**Problem Description:**A circular shaft AB of length \( L \) is fixed against rotation at the ends and loaded by a distributed torque \( t(x) \) that varies linearly in intensity from zero at end \( A \) to \( t_0 \) at end \( B \) (see figure). The reaction torque at \( B \) is known to be \( \frac{t_0L}{3} \). Find the reaction torque at \( A \), then plot the torsional moment diagram.**Diagram Explanation:**The accompanying diagram illustrates a circular shaft \( AB \) with length \( L \). It is subjected to a linearly varying torque \( t(x) \), shown as increasing from zero at end \( A \) to \( t_0 \) at end \( B \). The diagram features:1. **Shaft Representation:** The horizontal blue line represents the shaft.2. **Torque Representation:** Red arrows extending along the shaft indicate the direction and variation of torque \( t(x) \), increasing linearly from left (end \( A \)) to right (end \( B \)).3. **Measurement Indicators:** - \( x \) is the distance from end \( A \). - \( L \) is the total length of the shaft.4. **Support Conditions:** Both ends \( A \) and \( B \) are fixed, inhibiting rotation.The task requires calculating the reaction torque at \( A \) and constructing the torsional moment diagram based on the given conditions and distribution.

According to the given free body diagram , Consider the torque equilibrium in vertical direction RA+RB=12t0L......................1Here the reaction force are RAand RB, the distributed torque is t0,and length is L.Consider the moment about left end RBL-12t0L2L3=0 RB=t0L3Substitutet0L3for RB in equation 1 RA+RB = 12t0L RA+t0L3 = 12t0L RA= t0L6 Therefore reaction force at A is t0L6 Consider the torque momentum equation Tx= -RA+12t0xLxSubstitute t0L6 for RA Tx= -t0L6+12t0xLx =-t0L6+12t0x2L For x= 0, the corresp[onding torque is, Tx=0= -t0L6+12t002L =- t0L6For x= L, the corresponding torque is, Tx=L= -t0L6+12t0L2L =- t0L6+t0L2 = t0L3 Draw the internal moment diagram for the shaft. Therefore, the required torsional moment diagram for the shaft is drawn.

Engineering

Mechanical Engineering

A circular shaft AB of length L is fixed against rotation at the ends and loaded by a distributed torque (x) that varies linearly in intensity from zero at end A to to at end B (see figure). The reaction torque at B is known to be toL/3. Find the reaction torque at A, then plot the torsional moment diagram.

A circular shaft AB of length L is fixed against rotation at the ends and loaded by a distributed torque (x) that varies linearly in intensity from zero at end A to to at end B (see figure). The reaction torque at B is known to be toL/3. Find the reaction torque at A, then plot the torsional moment diagram.

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

Torsion

In mechanical engineering, torque, torsion, and twisting moment are three of the most important concepts which have different meanings. Torque is the consequence of a moment of a force that produces an angular acceleration in a body or induces rotational kinetic energy in a body. For instance, in an automobile, the power transmission shaft is a body that is always under rotation due to the external torque acting on it, this torque is created by the engine.

Question

**Problem Description:**

A circular shaft AB of length \( L \) is fixed against rotation at the ends and loaded by a distributed torque \( t(x) \) that varies linearly in intensity from zero at end \( A \) to \( t_0 \) at end \( B \) (see figure). The reaction torque at \( B \) is known to be \( \frac{t_0L}{3} \). Find the reaction torque at \( A \), then plot the torsional moment diagram.

**Diagram Explanation:**

The accompanying diagram illustrates a circular shaft \( AB \) with length \( L \). It is subjected to a linearly varying torque \( t(x) \), shown as increasing from zero at end \( A \) to \( t_0 \) at end \( B \). The diagram features:

1. **Shaft Representation:** The horizontal blue line represents the shaft.
2. **Torque Representation:** Red arrows extending along the shaft indicate the direction and variation of torque \( t(x) \), increasing linearly from left (end \( A \)) to right (end \( B \)).
3. **Measurement Indicators:**
- \( x \) is the distance from end \( A \).
- \( L \) is the total length of the shaft.
4. **Support Conditions:** Both ends \( A \) and \( B \) are fixed, inhibiting rotation.

The task requires calculating the reaction torque at \( A \) and constructing the torsional moment diagram based on the given conditions and distribution.

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