A "
50 N/ N/mm mm2 !
B
C
40 N/ N/mm mm2 35 N/ N/mm mm2
2 ! N/mm
2$ = 23° 10 Q1 (54,5) #II
O
10
#I
C
20 30 Q2 (30,–5)
40
50
2 # N/mm
60
–10
2 ! N/mm
10 Q2 (54,5) #II
O
10
#I
C
20 30 Q1 (30,–5)
40
50
2 # N/mm
60
–10 2$ = 23°
2 ! N/mm
2$ = 159°
10
Q1 (–60,5) 2 # N/mm
#II
–60
#I
C –50
–40
–30
–20
–10
O
Q2 (–36,–5) –10
! N/mm
2
Q1 (30,30)
30 20 10 #II
–60
–50
2$ = 37°
C –40
–30
–20
#I
–10 0
10
20
30
# N/mm
40
2
50
–10 –20 –30
Q2 (–50,–30)
10 N/mm2
10 N/mm2 (#y )
15 N/mm2
15 N/mm2
15 N/mm2
15 N/mm2
!
!max
Q1 (#x , !xy )
P2
O
B (#I )
C
#
P1
Q2 (#y ,– !xy ) !max
2p 4p
y
4p
P (2,3)
3p
3p O
x
4p 4p 2p
A
x D x x C
B
2 v 2
u 2
2'
3a !
7 v 7 u 7
7'
P A
B
P 2
C
D
F
EI /2
z
EI
L/4
L/4
L/4
P 2
L/4
B
z
R "
C W
4R
A
1
P
2 !
450 mm
4
3 600 mm
z
w
C B
EI
2EI
2EI l
w ' z
z D
H A
H D
A R A
R D 2l /3
8wl 2/45 B
7wl 2/45
C
8wl 2/45
7wl 2/45
0.173wl 2 29 45
Bending moment is drawn on the tension side of each member
l
A
D
B M c
3a 5a z 1
C
z 2
4a
R c
!
A P
100 kN
P A
C
R A
B
F
R B
z 3.05 m
3.05 m
3.05 m
z 2
3wa
1.5w /unit length
z 1 A
C
D
R A,H
B R A,V E
F
4a
4a
3a
G R G,H 4a
R G,V
P 2
N
" #
h
M
p S
M O N O
O
M A A
N A
p 0
a "
B
N B
C z
M B
7
S 7
8
S 8 z 1
q
9
S 9 z 3
z 2 4
5
q
q
z 5
z 4
6 P
q
P
a
3a
3a
1.17 Pa 0.48 Pa 3 0.27 Pa
0.27 Pa
1.08 Pa
2
1
0.69 Pa
Bending moments drawn on the tension side of each member
1.17 Pa 1.08 Pa
0.48 Pa 0.27 Pa
4 5
0.69 Pa
6
1.08 Pa
0.27 Pa 1.08 Pa
S 1 1
q ! "
45
°
S 2
x
4
2 S 3 3
z
D
C R C r "
F
B r
2000 N C
A
F
B
R A
D R B
z 360 mm
720 mm
720 mm
600 mm
B I
H B 30
°
"
r
C
B
P
y M B
v B
z
P
A
l
y
B
4EI
C
EI
EI v
P
P
z A
D
l /4
l /2
l /4
4P
y
!
k !
v z
l
y
v v 0
P
P
z
l
y
v
!
v 0
P
P
z
l/ 2
l/ 2
w
y
v z e
e
P
P wl
wl
2
2
l
y M B C
v
P
z
B
a y 1
B
M B
P
v 1 b
z 1
A
y A
C
z
v
V B
v B
P
B
P
P
V a
b
b
t
y x
y s c
Centroid of combined section
t s
d s
120 mm
y
x
3 mm
30mm
3.5 mm
N ma
M m U.C a 2.25 kN
135 kN
200 kN 200 kN
200 kN (a)
150 mm (b)
L AC
T
P CG D
M 0
nW
0.915 m
16.7 m
P + !P D
m 2 . 2 1
L M CG
CG
40
°
WV 2 gR V
W
L
0 .9 15 m
T 0.45 m
P
CG
M 0
10.2
AC D
°
W 7 .6 25 m
L " "
CG
V W
WV 2 gR
100 mm
y B
A 10mm E
30
°
C
y
F
x
125 mm
x
C
D
10mm
y
1
t 5a 3a
x
C
y
t 2
3 4a
W
2 A
2W 1
z
4
B
D 3
l /2
l /2
1
y x
24mm
1.25 1. 25 mm
x
C
y
1.25 1. 25 mm
3
2 36 mm
y t
B
N
r
"
x
C
!
r A D
a
1
t
2!
