Problem 1: In the figure below a solid bar with a 1.00 in diameter is subjected to a bending moment M and a twisting moment T. Given that the magnitude of the twisting moment and the bending moment are equal, so that M = T, answer the following questions: a) If the bar is made from a material that undergoes brittle failure under a tensile stress of 6000 psi, what is the value of the minimum moment that would produce brittle failure? Make a sketch of the bar; then determine and show the direction of the fracture plane with respect to the axial direction of the bar. Draw Mohr's circle and show your work. b) If the bar is made from a ductile material that yields plastically at a stress of 36000 psi, what is the value of the minimum moment that would produce yielding? Use von-Mises theory.

Problem 1: In the figure below a solid bar with a 1.00 in diameter is subjected to a bending moment M and a twisting moment T. Given that the magnitude of the twisting moment and the bending moment are equal, so that M = T, answer the following questions: a) If the bar is made from a material that undergoes brittle failure under a tensile stress of 6000 psi, what is the value of the minimum moment that would produce brittle failure? Make a sketch of the bar; then determine and show the direction of the fracture plane with respect to the axial direction of the bar. Draw Mohr's circle and show your work. b) If the bar is made from a ductile material that yields plastically at a stress of 36000 psi, what is the value of the minimum moment that would produce yielding? Use von-Mises 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

Problem 1: In the figure below a solid bar with a 1.00 in diameter is subjected to a bending moment M and a twisting
moment T. Given that the magnitude of the twisting moment and the bending moment are equal, so that M = T₁
answer the following questions:
M
a) If the bar is made from a material that undergoes brittle failure under a tensile stress of 6000 psi, what is the
value of the minimum moment that would produce brittle failure? Make a sketch of the bar; then determine and
show the direction of the fracture plane with respect to the axial direction of the bar. Draw Mohr's circle and
show your work.
b) If the bar is made from a ductile material that yields plastically at a stress of 36000 psi, what is the value of the
minimum moment that would produce yielding? Use von-Mises theory.

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