Advanced **Torsion Member Analysis****Problem Statement:**The left-hand section of the torsion member in Figure E6.8 is 2.00 meters long, and the right-hand section is 1.00 meter long. It is constructed from an aluminum alloy with a modulus of rigidity \( G \) of 27.1 GPa. The task is to determine the magnitude of \( T_2 \) given that \( T_1 = 350 \, \text{N} \cdot \text{m} \) and that the maximum shear stress is 45.0 MPa. In this problem, neglect stress concentrations at changes in the section. Additionally, determine the angle of twist of the free end. The support at the left end prevents the rotation of this cross-section but allows warping.**Diagram Description:**Figure E6.8 illustrates a torsion member. The left section of the bar is 2.00 meters in length with a diameter of 60 mm. The right section is 1.00 meter in length with a reduced diameter of 30 mm. Torque \( T_1 \) acts at the end of the left section, while torque \( T_2 \) acts at the free end of the right section. The diagram provides dimensions and indicates the positions where the torques are applied. The boundary conditions show that the left end is fixed in terms of rotation but not warping, which means the structure is free to deform axially.This problem involves calculating the unknown torque \( T_2 \) and the angle of twist using material properties and geometric dimensions provided.

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Answered: The left-hand section of the torsion…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Advanced

**Torsion Member Analysis**

**Problem Statement:**

The left-hand section of the torsion member in Figure E6.8 is 2.00 meters long, and the right-hand section is 1.00 meter long. It is constructed from an aluminum alloy with a modulus of rigidity \( G \) of 27.1 GPa. The task is to determine the magnitude of \( T_2 \) given that \( T_1 = 350 \, \text{N} \cdot \text{m} \) and that the maximum shear stress is 45.0 MPa. In this problem, neglect stress concentrations at changes in the section. Additionally, determine the angle of twist of the free end. The support at the left end prevents the rotation of this cross-section but allows warping.

**Diagram Description:**

Figure E6.8 illustrates a torsion member. The left section of the bar is 2.00 meters in length with a diameter of 60 mm. The right section is 1.00 meter in length with a reduced diameter of 30 mm. Torque \( T_1 \) acts at the end of the left section, while torque \( T_2 \) acts at the free end of the right section.

The diagram provides dimensions and indicates the positions where the torques are applied. The boundary conditions show that the left end is fixed in terms of rotation but not warping, which means the structure is free to deform axially.

This problem involves calculating the unknown torque \( T_2 \) and the angle of twist using material properties and geometric dimensions provided.

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Determine the minimum radius of gyration for the column cross and find the
slenderness ratio of the column.
b) Determine the buckling load for the column.
Take E = 72GPA

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