A cantilever beam with a length of 15 meters and a circular cross section with a diameter (d) of 250 mm, respectively, c

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A cantilever beam with a length of 15 meters and a circular
cross section with a diameter (d) of 250 mm, respectively, carries
a transverse end point load (𝑃𝑃1 = 25 𝑘𝑘𝑘𝑘) and a compressive load
(𝑃𝑃2 = 1500 MN) on its free end that is applied through its
centroid. (i) Starting from the general equation for bending,
derive the equation for the maximum longitudinal direct stresses
due to transverse concentrated load and calculate its maximum
tensile and compressive values. [12] (ii) Develop an equation for
the direct longitudinal stress due to the compressive end-load
acting on the beam and calculate its numerical value. [2] (iii) By
plotting these stresses on a diagram for the distribution of stress
through the depth of the beam, determine the maximum direct
stresses induced in the beam. [6] (iv) Use the plotted diagram to
determine the location of the neutral axis with reference to the
lower and upper surfaces of the beam cross-section. [7