il '.o~ ~~1 ~r,

682I ANSWERSIi 1-61 FAB = 20 kip (C) V= 1.60 !eN (- 2-45 611 FBC = 60 kip (T) M = 0.800 !eN . m ~ . E~. FCD = 10 kip (T) 1-93 (a) A = 1875 Ib t 2-47 f

1-62 FAB = 25 !eN (C) B = 7125 Ib j 2-48 (.FBc = 50 !eN (T) (b) P = 0 1 (FCD = 50 kN (C) V= 375 Ib !M = 9750 ft . Ib ~ 2-53 c1-65 P = 300 Ib (-

. V= 500 Ib ! 1-94 (a) A = 43.75 !eN j ,M= 3600 in. Ib r B = 11.25 !eN t 2-54

1-66 P = 225 N (- (b) P = 0V= 139.7 N ! V= 6.75 kN ! 2-57M= 95.9 N m r M = 6.75 kN m ~ ~~

.\

1-69 (a) A = 6000 Ib j 2-58B = 11,600 Ib i

Chapter 2(b) P = 0 2-61V= 3300 Ib ! 2-1 U'A = 700 psi (T)M= 13,950 ft Ib ~ U'B = 955 psi (T) 2-63

1-70 (a) A = 21.0 !eN i 2-2 U'A = 106.7 MPa (T)B = 9.00 kN i U'B = 133.3 MPa (T) 2-65(b) P = 0

U'c = 53.3 MPA (T)V = 11.0 kN !

2-5 U'AB = 23.1 ksi (C)M = 14.0 kN . m ~ 2-66U'BC = 30.0 ksi (C)

1-73 (a) P = 1238 Ib ! U'CD = 20.0 ksi (C)V= 600 Ib ~ AA = 4330 rnrrr' 2-692-6M = 900 ft . Ib J

AB = 10,000 mm"(b) P = 606 Ib ~ Ac = 20,000 mrrr' ~ 2-70

V= 743 Ib i2-9 d = 3.18 in.M = 1485 ft Ib J

2-731-74 (a) P = 162.0 N ~ 2-10 (a) P = 113.8 kN

V= 540N i (b) P = 156.0 kN(c) P = 54.3 !eN 2-74M = 162.0 N . m J

(b) P = 402 N? 59.0 (d) P = 216 kN "V= 52.0 N ~ 31.0 2-13 Pmax = 4.88 kip 2-77M = 15.20 N m J 2-14 Pmax = 589 kN >

1-81 T = 700 Ib ~ 20.0 2-17 PAB = 4.88 kip 2-83FA = 1316 Ib 5::", 60.0 2-18 a = 53.3 nun

1-82 Ax = 2.510 kN ~ 2-21 Pmax = 8.45 kip r- 2-84Ay = 0.399 !eN ! 2-22 (a) U'DE = 17.78 MPa (T)B = 3.42 kN ~ 60

(b) ABC = 389 mm'' 2-871-85 TAB = 732 N (C) 2-25 (a) TB=21.4ksi

TAD = 366 N (C) (b) TC= 18.11 ksi 2-88TBC = 732 N (C) 2-26 (a) TA = 34.7 MPaTBD = 0

(b) TB=31.4MPa 2-91TCD = 732 N (C)2-33 U'max = 22.5 ksi (T)1-86 (a) A = 21 kN j

Tmax = 11.25 ksi 2-92B=18kNj(b) P = 0 2-34 U'max = 110.0 MPa (T)

V= 9.00 kN ! Tmax = 55.0 MPa .' 2-95M= 6.0!eN m ~ 2-37 a.; = 18.29 psi (C)

t; = 73.4 psi ,1-89 P = 85.1 Ib tV= 206 lb (- 2-38 'min = 51.3 nunM = 789 ft . lb 1, 2-41 Pmax = 9.38 kip

1-90 P = 3.20 kN i 2-42 Pmax = 291 kN 2-96

ANSWERS 683

2-45 ()= 36.9 Tnt = 47.2 MPaP = 75.0 kip (b) a; = 5.98 MPa (T)

2-47 Pmax = 5.44 kip a, = 86.0 MPa (C)

2-48 (a) = 59.0 Tnt c= 19.64 MPa

(b) Pmax = 34.0 kN 2-99 (a) Tv "" Th = 5.33 ksi, Fj 2-53 U = 14.23 ksi (T)

(b) Tnt = 5.33 ksi

T = 11.82 ksi 2-100 (a) Ux = 221 MPa (T)

2-54 0' = 121.5 MPa (T)(b) Tnt = 61.0 MPa

T = 9.64 MPa 2-103 (a) Uaa = 11.50 ksi (C)

2-57 0' = 12.31 ksi (T)Taa = -8.50 ksi

T = 1.075 ksi(b) Ux= 16.25 ksi (C)

