The following illustration shows an idealized crane setup for lifting large machinery. The crane'srigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a compositecolumn. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strainin the composite column should not exceed 0.1%, determine the maximum mass (in kg) ofmachinery that the crane can carry. Use r = 3 m.2rBAluminum cable:L = 2mE = 70 GPaD = 10 mmrOuter:ConcreteL = 3mE = 150 GPaDouter= 60 mmAluminum rodL = 4 mE = 70 GPaD = 25 mm2rInner core:BronzeL = 3mE = 100 GPaD = 30 mmD Solution guide:1) Analyze how the rigid bar ABCD would move due to the machinery. What kind of force willthe aluminum cable, aluminum rod, and composite column C feel due to the movement of therigid bar ABCD? Draw the FBD considering your analysis. Make sure that the forces youassumed would yield equilibrium (Not all forces are upwards/downwards; there are forcesbalancing the rotation/tilting caused by the machinery)2) Set-up the equilibrium equations. Remember the restrictions on the number of equilibriumequations 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 ofthe system. Would there be a pivot point along the rigid bar? Where would it be located? Is itlocated at one of the points A, B, C, and D, or somewhere between the points? Note that if youset the pivot point in one of the points, you are assuming that the point will not go up or down; ifyou set it at B, C, or D, you are assuming that the aluminum rod, cable or the composite does notdeform and thereby experiences no force. How many compatibility equations can you formulatefrom this deformation diagram?

Given data, Maximum normal stress in the aluminium cable and aluminium rod, σmax,Al=70 MPa Maximum…

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

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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Clutches, Brakes, Couplings, and Flywheels

The clutch is described as a machine element used to connect or disconnect two shafts together to transmit torque or power. The clutch works on the principles of friction. The clutch is commonly used in automobiles to transfer power from the driving shaft to the driven shaft.

Question

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?

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