Uploaded by User2309

3Fackverk

!
$
"
%
#
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-
"