**Problem 5**The shaft is subject to a compressive force without the torque and the point loading. Its elastic modulus $ E $ is 100 GPa. Its both ends are pin connections: $ K $ of $ KL $ is 1. Please compute the $ P_{cr} $ of this column. ### Analysis of Stress on a Shaft#### (a) Overview of ShaftThis diagram shows a cylindrical shaft supported at both ends. Key elements include:- **P**: A downward force applied at the center.- **L**: Denotes the length of the shaft.- **T**: Represents torque or twisting force at the ends.- **Thrust bearing**: Highlighted near the center, providing axial support.#### (b) Zoom-in View of a Solid ParticleThis illustration focuses on a small segment located at the bottom, middle section of the shaft. Elements include:- **$\tau$**: Shear stress acting horizontally within the particle.- **$\sigma_x$**: Normal stress acting horizontally outward.- **Arrows indicating forces**: Directions of applied stresses on the particle.#### (c) Zoom-in "Top" View of the Solid ParticleThis view provides a perspective from above the solid particle at the bottom middle of the shaft. Key points are:- **$\sigma_x$**: Normal stress on the x-axis.- **$\tau_{xy}$, $\tau_{yx}$**: Shear stresses appearing as vector pairs.- **$\sigma_y = 0$**: Indicates no normal stress in the y-direction.This diagram series collectively explains how a symmetrical shaft with central load and end torques experiences both normal and shear stress across its structure.

Answered: Problem 5 point loading. Its elastic…

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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$**Problem 5** The shaft is subject to a compressive force without the torque and the point loading. Its elastic modulus $ E $ is 100 GPa. Its both ends are pin connections: $ K $ of $ KL $ is 1. Please compute the $ P_{cr} $ of this column.$

Transcribed Image Text:**Problem 5** The shaft is subject to a compressive force without the torque and the point loading. Its elastic modulus $ E $ is 100 GPa. Its both ends are pin connections: $ K $ of $ KL $ is 1. Please compute the $ P_{cr} $ of this column.

### Analysis of Stress on a Shaft

#### (a) Overview of Shaft

This diagram shows a cylindrical shaft supported at both ends. Key elements include:
- **P**: A downward force applied at the center.
- **L**: Denotes the length of the shaft.
- **T**: Represents torque or twisting force at the ends.
- **Thrust bearing**: Highlighted near the center, providing axial support.

#### (b) Zoom-in View of a Solid Particle

This illustration focuses on a small segment located at the bottom, middle section of the shaft. Elements include:
- **$\tau$**: Shear stress acting horizontally within the particle.
- **$\sigma_x$**: Normal stress acting horizontally outward.
- **Arrows indicating forces**: Directions of applied stresses on the particle.

#### (c) Zoom-in "Top" View of the Solid Particle

This view provides a perspective from above the solid particle at the bottom middle of the shaft. Key points are:
- **$\sigma_x$**: Normal stress on the x-axis.
- **$\tau_{xy}$, $\tau_{yx}$**: Shear stresses appearing as vector pairs.
- **$\sigma_y = 0$**: Indicates no normal stress in the y-direction.

This diagram series collectively explains how a symmetrical shaft with central load and end torques experiences both normal and shear stress across its structure.

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