending moment diagrams as a function of x for cylinders
3 and

4 at the crank angles
corresponding to maximum transverse shear force. At these crank angles, what is
the magnitude of torque applied to the crank shaft? Plot the torque in the
crank shaft as a function of x at these crank angles. This is called a torsion
diagram.

d) Determine the crank angles for cylinders 3
and 4 that correspond to maximum torque about the axis of the crankshaft. At
these angles, plot the torque in the crank shaft as a function of x and the
shear and bending moment diagrams.

e) Identify
the axial location
(the x coordinate
value) on the
crank shaft in
terms of maximum bending moment and calculate the
maximum bending stress at this section. The crank shaft has a diameter of 39
mm. Note that while the force delivered
by the connecting rod to the crank imposes a torque about the axis of the crank
shaft, there is no torsion in the crank shaft at the section where the crank
connects to the connecting rod.

f) The critical
section is identified as the section of the crankshaft that experiences the
maximum equivalent stress during the engine cycle. Equivalent stress for a
stress element which experiences one

normal stress and
one shear stress component
is given by the formula

eq =

2 +32

(1)

Determine the x coordinate value for
this section, the maximum equivalent stress that occurs over the engine cycle
at this section, and the corresponding crank angle.

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