solution manual for Applied Strength of Materials 7th Edition by Mott, 2022 (1)

CoversAll 13 Chapters
yt yt yt




SOLUTIONS MANUAL
yt

,Chapter 1 yt Basic Concepts in Strength of Materials yt yt yt yt yt




1.1 to 1.15 Answers in text.
yt yt yt yt yt




1.16 𝑊 = 𝑚 ∙ 𝑔 = 1800 kg ∙ 9.81 m/s2 = 17 658 (kg ∙ m)/s2 = 17 × 103 N
y t yt yt yt yt yt yt yt yt yt y t yt yt yt yt yt y t yt yt yt yt




𝑾 = 𝟏𝟕. 𝟕 𝐤𝐍
yt yt yt yt




1.17 Total Weight = 𝑚𝑔 = 4000 kg ∙ 9.81 m/s2 = 39.24 kN
yt yt yt yt yt yt yt yt yt y t yt yt




Each Front Wheel: 𝐹𝐹 = (12) (0.40)(39.24 kN) = 𝟕. 𝟖𝟓 𝐤𝐍
yt yt yt y t yt yt yt yt yt yt yt




Each Rear Wheel: 𝐹𝑅 = (12) (0.60)(39.24 kN) = 𝟏𝟏. 𝟕𝟕 𝐤𝐍
yt yt yt y t yt yt yt yt yt yt yt




1.18 Loading = Total Force / Area yt yt yt yt yt




Total Force = 𝑚𝑔 = 6800 kg ∙ 9.81 m/s2 = 66.7 kN
yt yt yt yt y t yt yt yt yt y t yt yt




Area = (5.0 m)(3.5 m) = 17.5 m2
yt yt yt yt yt yt yt




Loading = 66.7 kN⁄17.5 m2 = 3.81 kN⁄m2 = 𝟑. 𝟖𝟏 𝐤𝐏𝐚
yt yt yt yt y t yt yt y t yt yt yt




1.19 Force = Weight = 𝑚𝑔 = 25 kg ∙ 9.81 m/s2 = 245 N
yt yt yt yt yt yt yt yt yt yt y t yt yt




K = Spring Scale = 4500 N⁄m = 𝐹/Δ𝐿
yt yt yt yt yt yt yt yt




𝐹 245 N = 0.0545 m = 54.5 × 10−3 m = 𝟓𝟒. 𝟓 𝐦𝐦
Δ𝐿 = =
y t yt
yt yt yt yt yt yt yt yt yt yt yt
yt yt

𝐾 4500 N/m yt




1.22 𝑊 = 17.7 kN = 17 700 N ∙ 0.2248 (lb⁄N) = 𝟑𝟗𝟖𝟎 𝐥𝐛
y t yt yt yt yt yt yt yt yt yt yt yt yt




1.23 𝐹𝐹 = 7.85 kN = 7850 N ∙ 0.2248 (lb⁄N) = 𝟏𝟕𝟔𝟓 𝐥𝐛
y t yt yt yt yt yt yt yt yt yt yt yt




𝐹𝑅 = 11.77 kN = 11 770 N ∙ 0.2248 (lb⁄N) = 𝟐𝟔𝟒𝟔 𝐥𝐛
y t yt yt yt yt yt yt yt yt yt yt yt yt


3y t Ny t 2
1.24 Loading = 3.81 kPa = 3.81×10 yt yt yt yt yt × 0.2248 lb ×
yt yt yt
1m yt = 𝟕𝟗 yt y t
𝐥𝐛
m2 N (3.28 ft)2 yt 𝐟𝐭𝟐

1.25 𝐹 = 245 N ∙ 0.2248 (lb⁄N) = 𝟓𝟓. 𝟏 𝐥𝐛
yt yt yt yt yt yt yt yt yt yt




4500 N 0.2248 lb 1m = 𝟐𝟓. 𝟕 𝐥𝐛
𝐾= × ×
yt yt yt yt yt
yt yt y t
yt yt yt

m N 39.37 in yt 𝐢𝐧
𝐹 55.1 lb = 𝟐. 𝟏𝟒 𝐢𝐧
Δ𝐿 = =
y t yt
yt yt yt
yt yt

𝐾 25.7 (lb⁄in) yt


2y t



1.26 𝑚= yt yt
𝑤 y t

=
2750 lb yt
= 85.4 y t y t
lb∙s = 𝟖𝟓. 𝟒 𝐬𝐥𝐮𝐠𝐬 yt yt yt


𝑔 32.2 (ft/s2) yt ft
2y t



1.27 𝑚
lb yt = yt
𝑤 y t

= y t
12800 yt
= 398 y t y t
lb∙s = 𝟑𝟗𝟖 𝐬𝐥𝐮𝐠𝐬
y t yt



𝑔 32.2 (ft/s2) yt ft

1.29 𝑝 = 1200 psi ∙ 6.895 (kPa⁄psi) = 𝟖𝟐𝟕𝟒 𝐤𝐏𝐚
yt yt yt yt yt yt yt yt yt




1.30 𝜎 = 21 600 psi ∙ 6.895 (kPa⁄psi) = 149 000 kPa = 𝟏𝟒𝟗 𝐌𝐏𝐚
yt yt yt yt yt yt yt yt yt yt yt yt yt yt




