A 60 mm diameter shaft AB is rigidly attached to the beam CDFH of 30 mm by 40 mm rectangular cross-section as shown in Figure Q4. The beam is pin supported at C and H. A torque of 2 kN.m (moment about z axis) is applied to end B of the shaft. Determine: (a) the reactions at supports Cand H, (b) the rotation about z axis of end B of the shaft by using Castigliano's second theorem, (c) the slope (rotation about z axis) at point C of the beam by using Castigliano's second theorem. The shaft and the beam are made of an aluminum alloy for which E = 72 GPa and G=27 GPa. Assume that the hub DF is rigid and neglect the strain energy due to transverse shear.

A 60 mm diameter shaft AB is rigidly attached to the beam CDFH of 30 mm by 40 mm rectangular cross-section as shown in Figure Q4. The beam is pin supported at C and H. A torque of 2 kN.m (moment about z axis) is applied to end B of the shaft. Determine: (a) the reactions at supports Cand H, (b) the rotation about z axis of end B of the shaft by using Castigliano's second theorem, (c) the slope (rotation about z axis) at point C of the beam by using Castigliano's second theorem. The shaft and the beam are made of an aluminum alloy for which E = 72 GPa and G=27 GPa. Assume that the hub DF is rigid and neglect the strain energy due to transverse shear.

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

A 60 mm diameter shaft AB is rigidly attached to the beam CDFH of 30 mm by 40 mm rectangular
cross-section as shown in Figure Q4. The beam is pin supported at C and H. A torque of 2 kN.m
(moment about z axis) is applied to end B of the shaft. Determine:
(a) the reactions at supports Cand H,
(b) the rotation about z axis of end B of the shaft by using Castigliano's second theorem,
(c) the slope (rotation about z axis) at point C of the beam by using Castigliano's second theorem.
The shaft and the beam are made of an aluminum alloy for which E = 72 GPa and G=27 GPa. Assume
that the hub DF is rigid and neglect the strain energy due to transverse shear.

y
200 mm
-400 mm-
400 mm-
H
F
30 mm
60 mm
40 mm
-800 mm
hub
T=2 kN.m
Figure Q4 / Rajah S4

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