ScenarioA pipe made from martensitic steel, with inner and outer diameters of 56 mm and 60 mm,respectively, has been fixed perpendicularly to a wall, and the pipe lies along the X-axis, aspresented in Fig. 1a. Two steel arms of the same length have been welded perpendicularly(along the Y-axis) to the pipe, on the same X-Y plane (Fig. 1b, view along the X-axis), and thearms are parallel to the wall (Fig. 1c, view along the Z-axis). The two arms are subjected toexternal vertical loading (along the Z-axis) in opposite directions with equal magnitude (Fig.1a). The arms are made of the same material as the pipe, and they can be assumed to berigid (no deflection within the arms). Please note the lengths and diameters of the pipe/armsin the figure are not to scale.(a)(b)L31FValues UsedParameterL1 (cm)L2 (cm)L3 (cm)F (N)F2B12Value3552273527(c)I1Figure 1: A steel pipe with two horizontal arms. ScenarioA pipe made from martensitic steel, with inner and outer diameters of 56 mm and 60 mm,respectively, has been fixed perpendicularly to a wall, and the pipe lies along the X-axis, aspresented in Fig. 1a. Two steel arms of the same length have been welded perpendicularly(along the Y-axis) to the pipe, on the same X-Y plane (Fig. 1b, view along the X-axis), and thearms are parallel to the wall (Fig. 1c, view along the Z-axis). The two arms are subjected toexternal vertical loading (along the Z-axis) in opposite directions with equal magnitude (Fig.1a). The arms are made of the same material as the pipe, and they can be assumed to berigid (no deflection within the arms). Please note the lengths and diameters of the pipe/armsin the figure are not to scale.(a)(b)L31FValues UsedParameterL1 (cm)L2 (cm)L3 (cm)F (N)F2B12Value3552273527(c)I1Figure 1: A steel pipe with two horizontal arms.

Answered: Image /qna-images/answer/99415241-a5f7-4589-acf1-0b8a2beb597b.jpg

A1. Produce a Mohr's circle for the stress state of a 2D plane stress element at position C (located on the upper surface of the pipe) for your geometry and load, and calculate the values of the maximum in-plane shear stress and the maximum and minimum in- plane principal stresses. Show your working. A2. Calculate the von Mises equivalent stress at position C for your geometry and load, and state whether yielding occurs, assuming the material has a yield stress of 600 MPa. Show your working. A3. Providing the applied load F is no longer derived from your given parameter. Derive an expression for this and hence determine the maximum allowable applied load (F) to ensure a safety factor of 1.5 against yielding (considering the von Mises yield criterion), assuming the material has a yield stress of 600 MPa. Show your working.

A1. Produce a Mohr's circle for the stress state of a 2D plane stress element at position C (located on the upper surface of the pipe) for your geometry and load, and calculate the values of the maximum in-plane shear stress and the maximum and minimum in- plane principal stresses. Show your working. A2. Calculate the von Mises equivalent stress at position C for your geometry and load, and state whether yielding occurs, assuming the material has a yield stress of 600 MPa. Show your working. A3. Providing the applied load F is no longer derived from your given parameter. Derive an expression for this and hence determine the maximum allowable applied load (F) to ensure a safety factor of 1.5 against yielding (considering the von Mises yield criterion), assuming the material has a yield stress of 600 MPa. Show your working.

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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2
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