Problem B-2 [Statically Indeterminant Problem – Torsional Loading] A solid compound circular shaft (i.e., with segments AB and BC) are fixed to rigid walls at points A and C, respectively. As shown in the figure, an external torque is applied at point B. Determine the absolute maximum shear stress developed in the entire compound circular shaft ABC. B 480 N-m Bronze L1 = 1.8 m dz = 60 mm G2= 43 GPa Note: Corresponding length (L), diameter (d) and shear modulus (G) of the two segments are given in the figure, respectively. Ignore the effect of stress concentration. L = 0.6 m %3D Aluminum di = 40 mm G = 27 GPa

Problem B-2 [Statically Indeterminant Problem – Torsional Loading] A solid compound circular shaft (i.e., with segments AB and BC) are fixed to rigid walls at points A and C, respectively. As shown in the figure, an external torque is applied at point B. Determine the absolute maximum shear stress developed in the entire compound circular shaft ABC. B 480 N-m Bronze L1 = 1.8 m dz = 60 mm G2= 43 GPa Note: Corresponding length (L), diameter (d) and shear modulus (G) of the two segments are given in the figure, respectively. Ignore the effect of stress concentration. L = 0.6 m %3D Aluminum di = 40 mm G = 27 GPa

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

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

**Problem B-2: Statically Indeterminate Problem – Torsional Loading**

**Description:**

A solid compound circular shaft (i.e., with segments AB and BC) is fixed to rigid walls at points A and C, respectively. As depicted in the figure, an external torque is applied at point B. The task is to determine the absolute maximum shear stress developed in the entire compound circular shaft ABC.

**Note:**
The corresponding length (L), diameter (d), and shear modulus (G) of the two segments are given in the figure, respectively. Ignore the effect of stress concentration.

**Diagram Explanation:**

The diagram shows a compound circular shaft with two segments:
1. **Segment AB** - Made of aluminum
- Length (L₁) = 0.6 m
- Diameter (d₁) = 40 mm
- Shear modulus (G₁) = 27 GPa

2. **Segment BC** - Made of bronze
- Length (L₂) = 1.8 m
- Diameter (d₂) = 60 mm
- Shear modulus (G₂) = 43 GPa

A torque of 480 N·m is applied at point B, causing torsional loading on both segments. The shaft is fixed at walls at both ends, A and C.

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