Solutions Manual to accompany APPLIED STRENGTH OF MATERIALS Fourth Edition Robert L.. Mott Prentice BENT ee Upper Saddle River, New Jersey Columbus, Ohio... All rights reserved
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Solutions Manual
to accompany
APPLIED STRENGTH OF MATERIALS
Fourth Edition
Robert L Mott
Prentice
BENT
ee
Upper Saddle River, New Jersey
Columbus, Ohio
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Copyright © 2002 by Pearson Education, Inc., Upper Saddle River, New Jersey 07458 All rights
reserved Printed in the United States of America This publication is protected by Copyright and
permission should be obtained from the publisher prior to any prohibited reproduction, storage in a
retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,
recording, or likewise For information regarding permission(s), write to: Rights and Permissions
Department
Instructors of classes using Mott, Strength of Materials, Fourth Edition, may reproduce material from
the solutions manual for classroom use -
10987654321 Prentice
Hah
————
ISBN 0-13-088579-7
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CHAPTER B1 Basic Concepts in Strength of Materials
fol ro l-/S ANSWERS IN TEAT,
_——=— —
/-%
` a `
/-18
R ~ `Š
—` £ lad IN
ð us
4 ~ `
hi
Weems = /Booky 9.81 m/s? = l2 ÁSB Agem/S*2/22744`A/
We 127 4b
TOTAL Wh tangs on Ê2-9812%/6 >«2929Á2I
EA Front wieer: Fp *(‡)(a.V)(39,awl)= 2605 Á
EACH Rete wuert f2 =(‡)(0.40)( 2¢.2thw) = 4-774d)
(0Aø/aa > TOTAL FRCE/ARA ;
ToTAL FoRce= 6200ky-9.8/ a5? =66.7.4N
A#eA ~ (Z0) (3,6⁄2:) = /2-5⁄m ”
LoAoine = €Ẽ 24/72 „+ = 391 hilar? ZAb a Fo@(E = MT = m-4* 25kg -# on» 29322
Ke §P&IAlá SEALG = W700///me “BÉ
AL» Fo 295N
K %500A//2
W 2/77 Al = 19200 d/% 02208 LE/N © 298048
8 O0bSYS n= SISK = SYeTan0m
Fe = 78S 40° 7850N« 0.2298L0/w */765 48
Fp *MeIIAN® H7ION 4b, 32VAL8/ = 26Y6LE
Lodous = 38kf = 3.8/x10 HN, Ý_ 0.22,
F = 295+ 0.2298 8/4 = §5./ £8
es ca
ÁL ¬®— 8 a
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/-2€ mn oe cay 85:4 LES, Ø9 Su £
—D
/~2 “~m v.Ắ aa jane? F178 LBS '= B98 Sues “st
J-3o & 2/6oo @diké.f†S.k/6/Hi © 19,000 Ata Ht Mle
/-3/ %%= /Voao /0vá44090s Ml, f Ph? Ib, S00 ble +96 Sha