@@SSee
isis
mmiciicsis
oolala
titoionn

,1.31 𝑠𝑢 = 14 000 psi ∙ 6.895 (kPa⁄psi) = 96 500 kPa = 𝟗𝟔. 𝟓 𝐌𝐏𝐚
y t yt yt yt yt yt yt yt yt yt yt yt yt yt yt




𝑠𝑢 = 76 000 psi ∙ 6.895 (kPa⁄psi) = 524 000 kPa = 𝟓𝟐𝟒 𝐌𝐏𝐚
y t yt yt yt yt yt yt yt yt yt yt yt yt yt




1750 rev 2π rad 1 min 𝐫𝐚𝐝
𝑛= × × = 𝟏𝟖𝟑
yt yt yt yt yt y t

1.32 yt yt yt yt yt y t

min rev 60s 𝐬
2y t


1.33 𝐴 = 14.1 in2 ×
y t y t yt yt yt
(25.4 mm) yt = 𝟗𝟎𝟗𝟕 𝐦𝐦𝟐 y t yt


in2

1.34 𝑦 = 0.08 in ∙ 25.4 (mm⁄in) = 𝟐. 𝟎𝟑 𝐦𝐦
yt yt yt yt yt yt yt yt yt yt




1.35 Dimensions: 18 in × 25.4 (mm/in) = 457 mm yt yt y t y t yt yt yt yt




12 in × 25.4 (mm/in) = 305 mm
yt y t y t yt yt yt yt




Area = (18 in)2 = 𝟑𝟐𝟒 𝐢𝐧𝟐
yt yt yt y t yt yt




Area = (457 mm)2 = 𝟐. 𝟎𝟗 × 𝟏𝟎𝟓 𝐦𝐦𝟐
yt yt yt y t yt yt yt yt yt




Volume = 𝑉 = Area × Height yt yt yt yt yt yt




𝑉 = 324 in2 × 12 in = 𝟑𝟖𝟖𝟖 𝐢𝐧𝟑
yt yt yt yt yt yt yt yt yt




𝑉 = (1.5 ft)2 × 1.0 ft = 𝟐. 𝟐𝟓 𝐟𝐭𝟑
yt yt yt yt yt yt yt yt yt yt




𝑉 = (209 × 103 mm2) × 305 mm = 𝟔. 𝟑𝟕 × 𝟏𝟎𝟕 𝐦𝐦𝟑
yt yt yt yt yt yt yt yt yt yt yt yt yt yt




𝑉 = (0.457 m)2 × 0.305 m = 0.0637 m3 = 𝟔. 𝟑𝟕 × 𝟏𝟎−𝟐 𝐦𝟑
yt yt yt y t y t yt yt yt yt y t yt yt yt yt yt




1.36 𝐴 = 𝜋𝐷2⁄4 = 𝜋(0.505 in)2⁄4 = 𝟎. 𝟐𝟎𝟎 𝐢𝐧𝟐
yt yt yt yt yt yt yt yt yt



2y t


𝐴 = 0.200 in2 × (25.4 mm) = 𝟏𝟐𝟗 𝐦𝐦𝟐
y t y t yt yt yt yt y t yt


in2
1.37 𝜎=𝑃 = 3200 N 3200 N = 40.7 N = 𝟒𝟎. 𝟕 𝐌𝐏𝐚
=
yt
yt yt yt y t yt yt yt yt yt


