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This b o o k l e t is p a r t o f t h e " R u l e s f o r t h e design o f h o i s t i n g appliances" c o n c i s t i n g o f B b o o k l e t s : Booklet Booklet Booklet Booklet Booklet Booklet Booklet Booklet

1 - Object and scope 2 - C l a s s i f i c a t i o n a n d loading o n s t r u c t u r e s and m e c h a n i s m s 3 - C a l c u l a t i n g t h e ctresses i n s t r u c t u r e s 4 - C h e c k i n g f o r f a t i g u e and c h o i c e o f m e c h a n i c m c o m p o n e n t s 5 - Electrical equipment 6 - S t a b i l i t y and s e f e t y against m o v e m e n t b y t h e w i n d 7 - Safety rulec 8 - Test loads a n d tolerantes

and m u s t n o t be used s e p a r a t e l y .

PREFACE

The Rules f o r t h e ü e s i g n o f H o i s t i n g Appliances s e t up by t h e T e c h n i c a l Comnittee o f t h e S e c t i o n 1 o f t h e F.E.M., which have been p u b l i s h e d s o f a r i n two E d i t i o n s , t h e f i r s t one i n 1962 and t h e second i n 1970, have been i n c r e a s i n g l y widely used i n many c o u n t r i e s a l 1 over t h e world.

Taking a c c o u n t o f t h i s e n l a r g e d a u d i e n c e , S e c t i o n 1 o f t h e FEM d e c i d e d t o change t h e format o f t h e s e Design R u l e s and t o f a c i l i t e u p d a t i n g by abandoning t h e s i n g l e v o l m e f o m and d i v i d i n g t h e work i n t ü a n m b e r o f s e p a r a t e b o o k l e t s a s f o l l o w s :

Booklet 1 - O b j e c t and Scope B o o k l e t 2 - C l a s s i f i c a t i o n a n d l o a d i n g on s t r u c t u r e s a n d mechanisms Booklet 3 - Calculating t h e s t r e s s e s i n t h e s t r u c t u r e B o o k l e t 4 - C h e c k i n g f o r f a t i g u e a n d c h o i c e o f mechanism c o m p o n e n t s Booklet 5 - E l e c t r i c a l equipment B o o k l e t 6 - S t a b i l i t y a n d s a f e t y a g a i n s t movement by t h e wind Booklet 7 - S a f e t y r u l e s Booklet 8 - T e s t l o a d s and t o l e r a n c e s

Although n o t d i r e c t l y a p a r t o f t h e s e Design Rules, t h e o p p o r t u n i t y i s t a k e n t o draw a t t e n t i o n t o t h e new Terminology o f S e c t i o n 1.

INTRODUCTION

To f a c i l i t a t e t h e u s e o f t h e s e Rules by t h e p u r c h a s e r s , m a n u f a c t u r e r s and s a f e t y organizations concerned, i t is necessary t o give sane explanation i n regard t o t h e two f o l l o w i n g q u e s t i o n s . 1.

How s h o u l d t h e s e R u l e s be a p p l i e d i n p r a c t i c e t o t h e d i f f e r e n t t y p e s of a p p l i a n c e whose c o n s t r u c t i o n t h e y cover ?

2.

H o w s h o u l d a p u r c h a s e r u s e t h e s e Rules t o d e f i n e h i s r e q u i r e m e n t s i n r e l a t i o n

t o an a p p l i a n c e which he d e s i r e s t o o r d e r and what c o n d i t i o n s s h o u l d he s p e c i f y i n h i s e n q u i r y t o e n s u r e t h a t t h e m a n u f a c t u r e r s can submit a p r o p o s a l i n accordance with h i s requirements ?

1. I t i s n e c e s s a r y f i r s t t o r e c o g n i z e t h e g r e a t v a r i e t y of a p p l i a n c e s c o v e r e d by

t h e Design Rules. I t is obvious t h a t a c r a n e having very high s p e e d s and a r a p i d working c y c l e i s t n o t d e s i g n e d i n t h e same manner a s a s m a l l overhead c r a n e f o r i n f r e q u e n t d u t y . For such a machine t h e r e can be no q u e s t i o n o f making a l 1 t h e v e r i f i c a t i o n s which would appear t o be r e q u i r e d , f r m r e a d i n g through t h e R u l e s , because one would c l e a r l y f i n i s h w i t h a v o l m e of c a l c u l a t i o n s which would be t o t a l l y o u t o f p r o p o r t i o n t o t h e o b j e c t i v e i n view. The manufacturer must t h e r e f o r e d e c i d e i n each p a r t i c u l a r c a s e which p a r t s o f t h e machine, which he i s des i g n i n g , s h o u l d be a n a l y s e d and t h o s e f o r which c a l c u l a t i o n i s u n n e c e s s a r y , n o t because he must a c c e p t t h a t t h e r e s u l t s f o r t h e l a t t e r would n o t be i n accordance w i t h t h e r e q u i r e m e n t s o f t h e R u l e s , b u t because on t h e c o n t r a r y he i s c e r t a i n i n advance t h a t t h e c a l c u l a t i o n s f o r t h e l a t t e r would only confirm a f a v o u r a b l e o u t c m e . T h i s may be because a s t a n d a r d c m p o n e n t is b e i n g used which h a s been v e r i f i e d once and f o r a l 1 o r because i t h a s been e s t a b l i s h e d t h a t s m e o f t h e v e r i f i c a t i o n s imposed by t h e Rules cannot i n c e r t a i n c a s e s have an u n f a v o u r a b l e r e s u l t and t h e r e f o r e s e r v e no purpose.

I f one t a k e s , f o r example, t h e f a t i g u e c a l c u l a t i o n s , c e r t a i n v e r i f i c a t i o n s a r e unnecessary f o r appliances because t h e y always l e a d t o t h e c o n c l u s i o n s t h a t t h e a r e those r e s u l t i n g f r m checking s a f e t y i n r e l a t i o n

i t i s very e a s y t o s e e t h a t o f l i g h t o r moderate d u t y most u n f a v o u r a b l e c a s e s t o the elastic l i m i t .

These c o n s i d e r a t i o n s show t h a t c a l c u l a t i o n s made i n accordance w i t h t h e Rules can t a k e a v e r y d i f f e r e n t form a c c o r d i n g t o t h e type o f a p p l i a n c e which i s b e i n g c o n s i d e r e d , and may i n t h e c a s e o f a simple machine o r a machine embodying s t a n d a r d c a n p o n e n t s be i n t h e form o f a b r i e f s m a r y without p r e j u d i c i n g t h e compliance o f t h e machine w i t h t h e principies s e t out by t h e Design Rules.

2. As f a r a s t h e second q u e s t i o n i s concerned, s m e e x p l a n a t i o n i s f i r s t d e s i r a b l e

f o r t h e p u r c h a s e r , who may be s m e w h a t bewildered by t h e e x t e n t o f t h e document and confused when f a c e d with t h e v a r i e t y o f c h o i c e which i t p r e s e n t s , a v a r i e t y which i s , however, n e c e s s a r y i f one wishes t o t a k e account o f t h e g r e a t d i v e r s i t y o f problems t o be r e s o l v e d .

I n f a c t , t h e o n l y i m p o r t a n t m a t t e r f o r t h e p u r c h a s e r i s t o d e f i n e t h e d u t y which h e e x p e c t s f r m h i s a n p l i a n c e and i f possbb!? t o g i v e c m e i n d i c l t b m cif t h e d u t y o f t h e v a r i o u s motions.

As r e g a r d s t h e s e r v i c e t o b e performed by t h e a p p l i a n c e , two f a c t o r s rnust be s p e c i fied, i.e. :

- t h e c l a s s o f u t i l i z a t i o n , a s d e f i n e d i n 2.1.2.2

;

- t h e l m d s p e c t r u n , a s d e f i n e d i n 2.1.2.3. In o r d e r t o a r r i v e a t t h e nunber o f h o i s t i n g c y c l e s d e t e r m i n i n g t h e c l a s s o f u t i l i z a t i o n , t h e p u r c h a s e r rnay, f o r instante, f i n d t h e p r o d u c t o f :

- t h e nunber o f h o i s t i n g c y c l e s which t h e a p p l i a n c e

w i l l have t o a v e r a g e e a c h day

on which i t i s used ;

- t h e a v e r a g e nunber o f days of u s e p e r y e a r

;

- t h e nunber o f y e a r s a f t e r which t h e a p p l i a n c e rnay b e c o n s i d e r e d a s having t o be replaced.

S i r n i l a r l y , t h e l o a d spectrum may be c a l c u l a t e d by means o f t h e s i r n p l i f i e d formula s e t o u t i n t h e above rnentioned p a r a g r a p h .

