Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN: 9781305084766
Author: Saeed Moaveni
Publisher: Cengage Learning
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Concept explainers

Question
Chapter 6, Problem 35P
To determine

Convert the strength of selected materials from MPa to ksi.

Expert Solution & Answer
Check Mark

Answer to Problem 35P

The conversion for the strength of selected materials given in accompanying table from MPa to ksi as follows:

MaterialUltimate strength (MPa)Ultimate strength (ksi)
Aluminum alloys10055014.579.7

Concrete

(compression)

1070

1.410.1

Stee1  
Machine55086079.7124.7
Spring7001,900101.5275.5
Stainless4001,00058.0145.0
Tool900130.5
Structural Steel34083049.3120.3
Titanium alloys9001,200130.5174.0
Wood (Bending)  
Douglas fir50807.211.6
Oak501007.214.5
Southern pine501007.214.5

Explanation of Solution

Given data:

Refer to Problem 6.35 in textbook for the accompanying table.

1ksi=1000lbfin.2 (1)

Formula used:

Convert N to lbf,

1N=224.809×103lbf

Convert meter to foot,

1m=3.2808ft

Convert foot to inches,

1ft=12in.

Calculation:

Rearrange the equation (1) for conversion of unit as follows,

1lbfin.2=11000ksi (2)

Case 1:

For Aluminum alloys:

Ultimate strength=100MPa=100×106Pa (3)

Substitute the unit Nm2 for Pa in equation (3).

Ultimate strength=100×106Nm2 (4)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (4).

Ultimate strength=100×106(224.809×103lbf)(3.2808ft)2=(100×106)(224.809×103)3.28082lbfft2=2088594.746lbfft2 (5)

Substitute the unit 12in. for 1ft in equation (5).

Ultimate strength=2088594.746lbf(12in.)2=2088594.746122lbfin.2=14504.13lbfin.2 (6)

Substitute the unit 11000ksi for 1lbfin.2 in equation (6).

Ultimate strength=14504.13×11000ksi=14.5ksi (7)

For Aluminum alloys:

Ultimate strength=550MPa=550×106Pa (8)

Substitute the unit Nm2 for Pa in equation (8).

Ultimate strength=550×106Nm2 (9)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (9).

Ultimate strength=550×106(224.809×103lbf)(3.2808ft)2=(550×106)(224.809×103)3.28082lbfft2=11487271.1lbfft2 (10)

Substitute the unit 12in. for 1ft in equation (10).

Ultimate strength=11487271.1lbf(12in.)2=11487271.1122lbfin.2=79772.716lbfin.2 (11)

Substitute the unit 11000ksi for 1lbfin.2 in equation (11).

Ultimate strength=79772.716×11000ksi=79.7ksi (12)

Case 2:

For Concrete (compression):

Ultimate strength=10MPa=10×106Pa (13)

Substitute the unit Nm2 for Pa in equation (13).

Ultimate strength=10×106Nm2 (14)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (14).

Ultimate strength=10×106(224.809×103lbf)(3.2808ft)2=(10×106)(224.809×103)3.28082lbfft2=208859.475lbfft2 (15)

Substitute the unit 12in. for 1ft in equation (15).

Ultimate strength=208859.475lbf(12in.)2=208859.475122lbfin.2=1450.413lbfin.2 (16)

Substitute the unit 11000ksi for 1lbfin.2 in equation (16).

Ultimate strength=1450.413×11000ksi=1.4ksi (17)

For Concrete (compression):

Ultimate strength=70MPa=70×106Pa (18)

Substitute the unit Nm2 for Pa in equation (18).

Ultimate strength=70×106Nm2 (19)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (19).

Ultimate strength=70×106(224.809×103lbf)(3.2808ft)2=(70×106)(224.809×103)3.28082lbfft2=1462016.322lbfft2 (20)

Substitute the unit 12in. for 1ft in equation (20).

Ultimate strength=1462016.322lbf(12in.)2=1462016.322122lbfin.2=10152.89lbfin.2 (21)

Substitute the unit 11000ksi for 1lbfin.2 in equation (21).

Ultimate strength=10152.89×11000ksi=10.1ksi (22)

Case 3:

For Steel-Machine:

Ultimate strength=550MPa=550×106Pa (23)

Substitute the unit Nm2 for Pa in equation (23).

