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\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd 50 20 50 20 Figura 3.40: Figura do exerc´\u131cio 4 5. Um eixo de comprimento 1, 6 m e sec¸a\u2dco vazada representada na figura 3.41 (di- menso\u2dces em mm) esta´ sujeito a um torque de 90 Nm. Dado o mo´dulo de eslas- ticaidade transversal 80 GPa, calcular as tenso\u2dces nos pontos a e b e o a\u2c6ngulo de troc¸a\u2dco. Resposta 4, 732 MPa e 0, 005543 rad b 1540 15 40 R=38 4 o a 2 4 Figura 3.41: Figura do exerc´\u131cio 5 6. A figura 3.42 representa a sec¸a\u2dco transversal de um tubo de paredes finas, de alum\u131´nio com \u3c4 = 85 MPa e G = 27000 MPa. o trecho CD tem forma semi-circular. As dimenso\u2dces externas esta\u2dco indicadas em mm. As espessuras sa\u2dco e1 = 4 mm em AB e e2 = 3 mm em ACDB. calcular o momento de torc¸a\u2dco ma´ximo admiss´\u131vel e os valores correspondentes do fluxo de cisalhamento, das tenso\u2dces nos pontos P e M, e do a\u2c6ngulo de torc¸a\u2dco por metro de comprimento. Resposta 192, 56 kN; 255 N/mm; 85 MPa e 63, 75 MPa; 0, 009095 rad 7. Um eixo tubular de parede fina, com dia\u2c6metro interno de 100mm esta´ sujeito a um torque de 5675Nm. Calcular a espessura da parede para uma tensa\u2dco admissivel ao cisalhamento de 91Mpa, usando a teoria aproximada de tubos de paredes finas e usando a teoria exata de torc¸a\u2dco. Resposta 3, 7mm e 3, 8mm. 8. Deduzir as propriedades para ca´lculo de \u3c4 e \u3b8 em um tubo circular de parede fina (raio \u201dme´dio\u201dr e espessura e), sujeito a um torque T. comparar com as propriedades deduzidas para sec¸a\u2dco anular. 65 \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd 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