In n e i t h e r c a s e do t h e c a l c u l a t i o n s c a l l f o r a h i g h d e g r e e of a c c u r a c y , b e i n g more i n t h e n a t u r e o f e s t i m a t e s t h a n o f p r e c i s e c a l c u l a t i o n s . Moreover, t h e nunbers of h o i s t i n g c y c l e s d e t e r m i n i n g t h e c l a s s e s of u t i l i z a t i o n do n o t c o n s t i t u t e g u a r a n t e e d v a l u e s : t h e y a r e merely g u i d e v a l u e s , s e r v i n g a s a b a s i s f o r t h e f a t i g u e c a l c u l a t i o n s and c o r r e s p o n d i n g t o an a v e r a g e l i f e which can be expected w i t h a r e a s o n a b l e d e g r e e o f s a f e t y , p r o v i d e d t h e a p p l i a n c e , d e s i g n e d i n accordance w i t h t h e p r e s e n t d e s i g n r u l e s , is used under t h e c o n d i t i o n s s p e c i f i e d by t h e customer i n h i s c a l l f o r t e n d e r and a l s n t h a t i t i s o p e r a t e d and m a i n t a i n e d r e g u l a r l y i n c m p l i a n c e w i t h t h e manufacturer's instructions.

I f he i s u n a b l e t o d e t e r m i n e t h e c l a s s o f u t i l i z a t i o n and t h e l o a d s p e c t r m , t h e p u r c h a s e r may c o n f i n e h i m s e l f t o s t a t i n g t h e group i n which t h e a p p l i a n c e is t o b e c l a s s i f i e d . A g u i d e a s t o t h e c h o i c e o f group i s provided by Table 2.1.2.5., which i s n o t b i n d i n g b u t g i v e s s i m p l e examples which, by way o f c m p a r i s o n , may f a c i l i t a t e selection.

In t h e c a s e o f mechanisrns, t h e f o l l o w i n g s h o u l d a l s o be s p e c i f i e d

- t h e c l a s s o f u t i l i z a t i o n , a s d e f i n e d i n 2.1.3.2 - t h e load s p e c t r m , a s defined i n 2.1.3.3.

;

;

t h e same o b s e r v a t i o n s a p p l y a s were made c o n c e r n i n g t h e a p p l i a n c e a s a whole.

ihe t a b l e s i n Appendix A.2.1.1. may be used t o f a c i l i t a t e d e t e r m i n a t i o n o f t h e c l a s s of u t i l i z a t i o n . On t h e b a s i s o f t h e c l a s s o f u t i l i z a t i o n of t h e a p p l i a n c e , t h e y make i t p o s s i b l e t o d e t e r m i n e a t o t a l nunber of working h o u r s f o r t h e mechanism, a c c o r d i n g t o t h e a v e r a g e d u r a t i o n o f a working c y c l e and t h e r a t i o between t h e oper a t i n g time o f t h e mechanism and t h e d u r a t i o n o f t h e ccnnplete c y c l e .

Table T.2.1.3.5. may be used a s a g u i d e by a p u r c h a s e r wishing simply t o choose a group f o r e a c h o f t h e mechanisrns w i t h which t h e a p p l i a n c e he wants t o o r d e r i s t o be f i t t e d .

A s a g e n e r a l r u l e , t h e p u r c h a s e r h a s no o t h e r i n f o r m a t i o n t o supply i n c o n n e c t i o n w i t h t h e d e s i g n of t h e a p p l i a n c e , e x c e p t i n c e r t a i n c a s e s :

-

t h e a r e a o f h o i s t e d l o a d s p r e s e n t e d t o t h e wind, i f t h i s a r e a i s l a r g e r t h a n t h o s e d e f i n e d i n 2.2.4.1.2. ;

-

t h e v a l u e o f t h e o u t - o f - s e r v i c e wind, where l o c a l c o n d i t i o n s a r e c o n s i d e r e d t o n e c e s s i t a t e d e s i g n f o r an o u t - o f - s e r v i c e wind g r e a t e r t h a n t h a t d e f i n e d i n 2.2.4.1.2.

Q E J E C T OF THE R U L E S

The purpose of t h e s e r u l e s is t o determine t h e l o a d s and ccnnbinations o f l o a d s which must be t a k e n i n t o a c c o u n t when d e s i g n i n g h o i s t i n g a p p l i a n c e s , and a l s o t o e s t a b l i s h t h e s t r e n g t h and s t a b i l i t y c o n d i t i o n s t o be observed f o r t h e v a r i o u s l o a d combinations.

SCOPE

The R u l e s a p p l y t o t h e d e s i g n o f l i f t i n g a p p l i a n c e s o r p a r t s o f l i f t i n g a p p l i a n c e s which appear i n t h e i l l u s t r a t e d terminology f o r c r a n e s and heavy l i f t i n g a p p l i a n c e s o f S e c t i o n 1 o f t h e FEM.

Appliances n o t covered by S e c t i o n 1 1 ) L i f t i n g a p p l i a n c e s i n c l u d e d i n S e c t i o n V , f o r example :

-

mobile j i b c r a n e s on p n e m a t i c o r s o l i d rubber t y r e s , c r a w l e r t r a c k s , l o r r i e s , t r a i l e r s and b r a c k e t s .

2 ) L i f t i n g e q u i p n e n t which a c c o r d i n g t o t h e i n t e r n a 1 r e g u l a t i o n s of FEM, a r e i n c l u ded i n S e c t i o n IX, t h a t i s t o s a y :

- v a r i o u s itms o f s e r i e s l i f t i n g e q u i ~ e n t , - electric hoists,

- pneunatic h o i s t s , - accessories for l i f t i n g ,

- hand o p e r a t e d c h a i n b l o c k s , - e l e v a t i n g p l a t f o r m s , work p l a t f o r m s , dock l e v e l l e r s , - winches, - j a c k s , t r i p o d s , c m b i n e d a p p a r a t u s f o r p u l l i n g and l i f t i n g , - stacker cranes. For s e r i e s l i f t i n g equipment, t h o s e c h a p t e r s of t h e Design R u l e s o f S e c t i o n 1 which have been a c c e p t e d by S e c t i o n IX s h o u l d be used.

These r u l e s c m p r i . s e e i g h t b o o k l e t s . In a d d i t i o n s m e b o o k l e t s c o n t a i n appendices which g i v e f u r t h e r i n f o r m a t i o n on t h e method o f a p p l i c a t i o n .

LIST OF SYMBOLS A N D N O T A T I O N S

A

rn2

A r e a exposed t o w i n d (2-231 C o m b i n e d i n f l u e n c e o f r e s i d u a l t e n s i l e stresses w i t h dead w e i g h t ctresses (3-41

A l t o A%!

-

C r a n e groups [2-31

Ae

rn2

E n v e l o p e d area o f l a t t i c e [2-271

rnrn

Wheelbase o f c r a n e [2-201: D i m e n s i o n o f l a t t i c e i n w i n d l o a d c a l c u l a t i o n [2-271: L e n g t h o f s t r i p o f p l a t e i n b u c k l i n g c a l c u l a t i o n (3-383 S i z e o f f i l l e t w e l d i n n o t c h case 2.33 [3-621

a

rn/s2

A c c e l e r a t i o n [5-221

5

-

l n f l u e n c e o f t h i c k n e s s o f s t r u c t u r a l rnember [3-61

B

rnm

W i d t h o f l a t t i c e i n w i n d l o a d c a l c u l a t i o n [2-271

5 0 t o BICI

-

Classes o f u t i l i s a t i o n o f s t r u c t u r a l rnembers [2-1 11

mm

B r e a d t h o f s e c t i o n acrocs w i n d f r o n t [2-271: L a r g e s t dirnension o f r e c t a n g u l a r s t e e l c e c t i o n [3-61: L e n g t h o f p l a t e i n b u c k l i n g c a l c u l a t i o n [3-391: U s e f u l w i d t h o f r a i l i n w h e e l c a l c u l a t i o n [4-211 l n f l u e n c e o f c o l d [3-71: C o e f f i c i e n t used t o c a l c u l a t e t h e t i g h t e n i n g t o r q u e o f b o l t s [3-281: S e l e c t i o n c o e f f i c i e n t f o r c h o i c e o f r u n n i n g s t e e l w i r e ropes (4-151 Shape c o e f f i c i e n t i n w i n d load c a l c u l a t i o n [2-241 S t a r t i n g class (5-201 F a c t o r s c h a r a c t e r i s i n g t h e slope o f Wtihler c u r v e s [4-91 R o t a t i o n speed c o e f f i c i e n t s f o r wheel c a l c u l a t i o n (4-2 11 G r o u p c o e f f i c i e n t f o r w h e e l c a l c u l a t i o n (4-21 1 P o w e r f a c t o r [5-81 Syrnbol used i n p l a t e i n s p e c t i o n f o r l a r n i n a t i o n d e f e c t s (3-571 S e c t i o n d i a m e t e r i n chape f a c t o r d e t e r r n i n a t i o n (2-251