Ultimate strength=550×106Nm2 (24)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (24).

Ultimate strength=550×106(224.809×103lbf)(3.2808ft)2=(550×106)(224.809×103)3.28082lbfft2=11487271.1lbfft2 (25)

Substitute the unit 12in. for 1ft in equation (25).

Ultimate strength=11487271.1lbf(12in.)2=11487271.1122lbfin.2=79772.716lbfin.2 (26)

Substitute the unit 11000ksi for 1lbfin.2 in equation (26).

Ultimate strength=79772.716×11000ksi=79.7ksi (27)

For Steel-Machine:

Ultimate strength=860MPa=860×106Pa (28)

Substitute the unit Nm2 for Pa in equation (28).

Ultimate strength=860×106Nm2 (29)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (29).

Ultimate strength=860×106(224.809×103lbf)(3.2808ft)2=(860×106)(224.809×103)3.28082lbfft2=17961914.82lbfft2 (30)

Substitute the unit 12in. for 1ft in equation (30).

Ultimate strength=17961914.82lbf(12in.)2=17961914.82122lbfin.2=124735.519lbfin.2 (31)

Substitute the unit 11000ksi for 1lbfin.2 in equation (31).

Ultimate strength=124735.519×11000ksi=124.7ksi (32)

For Steel-Spring:

Ultimate strength=700MPa=700×106Pa (33)

Substitute the unit Nm2 for Pa in equation (33).

Ultimate strength=700×106Nm2 (34)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (34).

Ultimate strength=700×106(224.809×103lbf)(3.2808ft)2=(700×106)(224.809×103)3.28082lbfft2=14620163.22lbfft2 (35)

Substitute the unit 12in. for 1ft in equation (35).

Ultimate strength=14620163.22lbf(12in.)2=14620163.22122lbfin.2=101528.9113lbfin.2 (36)

Substitute the unit 11000ksi for 1lbfin.2 in equation (36).

Ultimate strength=101528.9113×11000ksi=101.5ksi (37)

For Steel-Spring:

Ultimate strength=1900MPa=1900×106Pa (38)

Substitute the unit Nm2 for Pa in equation (38).

Ultimate strength=1900×106Nm2 (39)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (39).

Ultimate strength=1900×106(224.809×103lbf)(3.2808ft)2=(1900×106)(224.809×103)3.28082lbfft2=39683300.18lbfft2 (40)

Substitute the unit 12in. for 1ft in equation (40).

Ultimate strength=39683300.18lbf(12in.)2=39683300.18122lbfin.2=275578.474lbfin.2 (41)

Substitute the unit 11000ksi for 1lbfin.2 in equation (41).

Ultimate strength=275578.474×11000ksi=275.5ksi (42)

For Steel-Stainless:

Ultimate strength=400MPa=400×106Pa (43)

Substitute the unit Nm2 for Pa in equation (43).

Ultimate strength=400×106Nm2 (44)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (44).

Ultimate strength=400×106(224.809×103lbf)(3.2808ft)2=(400×106)(224.809×103)3.28082lbfft2=8354378.985lbfft2 (45)

Substitute the unit 12in. for 1ft in equation (45).

Ultimate strength=8354378.985lbf(12in.)2=8354378.985122lbfin.2=58016.521lbfin.2 (46)

Substitute the unit 11000ksi for 1lbfin.2 in equation (46).

Ultimate strength=58016.521×11000ksi=58.0ksi (47)

For Steel-Stainless:

Ultimate strength=1000MPa=1000×106Pa (48)

Substitute the unit Nm2 for Pa in equation (48).

Ultimate strength=1000×106Nm2 (49)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (49).

Ultimate strength=1000×106(224.809×103lbf)(3.2808ft)2=(1000×106)(224.809×103)3.28082lbfft2=20885947.46lbfft2 (50)

Substitute the unit 12in. for 1ft in equation (50).

Ultimate strength=20885947.46lbf(12in.)2=20885947.46122lbfin.2=145041.302lbfin.2 (51)

Substitute the unit 11000ksi for 1lbfin.2 in equation (51).

Ultimate strength=145041.302×11000ksi=145.0ksi (52)

For Steel-Tool:

Ultimate strength=900MPa=900×106Pa (53)

Substitute the unit Nm2 for Pa in equation (53).