Su® Pb000gei x 6.895 bho/ Au = FLY 000K = SEV M Loe
=
[320 m= 1950 Rev Rev , ZI RAC, foun = rh Zee = 783 Rao/s oA
/33 A=/ữ./22*x Bevan)” = 909? anan®
L:3¢ W=0.0пuy 2%SW2ax//M "2,03 nản (3Š ỐC ÔA/neoAl4: /8/2AxX2SVx2s/205= 952 gam
/V+ 2% 2mm Jin = = 305m
A#EA = (29,0) °= 320/4}
Area = (IS9 mưa)" = 224/052 nạn 2
VYotume =V © AREA 4HGlGHtT
VE 32/⁄u†y /21 = 2888 //°
VF0.S#“rÌ`a¿ (0FT£2/2€ 73
V = (209x/0man ) 4 30S anim = u32 XA 2n"
¥™ (0.95 Im¥ * 0.308 © 6.6432 s 432v 12y8 1-360 28 ATO? Wlasisw)'/¥= 0.2000m* Ni 2
Ax 0200 w* (26m) a 24mm
i322 o- f> Lay TOUR = Lids © OTM gr 1007 Mle
138 one we 20K W ,
hs
Z-£- 6 teas = SB eet
/-3
TC + va = 250 pol
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J=J Lono ovSHe.r®W=xnd=/B†0Aly-9/8/2/6*= /0as0/
Laty =o= Ñfa£A')(&om=) =Cy220=^) Ee
Cy = 45/2 V —4+—=Ƒ ề
ep,
Tula Li, WEN = 1B Le —|z_«o
Wim)
3 /¬ =P 70242:6_ _ ‘
/-# 3 o= =f 2956 = 0 (6/2
;-#/ cz Shy = ook = SY.7 le
T lŠ yr sig = 100ky 481m /s* -.2Â 4, Ate
Aby= AB Ain 38° - scr
đây = 4ó caa 4S9 fk
ổc„= BC ainss*
BCy = a
ZF, 20 = AB, ~ BC
Aaa= 6c 2S = /28 8C Arn 3S”
O= (1928 BC) Ceaas* + BC Coa SS*-~HA24N
A,2Aw= Bc[//20*-0,Š7] = 4993 be
&c = ⁄224//11v4 23,6340
A6=z /22 ác = 33.7%Ân
ø Rap A8: đ=-AÊ 32.26xn 3V -
nhờn on Ge BIH e111 Ml 3
Sregss w Pid Bar đặc = BS « 236240 “A 7 Comm) ¥ 2120 95,2 she
3
Sreess is Rov B02 Op y+ BP = thee (31.1 lao
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“~t ('“#20/207 ym hm = (0.0/00 f2)(2.42)(3ose) *
£= 23¿0cC//
A= WUbam) /f = Zof mam ©
=» £- 2Ÿ697
(7 Ty muat “-20//2-,
/~#2 2=o 2mm) ”= o0 „xa °-
Foe 491 =(/0 -yora)ar =/sodd
“ fs» £50009 lh? tla TEwsin 90M ———————
FoR Be: f= yo-yo =Ắ 204
a yt 2 128/04 TENSION
FOR Cd! Fag « Ibn
% * TH MOAN, 2 122 Whe TEMS IOV
—— Akets: A-03 A* tF(Ae)/V* V92"
C-0 5 Á° 0/617" 200mm
POR AG: Fag ® — 265 -22.32 +495 2-/52hd
Ong © =——=
FoR BOt Fy © -9,65 -/2.32 = ~2/.92 MN
đạ, =.Eác „ ^2//424/03/
= BSI Moa, Conte
a Waa £ =Ÿ1⁄7/2Áv C01
FoRco: %;=-9,6 7Â
= Feo „ 9.67 VŨ
wh A* riko)" = 0.999 ye® (them Pree ~Aen A42)
Fok OL: Zặc= = -2200 có
D799 mee
FoR RB: Figs 2500 +2 (8.000 Cea 30) =/6 35048
đa, = -FAÊ Km =ðo H1! SẼ Ố reAs/ov
= 3/29 F3/ T#1/0v