D

mrn

R o p e w i n d i n g d i a r n e t e r [4-191: Wheel diarneter (4-211: S h a f t d i a r n e t e r i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i c m p a r t s [4-261.

mm

n i s r n e t ~ ro f b o l t h o l e s [ 3 - 1 5 )

mm

D e p t h o f section parallel t o wind direction i n wind load calculation [2-27): N o m i n a l d i a m e t e r o f b o l t [3-28): N o m i n a l d i a m e t e r o f r o p e (4-181: C h a f t d i a m e t e r i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i s m p a r t s (4-2':

mm

B o l t d i a r n e t e r a t t h r e a d r o o t [3-141

-

N u m b e r o f c o m p l e t e d s t a r t s p e r h o u r 15-201

-

N u r n b e r o f i m p u l s e s o r i n c o m p l e t e s t a r t s p e r h o u r [5-201

mm

M i n i m u m r o p e d i a m e t e r 14-331

mm

N o m i n a l b o l t d i a m e t e r (3-141

~

/

m

m

~ E l a s t i c m o d u l u s o f s t e e l 13-391

-

Groups o f components [2-14)

%

D u t y f a c t o r 15-191 T h i c k n e s s o f s t r i p o f p l a t e i n b u c k l i n g c a l c u l a t i o n (3-391: T h i c k n e s s o f p l a t e i n w e l d e d j o i n t s [3-621 P l a t e t h i c k n e c c e s i n w e l d e d j o i n t s (3-64) W i n d f o r c e (2-23): H o r i z o n t a l f o r c e d u r i n g a c c e l e r a t i o n [2-451: T e n s i l e l o a d i n b o l t s (3-191: C h m p r e s s i v e f o r c e o n m e m b e r i n c r i p p l i n g c a l c u l a t i o n (3-341 M i n i m u r n b r e a k i n g l o a d o f r o p e I4-171 P e r m i s s i b l e w o r k i n g l o a d o n b o l t s (3-151 P r o j e c t i o n o f r o p e l o a d o n t h e x a x i s d u r i n g t r a v e l l i n g 12-491 l n e r t i a f o r c e d u e t o t h e l o a d d u r i n g t r a v e l l i n g [2-461 M a x i m u m v a l u e o f Fc [2-5 1) F i l l f a c t o r o f r o p e [4-181: N u m b e r o f e l e c t r i c a l b r a k i n g s [ 5 - 2 0 1 R u n n i n g t i m e o f m o t o r [5-241 C o e f f i c i e n t f o r r e l a t i v e t i m e s o f deceleration and a c c e l e r a t i o n [5-251 A c c e l e r a t i o n d u e t o g r a v i t y . a c c o r d i n g t o ISO 9.80665 m / c 2 [ 2 - 4 6 1 C o e f f i c i e n t depending o n group for choice o f r o p e d r u m s and p u l l e y s I 4 - 191 M o m e n t o f i n e r t i a o f rnass i n s l e w i n g m o t i o n I2-561 M o m e n t o f i n e r t i a o f s t i f f e n e r s [3-451

S t a r t i n g c u r r e n t o f m o t o r [5-71 N o m i n a l c u r r e n t o f m o t o r [5-61 Sum o f c u r r e n t s I A a n d IN [5-81 M o m e n t o f i n e r t i a o f s t i f f e n e r s [3-441 M o m e n t o f i n e r t i a o f mass o f a p a r t i n r o t a t i o n (2-451 M o r n e n t o f i n e r t i a o f mass o f al1 p a r t s i n r o t a t i o n [2-493 M o r n e n t o f i n e r t i a o f mass o f m o t o r and b r a k e (5-221 G r o u p n u m b e r i n c o m p o n e n t groups E9 t o E8 (4-101 A c c e l e r a t i o n i n h o r i z o n t a l m o t i o n s (2-501 A v e r a g e a c c e l e r a t i o n / d e c e l e r a t i o n in h o r i z o n t a l m o t i o n s [2-461 C u b i c m e a n f a c t o r f o r c h o i c e o f b e a r i n g s (4-131 Empirical coefficient for determining m i n i m u m breaking strength o f r o p e [4- 1 El] Stress c o n c e n t r a t i o n classes f o r w e l d e d p a r t s (3-4B1 C o e f f i c i e n t f o r calculating force i n the direction o f the wind f o r l a t t i c e g i r d e r s and t o w e r s [2-291 P r e s s u r e o f w h e e l on r a i l [4-251

S p i n n i n g loss c o e f f i c i e n t [4-181 C o r r o s i o n c o e f f i c i e n t i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i c m p a r t s (4-261 S i z e c o e f f i c i e n t i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i s m p a r t s (4-261 C o r r e c t i o n c o e f f i c i e n t f o r a b n o r m a l l o c a t i o n [5-191 S p e c t r u m c o e f f i c i e n t f o r m e c h a n i s m s [2-El S p e c t r u m c o e f f i c i e n t f o r cranec í2-41 Chape c o e f f i c i e n t i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i s m p a r t s (4-261 S p e c t r u m c o e f f i c i e n t f o r c o m p o n e n t s [2-121 S p e c t r u m c o e f f i c i e n t f o r m e c h a n i s m p a r t s (4- 101 Surface finish [machiningl coefficient in fatigue verification of m e c h a n i s m p a r t s [4-261 B u c k l i n g c o e f f i c i e n t s used i n b u c k l i n g c a l c u l a t i o n s (3-391

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R a d i u s o f c y l i n d r i c a l s h e l l s i n b u c k l i n g c a l c u l a t i o n s (3-441: R a d i u s o f r o p e g r o o v e [4-201: R a d i u s o f r a i l h e a d (4-22): B l e n d i n g r a d i u s (4-261 C o e f f i c i e n t f o r t y p e o f e l e c t r i c b r a k i n g 15-20) O h m i c r e s i s t a n c e p e r u n i t l e n g t h (5-91 S t r e s s 12-8): M a x i m u m t e n s i l e f o r c e i n r o p e 14-16] A r e a o f al1 r n e m b e r s o f l a t t i c e g i r d e r s a n d t o w e r s 12-29) C r o s s s e c t i o n a l a r e a o f c o n d u c t o r [5-81 B e a r i n g d i a r n e t e r u n d e r b o l t h e a d 13-15) S p e c i a l q u a l i t y o f w e l d i n g [3-571 L o a d d u e t o d e a d w e i g h t . c o n s t a n t l o a d [2-15). (3-231 L o a d d u e t o h o r i z o n t a l m o t i o n s (2-19) L o a d due t o w o r k i n g l o a d [2-151 L o a d d u e t o t o r q u e s (2-331 M e a n t y p e M l o a d i n b e a r i n g c a l c u l a t i o n (4-131 M i n i m u m t y p e M l o a d i n b e a r i n g c a l c u l a t i o n (4-13) M a x i m u m t y p e M l o a d i n l o a d c a s e 1 (2-341 M a x i m u m t y p e M l o a d i n l o a d case 1 1 (2-351 M a x i m u m t y p e M l o a d i n l o a d c a s e 1 1 1 (3-351 L o a d d u e t o a c c e l e r a t i o n o r b r a k i n g 12-33] L o a d due t o r n a x i m u m m o t o r t o r q u e (2-371 L o a d d u e t o f r i c t i o n a l f o r c e s (2-331 L o a d due t o v e r t i c a l displacement o f rnoveable p a r t c o f a l i f t i n g a p p l i a n c e . e x c l u d i n g t h e w o r k i n g l o a d (2-331 L o a d d u e t o v e r t i c a l d i s p l a c e m e n t o f t h e w o r k i n g l o a d (2-331 L o a d due t o t h e e f f e c t o f l i r n i t i n g w i n d f o r appliance i n s e r v i c e [2-331 L o a d due t o w i n d e f f e c t f o r q

