### Problem Statement:**9-41.** A 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the yield stress for the steel is \((\sigma_y)_{st} = 640 \text{ MPa}\), and for the bronze \((\sigma_y)_{br} = 520 \text{ MPa}\), determine the magnitude of the largest elastic load \(P\) that can be applied to the assembly. The modulus of elasticity for steel \(E_{st} = 200 \text{ GPa}\) and for bronze \(E_{br} = 100 \text{ GPa}\).### Diagram Explanation:The diagram illustrates a vertical assembly where a steel bolt is concentrically surrounded by a bronze sleeve. Key dimensions and features include:- The bolt is located centrally with a diameter of 10 mm.- The bronze sleeve encases the bolt, with an inner diameter of 10 mm and an outer diameter of 20 mm.- Two arrows labeled \(P\) indicate the application of load from the top and bottom ends of the assembly.- The assembly is symmetric, and the load \(P\) acts along the longitudinal axis of the bolt and sleeve.The task is to determine the maximum elastic load \(P\) that can be applied to this assembly without exceeding the yield stress of either material.

Calculate the cross-sectional area of bolt and bronze sleeve.Ast =π4 d2 ⇒π4(10)2 =78.54 mm2Abr…

9-41. The 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the yield stress for the steel is (oy)s = 640 MPa, and for the bronze (oy)br = 520 MPa, determine the magnitude of the largest elastic load P that can be applied to the assembly. Eg = 200 GPa, E=100 GPa. 10 mm -20 mm P

9-41. The 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the yield stress for the steel is (oy)s = 640 MPa, and for the bronze (oy)br = 520 MPa, determine the magnitude of the largest elastic load P that can be applied to the assembly. Eg = 200 GPa, E=100 GPa. 10 mm -20 mm P

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

Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

Question

### Problem Statement:

**9-41.** A 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the yield stress for the steel is \((\sigma_y)_{st} = 640 \text{ MPa}\), and for the bronze \((\sigma_y)_{br} = 520 \text{ MPa}\), determine the magnitude of the largest elastic load \(P\) that can be applied to the assembly. The modulus of elasticity for steel \(E_{st} = 200 \text{ GPa}\) and for bronze \(E_{br} = 100 \text{ GPa}\).

### Diagram Explanation:

The diagram illustrates a vertical assembly where a steel bolt is concentrically surrounded by a bronze sleeve. Key dimensions and features include:

- The bolt is located centrally with a diameter of 10 mm.
- The bronze sleeve encases the bolt, with an inner diameter of 10 mm and an outer diameter of 20 mm.
- Two arrows labeled \(P\) indicate the application of load from the top and bottom ends of the assembly.
- The assembly is symmetric, and the load \(P\) acts along the longitudinal axis of the bolt and sleeve.

The task is to determine the maximum elastic load \(P\) that can be applied to this assembly without exceeding the yield stress of either material.

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