2-58 U = 60.8 MPa (T)uy = 6.75 ksi (C)

T = 14.40 MPaTxy = 7.05 ksi

2-61 U = 12.99 ksi (T)2-107 up! = 18.77 ksi (T)

T = 7.50 ksiUp2 = 2.77 ksi (C)

2-63 U = 7.38 ksi (C)up3 = a,= 0

'

684 ANSWERSTxy = -75.0 MPa 2-149 (a) Upl = 9.15 ksi (T) 3-5 (,8p = 18.43 ~ Up2 = 22.4 ksi (C) (l

2-123 Txy = -19.97 ksi Up3 = 31.7 ksi (C) 3-6 (;Tmax = 20.4 ksi (iupl = 27.0 ksi (T)

(b) 83x = 45.6 3-9Up2 = 37.0 ksi (C)Up3 = 0 83y=45.1 3-1083z = 96.42-125 o; = 6.62 ksi (T)

Upl = 131.3 MPa (T) 3-13Tnt = 11.03 ksi 2-150 (a)

Up2 = 28.4 MPa (T)2-126 a; = 23.6 MPa (T)

Up3 = 5.24 MPa (T) 3-14Tnt = -32.9 MPa

Tmax = 63.1 MPa2-129 Upl = 31.0 ksi (T) (b) 8lx = 44.6 3-17

Up2 = 1.000 ksi (T) (}ly = 61.20(Ip3 = 0 8lz = 59.2Tp = 15.00 ksi 2-153 (a) UAC = 5.28 ksiTmax = 15.50 ksi (b) ACD = 3.43 in.28pJ = 26.6 ~ 2-154 (a) AAB = 577 mm"

2-130 Upl = 77.7 MPa (T) ABc = 1155 mrrr' 3-18(Ip2 = 7.72 MPa (C) (b) dA = 23.5 rnm(Ip3 = 0 dc = 33.2 rnmTmax = Tp = 42.7MPa 2-157 (In = 19.48 ksi (T) 3-218p\ = 34.7 ~ Tnt = 10.62 ksi 3-22

2-133 (a) upl = 16.45 ksi (T) 2-159 (Ipl = 29.1 ksi (T) 3-25Up2 = 10.45 ksi (C) (Ip2 = 5.09 ksi (C) 3-26Up3 = 0 Up3 = a; = 0

3-29Tmax = Tp = 13.45 ksi Tmax = Tp = 17.09 ksi(b) (In = 1.160 ksi (C) 8p = 34.7 ~

Tnt = 12.79 ksi 2-160 Up! = 48.9 MPa (T)3-302-134 (a) upJ = 98.2 MPa (T) Up2 = 38.9 MPa (C)

(Ip2 = 118.2 MPa (C) (Ip3 = Uz = 0(Ip3 = 0 Tmax = Tp = 43.9 MPa

3-33Tmax = Tp = 108.2 MPa 8p = 12.11 ~(b) (In = 60.3 MPa (C) 2-163 (a) Upl = 15.00 ksi (T)

Tnt = -95.8 MPa (Ip2 = 5.00 ksi (T)3-342-137 (In = 21.0 ksi (T) Up3 = 0

Tn = 4.27 ksi Tp = 5.00 ksi2-138 (In = 71.9 MPa (T) Tmax = 7.50 ksi

(b) (In = 8.04 ksi (T) 3-37t; = 10.96 MPaTnt = -4.60 ksi

2-141 a; = 16.00 ksi (T)2-166 (a) a; = 87.1 MPa (T) 3-38

Tn = 1.642 ksiTn = 23.2 MPa

2-143 Up! = 22.2 ksi (T) (b) Up! = 91.7 MPa (T) 3-41(Ip2 = 7.30 ksi (T) (Ip2 = 16.57 MPa (T)(Ip3 = 19.47 ksi (C) (Ip3 = 47.3 MPa (C)Tmax = 20.8 ksi Tmax = 69.5 MPa

2-144 Upl = 73.8 MPa (T) (c) (}3x = 38.8Up2 = 9.41 MPa (T) (}3y = 86.4 3-42(Ip3 = 43.2 MPa (C) 83z = 51.4Tmax = 58.5 MPa

2-147 UpJ = 16.11 ksi (T)Chapter 3

(Ip2 = 5.75 ksi (C)Up3 = 10.36 ksi (C) 3-1 EO = 2080 f.L 3-45Tmax = 13.24 ksi 3-2 B = 0.480 rnm

3-5

1

3-6~

3-93-103-13

,, f 3-14

3-17

;

