Livro Hibbeler - 7ª ed Resistencia Materiais (Livro)

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RESPOSTAS 613 6.90. 6.91. 6.92. 6.93. 6.94. 6.95. 6.96. 6.97. 6.98. 6.99. 6.101. 6.102. 6.103. 6.105. 6.106. 6.107. 6.109. 6.110. 6.111. 6.113. 6.114. 6.115. 6.117. 6.118. 6.119. 6.121. 6.122. 6.123. 6.125. 6.126. 6.127. 6.128. 6.129. 6.130. 6.131. 6.133. 6.134. P = 1,67 kN Umáx = 9,00 MPa Umáx = 105,11 MPa a= 159,88mm Umáx = 160,45 MPa umáx = 166,7 MPa umáx = 142,2 MPa a= 156,2mm b = 89,3 mm b = 53,1 mm h 3M( + ) c= vE, vE,' (umáx)c = bh 2 vE, Et + Ec I a-8 = -77,5 MPa (C), a-D = 77,5 MPa (T), a= -36,87° IMI = 32,24 kN·m a-A = 21,97 MPa (T), a = 63,91 o a-11 = 1,30 MPa (C), a-8 = 0,587 MPa (T), a= -3,74° u A = 1,30 MPa (C), a = -3,74° d = 28,9 mm a-A = 7,40 MPa (T), a-Á = 6,40 MPa (T), a= 25,25° ( IyMz + Myfyz ) _ a = O, b = - 2 , c - lyfz - lyz d = 62,9 mm u A = 293 kPa (C) u; = 293 kPa (C) u A = 2,60 MPa (T) u A = 2,60 MPa (T) IzMy+M)yz IJz - 1;.z h= 41,3 mm, M = 6,60 kN·m ( Ua ç o)máx = 3,70 MP a, ( u m)máx = 0,179 MP a Ua ç o = 62,7 MPa, Um = 4,1 MPa Ua ç o = 10,37 MPa, Um = 0,62 MPa (umáx)aço = 9,42 MPa, (umáx)Iat = 6,63 MPa, Na junção: Uaço = 1,86 MPa, lTiat = 0,937 MPa M = 58,8kN·m Mactm = 127,98 kN·m w0 = 10,76 kN/m M = 6,91 N·m a-A = 9,91 MPa, a-s = -8,52 MPa P = 55,2kN u A = 3,82 MPa (T), a-8 = 9,73 MPa (C) a-c = 2,66 MPa (T) 6.135. 6.137. 6.138. 6.139. 6.141. 6.142. 6.143. 6.144. 6.145. 6.146. 6.147. 6.148. 6.149. 6.150. 6.151. 6.153. 6.154. 6.155. 6.156. 6.157. 6.158. 6.159. 6.161. 6.162. 6.163. 6.165. 6.166. 6.167. 6.169. 6.170. 6.171. 6.173. 6.174. 6.175. 6.176. 6.177. a-11 = 792 kPa (C), a-8 = 1,02 MPa (T) P = 3,09 N (a-1)máx = 4,77 MPa a-A = 1,3594 MPa (T), a-8 = -0,9947 MPa (C), uc = -0,0531 MPa (C) u A = 446 kPa (T), a-8 = 224 kPa (C). Não, por conta da concentração de tensão localizada no muro. M = 14,0 kN·m M = 56,57 N·m Umáx = 100,22 MPa r= 5,00 mm u máx = 54,4 MP a a-máx = 384 MP a M = 9,11N·m (u1)máx = 6,77 MPa, (u2)máx = 6,66 MPa L= 950 mm M = 4,46 kN·m M = 455,73 N·m Umáx = 276,48 MPa P = 468,75 N Umáx = 266,67 MPa M = 9,52 kN·m Uuperior = a-inferior = 67,1 MPa Usuperior = a-inferior = 43,5 MPa Me = 50,7 kN·m, MP = 86,25 kN·m 4r3 k = 1,70, z = 3 Me = 82,83 kN·m, MP = 140,63 kN·m Me = 50,35 kN·m,MP = 85,94 kN·m MP = 515 kN·m MP = 225,6 kN·m z = 0,0976bh2, k = 2,34 Me = 3,07 kN ·m,MP = 7,19kN·m - 3h [ 4bt(h - t) + t(h - 2tf] . k - 2 bh3 - ( b - t) (h - 2t ) 3 t 2 z = bt(h - t) + 4 (h - 21) w = 53,4kN/m w0 = 212,67 kN/m, w0 = 269,79 kN/m P = 218,66 N Me = 551,25 kN·m, M = 78,54 kN·m M = 9,03 kN·m

