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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