. f

3-21

3-22i 3-25

3-263-29

ANSWERS 685

3-18

(a) avg = 1543 fLin./in.(b) Eavg = 1400 fLin./in.(a) eavg = 2000 fLrn/rn(b) Eavg = 1583 fLrn/m'Y= 1396 fL rad'Y= 0.0279 rad(a) eA = 1000 fLin./in.(b) EA = 900 fLin./in.(a) Ec = 8100 fLrn/m(b) Ec = 7770 fLrn/m

L2(a) s =..E6E

(b) - 'YLEavg - 6E

(c) Emax = ~(a) {j = 5.00 mm(b) Eavg = 1667 fLrn/m(c) Emax = 5000 fLmJmen = 1541 fLin./in.En = -2410 JLm/meBD = - 1160 fLin./in.

eBD = 30.0 fLrn/rn

En = -633 fLe, = 473 J-t'Ynl = 1332 fLraden = 264 fLe, = -24.1 fL'Ynl = 1219 fLraden = 362 fLE, = 748 fL'Yn' = - 306 JLraden = -398 J-tE, = -=402 fL'Ynt ~ 721 fLIad(a) 'Yn' = 425 fLrad(b) Ey = 1675 fLin./in.

(a) Yry = -4040 fLrad(b) eQR = 2600 fLrn/m

tpl = 672 fLEp2 = -272 fLep3 = 0'Ymax = 'Yp = 943 fLradOp = 16.00 ~Ep! = 1004 fLep2 = -364 fLCp3 = 0')Imax = ')Ip = 1367 J-tradOp = 10.28 JlOp! = 1009 u.lOp2 = -759 fL

Cp3 = 0'Ymax = 'Yp = 1768 fLradOp = 4.07 ~

3-47 lOpl = 880 JLCp2 = 360 JLCp3 = 0')Ip = 2(260.0) = 520 fLrad'Ymax = 880 fLradOp = 33.7 ~

3-48 epl = -404 fLlOp2 = - 1116 JLCp3 = 0'Yp = 712 JLf3d'Ymax = 1116 JLfadOp = 25.9 J

3-51 lOp! = -233 fLp2 = -717 fLlOp3 = 0'Yp = 484 JLf3dYmax = 717 JLrado, = 25.9 1

3-53 Cp2 = -1360 fL'Yry = ::':2030 fL'Ymax = 'Yp = 2400 fL(jp = ::':28.9

3-54 Ep2 = -2400 JLYry = ::':3600 JL'Ymax = 'Yp = 3900 fL(jp = ::':33.7

3-57 e. = -295 fLEy = -1334 JLlOp2 = - 1853 fLYmax = 'Yp = 2080 fL

3-58 e. = 947 JLty = -54.0 fLlOp2 = -207 JL'Ymax = 'Yp = 1307 fL

3-61 e. = 500 fLEy = -300 JLYry = 600 JLrad'Ymax = 'Yp = 1000 fLrad

3-62 e. = 640 JLEy = -800 fLYry = 960 JLrad'Ymax = Yp = 1730 fLrad

3-65 lOpl = 966 fLCp2 = -241 JLCp3 = 0'Ymax = 'Yp = 1207 fLradOp = 6.59 ~

3-66 &,1 = 1072 JLep2 = -505 JLlOp3 = 0

3-30

3-33

3-34

3-37

3-38

3-41

3-42

3-45

686 ANSWERS'Ymax = 'Yp = 1576 fLrad 3-83 (a) Ex = -227 fLOp = 19.27 1 ty = 152 fL

4-2

3-69 'Yxy = :t641 fL 'Yxy = 1875 fLrad

Ep2= -774fL (b) Epl = 919 fL

Ep3 = 0 Ep2 = -994 u.4-5

'Ymax = Y = 1188 wad Ep3 = 25.0 fLOp = :t 16.35 'Ymax = 'Yp = 1913 fLrad

4-7

3-70 'Yxy = :t912 fL Op = 39.3 J

Ep2 = -180 fL 3-84 (a) Ex = 472 fLEp3 = 0

ty = -186.4 fL

'Ymax = 'Yp = 960 fLrad 'Yxy = -2124 fLradOp = :t35.9 (b) Epi = 1255 fL

3-73 (a) Ex = 750 fLEp2 = -969 j.L

ty = -250 fLEp3 = -122.6 fL : :'

'Yxy = -750 fLrad'Ymax = Y = 2220 fLrad

(b) pi = 875 fLe, = 36.4 J 4-8

Ep2 = -375 fL 3-87 (a) Eavg = 938 fLin./in.Ep3 = -214 fL

(b) tavg = 3 13 fLin.lin.

