Mechanical Principles for BMW: Shear Force, Bending Moment, Gyroscopic Reaction Torque, Power Transmission, Damped Vibration, Failure Analysis

Mechanical Principles 1
Mechanical Principles
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Mechanical Principles 2
Mechanical Principles for BMW
Section 1: Static Mechanical Systems
Part 1: For shear force, bending moment and shear due to bending calculate the distribution
into simply supported beams in BMW vehicles
Shear Forces refer to the unaligned forces which tend to push the body parts in a specified
direction and often another parametric body part in the overall opposite direction. The actions of
the shear force mainly represented in the figure below as follows:
Figure Illustrating the Actions of Shear Forces In the Plane
Shear Forces Computation
The figure below mainly demarcates the distribution of the shear force in the simply supported
and uniformly distributed beam.

Mechanical Principles 3
From the figure above, the overall total load carried in the span mainly given as loading intensity
multiplied by the length. But the length of the system is denoted by l, whereas the loading
intensity marked as w. Thus,
Total load=loading intensity x length
¿ w x l
Notably, there is support offered by the symmetry reactions at the parametric ends and thus, the
analysis at sections mainly represented as wl
2 . However, the overall distance cutting across the
sections from the makeable left beam hand is given as x.
On the other hand, the S.F at x-section x-x mainly represented as
= Wl
2 – Wx
= W (1/2 –x)
Additionally, using the given straight relation and taking the slope as equal to the parametric
loading rate or load intensity; then equations above changes to:

Mechanical Principles 4
Bending Moments
These are the reactions resulting from the actions of the applied external forces induced in the
structural elements which often cause the element to change or bend. The often and frequent
structural element subjected to the overall bending moments actions is the beam. Thus, the
diagram below illustrates the actions of the simply supported beam at the overall ends. However,
the supported mainly defined as the rotating of the beams at each end and thus, the resultant
bending moments is zero.
Figure Showing the Actions of the Moments and Shear in A Simply Supported Parametric
(Habibi and O’Connor 2017 p.317).
Beam