Problem 7: Non-circular cross section shaft related to torque problems are difficult to be solved using the basic heory as for circular shaft. Your role is to make use of FAE to analyze the stress in squared cross section shaft shown in Figure.5.

Problem 7: Non-circular cross section shaft related to torque problems are difficult to be solved using the basic heory as for circular shaft. Your role is to make use of FAE to analyze the stress in squared cross section shaft shown in Figure.5.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.48P: Use numerical integration to compute the product of inertia of the region show with respect to the...

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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

2. Justify the simplification of this problem to only modeling one-eighth of the cross section
3. Construct two-dimensional elements grid (i.e., grid/mesh region), make the correct numbering and labeling
of the nodes and elements.

Problem 7: Non-circular cross section shaft related to torque problems are difficult to be solved using the basic
theory as for circular shaft. Your role is to make use of FAE to analyze the stress in squared cross section shaft
shown in Figure.5.
g= 6.5(10%) N/cm?
e = 0.035 deg
0.5 cm
0.5 cm
0.5 cm- 0.5 cm
Figure.5: Squared cross section shaft applied to torque T as 3D model
Provide justified explanation and recommendations to simplify the problem from three-dimensional (3D) to
two- dimensional (2D).
b.
а.
If the governing boundary value problem equation of such a problem can be given by:
+ 2g0 = 0,
dy?
$(x,y) at boundary is 0
dx2

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