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/-Z2Ð0 — £ he 20.2 28001 YS) ~ fy, C32)
đập = ¥200 Le
G7,» £222 #200 eG _— cổ z32 (
ÉP A Baten 223 pul_ Tenshi
8O2/0.SkN
10.Sk0 “
Joint A
0 AD fin 30" = 62s Á
< Ao = A.ShW 260
A Ab AG = Ao Ces 202909 hy * be
S2sks
T 2
—_ ,, 2 4%" 2% ° 4.49 x42) =223//2 ?: ñ 2X = lợi On ENE
BO: Go= L052 19, Bool Bane LIS Mit, TENSION
40,۩bt A =(30)*-(20oy = Soomm*
Fo Fis * 18S LON a2), 1the Co/6/64/
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1-52 Ấ/!„ =o* Êo0u()+-/26oo(/v) ¬£v (8)
Rp = /0000 Le
Zp =0 ® [2000 (6) +600002)-8,08) Raw 800016
ae ,
AB = R, Joe BOC/o.2 = /000L8 Come,
ÁP* AB œ«eo* /0000(0-6)= 6060L6 Ems
gordo
c6 BE Arn £6000 ~AG OHO =O
6 6c Be = Abang ~Go0o , 10000(0.8) “CC - 260018 Teus, ane oF
se P\Xe BCE AC 42 O + BE cose = 10000606) + 2500.0 =
Be BC> 780046 Come
!2p0o Lổ 8£* C£ Cone
Cr ® b¢/cosa ™ 2500 /o.6* /2500L6 Come
¿ tô CE 2 /ÈO0b = CE đến ® = /20t0=/2StO0(0£)#2000LÊ C
Le
cé
ow EF ‘ STResses:
£ Oo = Wu = 6000/4, 9e4 = S/F fat
|&# ®/0000tó Ser = 7500/0968 ©] )¥E pd
[jo =0
AREAS OF Mensees ? ÍÍtPP, 47, A6) Ten * 2500/o,yey 25765 pus
AD, 0, £r— 200Y8)* 0.968 Cee 200 /o.yay 5/92 pl
BO, be Ce OY đạo = ~200/% và 2= (132/222
AG, BC, CF — 2Ch2/)2 24 w? | og © -750/2.v2= ~3099 pul
Mere? ComPhe sso MEMCERS MULT BE | Cte = ~RSWY/ 2.92 =~ Fes ped
CHE txto Fok Column Buckt Ina
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FA, 202 (ZEN 40) ABLES) Sz Ln
Ab= Zohn
Z= 201V = 0/0
Ø) nen
/a2.XÀM
_!-5f 4+ n(0so5)/V=o.200w*
= Lyn (260018 /y,209 py» 63 O00 ps
- SẼ 4= 2.6540) + 2LbvoVosyct)] = #41 2?
on ime (S2o00 16/y gp iy?) @M 79/ pros
LSS Ae (8040) ~ (60S) FT 40)' Y= 3557 men
đ«= ĐA SFO S2 mau >= 180 Mla
1-57) «= DIRECT SHEAR - SINGLE SHEAR
——— ————————————r=rsene
As= C#C20Y AY) man” 11 xman
7e FAs * BS OW) 3 nan = 146M,
Fz SS
/-§8 ẤF,*o* rz(//5)¬f,(253 * ¥ +
Fpx /2?A/
Á¿> L0, «3.01 2maY :0o tới
Te Ftp LY granan>? 2501 ban PIN Am Siete
SHEAR ' c|ẾT, Pbed Peae -¥6t F223695 N
Ase 2urlayr] = 757 mm™ Dovbre SHEAR
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c(cép —- 4:=(.oX3.3)*/0.f/,Y
y* F/As* Ê0eo Lê Jos ww SI CS, LBL Ás= (2/37) +r(ø) ÏỚ.g) = ¥95.9 am?