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T h i c k n e s s o f s t r u c t u r a l m e m b e r w h e n c h o o s i n g s t e e l q u a l i t y [3-61; T h i c k n e s s o f c y l i n d r i c a l s h e l l w a l l i n b u c k l i n g analysis [3-q41: T h i c k n e s s o f w e b o f t r o l l e y r a i l g i r d e r [a-61 D u r a t i o n o f d i f f e r e n t l e v e l s o f l o a d i n g [2-8) D u r a t i o n o f a c t i o n o f c o u p l e s M i . M 2 a n d M 3 [5-181 I d e a l s e c t i o n t h i c k n e s s w h e n c h o o s i n g s t e e l q u a l i t y [3-61 D u r a t i o n o f d e c e l e r a t i o n w h e n c a l c u l a t i n g loads due t o h o r i z o n t a l m o t i o n (2-5 11 A v e r a g e d u r a t i o n o f a h o i s t i n g c y c l e [2-391 Classes o f u t i l i s a t i o n o f l i f t i n g a p p l i a n c e s [2-33 P e r m i s s i b l e v o l t a g e d r o p í5-81 H o i s t i n g speed [2-161: [5-171 T h e o r e t i c a l w i n d speed (2-221 N o m i n a l t r a v e l speed o f a p p l i a n c e [2-2 1 1 S t e a d y h o r i z o n t a l s p e e d o f p o i n t o f suspension o f l o a d [2-451 Distance of e x t r e m e fibre f r o m centre o f gravity o f section in c r i p p l i n g c a l c u l a t i o n [3-341 T r a v e l speed [5-221 W o r k d o n e p e r u n i t t i m e d u r i n g s t a r t i n g [5-261 N o t c h cases o f u n w e l d e d m e m b e r s [3-481 Angular v e l o c i t y o f a mechanism p a r t about i t s c e n t r e o f r o t a t i o n w h e n c a l c u l a t i n g loads d u e t o h o r i z o n t a l m o t i o n [2-45) M a x i m u m v a l u e i n d i c a t e d f o r m o t o r o f w o r k done i n s t a r t i n g w i t h h o o k l o a d [5-261 R e a c t a n c e p e r u n i t l e n g t h [5-91 C o o r d i n a t e o f p o i n t o f suspension o f h o i s t r o p e a l o n g a n a x i s p a r a l l e l t o t h e d i r e c t i o n o f t r a v e l [2-471 C o o r d i n a t e o f p o s i t i o n o f c e n t r e o f g r a v i t y o f suspended l o a d a l o n g a n a x i s h a v i n g t h e s a m e d i r e c t i o n . cense and o r i g i n as t h e a x i s o f x [2-401 Assessing c o e f f i c i e n t f o r i n f l u e n c e A [3-41 Assessing c o e f f i c i e n t f o r i n f l u e n c e B [3-61 Assessing c o e f f i c i e n t f o r i n f l u e n c e C [3-71 M i n i m u m p r a c t i c a 1 f a c t o r o f s a f e t y For c h o i c e o f s t e e l w i r e r o p e s [4-1, C o o r d i n a t e expressing h o r i z o n t a l displacement o f load r e l a t i v e t o c r a n e [2-481

D i c p l a c e m e n t o f l o a d d u r i n g t r a v e l m o t i o n o f c r a n e [2-5

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D i s p l a c e m e n t o f l n a d d u r i n g tr=r\lel r n o t l o n o f r r a n e [2-5 1 3 R a t i o o f cidec o f p a n e l i n b u c k l i n g c a l c u l a t i o n [3-411

R a t i o o f d u r a t i o n o f use o f m e c h a n i c m during a hoicting c y c l e t o a v e r a g e d u r a t i o n o f c y c l e (2-391 Angle o f inclination o f rope during acceleration o f crane [2-4gl T i m e c o e f f i c i e n t r e l a t i n g t o a c c e l e r a t i o n o f c r a n e í2-461 Critica1 value of

6 (2-521

A m p l i f y i n g c o e f f i c i e n t o f l o a d i n g d e p e n d i n g o n c r a n e g r o u p (2-301 A m p l i f y i n g c o e f f i c i e n t o f loading depending on mechanism group [2-34 1 Shortening o f j o i n e d e l e m e n t s under t h e t i g h t e n i n g f o r c e i n b o l t e d j o i n t s [3-151 E x t e n c i o n o f b o l t u n d e r t i g h t e n i n g f o r c e (3-151 D i v e r g e n c e i n s p a n o f c r a n e [E-41: D i v e r g e n c e i n c r a n e r a i l c e n t r e s

[a-al E l a s t i c c o e f f i c i e n t o f b o l t e d j o i n t c (3-151 S h i e l d i n g c o e f f i c i e n t in c a l c u l a t i o n o f w i n d f o r c e (2-281: Poiccon's r a t i o í3-391: O v e r a l l e f f i c i e n c y o f m e c h a n i s m [5-171 A n g l e o f w i n d r e l a t i v e t o l o n g i t u d i n a l a x i c o f m e m b e r [2-291 S a f e t y c o e f f i c i e n t c a p p l y i n g t o b o l t e d j o i n t c [ 3 - 151 R a t i o o f t h e e x t r e m e s t r e s s v a l u e c i n f a t i g u e c a l c u l a t i o n (3-241 E l e c t r i c c o n d u c t i v i t y [5-0) R a t i o o f e x t r e m e i n d i v i d u a l strecces ax. [3-521

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S a f e t y c o e f f i c i e n t for calculation o f mechanism parts depending o n case o f l o a d i n g (4-31 s a f e t y c o e f f i c i e n t for calculation o f b o l t e d joints depending o n c a s e o f l o a d i n g [3-191

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=

+ 1 i n f a t i g u e c a l c u l a t i o n [3-501

A m p l i t u d e o f t h e permissible m a x i m u m stress i n b o l t s f o r f a t i g u e c a l c u l a t i o n s í3-161 A p p a r e n t e l a s t i c l i m i t o f s t e e l [3-101 T e n s i l e s t r e s s d u e t o p e r m a n e n t l o a d (3-41: S t r e s s due t o d e a d w e i g h t (3-231 U l t i m a t e t e n s i le s t r e n g t h (3-1 01 T h e E U L E R S t r e s s (3-391 S t r e s s due t o v a r i a b l e l o a d s !3-233 P e r m i s s i b l e t e n s i le s t r e s s f o r s t r u c t u r a l m e m b e r s 13-41; P e r m i s s i b l e s t r e s s f o r r n e c h a n i s m p a r t s !4-3) Permissible n o r m a l stress f o r v e r i f i c a t i o n o f fatigue s t r e n g t h o f m e c h a n i s m p a r t s (4- 1 1 1 I n i t i a l s t r e s s i n c a l c u l a t i n g b o l t e d j o i n t s I3-141 Endurance l i m i t o f m a t e r i a l s o f mechanism p a r t s under a l t e r n a t i n g b e n d i n g (4-61 Permissible f a t i g u e s t r e n g t h in compression for s t r u c t u r a l m e m b e r s (3-491: C a l c u l a t e d c o m p r e s s i v e s t r e s s f o r m e c h a n i s m p a r t s ( 4 - 4 ) C o m p r e s s i o n s t r e s s i n w h e e l and r a i l (4-25)

N/mmZ

E q u i v a l e n t s t r e s s u s e d i n c a l c u l a t i n g s t r u c t u r a l m e m b e r s ( 3 - 121 C r i t i c a 1 stress used i n c a l c u l a t i n g s t r u c t u r a l m e m b e r s subjected t o r a r g e d e t o r m a t i o n c (3-231 C r i t i c a l b u c k l i n g s t r e s s [3-391 C r i t i c a l c o m p a r i s o n s t r e s s u s e d i n b u c k l i n g c a l c u l a t i o n [3-401 E n d u r a n c e l i m i t o f m a t e r i a l s o f m e c h a n i s m p a r t s [4-81 C a l c u l a t e d b e n d i n g s t r e s s i n m e c h a n i s m p a r t s (4-41 I d e a l b u c k l i n g s t r e s s f o r t h i n w a l l e d c i r c u l a r c y l i n d e r s (3-441 L o w e r s t r e s s in d e t e r m i n a t i o n o f s t r e s s s p e c t r u m (2-131 F a t i g u e s t r e n g t h o f m e c h a n i s m p a r t s [4-101 F a t i g u e s t r e n g t h f o r n o r m a l stresses i n t h e x d i r e c t i o n (4-121 F a t i g u e s t r e n g t h f o r n o r m a l s t r e c s e s i n t h e y d i r e c t i o n ( 4 - 121 A r i t h m e t i c m e a n o f al1 u p p e r and l o w e r stresses d u r i n g t h e t o t a l d u r a t i o n o f use 12-131: P e r m i s s i b l e s t r e s s i n c o n f o r m i t y t e s t s t o ISO 3 6 0 0 / 1 (3-1 61

Omax

M a x i m u m s t r e s s i n f a t i g u e c a l c u l a t i o n f o r s t r u c t u r a l m e m b e r s (3-241

" m in

M i n i m u m stress i n f a t i g u e c a l c u l a t i o n f o r s t r u c t u r a l m e m b e r s (3-251

un

B e a r i n g p r e s s u r e i n r i v e t e d j o i n t s 13-13]

u P

T h e o r e t i c a l t e n s i l e s t r e s s i n b o l t due t o t i g h t e n i n g (3-14)

u S'JP

U p p e r s t r e s s i n d e t e r m i n a t i o n o f s t r e s s s p e c t r u m (2-131

