The rotating solid steel shaft (Fig.1 a) is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 150 mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point “A" of TA = 300 N.m. There is a step at point “C" as shown in Fig.1 (b), assume that D/d ratio is 1,09 and fillet radius (r) is 2,5 mm. Find the stress concentrations at point "C" due to bending and shear loads (Initially assume d=50mm). If the shaft is machined from quenched and drawn steel with Sy= 420 MPa and Sut=560 MPa and using a factor of safety of 2.5, determine the minimum allowable diameter of the shaft at "C" based on a static yield analysis using the distortion energy (DE) theory. If the shaft with a diameter (d) of 32 mm is made of a brittle material with Suc = 420 MPa and Sut=360 MPa, determine the factor of safety of the shaft at "C" based on a static analysis using the Brittle-Coulomb-Mohr (BCM) theory.

The rotating solid steel shaft (Fig.1 a) is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 150 mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point “A" of TA = 300 N.m. There is a step at point “C" as shown in Fig.1 (b), assume that D/d ratio is 1,09 and fillet radius (r) is 2,5 mm. Find the stress concentrations at point "C" due to bending and shear loads (Initially assume d=50mm). If the shaft is machined from quenched and drawn steel with Sy= 420 MPa and Sut=560 MPa and using a factor of safety of 2.5, determine the minimum allowable diameter of the shaft at "C" based on a static yield analysis using the distortion energy (DE) theory. If the shaft with a diameter (d) of 32 mm is made of a brittle material with Suc = 420 MPa and Sut=360 MPa, determine the factor of safety of the shaft at "C" based on a static analysis using the Brittle-Coulomb-Mohr (BCM) theory.

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

1) The rotating solid steel shaft (Fig.1 a) is simply supported by bearings at points B and C and is driven
by a gear (not shown) which meshes with the spur gear at D, which has a 150 mm pitch diameter. The
force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point “A" of
TA = 300 N.m. There is a step at point "C" as shown in Fig.1 (b), assume that D/d ratio is 1,09 and
fillet radius (r) is 2,5 mm.
a)
Find the stress concentrations at point "C" due to bending and shear loads (Initially assume
d=50mm).
If the shaft is machined from quenched and drawn steel with Sy= 420 MPa and Sut=560 MPa and
b)
using a factor of safety of 2.5, determine the minimum allowable diameter of the shaft at "C" based
on a static yield analysis using the distortion energy (DE) theory.
If the shaft with a diameter (d) of 32 mm is made of a brittle material with Suc = 420 MPa and
c)
Sut=360 MPa, determine the factor of safety of the shaft at "C" based on a static analysis using the
Brittle-Coulomb-Mohr (BCM) theory.
TA
250 mm
100 mm
20
Detail of the
shaft at point C
Fig.1 (a)
Fig.1 (b)

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