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Two solid circular shafts are connected by two rigid ab is a composite shaft. Determine the angle of twist at point 'a' in degrees to two decimal places. solid shaft 60 in b 4= 11-3535 TL GJ J= π/₂2r4 composite shaft C 35 in Notes:- gear b radius = 6.0 in - gear c radius= 4.0 in - shaft ab outer radius = 1.5 in - shaft ab inner radius= 1.1 in shaft cd radius= 1.0 in -shaft ab inner shear modulus = 12000 k -shaft ab outer shear modulus = 3000 ksi shaft ed shear modulus = 12000 ksi outer portion inner portion shaft ab cross-section 2.86 in-kip

Two solid circular shafts are connected by two rigid ab is a composite shaft. Determine the angle of twist at point 'a' in degrees to two decimal places. solid shaft 60 in b 4= 11-3535 TL GJ J= π/₂2r4 composite shaft C 35 in Notes:- gear b radius = 6.0 in - gear c radius= 4.0 in - shaft ab outer radius = 1.5 in - shaft ab inner radius= 1.1 in shaft cd radius= 1.0 in -shaft ab inner shear modulus = 12000 k -shaft ab outer shear modulus = 3000 ksi shaft ed shear modulus = 12000 ksi outer portion inner portion shaft ab cross-section 2.86 in-kip

Elements Of Electromagnetics
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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**Determining the Angle of Twist in a Composite Shaft** **Problem Statement:** Two solid circular shafts are connected by two rigid gears. Shaft AB is a composite shaft. Determine the angle of twist at point 'a' in degrees to two decimal places. **Equation:** \[ \phi = \frac{TL}{GJ} \] \[ J = \frac{\pi}{2} r^4 \] **Diagram Explanation:** The diagram shows a composite shaft system with a solid shaft connected to a composite shaft. Key components are: - **Fixed Support:** Located at the left end of the solid shaft. - **Solid Shaft:** 60 inches long. - **Composite Shaft:** Consists of an outer portion and an inner portion, 35 inches long, leading to point 'a'. - **Bearings:** Located at transition points, labeled along the shaft. **Shaft AB Cross-Section:** - The shaft consists of an outer portion and an inner portion. **Given Parameters:** - **Gear B radius:** 6.0 inches - **Gear C radius:** 4.0 inches - **Shaft AB outer radius:** 1.5 inches - **Shaft AB inner radius:** 1.1 inches - **Shaft CD radius:** 1.0 inch - **Shaft AB inner shear modulus:** 12000 ksi - **Shaft AB outer shear modulus:** 3000 ksi - **Shaft CD shear modulus:** 12000 ksi **Applied Torque:** 2.86 in-kip at the end of shaft AB. This problem involves calculating the angle of twist, which combines understanding of mechanical principles like torque and materials engineering to evaluate the behavior of composite shafts under load.
Transcribed Image Text:**Determining the Angle of Twist in a Composite Shaft** **Problem Statement:** Two solid circular shafts are connected by two rigid gears. Shaft AB is a composite shaft. Determine the angle of twist at point 'a' in degrees to two decimal places. **Equation:** \[ \phi = \frac{TL}{GJ} \] \[ J = \frac{\pi}{2} r^4 \] **Diagram Explanation:** The diagram shows a composite shaft system with a solid shaft connected to a composite shaft. Key components are: - **Fixed Support:** Located at the left end of the solid shaft. - **Solid Shaft:** 60 inches long. - **Composite Shaft:** Consists of an outer portion and an inner portion, 35 inches long, leading to point 'a'. - **Bearings:** Located at transition points, labeled along the shaft. **Shaft AB Cross-Section:** - The shaft consists of an outer portion and an inner portion. **Given Parameters:** - **Gear B radius:** 6.0 inches - **Gear C radius:** 4.0 inches - **Shaft AB outer radius:** 1.5 inches - **Shaft AB inner radius:** 1.1 inches - **Shaft CD radius:** 1.0 inch - **Shaft AB inner shear modulus:** 12000 ksi - **Shaft AB outer shear modulus:** 3000 ksi - **Shaft CD shear modulus:** 12000 ksi **Applied Torque:** 2.86 in-kip at the end of shaft AB. This problem involves calculating the angle of twist, which combines understanding of mechanical principles like torque and materials engineering to evaluate the behavior of composite shafts under load.
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Step 1: Given

Mechanical Engineering homework question answer, step 1, image 1

The radius of gear B is r subscript b equals 6 space i n

The radius of gear C is r subscript c equals 4 space i n

The outer radius of AB is R equals 1.5 space i n

The inner radius of AB is r equals 1.1 space i n

The radius of CD is r apostrophe equals 1 space i n

The outer shear modulus of CD is G subscript c d end subscript equals 12000 space k s i.

The shear modulus of AB is G subscript a b end subscript equals 3000 space k s i.

The inner shear modulus of CD is G subscript c d end subscript apostrophe equals 12000 space k s i.

The torque at end A is T equals 2.86 space k i p. i n

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