Solutions Manual for Applied Strength of Materials, 7th Edition - Mott (Ch 1 – 14) > Download as Pdf File <

,Chapter .1 Basic .Concepts .in .Strength .of .Materials
1.1 .to .1.11 .Answers .in .text.
1.12 𝑊 .= .𝑚 .∙ .𝑔 .= .1400 .kg .∙ .9.81 .m/s2 .= .13 .734 .(kg .∙ .m)/s2 .= .14 .× .103 .N
𝑾 .= .𝟏3. .𝟕 .𝐤𝐍
1.13 Total .Weight .= .𝑚𝑔 .= .3500 .kg .∙ .9.81 .m/s2 .= .34.34 .kN
1
Each .Front .Wheel: .𝐹𝐹 . = . ( ) .(0.40)(34.34 .kN) .= .6.87 .𝐤𝐍
1
Each .Rear .Wheel: .𝐹𝑅 . = . ( ) .(0.60)(34.34 .kN) .= .𝟏0.32 .𝐤𝐍

1.14 Loading .= .Total .Force ./ .Area
Total .Force .= .𝑚𝑔 .= .5900 .kg .∙ .9.81 .m/s2 .= .57.9 .kN
Area .= . (4.5 .m)(3.5 .m) . = . 15.8 .m2
Loading .= .57.9 .kN⁄15.8 .m2 .= .3.66 .kN⁄m2 .= .Ñ.66 .𝐤𝐏𝐚
1.15 Force . = 𝑚.𝑔 .= .35 .kg .∙ .9.81 .m/s2 .= .343 .N
K . = . Spring . Scale . =4800 .N⁄m .= .𝐹/Δ𝐿
Δ𝐿 .= 𝐹 .= .343 = .0.0715 .m .= .71.5 .× m .= .71. .Ó .&&
.N
.10−3
𝐾 4800 . N/m




1.16 𝑤 . 3250 . lb lb∙s2 = . 101 . ,%. .,
𝑚 .= . = = .101 .
𝑔 32.2 .(ft/s2) ft

1.17 𝑤. 11 lb∙s2 = .Ñ60 .,%. .,
𝑚
.600. =
.lb. = . = .360 .
𝑔 32.2 .(ft/s2) ft

1.19 𝑝 .= .1700 .psi .∙ .6.895 .(kPa⁄psi) .= .11 .722 .𝐤𝐏𝐚
1.20 𝜎 . = . 24 .300 .psi .∙ .6.895 .(kPa⁄psi) . = . 167 .549 .kPa . = . 168 . 𝐌𝐏𝐚

, 1.21 𝑠𝑢 .= .14 .000 .psi .∙ .6.895 .(kPa⁄psi) .= .96 .500 .kPa .= .×Ô. .Ó .𝐌𝐏𝐚
𝑠𝑢 . = .76 .000 .psi .∙ .6.895 .(kPa⁄psi) .= .524 .000 .kPa .= .ÓÐÒ .𝐌𝐏𝐚
3600 .rev . 2π .rad . 1 .min . 𝐫𝐚𝐝
1.22 𝑛 .= . ×. ×. = .377, .
min rev 60s
2
(25.4mm) .
1.23 𝐴 .= .26.1 .in2 .× . = .16 .839 .&&Ð
1.24 𝑦 .= .0.08 .in .∙ .25.4 .(mm⁄in) .= .Ð. .𝟎Ñ .&&
1.25 Dimensions: .18 .in . × . 25.4 .(mm/in) . = . 457 .mm
12 .in . × . 25.4 .(mm/in) . = . 305 .mm
Area .= .(18 .in)2 . = . ÑÐÒ .𝐢'Ð
Area .= .(457 .mm)2 . = . Ð. .𝟎× .× .1𝟎Ó . &&Ð
Volume .= .𝑉 . = .Area .× .Height
𝑉 . = .324 .in2 .× .12 .in .= .ÑÖÖÖ .𝐢'Ñ
𝑉 .= .(1.5 .ft)2 .× .1.0 .ft .= .Ð. .ÐÓ .𝐟-Ñ
𝑉 . = . (209 .× .103 .mm2) .× .305 .mm . = . Ô. .ÑÕ .× .1𝟎Õ .&&Ñ
𝑉 .= .(0.457 .m)2 . × . 0.305 .m .= .0.0637 .m3 . = .Ô. .ÑÕ .× .1𝟎−Ð .&Ñ
1.26 𝐴 .= .𝜋𝐷2⁄4 .= .𝜋(0.505 .in)2⁄4 .= .𝟎. .Ð𝟎𝟎 .𝐢'Ð
(25.4 .mm)2 .
𝐴 .= .0.200 .in2 .× . = .1Ð× .&&Ð
in2
𝑃 N
1.27 𝜎 . = . = 2800 .N = 2800 . N = . 35.7 = .35. .Õ .𝐌𝐏𝐚
𝐴 (𝜋𝐷2 .⁄4) [𝜋(10 .mm)2]⁄4 mm2
𝑃 . 3 . N N
1.28 𝜎 .= . = 18×10 = . 50.7 = .50. .Õ .𝐌𝐏𝐚
𝐴 (12)(30) . mm2 mm2
𝑃 . 1150 .lb .
1.29 𝜎 .= . = . . = .7188 .𝐩,𝐢
𝐴 (0.40 . in)2

