A beam made of Al 2014-T6 aluminum alloy is loaded by an oblique bending moment of M =5 kN.m as shown in the figure.a) Obtain the location of the centroid of the cross-section, ỹ.b) Calculate the moments of inertia about the axes y and z.c) Obtain the location and the orientation of the Neutral Axis and draw it on the figure.d) Calculate the max. tensile and the compressive stresses.Note: The cross-sectional dimensions are thesame with the one in the 3rd question of thefinal exam. Therefore, you do not need to findthe location of the centroid and the value of theтотеnt of inertia about the z axis, I, You candirectly use the values in the 3rd question.5 kN.m90 mm3010 mmX90 mm10 mm

Solution: a) Centroid of the cross-section y¯ can be calculated by, Let area A1 = 90×10=900mm2…

A beam made of Al 2014-T6 aluminum alloy is loaded by an oblique bending moment of M= 5 kN.m as shown in the figure. a) Obtain the location of the centroid of the cross-section, ỹ. b) Calculate the moments of inertia about the axes y and z.

A beam made of Al 2014-T6 aluminum alloy is loaded by an oblique bending moment of M= 5 kN.m as shown in the figure. a) Obtain the location of the centroid of the cross-section, ỹ. b) Calculate the moments of inertia about the axes y and z.

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 beam made of Al 2014-T6 aluminum alloy is loaded by an oblique bending moment of M =
5 kN.m as shown in the figure.
a) Obtain the location of the centroid of the cross-section, ỹ.
b) Calculate the moments of inertia about the axes y and z.
c) Obtain the location and the orientation of the Neutral Axis and draw it on the figure.
d) Calculate the max. tensile and the compressive stresses.
Note: The cross-sectional dimensions are the
same with the one in the 3rd question of the
final exam. Therefore, you do not need to find
the location of the centroid and the value of the
тотеnt of inertia about the z axis, I, You can
directly use the values in the 3rd question.
5 kN.m
90 mm
30
10 mm
X
90 mm
10 mm

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