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.

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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.

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

Scenario
A 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, as
presented 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 the
arms are parallel to the wall (Fig. 1c, view along the Z-axis). The two arms are subjected to
external 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 be
rigid (no deflection within the arms). Please note the lengths and diameters of the pipe/arms
in the figure are not to scale.
(a)
(b)
L3
1
F
Values Used
Parameter
L1 (cm)
L2 (cm)
L3 (cm)
F (N)
F
2
B
1
2
Value
35
52
27
3527
(c)
I
1
Figure 1: A steel pipe with two horizontal arms.

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