1. Lecture 4
STEEL INDUSTRIAL BUILDINGS
C.Teleman.StelStructuresIII.
Lecture4
1

2. dc
d
d
dc
c
c
KK
K
MM
KK
K
MM



 ;
111 hMI  N
i
M
iii IIII  0
DESIGNOFTHETRANSVERSALFRAME
Local effects of the fixing between column and truss: moments in the members of the truss
Hinged connection
Rigid connection

3. 1.STATICSCHEMES
• 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 rigid connection
between the column and the truss
Effect of redundancy (rigid connection): a)- the column on
the truss; b) the truss on the column; c) bending moment
effects upon the chords of the truss
Type of structure Ii/Is Ii1/Ii Is1/Ii
Equal bays 7…10 10…30 1,5…3
Internal bays bigger than marginal bays 20…60 2.5…7
Ratio between the stiffness of the current columns of the transversal frames

4. Stiffnessoftheelementsofthetransversalframe
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.

5. STIFFNESSOFTHESTRUCTURALELEMENTSINTHETRANSVERSALFRAME
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.

6. 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 FT 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 FT;
e)-if the seismic load is taken into account then neither the crab effects nor the wind are considered.
RULES FOR COMBINATIONS

7. C.Teleman.StelStructuresIII.
Lecture3
7
Fundamental group of actions:   





 

ik
1i
i0Fk1FminFmaxFFd QQGsauGS
iQ,11Q,1minG,1maxG,13
Accidental group of actions:   ik
1i
i2k11minmaxAd QQsauGGFS 


Rare combinations in limit state of serviceability:   ik
1i
i2k11minmaxAd QQsauGGFS 


Frequent combinations:   





 

ik
1i
i0Fk1FminFmaxFFd QQGsauGS
iQ,11Q,1minG,1maxG,13
Quasi-permanent combinations:   ik
1i
i2minmaxd QsauGGS 


 Permanent and quasi-permanent actions
a) dead loads transferred from the girder: 2
L
qV H
pp 
b) weight of the top (Gs) and bottom (Gi) of the column:
ii
ss
h150G
h100G


 Variable actions
a) snow, transferred from the girder:
ACTIONS,GROUPSOFACTIONSANDCOMBINATIONS
2
L
qV H
zz 
b) Reactions on the top of the column from wind on the roof, Vv, Hv and on the walls:
c) maximum vertical (R) and horizontal reactions (RF) transferred by the runway system
to the columns (determined with the influence lines):




Timin
Timax
LqPr
LqPR
 icF FR






T
'
v
'
v
Tvv
Lpq
Lpq

8. LOADINGSCHEMES(INTERNALFORCESANDMOMENTS)FORDESIGNOF THECOLUMN
FORFRAMESWITHCRANEGIRDERS
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
1654
321
;;
;;)(
eRMePMePM
ePMeGMeVVVM
sii
sssvzp


e
b b
e
b
e
t b
e
t bi s i
s
p s
i
p is


  



2 2 2 2
; ; ;

9.  11 1 1 0  X P








i
2
1
s
2
1
i
1P
s
1P
11
P1
1
dsmndsm
dsmMndsmM
X
11P XmMM 
 if XR
II Stage. Correction of internal forces and moments
  3
3
1
33
1
i
1
h
EI3
11n
n
h
EI3
r




I Stage. Determine the unknown force or translation on the frame considering the joint is blocked:
0RRf 
Area moment method applied
 irR


i
f
r
R
f
1
1111 R
R
r
XrXX 
)dsmndsm(
IE
1
dsm
IE
1
dsm
IE
1
ds
IE
m
ds
IE
m
i
2
1
s
2
1
s
i
2
1
is
2
1
si i
2
1
s s
2
1
1














)dsmMdsmM(
IE
1
dsmM
IE
1
dsmM
IE
1
ds
IE
mM
ds
IE
mM
i
1P
s
1P
s
i
1P
is
1P
si i
1P
s s
1P
P















Static computation of the frame with hinged joint between the column and the rafter

10. Reactions,bendingmomentsandstiffnesstohorizontaldisplacementsofcolumnswithvariablecross
sectionandhingedconnectiontotherafter(fixedinfoundations)
31
2s
2
1
K;
I
I
n;
h
h

 
     
n
11n
;
n
11n
;
n
11n 4
4
3
3
2
2












  2
23K1PX  
   1PXhM iA
 2
2
0
i
h
KM3
X  
0
iA MhXM 
4i phK
4
3
X 







2
ph
XhM iA
3
3
1
ii
1
h
EI3
RX


1;hRM iA 
n= 0.2 for cranes with small lifting capacity and heavy roofs;
n= 0.08 for cranes with heavy lifting capacity and light roofs.

11. C.Teleman.StelStructuresIII.
Lecture3
11
I. Sizing of the stiffness of the truss
k depends on the slope of the top chord of the girder (k = 0.9
for p = 0% and k = 0.7 for p = 10%).
I k I k A y A yx s s i i      ( )2 2
Static computation of the frame with rigid joint between the column and the rafter





11
P1
1
P11ii
r
r
0rr
Σr11 - the sum of the reactions at the top of the column when 1=1;
Σr1P - the sum of the horizontal reactions at the top of the stanchions due to the
external loads applied to the column.
II. Area moment applied considering the rafter is infinitely rigid

12. DETERMINATIONOFTHEREDUNDANCYEFFECTS UPONTRUSSMEMBERS
N N N
N N N
ik ik ik
I
ik ik ik
I
 
 
0
0
( )
( )
max
min




minBikikik
maxBikikik
)T(qN
)T(qN


    minmax/Bik
'
B'k'iBik
0
ikik )T(/MMNN 
a. Hinged connection
b. Rigid connection
II Stage. Effect
of the
redundancy
I Stage. Simply supported truss

13. 1 ,1
1 ik
ik ik
ik
l
N n
E A
   2 ,2
1 ik
ik ik
ik
l
N 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 ik
ik
ik
l
n
E A
   2
2 ,2
1 ik
ik
ik
l
n
E A
  
,1 ,1
1 ik
ik ik
ik
l
n n
E A
  
I. Rotations in the supports induced by unitary bending moments:
II. Rotations on the supports induced by external actions :
,1ikn internal forces 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 and the coefficients of transmission in the static computation, k12 and k21
2
1 2
1 2
k

  


1
2 2
1 2
k

  


12
2
k


 21
1
k



c. Particular situation – uneven restraining conditions

14. Designoftheconnectionbetweenthecolumnandtherooftruss
 
 
b,c
2
v
2
h
1
v
1
2
i
max
ih
11
NNNR
n
V
N;
n
HT
y
y
MN
eVeHTM






 
 
0
1
1
M
y2
shear
2
tech
angle
v
p2
v
t
2
h
t2
0
h
t
2
v
2
2
i
max
2h
22
f
3
td
N
;
4
d
N
4
d
N
;
4
d
N
n2
V
N;
n2
HT
h2
h
MN
eVeHTM

























M1=(H+T)e +Ve2
M2=(H+T)e - Ve1
M1=(H+T)e