The normal stress on the rectangular cross sec- varies linearly with respect to the tion ABCD y coordinate. That is, o, has the form o, = a + by, varying lin- early from oxb at the bottom edge of the cross section to ơxt at the top edge of the cross section. (a) Show that M, = 0 for this symmetrical normal-stress distribution. (b) Determine an expression for the axial force F, in terms of the stresses Oxb and ox and the dimensions of the cross section, width b and height h. (c) Determine an expression for the correspon- ding value of the bending moment M.

The normal stress on the rectangular cross sec- varies linearly with respect to the tion ABCD y coordinate. That is, o, has the form o, = a + by, varying lin- early from oxb at the bottom edge of the cross section to ơxt at the top edge of the cross section. (a) Show that M, = 0 for this symmetrical normal-stress distribution. (b) Determine an expression for the axial force F, in terms of the stresses Oxb and ox and the dimensions of the cross section, width b and height h. (c) Determine an expression for the correspon- ding value of the bending moment M.

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

The normal stress on the rectangular cross sec-
varies linearly with respect to the
tion ABCD
y coordinate. That is, o, has the form o, = a + by, varying lin-
early from oxb at the bottom edge of the cross section to ơxt
at the top edge of the cross section. (a) Show that M, = 0 for
this symmetrical normal-stress distribution. (b) Determine
an expression for the axial force F, in terms of the stresses
Oxb and ox and the dimensions of the cross section, width b
and height h. (c) Determine an expression for the correspon-
ding value of the bending moment M.

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