'Ymax = 'Yp = 1250 fLrad 3-88 (a) Eavg = 923 JLmlm

Op = 18.43 J tavg = 800 j.Lmlm

3-74 (a)(b) avg = 1327 JLmlm

' "

Ex = 665 JL",'

e; = 390 j.L E.vg = 1150 JLmlm.i: ,

'Yxy = -950 JLrad 3-91 Epi = 1085 JL~~

"

(b) pi = 1022 fL Ep2 = -885 j.L~

4-11

Ep2 = 33.0 JL p3 = 0~{-'

Ep3 = -143.9 JL 'Ymax = 'Yp = 1970 fLrad' ,

'Yp = 989 JLradOp = 11.98 J

'Ymax = 1166 JLrad 3-92 Epi = 1575 fLOp = 36.9 J Ep2 = 585 fL

3-77 (a) x=-35OfL Ep3 = 0

ty = 1150 fL 'Yp = 990 j.Lrad'Yxy = 520 j.Lrad 'Ymax = 1575 JLrad

(b) pi = 1194 fL Op = 38.0 J 4-13Ep2 = -394 JL 3-95 (b) pi = 1645 fLEp3 = -377 u. p2=-I045fL'Ymax = 'Yp = 1588 JLrad p3 = 0 4-14Op = 9.56 J 'Ymax = 'Yp = 2690 j.Lrad

t

3-79 (a) Ex = 875 fLOp = 24.0

e; = -525 JL 3-97 pi = 700 JL

'Yxy = - 1050 wad p2 = -300 fL! 4-17

(b) Epi = 1050 JLEp3=-171.4j.L : \

p2 = -700 fL 'Ymax = 'Yp = 1000 wad 4-18Ep3 = -172.4 JL Op = 18.43 1 . ,~

'Ymax = 'Yp = 1750 JLrad 3-98 pl = 2790 JLOp = 18.43 J tp2 = -1320 fL

3-80 (a) Ex = -555 JL p3 = -722 JL4-21

s, = 1295 JL 'Yp = 'Ymax = 4110 fLrad

'Yxy = -214 JLrad Op = 26.0 J(b) Epl = 1301 u. IEp2 = -561 j.L Chapter 4 ' I'

Ep3 = - 317 JL 4-1 (a) E = 10.65(103) ksi I'Ymax = Y = 1862 fLrad 4-22Op = 3.30 1 (b) v = 0.326(c) (TPL = 47.9 ksi. '.

ANSWERS 687\ 4-2 (a) E = 78.7 GPa 'Yyz = 1749 JLl1ld~ (b) v = 0.326

'Y== 2769 p,radf (c) O"PL = 354 MPa 4-25 (a) O"x= 18.96 ksi (T)'I,

4-5 (a) E= 10.58(103)ksi O"y= 1.813 ksi (C)(b) v = 0.325 'Txy = 6.35 ksi

4-7 (a) E = 10,000 ksi (b)O"p! = 20.7 ksi (T)(b) O"pL = 25 ksi O"p2 = 3.60 ksi (C)(c) O"ult = 69 ksi O"p3 = 0(d) O"ys(0.05%) = 31 ksi 'Tmax= Tp = 12.17 ksi(e) O"ys(0.20%) = 40 ksi Op= 15.71~(f) O"j= O"ult = 69 ksi 4-26 (a) a; = 64.7 MPa (T)(g) O"ft = 74.4 ksi O"y= 2.52 MPa (T)(h) E, = 133.3 ksi 'Txy = -42.8 MPa

?(i) E, = 1400 ksi (b) O"p! = 86.5 MPa (T)

4-8 (a) E = 69.5 GPa O"p2= 19.28 MPa (C)(b) O"PL = 139 MPa O"p3 = 0(c) O"ult = 450 MPa 'Tmax= 'Tp = 52.9 MPaCd) O"ys(0.05%) = 220 MPa ()p = 27.0 J(e) O"ys(0.20%) = 278 MPa 4-29 (a) O"x= 0.1593 ksi (T)(f) O"f= O"ult = 450 MPa O"y= 33.3 ksi (T) ~~(g) O"ft = 483 MPa 'Txy = 5.80 ksi(h) E, = 850 MPa (b)O"p! = 34.3 ksi (T)

I r~_

Un~ l' (i) E, = 6.83 GPa O"p2 = 1.135 ksi (C), i!l

4-11' (a) E = 26,700 ksi O"p3 = 0\rif::('

~.,' (b) O"PL = 38 ksi 'Tmax= 'Tp = 17.71 ksi ;;1:(c) O"ul! = 73.0 ksi Op = 9.56

0 J .!~~~.:H(d) O"ys = 43.5 ksi 4-31 (a) pI = 875 p: !i:!f(e) O"ys = 47.0 ksi Ep2 = -375 /.L ~ll~:i

, (f) O"f= 65.0 ksi Ep3 = -214 /.L ri!H~

(g) O"ft = 91.5 ksi 'Ymax= 'Yp = 1250 /.Lrad ,:!Ili(h) E, = 2.42(103) ksi e, = 18.430 J(i) E, = 14.4(103) ksi (b) O"p! = 25.1 ksi (T) ',:iUJ

4-13 O"x = 8.90 ksi (T) O"p2 = 3.71 ksi (C)::11Ii

O"y = 0.330 ksi (C) 'Tmax= 14.42 ksi :"1.,l'i~

'Txy = - 1.538 ksi 4-32 (a) tpl = 912 /.L:\',1'

,. 4-14 a; = 187.9 MPa (T) Ep2 = -383 /.Lilltf:

,. lilt\'! \ O"y = 126.4 MPa (T) tp3 = -261

/.L jljlliTxy = -43.1 MPa 'Ymax= Y = J 294 /.Lrad 'I'IIlilt!