Ultimate strength=900×106Nm2 (54)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (54).

Ultimate strength=900×106(224.809×103lbf)(3.2808ft)2=(900×106)(224.809×103)3.28082lbfft2=18797352.72lbfft2 (55)

Substitute the unit 12in. for 1ft in equation (55).

Ultimate strength=18797352.72lbf(12in.)2=18797352.72122lbfin.2=130537.172lbfin.2 (56)

Substitute the unit 11000ksi for 1lbfin.2 in equation (56).

Ultimate strength=130537.172×11000ksi=130.5ksi (57)

For Steel-Structural Steel:

Ultimate strength=340MPa=340×106Pa (58)

Substitute the unit Nm2 for Pa in equation (58).

Ultimate strength=340×106Nm2 (59)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (59).

Ultimate strength=340×106(224.809×103lbf)(3.2808ft)2=(340×106)(224.809×103)3.28082lbfft2=7101222.137lbfft2 (60)

Substitute the unit 12in. for 1ft in equation (60).

Ultimate strength=7101222.137lbf(12in.)2=7101222.137122lbfin.2=49314.043lbfin.2 (61)

Substitute the unit 11000ksi for 1lbfin.2 in equation (61).

Ultimate strength=49314.043×11000ksi=49.3ksi (62)

For Steel-Structural Steel:

Ultimate strength=830MPa=830×106Pa (63)

Substitute the unit Nm2 for Pa in equation (63).

Ultimate strength=830×106Nm2 (64)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (64).

Ultimate strength=830×106(224.809×103lbf)(3.2808ft)2=(830×106)(224.809×103)3.28082lbfft2=17335336.39lbfft2 (65)

Substitute the unit 12in. for 1ft in equation (65).

Ultimate strength=17335336.39lbf(12in.)2=17335336.39122lbfin.2=120384.281lbfin.2 (66)

Substitute the unit 11000ksi for 1lbfin.2 in equation (66).

Ultimate strength=120384.281×11000ksi=120.3ksi (67)

For Steel-Titanium alloys:

Ultimate strength=900MPa=900×106Pa (68)

Substitute the unit Nm2 for Pa in equation (68).

Ultimate strength=900×106Nm2 (69)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (69).

Ultimate strength=900×106(224.809×103lbf)(3.2808ft)2=(900×106)(224.809×103)3.28082lbfft2=18797352.72lbfft2 (70)

Substitute the unit 12in. for 1ft in equation (70).

Ultimate strength=18797352.72lbf(12in.)2=18797352.72122lbfin.2=130537.172lbfin.2 (71)

Substitute the unit 11000ksi for 1lbfin.2 in equation (71).

Ultimate strength=130537.172×11000ksi=130.5ksi (72)

For Steel-Titanium alloys:

Ultimate strength=1200MPa=1200×106Pa (73)

Substitute the unit Nm2 for Pa in equation (73).

Ultimate strength=1200×106Nm2 (74)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (74).

Ultimate strength=1200×106(224.809×103lbf)(3.2808ft)2=(1200×106)(224.809×103)3.28082lbfft2=25063136.96lbfft2 (75)

Substitute the unit 12in. for 1ft in equation (75).

Ultimate strength=25063136.96lbf(12in.)2=25063136.96122lbfin.2=174049.562lbfin.2 (76)

Substitute the unit 11000ksi for 1lbfin.2 in equation (76).

Ultimate strength=174049.562×11000ksi=174.0ksi (77)

Case 4:

For Wood (Bending)-Douglas fir:

Ultimate strength=50MPa=50×106Pa (78)

Substitute the unit Nm2 for Pa in equation (78).

Ultimate strength=50×106Nm2 (79)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (79).

Ultimate strength=50×106(224.809×103lbf)(3.2808ft)2=(50×106)(224.809×103)3.28082lbfft2=1044297.373lbfft2 (80)

Substitute the unit 12in. for 1ft in equation (80).

Ultimate strength=1044297.373lbf(12in.)2=1044297.373122lbfin.2=7252.065lbfin.2 (81)

Substitute the unit 11000ksi for 1lbfin.2 in equation (81).

Ultimate strength=7252.065×11000ksi=7.2ksi (82)

For Wood (Bending)-Douglas fir:

Ultimate strength=80MPa=80×106Pa (83)

Substitute the unit Nm2 for Pa in equation (83).