𝐴 (𝜋𝐷2⁄4) [𝜋(10 mm)2]⁄4 yt mm2

𝑃 20×103 N yt
= 66.7 N = 𝟔𝟔. 𝟕 𝐌𝐏𝐚
𝜎= =
y t

1.38 yt yt
yt yt yt yt


𝐴 (10)(30) mm2 yt mm2

1.39 𝜎=𝑃=yt yt yt y t y t
860 lb yt = 𝟓𝟑𝟕𝟓 𝐩𝐬𝐢 yt yt


𝐴 (0.40 in)2 yt




1.40 𝜎=
yt
𝑃
yt
y t

= [𝜋(0.375
1850 lb yt
= 𝟏𝟔 𝟕𝟓𝟎 𝐩𝐬𝐢 yt yt yt


𝐴 in)2]⁄4 yt




1.41 Load on Shelf = 𝑊 = 𝑚𝑔 = 1840 kg ∙ 9.81 m⁄s2 = 18 050 N
yt yt y t yt y t yt yt yt yt yt yt yt y t yt yt yt




𝑊/2 = 9025 N On each side
yt yt yt yt yt yt




∑ 𝑀𝐴 = 0 = (9025 N)(600 mm) − 𝐶𝑉(1200 mm)
yt yt yt yt yt yt yt yt yt yt




𝐶𝑉 = 4512 N
y t yt yt




𝐶 = 𝐶𝑉/ sin 30° = 9025 N
y t yt yt yt yt yt yt




𝑃 𝐶 9025 N = 𝟕𝟗. 𝟖 𝐌𝐏𝐚
𝜎= = =[𝜋(12
y t y t yt
yt yt yt
yt yt yt

𝐴 𝐴 mm)2]⁄4
yt




𝑃 70000 l = 𝟏𝟑𝟗𝟑 𝐩𝐬𝐢
𝜎 = =
y t yt

1.42 byt yt y t y t
yt yt



𝐴 [𝜋(8 in)2]/4 yt




@@SSee
isis
mmiciicsis
oolala
titoionn

, 1.43 𝜎 = 𝑃 = (29500 lb)/3 = 𝟖𝟎𝟑 𝐩𝐬𝐢
yt yt yt yt yt yt yt yt


𝐴 (3.5 in)2 yt




1.44 𝜎
N
=𝑃=
yt yt yt y t y t
3500 yt = 𝟓𝟒. 𝟕 𝐌𝐏𝐚 yt yt yt




𝐴 (8.0 mm)2 yt




1.45 𝑊 = 𝑚𝑔 = 4200 kg ∙ 9.81 m/s2 = 41.2 kN
y t yt yt yt yt yt yt yt y t yt yt




𝐴𝐵𝑋 = 𝐴𝐵 sin 35°yt yt yt yt




𝐴𝐵𝑌 = 𝐴𝐵 cos 35°y t yt yt yt




𝐵𝐶𝑋 = 𝐵𝐶 sin 55°yt yt yt yt




𝐵𝐶𝑌 = 𝐵𝐶 cos 55°yt yt yt yt




∑ 𝐹𝑋 = 0 = 𝐴𝐵𝑋 − 𝐵𝐶𝑋
yt yt yt yt yt yt yt




0 = 𝐴𝐵 sin 35° − 𝐵𝐶 sin 55°
yt yt yt yt yt yt yt yt




sin 55° yt yt


𝐴𝐵 = 𝐵𝐶 ∙ yt yt yt yt = 1.428 𝐵𝐶 si yt yt yt

n 35° yt




∑ 𝐹𝑉 = 0 = 𝐴𝐵𝑌 + 𝐵𝐶𝑌 − 41.2 kN = 𝐴𝐵 cos 35° + 𝐵𝐶 cos 55° − 41.2 kN
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt




0 = (1.428 𝐵𝐶) cos 35° + 𝐵𝐶 cos 55° − 41.2 kN
yt yt yt yt yt yt yt yt yt yt yt yt




41.2 kN = 𝐵𝐶[1.170 + 0.574] = 1.743 𝐵𝐶
yt yt yt yt yt yt yt yt




𝐵𝐶 = 41.2 kN = 23.63 kN
yt yt yt yt yt yt

1.743

𝐴𝐵 = 1.428 𝐵𝐶 = 33.75 kN
yt yt yt yt yt yt




Stress in Rod AB: 𝜎 𝐴𝐵 33.75×103 yt
= 𝟏𝟎𝟕. 𝟒 𝐌𝐏𝐚
= =
yt yt yt yt yt yt yt yt
yt y t
N
𝐴𝐵 𝐴 [𝜋(20 mm)2]/4 yt




Stress in Rod BC: 𝜎 𝐵𝐶 23.63×103 yt
= 𝟕𝟓. 𝟐 𝐌𝐏𝐚
= =
yt yt yt yt y t yt yt yt
yt y t
N
𝐵𝐶 𝐴 [𝜋(20 mm)2]/4 yt




Stress in Rod BD: 𝜎 yt yt yt yt
=
𝐵𝐷 y t

= = 𝟏𝟑𝟏. 𝟏 𝐌𝐏𝐚
yt yt yt


41.2×103
yt
yt



N
𝐵𝐷 𝐴 [𝜋(20 mm)2]/4 yt




1.46 𝐹 = 0.01097 𝑚𝑅𝑛2 = (0.01097)(0.40)(0.60)(3000)2 N
y t yt yt y t yt yt




𝐹 = 23 695 N
yt yt yt yt




𝜋(16 mm)2 y t


𝐴 = = 201 mm2
yt

y t y t yt yt


4

𝜎
Nyt = yt
𝐹 y t

= y t
23695 yt
= 𝟏𝟏𝟖 𝐌𝐏𝐚 yt yt



𝐴 201 mm2 yt




@@SSee
isis
mmiciicsis
oolala
titoionn