4-17 O"x = 8.20 ksi (T)Op = 18.59 J lin!liH

O"y = 0.624 ksi (T) (b) O"pl = 64.3 MPa (T) iiillTxy = -0.758 ksi O"p2 = 6.69 MPa (C) J!'Tmax = 35.5 MPa ~fl

4-18 o; = 201 MPa (T) :~!!'" = 39.2 MPa (T)

4-35 o"z = 12.00 ksi (C) !iif

Txy = 32.3 MPa 4-36 P = 4.72 kN (C)mf.

,:1

,I!~r

4-39 6.L = 48.7 in."'it

4-21 s, = 375 /.Lin.lin. iih,I:tty = -58.3 /.Lin.lin. 4-40 6.L = -72.0 mrn 'i:'!I;e; = 50.0 /.Lin.lin. 4-43 6.t = 1.960(10-3) in.

!l!~

(a)Ul

'Yxy = 477 /.Lrad 6.w = 3.92(10-3) in.li11Hil

'Yyz = 412 /.Lrad 6.L = 35.3(10-3) in. lill1'= = 277 /.Lrad (b)6.( = -1.568(10-3) in. i!~!

4-22 t;, = 1825 /.Lmlm Ilw = -3.14(10-3) in.

ililty = -1910 /.Lmlm 6.L = -28.2(10-3) in.Ez = 458 }-tmJm 4-45 Sp = 0.0472 in. t III'Yxy = 1275 /.Lrad 4-46 OA = 2.23 rom +-

il!-ml~l

1:

II 688 ANSWERSIIII 4-49 C = -0.257 in. 4-78 (a) EL = 200 Gpa 5-27 (a) i

4-50 (a) o; = 50.0 MPa (T) EH = 200 Gpa(b) Ca = -440 fLm/m (b) aL = 350 MPa (b) ((c) AD = -0.0338 rnm UH = 1030MPa 5-28 (a) ,

4-53 C\ = 1627 fL 4-81 ca = 440 JLinjin.2 = -7120 JL Cb = - 253 JLinjin. (b)Y12 = 1923 fLrad e; = 145.2 JLinjin.

4-54 \ = 829 JL 4-82 a = 619 JLm/m 5-31 uu'2 = -454 JL b = 81.6 JLm/m Ou =Y12 = 72.5 JLrad e; = 696 JLm/m 5-32 0=

4-57 Ox = 32.9(10-3) in. 5-35 (a)Oy = 1.369(10-3) in. Chapter 5 (b)

4-61 (a) FS = 1.947 (c)5-1 Pmax = 19.71 kip(b) FS = 1.980 5-36 (a)

5-2 Pmax = 187.5 kN (b)4-62 (a) FS = 2.50 5-5 o = 0.0549 in. (e)(b) FS = 4.50

5-6 (a) oa-a = 3.31 rnm 5-39 (a)4-65 (a) FSAC = 1.932 (b) Ob-b = 5.63 rnm

FSBC = 2.39 5-9 (a) OA = 0.00905 in. (b)(b) FSAC = 7.73 (b) 0 = 0.0727 in. (e)

FSBC = 8.54 5-11 (a) 0= 14.05(10-3) in. 5-41 (a)4-66 (a) dmin = 23.6 rnm (b) FS = 3.18

(b) dmin = 17.41 rnm (c) FS = 5.83 (b4-69 (a) UCD = 5.31 ksi (T) (d) Ux = 11.32 ksi (c

(b) TB = 3.42 ksi uy = 0 5-42 (a(c) FSCD = 7.73 Txy = 0(d) FSB = lLlI 5-12 (a) 0= 3.89 mm (I::

4-70 (a) UAB = 190.8 MPa (T) (b) FS = 3.24 (c(b) TC = 119.7 MPa (c) FS = 4.61 5-45 (2

(d) UxA = 80.0 MPa(c) FSAB = 1.310UyA = 0 (I(d) FSc = 2.26TxyA = 0

4-73 (a) a, = 23.9 ksi (T) UxB = 101.9 MPa C" = 14.58 ksi (C) UyB = 0Txy = 9.93 ksi TxyB = 0