PR Ƒˆ/He£ äP6xð”A 1S VIE? mm >* Off he
{6 Le Vig? t67 = 0.72) m —-
As* (2060) + rode +20 nose UN 6
T ® Flas? YS000c8/ yyy = 39327 0 —ả L—
£82 7
“su 7⁄4" 354m 20224 s Sea esta PP %
As = b:t.2 G0)(22)% 226 An Y
LEE Aix The s0mrem/y , = dooce
As beh 08022598 fl25n*
»z fy, = G00 Ey a sy s We ph
aE Le beveee swetes Ae» AMOS) = 0.393 we
Te ye 20000 L4/ 4,393 yt 2 50 O80¢%/
COLLAR SiENR COLLAR Áo“ Conwecron body
Ag = Wt t= los lost?) * asis4ia~
?= “4, = 2baao +4/2,%⁄„v` “46 700 FS)
Ây= 8doe
&~ Bykaw 2093 le by
Ase2 lates) py) =Q,2%
7⁄2 82, * Ê6/3(8/2,2/;ux “394% £/
v6 Az* (/0)//2) 80mm”
TP" Plage 8Ø8X40°Al nxue> “(83 M4,
£268 A4i= (2/20) * 2i0 mm”
Te Flags BB2KON/ yg gusgt * LEY Mob,
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„692 /:e mrot=rr(02)(8)220/,6xaa^—”
T= Ply = 22.3409 /3u,,6 mm * 23-9 Abbe
£222, 4»„* 2LT(/21V] =3%26.2A22⁄/H” Tựo KifFTi=5/lláce S/ehe
7= #/u = Bd xo W/azeranm™ ® $5/ba
T= Flag = 10.200'W/ysr,4 atm® © 22ST Mbt
BEARING STRESS
L292 ay Wests - on sran nares hy 4430" (Ath A-7)
* Đy,>26200/6Á43,v> 6969 /5/
As Svea piare ow Cowcrere: A,@l2)e WY m™
= Fig,= 26000 ley 4 * 181 Psi
€) conceere Ø0 ow CouceeTe Foorzet Ág*(Rt)°e$#2f/w>
CBF 22» « 26000 L8 1> * 80.2 f3 DP) Concears Foonne on Sot: Ay=Gb)” = 1296 w™
2: * Pip, > U4 00> LYjzag yy 920.1 ps}
£273, 0) pire ow Fiooe+ A,=Ÿ(2.31€”~2.062)* (61524
đ * Đ, 523509 03g jy ® sunt
at A) Boer HeAv OW WASHERS AS* Ayge “Azo (See att ot)
As * 0:26610,25)*= 7(2.sev)/V = 0.88 9
+ F/¿,« 2(€LÊ/2,230/2-® /Á/0 0$/
b) wasnet ov wooo: lụa {(430€°-6.463°) 823022
đ:* Fly - 38:0, 282/v+ + 3/2
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zE=É 2/474 “đu fan /-65! f= 2000048, Fie 1-28
đc « ZY, 20 000 th /8026yy* * /ÓÁ 200 Ø5/ (veer #164)
8) CoLtAR/yyzet Age Fl 0*-d Se Fln2s* 0.928) 90626 07
LB, Flom FG 1-94
OB) ON Monee PART? Aye’ 2 dt, *2M12)U15)* 360 anan*
Qe %, 2 M2 xo, ko xạ" ° 28.3 ///4,
4) ow ovrer /mers: A,^ #d6, *(V(/2X/0)* 862w ®
E1 re./-f7t 4,2 0oXo+£(ÊWÀ)* %3 2s ^
OS" a= SEM Ng xu "612/40
10
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CHAPTER 2 Design Properties of Materials
OMLY THOSE FRIBLEMS REQUIRING UMIEKICAL DATA ALE Shows
ZN Su* FoAsi (OU mea) 5 Sy* Cdat (HY at), 25K Bowe,
bettuse % evonsarton 75%, (7 15 overne (APA w-13)
2/5 10% HE: 36% erownatiw -GeEATe Dvenuiry
/oWo HRt 25% srowsnrionw (ee AAD
2716 Als! WW OOF 700% Hit Suc rue ALLey STEEL WITH Oy,
CAk6on), Quewchen Wi On , TEAR Ar joe, (rr A-13) YES, Sy = /72, Al @ 207100 , Sy" 1294 @ OOF 909
BY wreatotATiod Sy x/sool @ Ooraco (App A-13)
w 4 813) 6
7% DEMSTY = WeLuzs6 * (2,263 04/1 Ì(5o)(6)(2yg)Ÿ^ 503/90)/⁄y ⁄
(ÐF2A-8) U4Lug oF LoL" VALVE ol op este hry
“-⁄
.&cÑ E= 30x 5/61 (2096/w) Foe AL Chbau Aw Mery srees
27,
£20, VoLU2E2AeeAx(gex¿7z= FO) “« 22 © 4909510 Sean?