Ultimate strength=80×106Nm2 (84)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (84).

Ultimate strength=80×106(224.809×103lbf)(3.2808ft)2=(80×106)(224.809×103)3.28082lbfft2=1670875.797lbfft2 (85)

Substitute the unit 12in. for 1ft in equation (85).

Ultimate strength=1670875.797lbf(12in.)2=1670875.797122lbfin.2=11603.304lbfin.2 (86)

Substitute the unit 11000ksi for 1lbfin.2 in equation (86).

Ultimate strength=11603.304×11000ksi=11.6ksi (87)

For Wood (Bending)-Oak:

Ultimate strength=50MPa=50×106Pa (88)

Substitute the unit Nm2 for Pa in equation (88).

Ultimate strength=50×106Nm2 (89)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (89).

Ultimate strength=50×106(224.809×103lbf)(3.2808ft)2=(50×106)(224.809×103)3.28082lbfft2=1044297.373lbfft2 (90)

Substitute the unit 12in. for 1ft in equation (90).

Ultimate strength=1044297.373lbf(12in.)2=1044297.373122lbfin.2=7252.065lbfin.2 (91)

Substitute the unit 11000ksi for 1lbfin.2 in equation (91).

Ultimate strength=7252.065×11000ksi=7.2ksi (92)

For Wood (Bending)-Oak:

Ultimate strength=100MPa=100×106Pa (93)

Substitute the unit Nm2 for Pa in equation (93).

Ultimate strength=100×106Nm2 (94)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (94).

Ultimate strength=100×106(224.809×103lbf)(3.2808ft)2=(100×106)(224.809×103)3.28082lbfft2=2088594.746lbfft2 (95)

Substitute the unit 12in. for 1ft in equation (95).

Ultimate strength=2088594.746lbf(12in.)2=2088594.746122lbfin.2=14504.13lbfin.2 (96)

Substitute the unit 11000ksi for 1lbfin.2 in equation (96).

Ultimate strength=14504.13×11000ksi=14.5ksi (97)

For Wood (Bending)-Southern pine:

Ultimate strength=50MPa=50×106Pa (98)

Substitute the unit Nm2 for Pa in equation (98).

Ultimate strength=50×106Nm2 (99)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (99).

Ultimate strength=50×106(224.809×103lbf)(3.2808ft)2=(50×106)(224.809×103)3.28082lbfft2=1044297.373lbfft2 (100)

Substitute the unit 12in. for 1ft in equation (100).

Ultimate strength=1044297.373lbf(12in.)2=1044297.373122lbfin.2=7252.065lbfin.2 (101)

Substitute the unit 11000ksi for 1lbfin.2 in equation (101).

Ultimate strength=7252.065×11000ksi=7.2ksi (102)

For Wood (Bending)-Southern pine;

Ultimate strength=100MPa=100×106Pa (103)

Substitute the unit Nm2 for Pa in equation (103).

Ultimate strength=100×106Nm2 (104)

Substitute the units 224.809×103lbf for 1N and 3.2808ft for 1m in equation (104).

Ultimate strength=100×106(224.809×103lbf)(3.2808ft)2=(100×106)(224.809×103)3.28082lbfft2=2088594.746lbfft2 (105)

Substitute the unit 12in. for 1ft in equation (105).

Ultimate strength=2088594.746lbf(12in.)2=2088594.746122lbfin.2=14504.13lbfin.2 (106)

Substitute the unit 11000ksi for 1lbfin.2 in equation (106).

Ultimate strength=14504.13×11000ksi=14.5ksi (107)

Thus, the conversion for the strength of selected materials from MPa to ksi is tabulated in Table 1.

Table 1

MaterialUltimate strength (MPa)Ultimate strength (ksi)
Aluminum alloys10055014.579.7

Concrete

(compression)

1070

1.410.1

Stee1  
Machine55086079.7124.7
Spring7001,900101.5275.5
Stainless4001,00058.0145.0
Tool900130.5
Structural Steel34083049.3120.3
Titanium alloys9001,200130.5174.0
Wood (Bending)  
Douglas fir50807.211.6
Oak501007.214.5
Southern pine501007.214.5

Conclusion:

Hence, the conversion for the strength of selected materials from MPa to ksi has been explained.

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