Previous research has established the following criterion of the wind turbine to be:

The tubular steel tower hub of the wind turbine stands 75 metres high above the concrete platform base serving as a foundation of the structure with a blade length of 35 metres long for each of the three blades. The mass of the tower hub is 210 tonnes and the total mass of the nacelle and the rotor is 92 tonnes.

The tube outer diameter ranges from 4.5 meters at the bottom to 3 meters at the top of the tower. The shell thickness is 100 mm.

The data on wind speed variation with height on the windiest days of the year has revealed the following information:

Height above the see level in m	Wind speed in m/s
0	8.6
5	10.1
10	11.6
15	12.6
20	13.3
25	13.9
30	14.5
35	14.9
40	15.3
45	15.7
50	16.0
55	16.3
60	16.6
65	16.9
70	17.1
75	17.4
80	17.6
85	17.8

The research on average air density throughout the year for the location of the turbine has indicated a figure of 1.2 kg/m³

In all calculations below take:

g , the acceleration due to gravity as 10 m/s²

E, the modulus of elasticity for steel as 200 GN/m².

I, the second moment of area for the hub as 0.2898 m⁴.

Que

1. By making appropriate simplifying assumptions (at least 2) about the tower hub and the loading conditions under which it operates and considering the structure to be a cantilever draw the graphs of the shear force and the bending moment.
2. Calculate the bending moment and the resulting bending stress on the hub as a result of the wind shear without any simplifying assumptions being made. How would you expect these values to be different from those calculated in part (1)?