| (APeA-R)~ ng WS Sy ae ea? ISS 2680 RF 4.969 eit Anan 7 ' m3 =3.?? 4>
i WE Any = 2T1ky, Ul an] 26 98 hig /g? « 56,98 A/
đụ: 2S ¡6n = U40 Tỉ 6 snrfee, (42A-/)
ALLOY oF C01041 WITH Sitilad Ano MANES IVA Hear TReateo To TẾ remPER
Sa sy £ DEMS ITY en 427?
boi-o JBkKÍ 8&k£(- (0xe f7 0.40 48/103
Sh Sue YOks/ 3 Sue 140 ksi lara A-te)
iN ,
231 Bewome O%* Hfso/; T€uteu 03* ÐZQVÝ ; Cha, /Dob tsi CARLA
7o 644w, 365 fšì few€ruPituLĐE To đi; đe 13 © 46/S/
(App, A-18)
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2-44 Graphite fibers
2-45 S-glass, quartz fibers, tungsten fibers coated with silicon carbide
2-51 Material
Graphite/Epoxy (High Strength) Aramid/Epoxy Composite Boron/Epoxy Composite Graphite/Epoxy (Ultra-hi mod) Glass/Epoxy Composite
Titanium Ti-6AI-4V
AISI 5160 OQT 700 Steel
Aluminum 7075-T6
Aluminum 6061-T6 AIS! 1020 HR Steel 2-52 Material
Graphite/Epoxy (Ultra-hi mod) Boron/Epoxy Composite
Graphite/Epoxy (High Strength)
Aramid/Epoxy Composite AISI 1020 HR Steel AISI 5160 OQT 700 Steel Titanium Ti-6AI-4V
Aluminum 6061-T6 Aluminum 7075-T6 Glass/Epoxy Composite
2-60 Vm = 1 - Vf = 1.0 - 0.60 = 0.40
2-61 See Equation (2-5)
Specific strength
(in)
4.86x106
4.00x106
3.60x106
2.76x106 1.87x106 1.00x108 0.929x108 0.822x108 0.459x 106 0.194x106
Specific modulus
(in)
8.28x108 4.00x 108 3.45x108 2.20x108 1.06x108 1.06x108 1.03x 108 1.02x108 0.99x108 0.66x108
2-62 See Equations (2-6), (2-7), (2-8), (2-9)
12
Ratio Als!
25.0 20.6 18.5 14.2 9.63 5.18 4.78 4.23 2.36 1.00
Ratio Als!
