(a) The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50 mm and 40 mm outer and inner diameters respectively, and it is expected to be subjected to the following extreme loading conditions which act simultaneously: A torque of 2.5KNM about the axis. • A bending moment of 3.6kNm acting on the vertical plane containing the shaft axis. 3.6 ENm Figure 3(a) Calculate the following: i. The polar second moment of area, J i. The shear stress at point A on the outer surface of the shaft (where the vertical plane containing the shaft axis intersects the outer periphery of the shaft). i. The second moment of area / about a diametric axis (i.e., an axis across a diameter of the cross-section). iv. The bending stress at point A. (b) The spherical LPG storage tank shown in Figure 3(b) has the following design specifications: Tank diameter of 22 m, shell plate thickness of 24 mm, yield stress of steel plates 550 MPa, a factor of safety of 2. Calculate the design pressure, i.e., the maximum safe operating pressure, if the tank is designed simply on the basis of maximum allowable stress.

(a) The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50 mm and 40 mm outer and inner diameters respectively, and it is expected to be subjected to the following extreme loading conditions which act simultaneously: A torque of 2.5KNM about the axis. • A bending moment of 3.6kNm acting on the vertical plane containing the shaft axis. 3.6 ENm Figure 3(a) Calculate the following: i. The polar second moment of area, J i. The shear stress at point A on the outer surface of the shaft (where the vertical plane containing the shaft axis intersects the outer periphery of the shaft). i. The second moment of area / about a diametric axis (i.e., an axis across a diameter of the cross-section). iv. The bending stress at point A. (b) The spherical LPG storage tank shown in Figure 3(b) has the following design specifications: Tank diameter of 22 m, shell plate thickness of 24 mm, yield stress of steel plates 550 MPa, a factor of safety of 2. Calculate the design pressure, i.e., the maximum safe operating pressure, if the tank is designed simply on the basis of maximum allowable stress.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

3. (a) The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50
mm and 40 mm outer and inner diameters respectively, and it is
expected to be subjected to the following extreme loading conditions
which act simultaneously:
A torque of 2.5kNm about the axis.
• A bending moment of 3.6kNm acting on the vertical plane
containing the shaft axis.
3.6 ENm
25m
Figure 3(a)
Calculate the following:
i.
The polar second moment of area, J
ii. The shear stress at point A on the outer surface of the shaft
(where the vertical plane containing the shaft axis intersects the
outer periphery of the shaft).
i. The second moment of area I about a diametric axis (i.e., an
axis across a diameter of the cross-section).
iv. The bending stress at point A.
(b) The spherical LPG storage tank shown in Figure 3(b) has the following
design specifications: Tank diameter of 22 m, shell plate thickness of
24 mm, yield stress of steel plates 550 MPa, a factor of safety of 2.
Calculate the design pressure, i.e., the maximum safe operating
pressure, if the tank is designed simply on the basis of maximum
allowable stress.

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