614 RESISTtNCIA DOS MATERIAIS 6.178. 6.179. 6.181. 6.182. 6.183. 6.184. 6.186. 6.188. 6.189. 6.190. 6.191. Capítulo 7 7.1. 7.2. 7.3. 7.4. 7.5. 7.6. 7.7. 7.9. 7.10. 7.11. 7.13. 7.14. 7.15. 7.17. 7.18. 7.19. 7.21. 7.22. 7.23. 7.24. 7.25. M = 96,48 kN·m M = 46,84 kN·m M = 94,7N·m FR = 5,88 kN (amáx)1 = 3,43 MPa (T), (amáx)c = 1,62 MPa (C) 1 V:(x ) = (A - w· x ) ·- 1 · 1 · 1 kN M1(x1)= (-MA + A·x1 - 0,5w · Z = 0,963(10-3) m3, k = 1,22 amáx = 51,51 MPa F = 354,10 kN a A = 2,08 MPa (C) x 1 kN ·m ) · -- 6M a= 3 (cos () + sen8), () = 45°, a = -45° a r A = 1,99 MPa, r8 = 1,65 MPa r máx = 4,62 MP a Vw = 27,lkN Tmáx = 19,87 MPa Vw = 115,04 kN a= 42,26 mm T máx = 0,320 MP a V= 190 kN T máx = 3,16 MP a, (r A )alma = 1,87 MP a, (r A)aba = 1,24 MPa Tmáx = 43,17 MPa Tmáx = 11,79 MPa Tmáx = 3,993 MPa, Taba/AB = 1,327 MPa, TaJma/AB = 3,982 MPa Vaba = 19,08 kN P = 373,42 kN Tmáx = 0,750 MPa 4 3 Tmáx = 5 MPa 3wL Tmáx = 8bd d = 62,5 mm r A = 0,747 MPa, Ts = 0,747 MPa TA = 2,24 MPa, r8 = 2,24 MPa 7.26. 7.27. 7.28. 7.29. 7.30. 7.31. 7.36. 7.37. 7.38. 7.39. 7.41. 7.42. 7.43. 7.44. 7.45. 7.46. 7.47. 7.50. 7.51. 7.53. 7.54. 7.55. 7.57. 7.58. 7.59. 7.60. 7.61. 7.62. 7.63. 7.64. 7.65. 7.66. 7.67. 7.69. V.ba = 2,36 kN r8 = 0,572 MPa, r c= 0,572 MPa Tmáx = 1,467 MPa r A = 0,225 MPa, r8 = 0,225 MPa Vaba = 0,30 kN Para O :=:; y < r;: 4V [ (, ; - J')l - (,J - y ')l 7 = 377 (r - ri)[(r - l) (r[ - i)!] Para r; < y :=:; r0: r = - 4Vc -l) 37T r0 - r; -4--4 ['' ] 4V + '' + ,, 1 .. o o l Entao, Tmáx = 3 77 ( r - rf ) V máx = 2,222 kN F= 3,37kN F = 5,31 kN s = 733 mm s11 = 138,0mm V= 172,5 kN S11 = 303,2 mm P = 30,32 kN P = 238 N s11 = 216,6 mm,s;, = 30,7 mm s11 = 137,6 mm w = 7,06 kN/m q = 21,24 kN/m P = 6,60 kN w0 = 9,73 kN/m Tmáx = 21,58 MPa qc = 38,6 kN/m qA = 215 kN/m qmáx = 232 kN/m VAB = 7,43 kN qA = 1,39 kNjm, q8 = 1,25 kN/m qmáx = 1,63 kN/m qmáx = 84,85 kN/m qA = 65,09 kN/m, q8 = 43,63 kN/m qmáx = 82,88 kN/m d = 72,5 mm qA = 0,00 kN/m, q8 = 83,48 kN/m 3b2 e= 2(d + 3b) ]

