treliças, Notas de estudo de Engenharia Civil

Baixe treliças e outras Notas de estudo em PDF para Engenharia Civil, somente na Docsity! ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS 2 m 2 m 1,5 m 2 tf 1 tf 4 2 1 3 a b c d 2 tf Fc Fd 1 tf Fa Fb 1 tf 2 tf 1 2 Fb Fc Fd 3 1 2 ! sen! = 1.5 / 4,27 = 0,35 cos! = 4 / 4,27 = 0,94 "X = Fa.x 0,94 + Fb = 0 0,94Fb + Fa = 0 "Y = Fa.x 0,35 -- 1 = 0 Fa = 2,84 Fb = -2,67 2,84 "X = -Fc.x 0,94 -Fd.x 0,94 +2,84.x 0,94 = 0 "Y = Fc.x 0,35 -Fd. x 0,35 -2,84. x 0,35 - 2 = 0 Fc = 5,69 Fd = -2,84 "M3 = 0 1 x 4 + 2 x 2 – Fc x 4 x 0,35 = 0 Fc = 5,69 "M1 = 0 2 x 2 + Fd x 4 x 0,35 = 0 Fd = 2,84 "M2 = 0 1 x 2 + Fb x 0,75 = 0 Fb = - 2,67 T C a 2,84 b 2,67 c 5,69 d 2,84 ! ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS 3 tf Fd Fe 1 tf 2 tf 2 tf 1 tf 1 2 3 4 a b c d e f g h i 6 x 2 m 3 m 4,5 tf 4,5 tf De imediato: Fc = Fi = 0 Fb = Ff !# !2 Fa Fb ! 4,5 tf 1 ! 2 tf # ! Fg Fh 1 tf sen! = 0,45 cos! = 0,89 sen# = 0,83 cos# = 0,55 "X = Fa. x 0,89 + Fb = 0 "Y = 4,5 - 1+ Fa. x 0,45 = 0 Fa = -7,83 Fb = 7,0 7,83 "X = Fd. x 0,89 + Fe. x 0,89 +7,83. x 0,89 = 0 "Y = Fd. x 0,45 - Fe. x 0,45 +7,83. x 0,45 - 2 = 0 Fd = - 5,59 Fe = - 2,24 7,0 2,24 "X = Fh + Fg. x 0,55 + 2,24 x 0,89 - 7,0 = 0 "Y = - 2,24. x 0,45 + Fg. x 0,83 = 0 Fg = 1,2 Fh = 4,33 ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS 4 2 tf Fg Fh Fi Fj 5 Fe Ff 2 tf # 3 11 "X = Ff – 11 + Fe x cos# + Ff = 0 "Y = -2 + Fe x sen# = 0 Fe = 2,83 tf Ff = 9,0 tf 12 3 2,83 "X = Fg x cos! + 12,3 x cos! - 2,83 x cos# = 0 "Y = Fg x sen! + 12,3 x sen! - 2,83 x sen# - 2 - Fh = 0 Fg = - 3,0 tf Fh = - 10,1 tf "X = Fj – 9 + Fi x cos$ = 0 "Y = - 10,1 + Fi x sen$ = 0 Fj = 7,0 tf Fh = 3,61 tf 10,1 9,0 ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS 6,5 tf 1 tf 2 tf 2 tf 1 2 3 4 5 Fh 6,5 tf 1 tf 2 tf 2 tf 1 2 3 4 5 Fh Fi Fj 6 Fg Ff "M1 = 0 2 x 4 + 2 x 2 – Fi x 4 x 0,832 = 0 Fi = 3,61 "M6 = 0 5,5 x 6 – 2 x 4 – 2 x 2 – Fj x 3 = 0 Fj = 7,0 "M5 =0 5,5 x 4 – 2 x 2 + Fh x 4 x 0,447 = 0 Fh = - 10,1 "M4 =0 5,5 x 4 – 2 x 2 – Ff x 2 = 0 Ff = 9,0 "M1 =0 2 x 2 + 2 x 4 + Fg x 4 = 0 Fg = - 3,0 ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS 6,5 tf 1 tf 2 tf 1 2 3 Fd Fc Fb 6,5 tf 1 tf 2 tf 1 2 3 4 Fd Fe Ff "M3 = 0 5,5 x 2 + Fd x 2 x 0,447 = 0 Fd = - 12,3 "M1 = 0 2 x 2 – Fe x 2 x 0,707 = 0 Fe = 2,83 "M1 = 0 2 x 2 + Fc x 2 = 0 Fc = - 2 "M2 = 0 5,5 x 2 – Fb x 1 = 0 Fb = 11,0 Barra T C a 12,3 b 11,0 c 2,0 d 12,3 e 2,83 f 9,0 g 3,0 h 10,1 i 3,61 j 7,0 k --- --- ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS 3 tf 1 tf 1 2 3 Fd Fc Fb 3 tf 1 tf 1 2 3 4 Fd Fe Ff "Y = 3 – 1 + Fe x 0,707 = 0 Fe = - 2,83 "M3 = 3 x 4 – 1 x 2 + Fd x 2 = 0 Fd = -5 "Y = 3 – 1 – Fc x 0,707 = 0 Fc = 2,82 "M2 = 3 x 2 – Fb x 2 = 0 Fb = 3,0 3 tf 1 tf 2 tf 1 2 3 4 5 Fh Fg Ff "Y = 3 – 1 – 2 – Fg x 0,707 = 0 Fg = 0 "M4 = 3 x 6 – 1 x 4 – Ff x 2 = 0 Ff = 7,0 "M5 = 3 x 8 – 1 x 6 – 2 x 2 + 2 x Fh = 0 Fh = - 7,0 ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS 2 m 6 x 2 m 1 tf 2 tf 2 tf 2 tf 2 tf 2 tf 1 tf a b c d e f g h i j k l m 1 2 3 4 5 6 7 8 6 tf 6 tf 6 tf Fa Fb 1 2 6 tf 1 tf Fd Fc "Y = 6,0 + Fa = 0 Fa = - 6,0 "X = Fb = 0 "X = Fd + 0,707 x Fc = 0 "Y = 6,0 – 1,0 – 0,707 x Fc = 0 Fc = 7,07 Fd = - 5,0 Fe Fh 3 7,07 0,0 "X = Fh – 7,07 x 0,707 = 0 Fh = 5,0 "Y = Fe + 5 x 0,707 = 0 Fe = - 5,0 ESTÁTICA DAS CONSTRUÇÕES - TRELIÇAS Fi Fl 5 2 tf Ff Fg 4 "X = 5,0 + Ff + Fg x 0,707 = 0 "Y = 5,0 – 2,0 – Fg x 0,707 = 0 Fg = 4,24 Ff = -8,0 5,0 5,0 "X = Fl – 5,0 – 4,24 x 0,707 = 0 Fl = 8,0 "Y = Fi + 4,24 x 0,707 = 0 Fi = - 3,0 4,24 5,0 2 tf Fj Fk 6 2 tf Fm Fn 8 8,0 3,0 "X = Fj + 8,0 + Fk x 0,707 = 0 "Y = 3,0 – 2,0 – Fk x 0,707 = 0 Fk = 1,414 Fj = - 9,0 "X = Fn + 9,0 = 0 Fn = -9,0 "Y = 2 + Fm = 0 Fm = -2,0 9,0