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Centro Universita´rio Internacional Uninter Disciplina: Princ´ıpios de Mec. e Resisteˆncia dos Materiais Professor: Neil Franco de Carvalho LISTA DE EXERCI´CIOS 1) Encontre as reac¸o˜es de apoio sendo : • P1 = 1000 N (para baixo) • P2 = 500 N (para baixo) Resp.: a) Ay = 875N(↑);By = 625N(↑) b) Ay = 650N(↑);By = 800N(↑) c) Ay = 650N(↓);By = 800N(↑) d) Ay = 650N(↑);By = 800N(↓) e) N.D.A 1 Load Diagram P1 = 1000, N (down) Ay = 875,00 N (up) P2 = 500, N (down) By = 625,00 N (up) (m) X 0 0,5 1,5 2, A B P1 P2 exercicio1 Shear Diagram (N) (m) X 875,0 875,0 -125,0 -125,0 -625,0 -625,0 0,0 Moment Diagram (N-m) (m) X 2,0 0,0 437,5 312,5 0,0 2) Encontre as reac¸o˜es de apoio sendo : • P1 = 1000 N (para baixo) • P2 = 500 N (para baixo) Resp.: a) Ay = 250N(↑);By = 500N(↑) b) Ay = 750N(↓);By = 500N(↑) c) Ay = 250N(↑);By = 1250N(↑) d) Ay = 250N(↑);By = 750N(↓) e) N.D.A 3 Load Diagram P1 = 1000, N (down) Ay = 250,00 N (up) P2 = 500, N (down) By = 1.250,00 N (up) (m) X 0 0,5 1, 1,5 2, A B P1 P2 exercicio2 Shear Diagram (N) (m) X 250,0 250,0 -750,0 -750,0 500,0 500,0 0,0 0,0 Moment Diagram (N-m) (m) X 0,67 1,5 0,0 125,0 -250,0 0,0 0,0 3) Encontre as reac¸o˜es de apoio sendo : • P1 = 100 N (para cima) • P2 = 500 N (para baixo) Resp.: a) Ay = 100N(↑);By = 200N(↑) b) Ay = 200N(↑);By = 500N(↑) c) Ay = 200N(↑);By = 300N(↑) d) Ay = 200N(↑);By = 300N(↓) e) N.D.A 5 Load Diagram P1 = 100, N (up) Ay = 100,00 N (up) P2 = 500, N (down) By = 300,00 N (up) (m) X 0 1, 2, 3, A B P1 P2 Exercicio3 Shear Diagram (N) (m) X 100,0 100,0 200,0 200,0 -300,0 -300,0 0,0 Moment Diagram (N-m) (m) X 3,0 0,0 100,0 300,0 0,0 4) Encontre as reac¸o˜es de apoio sendo : • P1 = 1 kN (para baixo) Resp.: a) Ay = 1kN(↑);MA = 500N.m( ) b) Ay = 1kN(↑);MA = 500N.m(�) c) Ay = 1kN(↑);MA = 3 kN.m( ) d) Ay = 1kN(↓);MA = 1 kN.m(�) e) N.D.A 7 Load Diagram P1 = 1, kN (down) Ay = 1,00 kN (up) Moment A = 3,00 kN-m (ccw) (m) X 0 3, A B P1 Exercicio4 Shear Diagram (kN) (m) X 1,0 1,0 0,0 Moment Diagram (kN-m) (m) X 3,0 -3,0 0,0 9 5) Encontre as reac¸o˜es de apoio sendo : • P1 = 1 kN (para baixo) • P2 = 1 kN (para baixo) Resp.: a) Ay = 2kN(↑);MA = 4, 5 kN.m( ) b) Ay = 4, 5kN(↑);MA = 2 kN.m( ) c) Ay = 2kN(↑);MA = 4, 5 kN.m(�) d) Ay = 2kN(↓);MA = 5 kN.m(�) e) N.D.A 10 Load Diagram P1 = 1, kN (down) Ay = 2,00 kN (up) P2 = 1, kN (down) Moment A = 4,50 kN-m (ccw) (m) X 0 1,5 3, A B P1P2 Exercicio5 Shear Diagram (kN) (m) X 2,0 2,0 1,0 1,0 0,0 Moment Diagram (kN-m) (m) X -4,5 -1,5 0,0 6) Encontre as reac¸o˜es de apoio sendo : • P1 = 2 kN (para cima) • P2 = 2 kN (para baixo) Resp.: a) By = 2kN(↑);MB = 2 kN.m( ) b) By = 2kN(↑);MB = 2 kN.m(�) c) By = 2kN(↓);MB = 0 kN.m(�) d) By = 0kN(↑);MB = 2 kN.m( ) e) N.D.A 12 Load Diagram P1 = 2, kN (up) By = 0,00 kN (down) P2 = 2, kN (down) Moment B = 2,00 kN-m (ccw) (m) X 0 1, 3, A B P1 P2 Exercicio6 Shear Diagram (kN) (m) X 0,0 2,0 2,0 0,0 0,00,0 Moment Diagram (kN-m) (m) X 3,0 0,0 2,0 2,0 0,0 14 7) Encontre as reac¸o˜es de apoio sendo : • P1 = 150 N (para baixo) • P2 = 150 N (para baixo) • P3 = 300 N (para cima) • P2 = 300 N (para baixo) Resp.: a) Ay = 300N(↑);By = 300N(↑) b) Ay = 75N(↑);By = 225N(↑) c) Ay = 225N(↑);By = 75N(↑) d) Ay = 150N(↓);By = 300N(↑) e) N.D.A 15 Load Diagram P1 = 150, N (down) Ay = 75,00 N (up) P2 = 150, N (down) By = 225,00 N (up) P3 = 300, N (up) P4 = 300, N (down) (in) X 0 0,5 1, 1,5 2, 3, A B P1 P2 P3 P4 Exercicio7 Shear Diagram (N) (in) X 0,0 -150,0 -150,0 -300,0 -300,0 -225,0 -225,0 75,0 75,0 300,0 300,0 0,0 Moment Diagram (N-m) (in) X 3,0 0,0 -1,9 -5,7 -8,6 -7,6 0,0 17
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