Osup rnax

M a x i m u m u p p e r s t r e s s i n d e t e r m i n a t i o n f o s t r e s s s p e c t r u m (2-131

"sup rniri

M i n i m u m u p p e r s t r e s s i n d e t e r m i n a t i o n o f s t r e s s s p e c t r u m ( 2 - 131

"t

Permissible tensile stress in fatigue v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s I3-491: C a l c u l a t e d t e n s i l e s t r e s s i n r n e c h a n i s m p a r t s (4-4.1: Tensile stress i n r o p e (4-341 R e d u c e d b u c k l i n g s t r e s s o f t h i n w a l l e d c i r c u l a r c y l i n d e r s (3-441 P e r m i s s i b l e s t r e s s i n a l t e r n a t i n g t e n s i o n / c o m p r e s s i o n in f a t i g u e v e r i f i c a t i o n o f m e c h a n i s m p a r t s [3-481 Permissible a l t e r n a t i n g stress i n f a t i g u e v e r i f i c a t i o n o f mechanism p a r t s (4-71

N o r m a l stress i n t h e x d i r e c t i o n when c a l c u l a t i n g s t r u c t u r a l m e r n b e r s 13- 1 21 Permissible stress in fatigue v e r i f i c a t i o n o f s t r u c t u r a l mernbers [3-521

max

M a x i m u m stress i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s (3-521

Ox m i n

M i n i m u m s t r e s s i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s 13-521

O

N o r m a l stress i n t h e y d i r e c t i o n when c a l c u l a t i n g s t r u c t u r a l m e m b e r s ( 3 - 121

UX

Y

P e r m i s s i b l e s t r e s s i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s 13-52' max

M a x i m u m stress i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s I3-521

min

M i n i m u m s t r e s s i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s [3-521 Shear s t r e s s i n g e n e r a l (3-1 21: 3 l c u l a t e d s h e a r s t r e s s f o r m e c h a n i s m p a r t s (4-4) Permissible shear stress when c a l c u l a t i n g s t r u c t u r a l m e m b e r s í 3 - 1 1 1 Permissible shear stress i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i s m p a r t s 14-1 1 1 T o r s i o n a l s t r e s s i n b o l t s d u e t o t i g h t e n i n g I3-141 C r i t i c a l b u c k l i n g s h e a r s t r e s s 13-39) E n d u r a n c e l i m i t o f m a t e r i a l s o f m e c h a n i s m p a r t s (4-81 F a t i g u e s t r e n g t h o f m e c h a n i s m p a r t s (4- 101 M a x i m u m shear stress i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i c m p a r t s [3-251

min

M i n i m u m shear s t r e s s i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i s m p a r t s (3-251 E n d u r a n c e l i m i t u n d e r a l t e r n a t i n g shear o f m a t e r i a l s o f m e c h a n i s m p a r t s [4-71 Ratio o f duration of action of a known torque t o motor running t i m e 15-24]

'wk

E n d u r a n c e l i m i t u n d e r a l t e r n a t i n g shear i n f a t i g u e v e r i f i c a t i o n o f m e c h a n i s m p a r t s [4-71

' XY

S h e a r s t r e s s w h e n c a l c u l a t i n g s t r u c t u r a l m e m b e r s 13-121

xya

P e r m i s s i b l e shear s t r e s s i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s (3-521

xy m a x

M a x i m u m shear s t r e s s i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s (3-521

'xy m i n

M i n i m u m shear s t r e s s i n f a t i g u e v e r i f i c a t i o n o f s t r u c t u r a l m e m b e r s (3-521 S l o p e o f W o h l e r c u r v e [4-91

U y n a r n i c c o e f f i c i e n t f o r h o i s t m o t i o n [2-161: R a t i o o f s t r e s s e s a t p l a t e edges i n b u c k l i n g c a l c u l a t i o n [3-223 Dynarnic coeff i c i e n t when c a l c u l a t i n g loads due t o a c c e l e r a t i o n o f h o r i z o n t a l m o t i o n s (2-461

Tolerante f a c t o r i n b o l t e d j o i n t s [3-141 C r i p p l i n g c o e f f i c i e n t [3-221 A n g u l a r v e l o c i t y oF s h a f t w h e n c a l c u l a t i n g l o a d s d u e t o h o r i z o n t a l m o t i o n (2-561 F r e q u e n c i e s o f o s c i l l a t i o n d u r i n g l o a d s w i n g (2-501 A n g u l a r v e l o c i t y o f m o t o r [2-491

-

-

-

-

-

This b o o k l e t i s p a r t o f t h e "Rules f o r t h e design o f h o i s t i n g appliances" consisting o f 8 bookletc : Booklet Booklet Booklet Booklet Booklet Booklet Booklet Booklet

1

1 - O b j e c t and scope 2 - C l a s s i f i c a t i o n and loading on structures and mechanisms 3 - C a l c u l a t i n g t h e stressec i n s t r u c t u r e s - C h e c k i n g f o r f a t i g u e a n d c h o i c e o f m e c h a n i s m componenies 5 - Electricai equipment 6 - S t a b i l i t y and s a f e t y against m o v e m e n t b y t h e w i n d 7 - Safety rules 8 - Test loads and t o l e r a n c e s

and m u c t n o t b e used separately.

B O O K L E T

2

ICAI I O N A N D L Q A D I N G QN S T R U C T U R E S A N D M E C H A N I S N S CLASSIF

CONTENTS

Clause GROlP CLASSIFICATION ff HOISTING APPLIANCES AND T E I R C O W M N T PARTS

- General plan of classification - Classification of hoisting appliances as a whole Classification system Classes of utilization . Load spectrum Group classification of hoisting appliances . Guidance on group classification of an appliance ,

- Classification of individual mechanisms as a whole

Classification system Class of utilization . Loading spectrum . Group classification of individual mechanisms as a whole Guidance for group classification o: individual mechanisms as a whole .

- Classification o f components . Classification system

. Classes of utilization . Stress spectrum . Group classification of components

L.OADS ENTERIK INTO T E DESIGN ff STRUCTURES - Principal loads - Loads due to vertical motions

. Loads due to hoisting of the working load

. . Values of the dynamic coefficient '? . Loads due to acceleration (or deceleration) of the hoisting motion and to vertical shock loadings when travelling along rail tracks . Special case

- Loads due to horizontal motions SH Horizontal effects due to accelerations (or decelerations)

. . Traverse and travel motions

..

Slewing and luffing (derricking) motions

. Effects of centrifugal force

. Transverse reactions due to rolling action

.

Euffer effects ST

. . k f f e r effects on the structure . . Euffer effects on the suspended load

2.1

-

Loads due t o c l i m a t i c e f f e c t s

. Wind a c t i o n . . Wind p r e s s u r e .. D e s i g n w i n d c o n d i t i o n s ..

Wind l o a d c a l c u l a t i o n s

. . F o r c e coef f i c i e n t s . Snow l o a d . Temperature v a r i a t i o n s - Miscellaneous ioads

.

Loads c a r r i e d by p l a t f o r m s

CASES OF LOADING

-

Case 1 Case 1 1 - Case 111 - Choosiny

: PQpliance working w i t h o u t wind : PQpliance working w i t h wind

: Appliance subject t o exceptional loads t h e a m p l i f y i n g c o e f f i c i e n t yc

SEISMIC EFFECTS LOADS ENTERING INTO Ti€

DESIGN

ff MECHANISMS

- Type SM l o a d s - Type SR l o a d s CASES OF LOADING

- Case 1 : M r m a l s e r v i c e w i t h o u t w i n d

.

Type SM l o a d s

. Type

SR l o a d s

Case 11 : bbrmal s e r v i c e w i t h w i n o

. .

Type SM l o a d s Type SR l o a d s

- Case 111 : E x c e p t i o n a l l o a d s

.

Type SM l o a d s Type SR l o a o s

-

b p l i c a t i o n f o r c a l c u l a t i n g SM

.

H o i s t i n y motions

.

.

H o r i z o n t a l motions Combined m o t i o n s

APPENDIX HARMONISATION OF T E CLASSIFICATIONS OF APPLIANCES AND MCHANISMS CALCU.ATI0N OFLOADS D E T0 ACCELERATION MOTIONS LIST OF SYEIOLS AND NOTATIONS

ff HORIZONTAL A-2.2.3. See b o o k l e t 1

2-45

G R O U P C L A S S I F I C A T I O N OF H O I S T I N G A P P L I A N C E S A N D I H E I H COMPONENT PARTS

G E N E R A L P L A N OF C L A S S I F I C A T I O N I n t h e d e s i g n o f a h o i s t i n g a p p l i a n c e and i t s component p a r t s , account must be t a k e n of t h e duty which they w i l l be r e q u i r e d t o perform d u r i n g t h e i r d u r a t i o n o f use ; f o r t h i s purpose group c l a s s i f i c a t i o n i s employed of :

-

t h e a p p l i a n c e a s a whole ;

-

t h e i n d i v i d u a l mechanisms a s a whole ;

-

t h e s t r u c t u r a l and mechanical components.