(b) ap\ = 26.3 ksi (T) 5-15 (a) o = 0.00700 in.Up2 = 16.99 ksi (C) (b) UA = 2.00 ksi

5-49Up3 = 0 TmaxA = 1.000 ksiTmax = Tp = 21.7 ksi aB = 5.00 ksiIJp = 13.65 ~ TmaxB = 2.50 ksi

5-504-74 (a) ax = 93.3 MPa (T) ac = 2.50 ksiuy = 100.1 MPa (T) TmaxC = 1.250 ksiTxy = 18.66 MPa 5-16 (a) OA = 0.313 rnm

(b) Upl = 115.7 MPa (T) (b) 0 = 1.865 rnm 5-53ap2 = 77.7 MPa (T) (c) aA = 156.3 MPa (T)Up3 = 0 TmaxA = 78.1 MPa 5-54Tp = 18.98 MPa (d) UB = 135.0 MPa (T) 5-57Tmax = 57.8 MPa Uc = 91.7 MPa (T)IJp = 39.8 J TmaxB = 67.5 MPa

4-77 (a) EL = 25,000 ksi 5-19 o = 0.0638 in.EH = 14,500 ksi 5-20 0= yL

2 5-58(b) UL = 56.5 ksi 6E

UH = 21.5 ksi 5-23 [; = 0.000225 in.

ii'

. i' ANSWERS 689tit,} 5-.27 (a) OAe == 0.1655 in. 5-61 (a) UA = 18.93 ksi

OBe = 0.1780 in. UB == 19.02 ksi(b) Oy = 0.449 in. t (b) FSA = 3.27

,

,:-il'.UA690 ANSWERS ~.~~

5-102 (a) L; = 327 mm 5-145 (Tm = 75.0 psi ?L2 == 131.0 mrn (Ta = 158.3 psi {

(b) Li = 390 mm 5-150 (a) (T, = 171.2 MPa t 6-2 (a:"L2 = 106.8 mm (b) (T, = 96.2 MPa \,5-105 Pmax = 16.63 kip (e) Tmax = 123.1 MPa i5-106 Pmax = 332 kN 5-151 Pmax = 18.00 ksi { 6-5 (a

~.

5-109 Pmax = 3.28 kip 5-153 (a) Tmax = 37.1 ksi ~ (b5-111 B = 2.90 in. (b) a; = -7.51 ksi ~ 6-6 (a,

(t5-113 (a) I1L = 0.0293 in. (T, = 31.8 ksi s~(b) I1L = 0.0789 in. 5-155 (a) b = 14.97 in. t (c

5-114 (a) I1L = 5.71 mm (b) Wi = 0.0223 in. .~ (l. 6-9 (c(b) I1L = 11.87 mrn 5-157 Pmax = 39.0 ksi a*~.5-117 (a) (TA = 40.0 ksi 5-158 (a) 1= 0.268 mm

i (l(TB = 44.4 ksi (b) (Tmax = 318 MPa (T) i ((b) TD = 25.7 ksi 5-161 (a) (T, = 13.00 ksi (T) 'I!(e) TmaxA = 20.0 ksi (b) Ps = 1.875 ksi J; 6-11 (

TmaxB = 22.2 ksi 5-163 (a) F = 900 Ib

f(

(d) oe = 0.419 in. (b) (T, = 100.0 ksi (5-118 (a) (TA = 245 MPa 5-165 D = 3 112 in. 6-12l

(TB = 275 MPa 5-166 W406 X 39 t(b) Te = 119.5 MPa5-169 (a) L = 10.00 in. I(e) TmaxA = 122.7 MPa 6-15TmaxB = 137.5 MPa (b) a = 5.00 in.(d) OD = 8.40 mm (e) b = 7.00 in. 6-16(d) d = 20.0 in.

t5-121 (a) (TA.= 32.0 ksi

5-170 Wmin = 65.2 mm(TB = 36.0 ksi

5-173 dAB = 0.921 in. 6-19(b) ~D = 0.1829 in.(e) tc = 32.6 ksi dBe = 1.128 in.

i 6-21(d) TmaxA = 16.00 ksi 5-174 Dnom = 127 mmTmaxB = 18.00 ksi 5-177 (TAB = 4.07 ksi (C) ~.

