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static engineering systems for stress and bending moments

As per attachement.
includes; maximum bending moment
maximum stress in a beam
graph sketches for tensil and compressive stresses
dimensions for cross section that minimise stress with given values
percentage reduction of the maximum stresswith new calculated cross section

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(a) In order to identify the features of the loaded beam, some additional notations were added on the given figure, which will be used in the next calculations.
The vertical reactions can be determined by writing the balance of forces and moments:
- forces:
( 1)
- moments (about the support A):
( 2)
The last equation will give R2:
( 3)
( 4)
It follows from (1) that ( 5)
Consequently, the bending moments at locations B and C will be:

Solution Summary

The static engineering systems for stress and bending moments are examined.