T h i s c l a s s i f i c a t i o n i s based on two c r i t e r i a , namely : - t h e t o t a l d u r a t i o n o f use of t h e item c o n s i d e r e d ; - t h e hook l o a d , l o a d i n g o r s t r e s s s p e c t r a t o which t h e item i s s u b j e c t e d .

2.1.2.

2.1.2.1.

C L A S S I F I C A T I O N OF H O I S T I N G A P P L I A N C E S A S A W H O L E CLASSIFICATION SYSTEM Appliances a s a whole a r e c l a s s i f i e d i n e i g h t groups, d e s i g n a t e d by t h e symbols Al, A2, . , A8 r e s p e c t i v e l y ( s e e s e c t i o n 2 . 1 . 2 . 4 . ) , on t h e b a s i s o f t e n c l a s s e s o f u t i l i z a t i o n and f o u r l o a d s p e c t r a .

..

2.1.2.2.

CLASSES O F U T I L I Z A T I O N By d u r a t i o n of o s e o f a h o i s t i n g a p p l i a n c e i s meant t h e number of h o i s t i n g c y c l e s which t h e a p p l i a n c e performs. A h o i s t i n g c y c l e i s t h e e n t i r e sequence o f o p e r a t i o n s c o m e n c i n g when a l o a d i s h o i s t e d and ending a t t h e mment when t h e a p p l i a n c e is ready t o h o i s t t h e n e x t l o a d . The t o t a l d u r a t i o n of u s e i s a computed d u r a t i o n o f u s e , c o n s i d e r e d as a guide v a i u e , c o m e n c i n g when t h e a p p l i a n c e i s put i n t o s e r v i c e and ending when i t i s f i n a l l y taken o i ~ to f s e r v i c e . On t h e b a s i s o f t h e t o t a l d u r a t i o n o f u s e , we have t e n c l a s s e s o f u t i l i z a t i o n , d e s i g n a t e d by t h e symbols UO, U1, ..., U9. They a r e d e f i n e d i n t a b l e 1.2.1.2.2.

-

Table T.2.1.2.2.

C l a s s e s of u t i l i z a t i o n

T o t a l d u r a t i o n o f use ( n m b e r "max o f h o i s t i n g c y c l e s ) I x

< < < < < < < < <

2.1.2.3.

"max "max "max "max "max "max nmax nmax "max

L O A D SPECTRUM The l o a d spectrum c h a r a c t e r i z e s t h e t o t a l nunber o f l o a d s h o i s t e d d u r i n g t h e t o t a l d u r a t i o n o f u s e ( s e e 2 . 1 . 2 . 2 . ) o f an a p p l i a n c e . I t i s a d i s t r i b u t i o n f u n c t i o n ( s m e d ) y = f ( x ) , e x p r e s s i n g t h e f r a c t i o n x ( O ,< x 6 1 ) of t h e t o t a l d u r a t i o n o f u s e , d u r i n g which t h e r a t i o c f t h é hoisted ;oad r o íhe s o f e work:?~ 13cd a t t a i n s a t l e a s t a given value y (O 4 y 4 1 ) . Examples o f a l o a d spectrum a r e given i n f i g s . 2 . 1 . 2 . 3 . 1 .

o

03

o

F i g u r e 2.1.2.3.1.

mq

n

1

-

a

-6

-5

-4

-J

-

a and b .

-2

O

-1

1.g

F i g u r e 2.1.2.3.1.

-

(&)

b

= loads ;

m f m a x = s a f e working l o a d ;

n

= nunber of h o i s t i n g c y c l e s i n r e s p e c t o f which t h e h o i s t e d l o a d i s g r e a t e r than or equal t o m q ;

nmaX = nunber o f h o i s t i n g c y c l e s d e t e r m i n i n g t h e t o t a l d u r a t i o n o f use. Each spectrum i s a s s i g n e d a spectrum f a c t o r kp, d e f i n e d by :

For t h e purposes of group c l a s s i f i c a t i o n t h e exponent d i s t a k e n by c o n v e n t i o n 22 rquul ts 3 . In many a p p l i c a t i o n s t h e f u n c t i o n f ( x ) may be approximated by a f u n c t i o n cons i s t i n g o f a c e r t a i n number r o: s t e p s ( s e ? f i g . 2 . ¡ . 2 . 3 . 2 . ) , cornprising r e s p e c t i v e l y n l , n 2 , ..., nr h o i s t i n g c y c l e s , t h e l o a d may be c o n s i d e r e d a s p r a c t i c a l l y c o n s t a n t and e q u a l t o m& d u r i n g t h e n i c y c l e s o f t h e i t h s t e p . I f nmax r e p r e s e n t s t h e t o t a l d u r a t i o n o f u s e and t h e g r e a t e s t among t h e m f i l o a d s , t h e r e exists a relation :

mema,

o r i n approximated forrn :

, "NI

.

"2

-

"3

"m. "m81

"r " max

F i g u r e 2.1.2.3.2. According t o i t s l o a d ipectrurn, a h o i s t i n g a p p l i a n c e is p i a c e d i n one of t h e f 0 u r spectrum c l a s s e s Q1, Q2, Q 3 , Q4 d e f i n e d i n t a b l e 1.2.1.2.3. Table T.2.1.2.3. Spectrwn c l a s s e s

I

Symbol

Spectrum f a c t o r kp

l

2.1.2.4.

GROUP CLASSIFICATION OF HOISTING APPLIANCES Group c l a s s i f i c a t i o n o f h o i s t i n g a p p l i a n c e s a s a whole i s deterrnined frorn t a b l e T.2.1.2.4. Table T.2.1.2.4. Appliance qroups

2,1,2.5.

GUIDANCE ON GROUP CLASSIFICATION OF A N APPLIANCE D i r e c t i o n s concerning t h e c l a s s i f i c a t i o n of h o i s t i n g a p p l i a n c e s a r e given i n t a b l e T.2.1.2.5. S i n c e a p p i i a n c e s o f t n e sarne t y p e rnay be used i n a wide v a r i e t y o f ways, t h e grouping shown i n t h i s t a b l e can o n l y be taken a s a rnodel. In p a r t i c u l a r , where s e v e r a 1 groups a r e shown a s a p p r o p r i a t e t o an a p p l i a n c e o f a given t y p e , i t i s n e c e s s a r y t o a s c e r t a i n , on t h e b a s i s o f t h e a p p l i a n c e ' s cornputed t o t a l d u r a t i o n o f use and l o a d spectrurn, i n which c l a s s e s of u t i l i z a t i o n and load spectrurn i t h a s t o be p l a c e d , and consequently i n which group.

2.1.3.

2.1.3.1.

C L A S S I F I C A T I O N OF

I N D I V I D U A L MECHANISMS A S A WHOLE

CLASSIFICATION SYSTEM I n d i v i d u a l rnechanisrns a s a whole a r e c l a s s i f i e d i n e i g h t groups, d e s i g n a t e d r e s p e c t i v e l y by t h e syrnbols M1, M2, M8 ( s e e 2 . 1 . 3 . 4 . ) , on t h e b a s i s o f t e n c l a s s e s o f u t i l i z a t i o n and f o u r c l a s s e s of l o a d i n g spectrurn.

...,

Table T.2.1.2.5.

I1

2

4

qrsup

1 Erection

I

cranes

( Stocking

and r e c l a i m i n g t r a n s p o r t e r s

S t o c k i n g and r e c l a i m i n g t r a n s p o r t e r s

6

Workshop c r a n e s

1

I

A1 - A2

1

1

A1

1 kbok

duty

1

l l l 11

ii

(

Overhead t r a v e l l i n g c r a n e s , p i g - b r e a k i n g cranes, scrapyard cranes

A6

S t r i p p e r c r a n e s , open-hearth f u r n a c e charging cranes Forge c r a n e s

A8

/

I

I Hook o r s p r e a d e r d u t y

12.b

Other b r i d g e c r a n e s ( w i t h c r a b and/or slewing j i b c r a n e )

kbok duty

Bridge c r a n e s f o r u n l o a d i n g , b r i d g e c r a n e s ( w i t h c r a b and/or s l e w i n g j i b c r a n e )

Grab o r rnagnet

Drydock c r a n e s , s h i p y a r d j i b c r a n e s , j i b cranes for dismantling

Hook duty

Dockside c r a n e s ( s l e w i n g , on g a n t r y ) , f l o a t i n g c r a n e s and pontoon d e r r i c k s

t-bok duty

Dockside c r a n e s ( s l e w i n g , on g a n t r y 1, f l o a t i n q c r a n e s and pontoon d e r r i c k s

Grab o r rnagnet

l4 l5

l7

18

11

- A8 A8

Bridge cranes f o r unloading, bridge cranes for containers

I I l

1

Grab o r magnet

12.a

l3

A5 A6

Soaking-pit c r a n e s

1

1

- A8 A3 - A5

Grab o r magnet

Ladle c r a n e s 1O

- A2

E r e c t i o n and d i s m a n t l i n g c r a n e s f o r power s t a t i o n s , rnachine shops, e t c .