7.81 3.77 3.25 2.07 1.00 1.00 0.97 0.36 0.93 0.62
to
1020
to
1020
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2-63
2-64
2-65
Given: Vs = 0.50; Fibers are high strength carbon-PAN; Matix is Epoxy See Table 2-Ffor data Vm = 1- V/ = 1 0 - 0.50 = 0.50
Use Equation (2-5): sục = Su V + om' Vm Strain at which fibers would fail: ct = suf /Ef = (820x 103 psi)/(40x106 psi)
ef = 0.0205
Stress in matrix at this strain: om' = Em € = (0.56x106 psi)(0.0205) = 11 480 psi
Then: suc = (820x 103 psi)(0.50) + (11 480 psi)(0.50) = 415x103 psi
Modulus of elasticity: Ec = Ef Vf + Em vm = (40x106)(0.5) + (0.56x106)(0.50)
Ec = 20.3x106 psi
Specific weight: yc = yf Vf + ym Vm = (0.065)(0.50) + (0.047)(0.50)
Ye = 0.056 lb/in3
Given: V¢ = 0.50; Fibers are high modulus carbon; Matrix is Epoxy
See Table 2-9 for data Vm = 1- Vị = 1:0 - 0.50 = 0.50
Use Equation (2-5): suc = Suf Vf + am' Vm
Strain at which fibers would fail: ef = suf /Ef = (325x 103 psi)/(100x106 psi)
ef = 0.00325
Stress in matrix at this strain: om! = Em & = (0.56x106 psi)(0.00325) = 1820 psi
Then: Suc = (325x 103 psi)(0.50) + (1820 psi)(0.50) = 163x103 psi
Modulus of elasticity: Ec = Ef Vf + Em vm = (100x106)(0.5) + (0.56x106)(0.50)
Eg = 50.3x106 psi
Specific weight: yo = yf Vf + ym vm = (0.078)(0.50) + (0.047)(0.50)
Yo = 0.0625 Ib/in3
Given: V¢ = 0.50; Fibers are aramid; Matrix is Epoxy
See Table 2-4for data Vm = 1- Vf = 10 - 0.50 = 0.50 Use Equation (2-5): Suc = Suf Vf + om' Vm
Strain at which fibers would fail: ef = Sut /Ef = (500x 103 psi)/(19x106 psi)
ef = 0.0263 Stress in matrix at this strain: om' = Em € = (0.56x106 psi)(0.0263) = 14 740 psi Then: suc = (500x 103 psi)(0.50) + (14 740 psi)(0.50) = 257x103 psi
Modulus of elasticity: Eo = Ef Vf + Em vm = (19x106)(0.5) + (0.56x106)(0.50)
Ec = 9.78x106 psi
Specific weight: yc = yf Vf + ym Vm = (0.052)(0.50) + (0.047)(0.50)
Ye = 0.0495 Ib/in3
13
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Sofutions to Problems 2-66 to 2-67: Some data approximated from Figure P2-66
Most accurate vaiues are for Ultimate strength (b.)and % elongation (f)
Elastic limit (d.) estimated between proportional limit (c.) and yield strength (a.)
Modulus of elasticity (e.) computed from (A stress / A strain) Data are approximated
Materials found from Appendixes A-13 through A-17 matching s,, s,, % Elongation, and E
2-66 a S,= 73 ksi -~ Offset
b s, = 83 ksi
Sp = 60 ksi Se) = 67 ksi
E = 10.0x10° psi
11% Elongation Ductile
Aluminum 7075-T6
Sy = 75 ksi
Sp = 50 ksi
Sei = 56 ksi
E = 16.7x10° psi
15% Elongation
Ductile
Copper Alloy C54400 Bronze-hard
S, = 55 ksi
Sp = 50 ksi
Se = 53 ksi
E = 20.0x10° psi
0.5% Elongation
Brittle
Cast fron
ASTM A48 Grade 60
Sy = 57 ksi
Sp = 30 ksi Set = 27 ksi
E = 26x10° psi
21% Elongation Ductile
Structural Steel
ASTM A36
-penpag
2-69
2-71
2-73
14
2-67 a sy = 173 ksi Yield point
Sp = 162 ksi
Sq = 188 ksi
E = 29.0x10° psi
15% Elongation
Ductile Steel AiSi 4140 OQT 900
%= 49 ki - Yield point
Sy = 65 ksi
Sp = 46 ksi
Sa = 48 ksi
E = 26.5x10° psi
36% Elongation Ductile
Steel AlSI 1020 GD
%y= 53 ksi - Offset
Sy = 59 ksi
Sp = 31 ksi
Se = 42 ksi
E = 12.0x10° psi
5.0% Elongation Borderline Brittle/Ductile Zinc
Cast ZA-12
%= 19 ksi - Offset
$y = 40 ksi
Sp 14 ksi
Se = 17 ksi
E=6x10” psi
5% Elongation Bordertine Brittle/Ductile Magnesium
ASTM AZ 63A-T6