RESPOSTAS 613<br />

6.90.<br />

6.91.<br />

6.92.<br />

6.93.<br />

6.94.<br />

6.95.<br />

6.96.<br />

6.97.<br />

6.98.<br />

6.99.<br />

6.101.<br />

6.102.<br />

6.103.<br />

6.105.<br />

6.106.<br />

6.107.<br />

6.109.<br />

6.110.<br />

6.111.<br />

6.113.<br />

6.114.<br />

6.115.<br />

6.117.<br />

6.118.<br />

6.119.<br />

6.121.<br />

6.122.<br />

6.123.<br />

6.125.<br />

6.126.<br />

6.127.<br />

6.128.<br />

6.129.<br />

6.130.<br />

6.131.<br />

6.133.<br />

6.134.<br />

P = 1,67 kN<br />

Umáx = 9,00 MPa<br />

Umáx = 105,11 MPa<br />

a= 159,88mm<br />

Umáx = 160,45 MPa<br />

umáx = 166,7 MPa<br />

umáx = 142,2 MPa<br />

a= 156,2mm<br />

b = 89,3 mm<br />

b = 53,1 mm<br />

h 3M( + )<br />

c= vE, vE,' (umáx)c = bh 2 vE,<br />

Et + Ec I<br />

a-8 = -77,5 MPa (C), a-D = 77,5 MPa (T),<br />

a= -36,87°<br />

IMI = 32,24 kN·m<br />

a-A = 21,97 MPa (T), a = 63,91 o<br />

a-11 = 1,30 MPa (C), a-8 = 0,587 MPa (T),<br />

a= -3,74°<br />

u A = 1,30 MPa (C), a = -3,74°<br />

d = 28,9 mm<br />

a-A = 7,40 MPa (T), a-Á = 6,40 MPa (T),<br />

a= 25,25°<br />

( IyMz + Myfyz ) _<br />

a = O, b = - 2 , c -<br />

lyfz - lyz<br />

d = 62,9 mm<br />

u A = 293 kPa (C)<br />

u; = 293 kPa (C)<br />

u A = 2,60 MPa (T)<br />

u A = 2,60 MPa (T)<br />

IzMy+M)yz<br />

IJz - 1;.z<br />

h= 41,3 mm, M = 6,60 kN·m<br />

( Ua ç o)máx = 3,70 MP a, ( u m)máx = 0,179 MP a<br />

Ua ç o = 62,7 MPa, Um = 4,1 MPa<br />

Ua ç o = 10,37 MPa, Um = 0,62 MPa<br />

(umáx)aço = 9,42 MPa, (umáx)Iat = 6,63 MPa,<br />

Na junção: Uaço = 1,86 MPa, lTiat = 0,937 MPa<br />

M = 58,8kN·m<br />

Mactm = 127,98 kN·m<br />

w0 = 10,76 kN/m<br />

M = 6,91 N·m<br />

a-A = 9,91 MPa, a-s = -8,52 MPa<br />

P = 55,2kN<br />

u A = 3,82 MPa (T), a-8 = 9,73 MPa (C)<br />

a-c = 2,66 MPa (T)<br />

6.135.<br />

6.137.<br />

6.138.<br />

6.139.<br />

6.141.<br />

6.142.<br />

6.143.<br />

6.144.<br />

6.145.<br />

6.146.<br />

6.147.<br />

6.148.<br />

6.149.<br />

6.150.<br />

6.151.<br />

6.153.<br />

6.154.<br />

6.155.<br />

6.156.<br />

6.157.<br />

6.158.<br />

6.159.<br />

6.161.<br />

6.162.<br />

6.163.<br />

6.165.<br />

6.166.<br />

6.167.<br />

6.169.<br />

6.170.<br />

6.171.<br />

6.173.<br />

6.174.<br />

6.175.<br />

6.176.<br />

6.177.<br />

a-11 = 792 kPa (C), a-8 = 1,02 MPa (T)<br />

P = 3,09 N<br />

(a-1)máx = 4,77 MPa<br />

a-A = 1,3594 MPa (T), a-8 = -0,9947 MPa (C),<br />

uc = -0,0531 MPa (C)<br />

u A = 446 kPa (T), a-8 = 224 kPa (C). Não,<br />

por conta da concentração de tensão localizada<br />

no muro.<br />

M = 14,0 kN·m<br />

M = 56,57 N·m<br />

Umáx = 100,22 MPa<br />

r= 5,00 mm<br />

u máx = 54,4 MP a<br />

a-máx = 384 MP a<br />

M = 9,11N·m<br />

(u1)máx = 6,77 MPa, (u2)máx = 6,66 MPa<br />

L= 950 mm<br />

M = 4,46 kN·m<br />

M = 455,73 N·m<br />

Umáx = 276,48 MPa<br />

P = 468,75 N<br />

Umáx = 266,67 MPa<br />

M = 9,52 kN·m<br />

Uuperior = a-inferior = 67,1 MPa<br />

Usuperior = a-inferior = 43,5 MPa<br />

Me = 50,7 kN·m, MP = 86,25 kN·m<br />

4r3<br />

k = 1,70, z = 3<br />

Me = 82,83 kN·m, MP = 140,63 kN·m<br />

Me = 50,35 kN·m,MP = 85,94 kN·m<br />

MP = 515 kN·m<br />

MP = 225,6 kN·m<br />

z = 0,0976bh2, k = 2,34<br />

Me = 3,07 kN ·m,MP = 7,19kN·m<br />

- 3h [ 4bt(h - t) + t(h - 2tf] .<br />

k - 2 bh3 - ( b - t) (h - 2t ) 3<br />

t<br />

2<br />

z = bt(h - t) + 4 (h - 21)<br />

w = 53,4kN/m<br />

w0 = 212,67 kN/m, w0 = 269,79 kN/m<br />

P = 218,66 N<br />

Me = 551,25 kN·m, M = 78,54 kN·m<br />

M = 9,03 kN·m

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