5 r

clas;ifi¿atioll o f appliami~cc

knd-operated appliances

1

1

- Lidunce for

A6

- A8

A5

- A6

1

A4

I

A6

- A8

A3

- A4

F l o a t i n g c r a n e s and pontoon d e r r i c k s f o r v e r y heavy l o a d s ( u s u a l l y g r e a t e r t h a n 100 t ) Deck c r a n e s

19

Deck c r a n e s

20

Tower c r a n e s f o r b u i l d i n g

21

Derricks

22

Railway c r a n e s allowed t o r u n i n t r a i n

(

Hook duty

1

A4 - A5

Grab o r rnagnet

- A4 A2 - A3 A3

A4 -

-

( 1 ) Only a few t y p i c a l c a s e s o f u s e a r e shown, by way of g u i d a n c e , i n t h i s column.

1

2.1.3.2.

CLASSES OF U T I L I Z A T I O N By a i r a t i o n o f u s e o f a mechanism i s meant t h e time d u r i n g which t h e mechanism i s a c t u a l l y i n motion. The t o t a l d u r a t i o n o f u s e i s a c a l c u l a t e d d u r a t i o n o f u s e , c o n s i d e r e d a s a guide v a l u e , a p p l y i n g up t o t h e time o f replacement of t h e mechanism. I t i s e x p r e s s e d i n terms of hours. On t h e b a s i s o f t h i s t o t a l d u r a t i o n o f u s e , we have t e n c l a s s e s o f u t i l i z a t i o n , T O , T1, T2, T9. They a r e d e f i n e d i n t a b l e T.2.1.3.2.

...,

Table T.2.1.3.2. Classes of u t i l i z a t i o n

1

2.1.3.3.

Symbol

1

Total d u r a t i o n o f use T (h)

LOADING SPECTRUH The l o a d i n g spectrum c h a r a c t e r i z e s t h e magnitude of t h e l o a d s a c t i n g on a mechanism d u r i n g i t s t o t a l d u r a t i o n o f use. I t is a d i s t r i b u t i o n f u n c t i o n (summed) y = f ( x ) , e x p r e s s i n g t h e f r a c t i o n x ( O < x 6 1 ) o f t h e t o t a l d u r a t i o n o f u s e , d u r i n g which t h e mechanism is s u b j e c t e d t o a l o a d i n g a t t a i n i n g a t l e a s t a f r a c t i o n y (O 4 y 1) o f t h e maximm l o a d i n g ( s e e f i g u r e 2.1.2.3.1. ). Each spectrum i s a s s i g n e d a s p e c t r m f a c t o r ,k,

d e f i n e d by :

For t h e purposes o f group c l a s s i f i c a t i o n , d i s taken by convention a s equal t o 3. In many a p p l i c a t i o n s t h e f u n c t i o n f ( x ) may be approximated by a f u n c t i o n c o n s i s t i n g o f a c e r t a i n nunber r of s t e p s ( s e e f i g . 2 . 1 . 2 . 3 . 2 . ) , o f r e s p e c t i v e d u r a t i o n s t l , t2, t r ; t h e l o a d i n g s S may be c o n s i d e r e d a s p r a c t i c a l l y c o n s t a n t and equal t o Si d u r i n g t h e d u r a t i o n ti. I f T r e p r e s e n t s t h e t o t a l d u r a t i o n o f u s e and SmaX t h e g r e a t e s t o f t h e l o a d i n g s S1, S2, ..., S r , t h e r e e x i s t s a r e l a t i o n :

...

a n 3 i n approximated form :

1i+

k m = (- 51-) 3

hax

T

52 ) 3 (__

t2 +

. ..

(Srj'5

+

hax

Smax

T

=

r i=l

(-1

si

3

ha,

ti

T

Depending on i t s l o a d i n g spectrum, a mechanism i s p l a c e d i n one of t h e f o u r spectrum c l a s s e s L1, L2, L3, La, d e f i n e d i n t a b l e T.2.1.3.3. Table T.2.1.3.3. Spectrum c l a s s e s

k,

Spectrum f a c t o r

,<

km O. 125

<

0.250 O. 500

< <

k km km

G R O U P C L A S S I F I C A T I O N OF I N D I V I D U A L

2 . 1 3.4,

,

< ,< ,<

0.125 0.250 O. 500 1.000

MECHANISMS AS A UHOLE

On t h e b a s i s o f t h e i r c l a s s of u t i l i z a t i o n and t h e i r spectrurn c l a s s , i n d i v i d u a l mechanisms a s a whole a r e c l a s s i f i e d i n one of t h e e i g h t groups M1, M 2 , ..., M8, defined i n t a b l e 1.2.1.3.4. Table T.2.1.3.4. Mechanism qroups

(

2.1.3,5.

~ l a s so f

1

Class of u t i l i z a t i o n

GUIDANCE FOR GROUP CLASSIFICATIDN OF INDIVIDUAL MECHNISMS AS A WHOLE

Guidancc f o r group c l a s s i f i c a t i o n o f an i n d i v i d u a l mechanisrn a s a whole is given i n t a b l e T.2.1.3.5. 5 i n c e a p p l i a n c e s of t h e sane type rnay be used i n a wide v a r i e t y o f ways, t h e grouping d i r e c t i o n s i n t h i s t a b l e can only be taken a s a model. I n p a r t i c u l a r , where s e v e r a l groups a r e shown a s a p p r o p r i a t e t o a mechanism of a g i v e n t y p e , i t i s n e c e s s a r y t o a s c e r t a i n , on t h e b a s i s o f t h e mechanism's c a l c u l a t e d t o t a l d u r a t i o n o f u s e and l o a d i n g spectrurn, i n which c l a s s of u t i l i z a t i o n ( s e e 2 . 1 . 3 . 2 . ) and spectrum ( s e e 2 . 1 . 3 . 3 . ) i t h a s t o be p l a c e d , and consquently i n which group o f mechanisms ( s e e 2 . 1 . 3 . 4 . ) .

1

T a b l e T.2.1.3.5

Guidance f o r q r o g p c l a s s i f i c a t i o n o f a rnechanism

Type o f a p p l i a n c e Re f erence 1

1

Designation

4

1

1

1 Stocking

A

and r e c l a i m i n g t r a n s -

t /

8 9

1 Workshop

Grab o r magnet

1

M7-M8

I

1

1 b0verhead t r a v e x i n g cranes, sgr e a k i n g cranes, s c r a p y a r d c r a n e s

M6 1

cranes

! M 6 -

-

M4

M5-M6

Hook d u t y

S t o c k i n g and r e c l a i m i n g t r a n s -

1 porters 7

Type o f mechanism

I E r e c t i o n and d i s m a n l l i n g c r a n e s f o r power s t a t i o n s , machine shops, e t c .

5 6

1

E r e c t i o n cranes

porters

I

~articulars concerning nature of use (1)

Hand-operated a p p l i a n c e s

2 3

1

M

1

l

M4-M5

-

1

%-M7

-

1

M4

1

4

1 11

1

M5-Mó M7-M8

'

M5

I

7

1

Grab o r magnet

;

M8

Ladle cranes

/ Soaking-pit

cranes S t r i p p e r cranes, open-hearth furnace-charging cranes

1

1

Forge c r a n e s

1

Bridge cranes f o r dnloading, b r i d g e cranes f o r c o n t a i n e r s

a. Hook o r s p r e a d e r ! ! duty 1

Other b r i d g e cranes ( w i t h c r a b and/or s l e w i n g j i b c r a n e )

b. Hook d u t y

Bridge cranes for unloading, bridge cranes ( w i t h crab a n d l o r slewing j i b crane)

M6-M7

i

M3-M4

M6-M7 I

i

l ~ r a bo r magnet

M5-M6

M8

(

1 M5-MS

1

Drydock cranes, s h i p y a r d j i b c r a n e s , Hook d u t y j i b cranes f o r d i s m a n t l i n g

M5-N.5

M-M5

D o c k s i d e c r a n e s ( s l e w i n g , on g a n t r y , e t c . ) , f l o a t i n g c r a n e s and p o n t o o n Hook d u t y derricks

%-M7

M5-MS

1

1 M3-M4

1

M5-Wt

i

¡ M7-M8

1 M4-M5

-

1

M3-M4

1

Dockside c r a n e s ( s l e w i n g , on g a n t r y , p t c . ) , f l o a t i n g c r a n e s and p o n t o o n Grab o r magnet derricks F l o a t i n g c r a n e s and p o n t o o n d e r r i c k s f o r v e r y heavy l o a d s ( u s u a l l y g r e a t e r t h a n 100 t ) 18

Deck c r a n e s

Hook d u i y

19

Deck c r a n e s

Grab o r magnei

20

1

Tower c r a n e s f o r b u i l d i n g

í1)

l

i M3-M4

P,5-Wt

M3-M

t.u4

M5

[

M3-M4

M2

M3

M3-M4

M4-M5

M3-M4

M4

M3

M3

Only a f e k t y ~ i c a ! cases o f use a r e shown, by way o f guidance, i n t h i s column.