5-122 (a) P = 1225 kN (TBe = 34.0 ksi (T) I 6-22(b) OD = 6.00 mm (TeD = 12.73 ksi (T)(e) ~D = 60.0 mm 8 = 0.0213 in. I5-127 (T = 11.95 ksi 5-180 (TBD = 120.0 MPa (T)5-128 (T = 3.70 MPa (TCE = 133.3 MPa (C) 6-26OA = 3.49 mrn ! l5-131 t = 0.400 in. 5-181 Pmax = 167.9 kip t 6-295-132 t = 8.38 mm 5-184 (TB = 87.8 MPa (T) I5-135 t = 0.311 in. (Ts = 285 MPa (T) 6-355-136 t = 6.00 mm 5-185 t = 0.1833 in.5-140 (a) a.; = 5.34 MPa 5-188 (a) (Te = 240 MPa (T) I(b) t; = -1.851 MPa (TD = 156.0 MPa (C)(e) Tmax = 4.75 MPa (b) OA = 1.944 mm 6-365-141 (a) (TI = 23.5 ksi 5-189 (Ta = 496 psi (T) 6-39(T2 = 16.78 ksi (T, = 1489 psi (T)

(b) P = 340 psi 5-192 (a) (Trnax = 186.5 MPa I(e) FS = 3.13 (b) W = 0.213 mm J

5-142 (a) (Tn = 56.0 MPa 6-40(b) r; = 21.1':)MPa Chapter 6(c) Tmax = 42.0 MPa(d) Tmax = 43.4 MPa 6-1 (a) TAB = 80 ft . kip ~

TBe = 20 ft . kip r

ANSWERS 691

T CD = 20 ft . kip 1. (e) (}EIA = 0.1319 rad -1.-TDE = 45 ft . kip 1. 6-43 (a) T! = 32.0 in .. kip

6-2 (a) TBe = 500 N . ill 1. (b) O"max = 20.4 ksi (T)T CD = 400 N . ill 1. (e) O"max = 6.05 ksi (C)TDE = 250 N . m 1. 6-45 Power = 9340 hp

6-5 (a) T = 11.46 ksi 6-46 d = 85.9 mID(b) 0 = 0.0688 rad 6-49 Power = 170.3 hp

6-6 (a) T = 65.8 MPa(b) T = 43.9 MPa

6-50 (a) Power = 286 kW

(c) (J = 0.0274 rad(b) ()= 0.0600 rad

(d) 0 = 0.0713 rad 6-53(a) d = 1.399 in.

6-9 (a) TAB = 5.66 ksi(b) d, = 2.92 in.

TBe = 2.26 ksi(c) ,1W= 76.5%

(b) (JBIA = 0.01886 rad6-54 dmin = 84.4 mm

(c) ()ClA = 0.0245 rad 6-57(a) Tmax = 19.26 ksi

6-11 (a) Tmax = 11.21 ksi(b) Tmax = 3.80 ksi

(b) ODIB = 0.00764 rad -r- (e) (}C/A = 0.0355 rad(c) (JDIA = 0.00611 rad -1.- 6-58

(a) d, = 80.4 mID

6-12 (a) TDE = 139.3 MPa(b) d2 = 57.9 mID

(b) (JDIB = 0.00389 rad -1.-(e) (JCIA = 0.0538 rad

(e) ()EIA = 0.0894 rad -1.- 6-61Tb = 8.91 ksi

6-15 (a) Tmax = 4.75 ksi6-62 (a) Ts = 13.49 MPa

(b) BClA = 0.00335 rad -f-Tm = 15.35 MPa

6-16 (a) d, = 70.5 mID(b) 0= 0.01349 rad

(b) d, = 70.0 mID6-65 (a) (}max = 16.04 ksi

6-19 (a) Tmax = 9.94 in .. kip(b) OB = 0.0321 rad -r-

(b) OA = 0.01559 rad(e) O"max = 16.04 ksi (C)

6-67 (a) Tb = 6.11 ksi6-21 (a) dAB = 0.546 in. Ts = 18.99 ksi

(b) dCD = 0.402 in. Ta = 7.64 ksi(c) L = 2.12 ft (b) (Jb = 0.1048 rad

6-22 (a) dAB = 68.8 rom 6-68 (a) t = 71.0 MPa(b) dBC = 93.4 rom Ts = 72.8 MPa(e) d = 74.9 nun i; = 63.8 MPa

- 6-26 ()=3TL -

(b) ()b = 0.0911 rad

16Gt7fr3 6-71 t = 0.0393 in.

6-29 0=6-72 t = 4.53 mID

7TGC4 6-75 (a) T = 38.2 in .. kip

6-35 (a) a; = 4.12 ksi (T)(b) Tmax = 600 psi

Tnt = 1501 psi(e) T = 674 in .. kip

(b) O"max = 4.39 ksi (T) and (C) 6-77 Ts = 12.72 ksiTmax = 4.39 ksi Tb = 5.26 ksi

6-36 Tmax = 9.71 kN' ill 6-78 (a) T= 15.81 kN ill

6-39 (a) TBe = 500 ft Ib(b) Ts = 158.3 MPa

(b) TCD = 250 ft Ib (c) Ta = 32.6 MPa(c) O"maxA = 11.46 ksi (T) and (C) 6-81 T = 201 in .. kip

