transversal frame.ppt
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7/29/2019 TRANSVERSAL FRAME.ppt
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DESIGN OF THE TRANSVERSAL FRAME
1. Static scheme-preliminary conditions
2. Actions and combinations
3. Connection between the truss and the column
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I k I k A y A yx s s i i ( )2 2
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dc
d
ddc
c
c KK
K
MMKK
K
MM
;
111 hMI Ni
M
iii IIII 0
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1. STATIC SCHEMES
Articulated (hinged) connection between the truss and the column
Rigid (fully restraint) connection between the truss and the column
Left- Static scheme and rigidities (Ir, I -second moment area of the truss and of the column with constant cross section);
Right- Transversal frames carrying crane girders ( Is, Ii - second moment areas of the top and bottom part of the columns)
Models of the frame geometry for different layouts ofthe connection between the column and the truss
Effect of the redundancy of a rigid connection: a)- the column on the truss;b) the truss on the column; c) bending moment effects upon the chords of the truss
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Determination of the redundancy effects upon the truss members
N N N
N N N
ik ik ik
I
ik ik ik
I
0
0
( )
( )
max
min
N q T
N q T
ik ik ik B
ik ik ik B
( )
( )
max
min
minmax/Bik'B'k'iBik0ikik )T(/MMNN
a. Articulated connection
b. Rigid connection
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1 ,1
1 ikik ik
ik
lN n
E A 2 ,2
1 ikik ik
ik
lN n
E A
,2ikn
ikN
Knowing the values in the restrained joints 1 and 2 and the rotations of the supports for the simple supported truss under
external loading the equilibrium equations may be written.
2
1 ,1
1 ikik
ik
ln
E A
2
2 ,2
1 ikik
ik
ln
E A ,1 ,1
1 ikik ik
ik
ln n
E A
Rotations in the supports induced by unitary bending moments:
Rotations on the supports induced by external actions :
,1ikn internal efforts in the members ik when at the extremities 1 and 2 unitary bending moments are acting
internal forces in the members ik undder external actions
The stiffness of the members k1 and k2 also the coefficients for the transmission necessary in the static computation, k12 and k21
21 2
1 2
k
1
2 2
1 2
k
12
2
k
21
1
k
c. Particular situation uneven restraining conditions
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Stiffness of the elements of the transversal frame
The static computation follows the stages:
a)-preliminary design of the cross section of the girder considered simply supported for determining the moment of inertia Ir;
b)-preliminary design of the top and bottom part of the stanchion on the basis of a simplified scheme for determining the moments
of inertia Is
and Ii
;
c)-static computation of the frame for certain loads in order to determine the maximum sectional efforts.
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LOADING SCHEMES ON THE TRANSVERSAL FRAME WITHOUT CRANE GIRDERS
a)-the dead and live loads are always present;
b)-only one alternative of each temporary loads presented on the schemes may taken once (for ex. snow on the left side or on the
right side of the roof or on the whole roof, and so on);
c)-the snow and the maximum temperature effects are not possible together;
d)-the action of the force RF is always taken together with the action of the pair of forces R-r (or R-r); the action of the forces R-r
may be taken without the action of the force RF;
e)-if the seismic load is taken into account then neither the crab effects nor the wind are considered.
RULES FOR COMBINATIONS
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LOADING SCHEMES AND INTERNAL FORCES AND MOMENTS FOR DESIGN OF
THE COLUMN IN FRAMES WITH CRANE GIRDERS
M N T N M Tcoresp corespmax max, , ; , ,
Reactions from crane girder on the columns
Simplified schemes for the determinations of
sectional efforts on columns
Combinations of the sectional efforts for the design of the columns
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V qL
p p
H 2
ii
ss
hG
hG
150
100V q
Lz z
H 2
Ti
Ti
LqPr
LqPR
min
ma x R FF c i
Tvv
Tvv
Lpq
Lpq
''
1654
321
;;
;;)(
eRMePMePM
ePMeGMeVVVM
sii
sssvzp
e
b be
be
t be
t bi s is
p s
i
p is
2 2 2 2; ; ;
i
s
I
In 0
-no= 0.2 for cranes with low lifting capacity and heavy roofs;
-no= 0.08 for cranes with heavy lifting capacity and light roofs.
STAGE II: the static computation of the transversal frame is started considering a certain ratio I Is i/
One span, hinged connection 11 1 1 0 X Pn
I
I
s
i
X
M m ds M m ds
m ds n m ds
P
P
s
P
i
s i
1
1
11
1 1
1
2
1
2
11 12
1
2
12
12
1
2
1
2
1 1
1
mE I
ds mE I
dsE I
m dsE I
m ds
E Im ds n m ds
s i sis s i i
s s i
( )
11 1
1 1
1 1
1 1
1
P
P
ss
P
ii s
P
s i
P
i
s
P
s
P
i
M m
E Ids
M m
E Ids
E IM m ds
E IM m ds
E IM m ds M m ds
( )
M M m XP 1 1
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11 1 1 0 X P
is
iP
sP
P
dsmndsm
dsmMndsmM
X2
1
2
1
11
11
1
1M M m XP 1 1
if XR
II Stage. Correction of the reactions
33
1
33
1i
1
h
EI3
11n
n
h
EI3r
I Stage. Determine the reactions frame considering the joint is blocked
0RRf
The stages for the computation of the one redundancy degree system
irR
i
f
r
R
f1
1111 RR
rXrXX
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I Stage. Reactions, bending moments in the restraint at the base and stiffness to
horizontal displacements of the columns with variable cross section hinged at the top
31
2s
2
1K;
I
In;
h
h
n
11n;
n
11n;
n
11n 4
4
3
3
2
2
223K1PX
1PXhM iA
220ih
KM3X
0
iA MhXM
4i phK4
3X
2
phXhM iA
3
3
1ii
1
h
EI3RX
1;hRM iA
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Connection between the column and the roof truss
b,c
2
v
2
h
1
v
1
2
i
maxih
11
NNNR
n
VN;
n
HT
y
yMN
eVeHTM
0
1
1
M
y2
shear
2
tech
angle
vp2
vt
2
ht2
0
ht
2
v
22i
ma x2h
22
f3
td
N;
4
d
N
4
d
N;
4
d
N
n2
VN;
n2
HT
h2
hMN
eVeHTM
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