! $ " % # Ledad knutpunkt Stabil Instabil Stabil & ' # $ ! ( $ ( # ! " ) # " $ # & E F A Modell B R1 C Friläggning L y Tryckt A R1 Dragen x Knutpunktskrafter #$ * + # " , $ Fx = 0, Fy = 0, MA = 0 # * -$ - + " D R2 . # $ $ $ Fx = 0, + . %0 , Fy = 0 ' *1 2 $ & 0 / ( $ . $ ! # 3 & '" ! 34- 5 $ . θ 7 56 $ ' 6 # $ # 34 - . $ & 34- 5 5 # . / x $ ( ! x’ $ $ 8 ) F2 9 $ ! # # & P $ F1 * : $ + . ' " + M E = 0 : 5T − 30 ⋅10 − 20 ⋅ 5 = 0 T = 80 kN Fx = 0 : T cos 30 − Ex = 0 Ex = 69.3 kN Fy = 0 : E y + T sin 30 − 50 = 0 E y = 10 kN ; $ + Fy = 0 : AB sin 60 − 30 = 0 AB = 34.6 kN, D Fx = 0 : AC − AB cos 60 = 0 AC = 17.3 kN, T . 7 # < , *+ 1+ Fy = 0 : BC sin 60 − AB sin 60 = 0 BC = 34.6 kN, T Fx = 0 : BD − AB cos 60 − AB cos 60 = 0 BD = 34.6 kN, D ( " + Fy = 0 : CD sin 60 − BC sin 60 − 20 = 0 CD = 57.7 kN, D Fx = 0 : AC + cos 60 ( BC + CD ) − CE = 0 CE = 63.5 kN, T 7 + Fy = 0 :10 − DE sin 60 = 0 DE = 11.6 kN, T 2 Fx = 0! 0 ! $ ! $ #$ + $ ' * ' = 9 # ! ! * *+ =4- > $ $ =4 - , ' $ Fx = 0, Fy = 0, . MA = 0 ) $ ) 4 ? * *+ . * $ 0 # 3 -. ! ! * / $0 +0 +* * "66 ( : > + ; ; : +* M L = 0 : 200 ⋅15 −5.25CB = 0 CB = 571 kN,Tryck ( / (+ M C = 0 : 200 ⋅12 − 4 KL cos θ = 0 $ + / *0 β = tan −1 ( 3 5.25 ) = 29.72 BL = 4 + 3 M P = 0 : (12 − 9.60 ) 200 − −9.60CL cos β = 0 CL = 57.6 kN, Tryck 0 /β 1 θ = tan −1 ( 2.5 6 ) = 22.62 KL = 650 kN, Drag . θ . + 6.5 − 4 = 5.25 m 6 PC = 4 tan θ = 9.60 m 2 + / Fx = 0 : KL cos θ − CB − CL sin β = 0 < = - 3 * : + ,+ 4 M G = 0 :10 ⋅ 8 + 10 ⋅16 + 10 ⋅ 20 = RA ⋅ 24 RA = 18.3 kN / + CK AK = DJ AJ CK = 6 ⋅ 8 12 = 4 m . . " # @ 3 #% + / ( + " ' + M A = 0 : 12 CJ sin 45 − 10 ⋅ 4 − 10 ⋅ 8 = 0 CJ = 14.1 kN, Tryck ' "+ . 4 $ $ 3 + M G = 0 :12 DJ + 10 ⋅16 + 10 ⋅ 20 − −18.3 ⋅ 24 − 14.1sin 45 ⋅12 = 0 Svar: DJ = 16.6 kN, Drag ? / /$ ! " B " 3 =C " # # " * ' + 5 * 5 " 2 ( 4. *+ 5 " 22 ( 47 # 5 + 5 6A? ( 4. - # " * ' + 5 * 5 2 ( 4.-*+ 5 24"- ( 47+ 3 5 2 ( 47-5 + 5 242- ( 4.5 3 56 ( # " * , ' + 5 * 5 " 2 ( 47-*+ 5A ( 47+ 3 5 = 2 ( 47-3 5 & 2 ( 4.5 5 + 5 = 2 ( 4.* 5 " 2 ( 4.- # " $ ' 9 # ' + 5 * 5 *+ 56 5 *6 5 3 + 5+ 6 5 + 3 5 3 5 2 ( 475 66 ( 4.5 66 ( 475 & ( 4.- A 4 5 46 5 " 66 ( 4.- 1> 5 6 ( # " % > & 9 # " D E # @ & & * ' + 5 45+ 45 5+ 5 * 5 *+ 5 *4 5 3 # " 5 22 ( 475+ 3 53 56 ( ' *+ * * ' + *+ 5 & " 47* 5 6A6 ( 4.5 ? ( 4.- # " ( * +3 + ' + + 3 5 & &= 4.+ 56 ( 5 & 66 ( 47- 6 # " ) 7 4 , *+3 * + ' + + 3 5 366( 47+ 5 ?66( 475 "6?6( 4.- # " * *+ * * # ' + *+ 5 ?" ( 4.* 5 "6"6( 4.5 ?"=6( 47- # " 7 * 6 4 ' + *6 5 2 3 ( 4.6 4 5 " ( 4.- 3 6 36 *6 A6 # " # * 3 3 4 6 4 ' + 3 5 3 ( 4.3 4 5 A ( 4.6 4 5 &6 ( 47- "