O"maxB = 15.64 ksi (T) and (C) 6-82 (a) Tb = 87.3 MPa

6-40 (a) TAB = 47.8 MPa(b) Ts = 116.4 MPa

~ TBe = 9.55 MPa (c) (JBIA = 0.0582 rad -r-TCD = 66.9 MPa 6-91 up! = 5.10 ksi (T)TDE = 9.55 MPa O"p2 = 1.1 19 ksi (C)

(b) O"max = 66.9 MPa (T) or (C) Up3 = 0

692 ANSWERS

Tmax = Tp = 3.11 ksi 6-151 d = 3.00 in. , 7-33 V= -(Jp=25.lo~ 6-152 (a) d = 203 mm M= -

6-92 upl = 56.6 MPa (T) (b) d = 140 mm 7-34 V=wUp2 = 29.3 MPa (C) (e) W)Wh = 2.85

M=~up) = 0 6-155 d60 = 4 lI8 in.Tmax = Tp = 43.0 MPa d6000 = 7/8 in. 7-37 (a) V(Jp = 35.70 ~ Use 6000 rpm M

6-95 Pmax = 182.0 kip 6-156 d= 50.0mm (b) V6-97 Upl = 8.25 ksi (T) 6-159 d.Id, = 1.221

N.Up2 = 2.06 ksi (C) Independent (e) Vup) = 0 ~ '"6-160 (a) d = 75 mmTmax = Tp = 5.16 ksi '. (d)fe, = 26.60 ~ (b) d = 20 mm A

6-163 (a) Tmax = 9.05 ksi f;6-98 Pmax = 1710 kN (C)(b) ()BIA = 0.01811rad -r- {. 7-38 (a) J6-101 dmin = 1.662 in. ~ }(e) (JCIA = 0.0487 rad -r- .>~ (b) I6-103 P = l l.Ll kip 6-164 (a) dAB = 63.4 mfn ~'

T = 4.16 in .. kip :,dBC = 79.9 mm ~ (e)6-104 P = 674 kN (b) (JAIC = 0.0483 rad ti

~cT= 3.07 kN m 6-167 (a) Tmax = 1091 in.. Ib t (d)6-109 T = 18.11 ksi (b) (J = 0.1l12 rad f6-110 r= 81.5 MPa t;6-169 Power = 175.8 hp ~ 7-41 (a)a6-113 r = 0.540 in. 6-172 (a) TmaxS = 105.7 MPa i6-115 n= 13.37 ksi Tmaxn = 31.6 MPa ~ (b)

(b) BDIA = 0.00936 rad -L- ~ (e)6-117 (a) T = 360 in.. kip ~(b) T = 390 in.. kip 6-175 d = 2 3/4 in. t

~.6-118 (a) T= 23.6 kN m l 7-42 (a)(b) %! = 33.3% Chapter 7 t (b)6-121 (a) Ymax = 0.00364 (e)(b) T = 296 in.. kip 7-1 M; = 64.0 in .. kip f(e) Tp = 10.91 ksi 7-2 M; = 33.8 kN . m

~.

6-123 (a) T = 400 in.. kip 7-5 M; ~ 102.7 in.. kip i 7-45 (a(b) (J= 0.216 rad 7-6 (a) o = 5.00 MPa (T)6-124 (a) T = 54.4 kN . m (b) Uc = 2.50 MPa (C) l(b) () = 0.500 rad (e) UD = 6.25 MPa (T) ! (\:6-127 T = 756 in .. kip 7-9 (a) Ubot= 8.51 ksi (T) t6-128 T= 20.9 kN m (b) utop = 5.41 ksi (C)

6-131 (a) T = 295.3 in.. kip 7-10 (a) U = 252 MPa 7-46 C(b) TmaxS = 18 ksi (b) M; = -5.25 kN m

Tmaxb = 23.7 ksi 7-13 (a) M; = 2630 in.. kip6-137 Tmax = 2.52 in .. kip (b) M; = 4630 in.. kip

6-138 (a) TmaxR = 1176 N m 7-14 M; = 8.08 kN . m ITmaxS = 1380 N m 7-17 utop = 19.67 ksi (C) t 7-49

(b) OR = 0.00968 rad CTbot= 14.50 ksi (T) 7-54(Js = 0.00909 rad 7-18 M; = 2.46 kN . m

6-141 tmin = 0.0983 in. 7-21 Ubot= 15.00 ksi (T)6-143 (a) Tmax = 7.25 ksi 7-22 Mmax = 37.0 kN m J

(b) Bc/A = 0.01042 rad -1- 7-29 V= -1000 Ib 7-556-144 T= 2.47 kN m M = -1000x ft . lb6-147 T = 320 in .. kip 7-30 V=-2xkN

6-148 t = 1.750 mm M= -~ kN m

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