The cantilevered tube shown in the figure is to be made of 2014 aluminum alloy and is acted upon by external forces \( F \), \( P \) and torque \( T \). The bending load is \( F = 1.75 \, \text{kN} \), the axial tension is \( P = 9.0 \, \text{kN} \), and the torque is \( T = 72 \, \text{N} \cdot \text{m} \). If the tube has an outer diameter of (\( OD \)) 40 mm and an inner diameter (\( ID \)) of 30 mm, find all the stresses due to external loads at point A.### Diagram Explanation:- **Description**: The image is a visual representation of a cantilevered tube fixed at one end and subjected to various external forces.- **Diagram Details**: - The tube is horizontal and anchored at one end to a wall. - A bending force \( F \) is applied perpendicular to the length of the tube at its free end. - Axial tension \( P \) is shown as a force applied along the length of the tube. - Torque \( T \) is represented by an arrow in a circular motion around the axis of the tube. - The length of the tube from where it is fixed to the point of force application is given as 1000 mm. - The external and internal diameters are indicated, allowing calculations for stress analysis at point A.This setup is used to determine and analyze the stresses on the material at the fixed end of the tube caused by these external loads.

The tube is subjected to axial loading, bending, and torsion simultaneously, thus there will be axial normal stress, normal bending stress, and torsional shear stress in the tube. The axial normal stress can be calculated as- σ=FA where F is the axial loading in the tube A is the cross-sectional area of the tube The bending normal stress can be calculated as- σb=MyI where M is the bending moment at that point y is the distance of the fiber in the beam from the neutral axis of the beam I, the area moment of inertia of the beam The torsional shear stress can be calculated as- ζ=TrJ where T is the torsional loading acting in the tube r is the radius of that point in the tube J is the polar moment of inertia Writing all the relevant information given in the question as- The bending force acting in the tube, F=1.75kN The axial force acting in the tube, P=9.0kN The Torsional loading acting in the tube, T=72 Nm thus, the axial normal stress produced by force P at point A in the tube be, σ=PA=Pπ4×D2-d2σ=9.0×103π4×0.0402-0.0302σn=16.37MPa Thus, the normal stress produced by axial force be 16.37MPa. The normal bending stress produced by force F at point A in the tube be, σb=Fl×D2π64×D4-d4σb=1.75×103×0.120×0.0402π64×0.0404-0.0304σb=48.89MPa Thus, the normal stress produced by bending force F be 48.89MPa. The Torsional shear stress produced by the torque T on point A of the tube be- ζ=T×D2π32×D4-d4ζ=72×0.0402π32×0.0404-0.0304ζ=8.38MPa Thus, the shear stress produced by torsional loading be 8.38MPa.1. The Stress produced by axial force P on point A in the tube be 16.37MPa. 2. The normal stress produced by bending force F at point A in the tube be 48.89MPa. 3. The shear stress produced by torque at point A in the tube be 8.38MPa.

Engineering

Mechanical Engineering

The cantilevered tube shown in the following figure is to be made of 2014 aluminum alloy and is acted upon by external forces F, P and torque T. The bending load is F= 1.75 kN, the axial tension is P= 9.0 kN, and the torque is T= 72 N.m. If the tube has an outer diameter of (OD) 40 mm and an inner diameter (ID) of 30 mm, find all the stresses due to external loads at point A.

The cantilevered tube shown in the following figure is to be made of 2014 aluminum alloy and is acted upon by external forces F, P and torque T. The bending load is F= 1.75 kN, the axial tension is P= 9.0 kN, and the torque is T= 72 N.m. If the tube has an outer diameter of (OD) 40 mm and an inner diameter (ID) of 30 mm, find all the stresses due to external loads at point A.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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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 cantilevered tube shown in the figure is to be made of 2014 aluminum alloy and is acted upon by external forces \( F \), \( P \) and torque \( T \). The bending load is \( F = 1.75 \, \text{kN} \), the axial tension is \( P = 9.0 \, \text{kN} \), and the torque is \( T = 72 \, \text{N} \cdot \text{m} \). If the tube has an outer diameter of (\( OD \)) 40 mm and an inner diameter (\( ID \)) of 30 mm, find all the stresses due to external loads at point A.

### Diagram Explanation:

- **Description**: The image is a visual representation of a cantilevered tube fixed at one end and subjected to various external forces.
- **Diagram Details**:
- The tube is horizontal and anchored at one end to a wall.
- A bending force \( F \) is applied perpendicular to the length of the tube at its free end.
- Axial tension \( P \) is shown as a force applied along the length of the tube.
- Torque \( T \) is represented by an arrow in a circular motion around the axis of the tube.
- The length of the tube from where it is fixed to the point of force application is given as 1000 mm.
- The external and internal diameters are indicated, allowing calculations for stress analysis at point A.

This setup is used to determine and analyze the stresses on the material at the fixed end of the tube caused by these external loads.

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