2
S y ! !
S 4
3
x
2!
s
5
# s
3
t r S y
2
x
S
q 12
"
s 1 # s
# s
t
t/ $ t
S y
h
x S
1
2
s 1 d
s 2
3
$ d
4
t
S y
# S
5
3
1
!
S
s 1
x h
s 2 a
b 2
p
l
4
5
3
1
3Sy 2h 2 3Sy b 2h (b + a )
y 3
2
4
T 5
1
x
C (S)
s 2 6 30
8
°
a
s 1
7
2
0.8 mm 1
S y
# S
1.2 mm
100 mm
x
S 1.0 mm
100 mm
3
0.8 mm 4 500 mm
–3
2.14 x 10
0.61 x 10 –3 S y
2
S y
1
S y
# S
0
2.86 x 10 –3 S y
S
3
4
0.61 x 10 –3 S y
h /
12
h /
12
S y 2 (h + 2d )
S y (h + 3d ) h (h + 2d ) S y (h + 2d )
+
3.82 x 10 –3 rad "
2.13 x 10 –3 rad
1.6 mm
2 %
3
1.6 mm C
100 mm
2 mm 50mm 1
4
1.6 mm 200 mm
2
3
1 100 mm
4450 N
75mm
S
x
100 mm
75mm
6 4
5 250 mm
m 3 0 0 m
4450 N B
C
A
D
z R B
4450 N
R C
1250 mm
500 mm
1250 mm
SF in panels = 26669.8 N
y
3
1
5
x
C
2
225 mm
6
4 100 mm 250 mm
250 mm
50kN y
250 mm 15.4
1
28.9
10
2 A10 1
4.5
9
A12
39.8
A9 10
A23
A89
3
A34
44.3
x
C 8
4
4.5 39.8 7
5
15.4
6
Shear flows in N/mm
28.9
y
1
2
240 mm
3
x
8
4 x
C
y
7
6
400 mm
400 mm
180 mm
5 400 mm
44500N 5
6
4 I
II
254 mm
101 mm x
406 mm
101 mm 3
1
2 635 mm
763 mm
A
B
C
q 1
F
1000 mm
q 2
E
D
6 kN R F
R D
1000 mm
2000 mm
B
q 1
q 2
1000 mm h
E 6 kN
A P AB
q 1
1000 mm
P FE
F z R F
z
A
B
C
10 N/mm
21.6 N/mm
300 mm
300 mm
10 N/mm
1.6 N/mm
H
G
F z
300 mm
300 mm
E
21.6 N/mm
D
1.6 N/mm z
30
°
8000 N
300 mm
C
h
21.6 N/mm
200 mm
D 30
°
8000 N
1.6 N/mm
200 mm
F
B
21.6 N/mm h
200 mm
E
10 N/mm
1.6 N/mm
200 mm
G
q 12
2
1
q 1
q 2
q 51
6
200 mm
5 12000N q 3
200 mm
q 45
200 mm
q 23
8000 N
3
q 34
4
600 mm
2
P 2
q 1
400 mm 200 mm
4.0 N/mm P 3
3
1
16.0 N/mm h 200 mm
q 2
5
12000N 16.0 N/mm
q 3
200 mm
4
q 2
5
6
12000 N
q 3 z
600 mm
2
24.0 N/mm
1
26.0 N/mm z
600 mm
3
6.0 N/mm
4
4.0 N/mm z
600 mm
2
26.0 N/mm h
4.0 N/mm
200 mm
6
6.0 N/mm
200 mm
3 8000 N
Bay 1 q 1
Bay 2 q 2
3
q 1
200 mm 2 q 2
500 mm
4 2000 N 1
500 mm
400 mm
Bay 1
q 1
Bay 2
q 3
q 1
q 2
3 200 mm
2 q 2
4
500 mm
1000 Nm
q 3
1 500 mm
400 mm
P 2
Bay 1
q 1
2
P 2
P 1
1
P 1
500 mm
111 250 N q 12
2
q 23
1
!
