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The following illustration shows an idealized crane setup for lifting large machinery. The crane's rigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a composite column. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strain in the composite column should not exceed 0.1%, determine the maximum mass (in kg) of machinery that the crane can carry. Use r = 3 m. 2r B Aluminum cable: L = 2m E = 70 GPa D = 10 mm Outer: r C Aluminum rod L = 4 m E = 70 GPa D = 25 mm 2r Inner core: D

The following illustration shows an idealized crane setup for lifting large machinery. The crane's rigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a composite column. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strain in the composite column should not exceed 0.1%, determine the maximum mass (in kg) of machinery that the crane can carry. Use r = 3 m. 2r B Aluminum cable: L = 2m E = 70 GPa D = 10 mm Outer: r C Aluminum rod L = 4 m E = 70 GPa D = 25 mm 2r Inner core: D

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
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The following illustration shows an idealized crane setup for lifting large machinery. The crane's rigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a composite column. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strain in the composite column should not exceed 0.1%, determine the maximum mass (in kg) of machinery that the crane can carry. Use r = 3 m. 2r B Aluminum cable: L = 2m E = 70 GPa D = 10 mm r Outer: Concrete L = 3m E = 150 GPa Douter= 60 mm Aluminum rod L = 4 m E = 70 GPa D = 25 mm 2r Inner core: Bronze L = 3m E = 100 GPa D = 30 mm D
Transcribed Image Text:The following illustration shows an idealized crane setup for lifting large machinery. The crane's rigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a composite column. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strain in the composite column should not exceed 0.1%, determine the maximum mass (in kg) of machinery that the crane can carry. Use r = 3 m. 2r B Aluminum cable: L = 2m E = 70 GPa D = 10 mm r Outer: Concrete L = 3m E = 150 GPa Douter= 60 mm Aluminum rod L = 4 m E = 70 GPa D = 25 mm 2r Inner core: Bronze L = 3m E = 100 GPa D = 30 mm D
Solution guide: 1) Analyze how the rigid bar ABCD would move due to the machinery. What kind of force will the aluminum cable, aluminum rod, and composite column C feel due to the movement of the rigid bar ABCD? Draw the FBD considering your analysis. Make sure that the forces you assumed would yield equilibrium (Not all forces are upwards/downwards; there are forces balancing the rotation/tilting caused by the machinery) 2) Set-up the equilibrium equations. Remember the restrictions on the number of equilibrium equations in a single FBD. 3) Set-up the equation for the composite. 4) Considering the forces, you assumed in guide question #1, draw the deformation diagram of the system. Would there be a pivot point along the rigid bar? Where would it be located? Is it located at one of the points A, B, C, and D, or somewhere between the points? Note that if you set the pivot point in one of the points, you are assuming that the point will not go up or down; if you set it at B, C, or D, you are assuming that the aluminum rod, cable or the composite does not deform and thereby experiences no force. How many compatibility equations can you formulate from this deformation diagram?
Transcribed Image Text:Solution guide: 1) Analyze how the rigid bar ABCD would move due to the machinery. What kind of force will the aluminum cable, aluminum rod, and composite column C feel due to the movement of the rigid bar ABCD? Draw the FBD considering your analysis. Make sure that the forces you assumed would yield equilibrium (Not all forces are upwards/downwards; there are forces balancing the rotation/tilting caused by the machinery) 2) Set-up the equilibrium equations. Remember the restrictions on the number of equilibrium equations in a single FBD. 3) Set-up the equation for the composite. 4) Considering the forces, you assumed in guide question #1, draw the deformation diagram of the system. Would there be a pivot point along the rigid bar? Where would it be located? Is it located at one of the points A, B, C, and D, or somewhere between the points? Note that if you set the pivot point in one of the points, you are assuming that the point will not go up or down; if you set it at B, C, or D, you are assuming that the aluminum rod, cable or the composite does not deform and thereby experiences no force. How many compatibility equations can you formulate from this deformation diagram?
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