The experimental set-up depicted in fig. 2 is aimed at studying the behavior of materials under complex stress states. A thin-walled pressure vessel of radius R = 11 mm and thickness t = 2.0 mm is subjected to an inter- nal pressure pi. At the same time, a normal force, N, and a torque, Q, are applied to the sample. In a specific experiment, the applied normal force is N = 16 kN and Figure 2: Pressure vessel subjected to the internal pressure p¿ = 20 MPa. The applied torque internal pressure, external torque and is slowly increased. The first permanent deformations are axial force. 2R P. observed at the outer surface of the sample when Q = 120 N-m. (1) Find the yield stress for the material if it is assumed to follow von Mises' yield criterion. (2) Find the yield stress for the material if it is assumed to follow Tresca's yield criterion. (3) Based on von Mises' yield criterion, find and plot the yield surface in the space defined by the three loading components, the internal pressure, the applied axial force, and the applied torque.

The experimental set-up depicted in fig. 2 is aimed at studying the behavior of materials under complex stress states. A thin-walled pressure vessel of radius R = 11 mm and thickness t = 2.0 mm is subjected to an inter- nal pressure pi. At the same time, a normal force, N, and a torque, Q, are applied to the sample. In a specific experiment, the applied normal force is N = 16 kN and Figure 2: Pressure vessel subjected to the internal pressure p¿ = 20 MPa. The applied torque internal pressure, external torque and is slowly increased. The first permanent deformations are axial force. 2R P. observed at the outer surface of the sample when Q = 120 N-m. (1) Find the yield stress for the material if it is assumed to follow von Mises' yield criterion. (2) Find the yield stress for the material if it is assumed to follow Tresca's yield criterion. (3) Based on von Mises' yield criterion, find and plot the yield surface in the space defined by the three loading components, the internal pressure, the applied axial force, and the applied torque.

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

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

Problem 2
The experimental set-up depicted in fig. 2 is aimed at
studying the behavior of materials under complex stress
states. A thin-walled pressure vessel of radius R = 11
mm and thickness t = 2.0 mm is subjected to an inter-
nal pressure pi. At the same time, a normal force, N,
and a torque, Q, are applied to the sample. In a specific
experiment, the applied normal force is N = 16 kN and Figure 2: Pressure vessel subjected to
the internal pressure p; = 20 MPa. The applied torque internal pressure, external torque and
is slowly increased. The first permanent deformations are axial force.
observed at the outer surface of the sample when Q = 120
N-m. (1) Find the yield stress for the material if it is assumed to follow von Mises' yield criterion.
(2) Find the yield stress for the material if it is assumed to follow Tresca's yield criterion. (3)
2R P.
Based on von Mises' yield criterion, find and plot the yield surface in the space defined by the three
loading components, the internal pressure, the applied axial force, and the applied torque.

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