3
254 25 4 mm
127 12 7 mm
q 52 x
O
q 34 127 12 7 mm
254 25 4 mm 4 q 45
305 m m
5
q 56
6
254 mm
q 12
2
q 23
1
11000 Nm q 51
3
125 12 5 mm x
O 125 12 5 mm
q 24
q 34 4
q 45
300 mm
5
250 mm
3 q 31
q 23 R
10000N
"
2
30
°
x
O
q 12 1
S /unit length P b
q P S AS
q
b
B P z l
S P B +
P B
$P B $z
#z
q #z
q P A +
P A
$P A $z
#z
q #z
S P
P B
P S
P A
P
P B S z
(I + % B ) #z
& +
&
$& $z
#z
b
(I + % A ) #z
1 B 1 q
d
B 2
2
d
q B 1 z l /2
P 1 +
$P 1 $z
#z
P 1 q #z
q P 2 +
$P 2 $z
P 2
#z
q #z
P 1
P 2
P 1 z
(I + % 1 ) #z
& +
$& $z
#z
&
d
(I + % 2 ) #z
S 1
P 1,0
b
q 1 A ' 3
b
q 2
P 2,0
z l
S 2
S 1 P 1 +
P 1
$P 1 $z
#z
q 1 #z
q 1 P 3 +
P 3
$P 3 $z
#z
q 2 #z
q 2 P 2 +
P 2
$P 2 $z
#z
S 2 #z
P 1,0
S 1 P 1
b P 3 b P 2 P 2,0
S 2 z
( I + % )
1 # z
& 1 +
$ v $z
& 1 +
$ v $z
+
$& 1 $z
#z
+
$v $z
#z
( I + % )
3 # z
S /2h
3B
q
1
h
2 h
B
q
S /2h
h
z
l
S /2h P 1 +
$P 1 $z
#z
P 1 q #z
q
P 2 +
$P 2 $z
#z
P 2 #z
S /2h
P 1
P 2
P 2
P 1 S /2h z
(I + % 1 ) #z
& +
$& $z
#z
&
h
(I + % 2 ) #z
S
4
3
2
1
5
6
7
8
y s
2
1
s
d
4 3
x
S
d
6
d
5
2 s
3
s
!
!
1
S 6
4
5
y
p AR,0
S (r
C G
F
3
) 1
B
x D
O
y ) 2
(r
3
S
K M G
J ) 2
O
x I
2AR,0
3'
5' hd 4
2AR 2'
4'
2A'R
hd 4 6'
1' 1
2 d /2
d /2
3
4
6
s
d /2
h
A t
T
B
2t z 2
C
l
z 1 T l
9
F 29 !
l
v 2 !
M 2
2
P /2
3
M 3
F y ,3
P /3
+ 3 1
2
– (b)
P /3
PL/9
– PL/9
– +
(c)
2PL/9
1
PL/4
2
P /3 – P
3
P 2 P = 3 3
4
PL/4
P /3
P 2 P = 3 3
– P
P /3
+ 4 1
2
3
–
(b)
P /3 PL/4
PL/4
–
– 2
3
1
4
+
(c)
PL/12
PL/12
1
M 2
2
P /2
F y ,2
F y ,1
M 3
3
l /2
l
Pl /12
Pl /16
– 1
3 2
+
Pl /6
y 3 (0,a )
x 2 (a , 0)
1 (0,0)
y 3 (2,2)
1 (1,1)
2 (2,1)
x
y 4 (0,2b )
3 (2a ,2b )
x 1 (0,0)
2 (2a ,0)
B (2)
A
D (1)
C
z l
l
l
f 1 =
1 2!
3EI 4ml 3
f 2 =
(b)
1 2!
3EI ml 3
(c)
4
x
EI
1
3EI
2
l
EI
3
z l
l
C (1,2) A
y a z
B
2a
2
"
= 15.1 2
"
= 0.31
(b)
(c)
y
x #
a q i = q j
0
2 1.25 mm
1
150 mm 100 mm O 1.0 mm
x 1.0 mm
4 m 6 0 0 m
3