𝑃. 1850 .lb = . 1Ô .ÕÓ𝟎 .𝐩,𝐢
1.30 𝜎 . = . =[𝜋(0.375
𝐴 .in)2]⁄4

1.31 Load .on .Shelf . = .𝑊 .= .𝑚𝑔 .= .1650 .kg .∙ .9.81 .m⁄s2 .= .16 .187 .N
𝑊/2 .= .8093 .N .On .each .side
∑ .𝑀𝐴 .= .0 .= .(8093 .N)(600 .mm) .− .𝐶𝑉(1200 .mm)
𝐶𝑉 .= .4047 .N
𝐶 .= .𝐶𝑉/ .sin .30° .= .8093 .N
𝑃 . 𝐶 . . 9025 .N
𝜎 .= . =.
𝐴 . . =𝐴 [𝜋(12 . mm)2]⁄4 . . = . 71.6 . 𝐌𝐏𝐚
𝑃 70000 . lb . .
1.32 𝜎 .= . = . . = .891 .𝐩,𝐢
𝐴 [𝜋(10 .in)2]/4

, (29500 .lb)/3 .
1.33 𝜎 .= =. = .Ö𝟎Ñ .𝐩,𝐢
𝑃 𝐴 (3.5 .in)2
.

3500 .N
1.34 𝜎 .= =. . = . ÓÒ. . Õ . 𝐌𝐏𝐚
𝑃 𝐴 (8.0 .mm)2
.

1.35 𝑊 .= .𝑚𝑔 .= .4200 .kg .∙ .9.81 .m/s2 .= .41.2 .kN
𝐴𝐵𝑋 . = . 𝐴𝐵 .sin .35°
𝐴𝐵L . = . 𝐴𝐵 .cos .35°
𝐵𝐶𝑋 . = . 𝐵𝐶 .sin .55°
𝐵𝐶L . = . 𝐵𝐶 .cos .55°
∑ .𝐹𝑋 .= .0 .= .𝐴𝐵𝑋 .− .𝐵𝐶𝑋
0 . = . 𝐴𝐵 .sin .35° .− .𝐵𝐶 .sin .55°
sin .55°
𝐴𝐵 .= .𝐵𝐶 .∙ = .1.428 .𝐵𝐶
.sin .35°

∑ .𝐹𝑉 .= .0 .= .𝐴𝐵L .+ .𝐵𝐶L .− .41.2 .kN .= .𝐴𝐵 .cos .35° .+ .𝐵𝐶 .cos .55° .− .41.2 .kN .0
.= .(1.428 .𝐵𝐶) .cos .35° .+ .𝐵𝐶 .cos .55° .− .41.2 .kN

41.2 .kN . = . 𝐵𝐶[1.170 .+ .0.574] . = . 1.743 .𝐵𝐶
41.2 .kN .
𝐵𝐶 . = . = . 23.63 .kN
1.743

𝐴𝐵 . = . 1.428 .𝐵𝐶 . = . 33.75 .kN
𝐴𝐵 . 33.75×10 .3N .
Stress .in .Rod .AB: .𝜎 = . = . = .1𝟎Õ. .Ò .𝐌𝐏𝐚
𝐴𝐵 𝐴 [𝜋(20 .mm)2]/4
𝐵𝐶 . 23.63×10 . 3N .
Stress .in .Rod .BC: .𝜎 = . = . = .ÕÓ. .Ð .𝐌𝐏𝐚
𝐵𝐶 𝐴 [𝜋(20 .mm)2]/4
𝐵𝐷 . 41.2×10 3. . N
Stress .in .Rod .BD: .𝜎 =. = = .1Ñ1. .1 .𝐌𝐏𝐚
𝐵𝐷 𝐴 [𝜋(20 .mm)2]/4

1.36 𝐹 .= .0.01097 .𝑚𝑅𝑛2 .= .(0.01097)(0.40)(0.60)(3000)2 .N
𝐹 . = . 23 .695 .N
𝜋(16 . mm)2 .
𝐴 .= . = . 201 . mm2
4
𝐹. 23695 .N .
𝜎 .= . = . = .11Ö .𝐌𝐏𝐚
𝐴 201 .mm2