2-10

1

I 1

M4-M5

(

j M4-M5

2.1.4.

2.1.la.l.

C L A C S I F I C A T I O N OF COMPONENTS

C L A S S I F I C A T I O N SYSTEM Ccnnponents, b o t h s t r u c t u r a l and mechanical, a r e c l a s s i f i e d i n e i g h t groups, designed E8, on t h e b a s i s o f e l e v e n c l a s s e s o f u t i l i z a r e s p e c t i v e l y b y t h e symbols E l , E2, t i o n and four c l a s s e s o f s t r e s s spectrum.

...,

2.1.4.2.

CLASSES OF U T I L I Z A T I O N By d u r a t i o n of use o f a cmponent i s meant t h e nllmber of s t r e s s c y c l e s t o which t h e component i s subjected. A s t r e s s c y c l e i s a complete s e t o f successive s t r e s s e s , c m e n c i n g a t t h e moment when t h e s t r e s s under c o n s i d e r a t i o n exceeds t h e s t r e s s 0, defined i n f i g . 2.1.b.3. and ending a t t h e moment when t h i s s t r e s s i s , f o r t h e f i r s t time, about t o exceed a g a i n 0, i n t h e same d i r e c t i o n . F i g . 2.1.4.3. therefore represents the trend of t h e s t r e s s a over a d u r a t i o n o f use equal t o f i v e s t r e s s c y c l e s . The t o t a l d u r a t i o n of use i s a c m p u t e d d u r a t i o n o f use, considered as a guide value, a p p l y i n g u p t o t h e t i m e o f replacement of t h e cmponent. I n t h e case o f s t r u c t u r a l components t h e nunber c f s t r e s s c y c l e s i s i n a constant r a t i o w i t h t h e n m b e r o f h o i s t i n g c y c l e s o f t h e appliance. C e r t a i n c m p o n e n t s may be s u b j e c t e d t o severa1 s t r e s s c y c l e s d u r i n g a h o i s t i n g c y c l e depending on t h e i r p c s i t i o n i c the s t r ü c t i i r e . iience t h e r a t i o i n q u e s t i o n may d i f f e r from one cmponent t o another. Once t h i s r a t i o i s known, t h e t o t a l d u r a t i o n o f use of t h e component i s d e r i v e d frm t h e t o t a l d u r a t i o n o f use which determined t h e c l a s s o f u t i l i z a t i o n of t h e appliance. As r e g a r d s mechanical cmponents, t h e t o t a l d u r a t i o n o f use i s d e r i v e d from t h e t o t a l d u r a t i o n o f use o f t h e mechanism t o which t h e cmponent under c o n s i d e r a t i o n belongs, account b e i n g taken of i t s speed of r o t a t i o n and/or o t h e r c i r c m s t a n c e s affecting i t s operation. On t h e b a s i s of t h e t o t a l d u r a t i o n o f use, we have eleven c l a s s e s of u t i l i z a t i o n , designe010. They a r e d e f i n e d i n t a b l e T.2.1.4.2. t e d r e s p e c t i v e l y by t h e symbols BO, B l ,

...,

Table T.2.1.4.2. Classes o f u t i l i z a t i o n

S T R E S S SPECTRUM The s t r e s s s p e c t r u n c h a r a c t e r i z e s t h e m a g n i t u d e o f t h e l o a d a- -c- t i n g on t h e component d u r i n g i t s t o t a l d u r a t i o n o f use. I t i s a d i s t r i b u t c o n f u n c t i o n ( s m e d ) y = f ( x ) , x 4 1) o f t h e t o t a l d u r a t i o n o f use ( s e e 2.1.4.2.1, e x p r e s s i n g t h e f r a c t i o n x (O d u r i n g which the cmponent i s subjected t o a s t r e s s a t t a i n i n g a t l e a s t a f r a c t i o n y (O ,< x 4 1 ) o f t h e maximm s t r e s s . -

<

Each s t r e s s spectrum i s a s s i g n e d a spectrum f a c t o r ksD, d e f i n e d b y

Where c i s an exponent depending o n t h e p r o p e r t i e s o f t h e m a t e r i a l concerned, t h e shape and s i z e o f t h e c m p o n e n t i n q u e s t i o n , i t s s u r f a c e roughness and i t s degree o f c o r r o s i o n (see b o o k l e t 4). I n rnany a p p l i c a t i o n s t h e f u n c t i o n f ( x ) rnay be approximated b y a f u n c t i o n c o n s i s t i n g o f a c e r t a i n number r o f s t e p s , c o m p r i s i n g r e s p e c t i v e l y nl, n2, nr s t r e s s c y c l e s ; t h e s t r e s s 0 may be c o n s i d e r e d as p r a c t i c a l l y c o n s t a n t and e q u a l t o 0 i d u r i n g n i c y c l e s . Ifn r e p r e s e n t s t h e t o t a l d u r a t i o n o f use and ,,U , t h e g r e a t e s t of t h e s t r e s s e s 0 1 , 0 2 , ..., 0, t h e r e e x i s t s a r e l a t i o n :

...

and i n a p p r o x i m a t e d f o r m :

Depending on i t s s t r e s s spectrum, a cornponent i s p l a c e d i n one o f t h e spectrum ( 1 1. c l a s s e s P1, P2, P3, P4, d e f i n e d i n t a b l e 7.2.1.4.3. T a b l e T.2.1.4.3. Spectrum c l a s s e s

(1)

There which load. kSp =

a r e c m p o n e n t s , b o t h s t r u c t u r a l and rnechanical, such as s p r i n g l o a d e d components, a r e s u b j e c t e d t o l o a d i n g t h a t i s q u i t e o r a l m o s t independent o f t h e w o r k i n g S p e c i a l c a r e s h a l l be t a k e n i n c l a s s i f y i n g such components. I n most cases 1 and t h e y b e l o n g t o c l a s s P4.

For s t r u c t u r a l c m p o n e n t s , t h e s t r e s s e s t n hp t a k ~ ni n t a r o n s i r i o r ? t i c n f r r dct@rrr,i-n a t i o n o f t h e spectrum f a c t o r a r e t h e d i f f e r e n c e s Usup - U,,, between t h e upper s t r e s s e s aSupand t h e a v e r a g e s t r e s s U,, t h e s e c o n c e p t s b e i n g d e f i n e d by f i g . 2.1.4.3. r e p r e s e n t i n g t h e v a r i a t i o n o f t h e s t r e s s over time d u r i n g f i v e s t r e s s c y c l e s .

F i g . 2.1.4.3.

- V a r i a t i o n o f s t r e s s a s a f u n c t i o n of time d u r i n q f i v e s t r e s s

%up

:

upper s t r e s s

-

" S U ~ max

-

-~~~dximum upper s t r e s s

GSupmin

=

minimurn upper s t r e s s

Ginf

=

lower s t r e s s

m

=

a r i t h m e t i c mean o f a l 1 upper and lower s t r e s s e s d u r i n g t h e t o t a l duration of use

C Y C ~ ~ S

In t h e c a s e of mechanical components, we can p u t U, = O t h e s t r e s s e s t o be i n t r o d u c e d i n t o t h e c a i c u l a t i o n of t h e spectrum f a c t o r then b e i n g t h e t o t a l s t r e s s e s o c c u r r i n g i n t h e r e l e v a n t s e c t i o n of t h e component.

2.1.4.4.

GROUP CLASSIFICATION OF COWPONFNTc ai the basis of their class of utilization and their stress spectrum class, c m p o nents are classified in one of the eight groups E l , E2, ..., E8, defined in table

T . z . ~.4.4. Table T.2.1.4.4. Cornponent qroups -

-t

Stress Spectrum class

-

Class o f utilization 80

El El

81

j

82

7

,

El

I

El

1

El

F2

El l

El E2

1

ES

,

El

E2

E3

E2

E3

E4

E3

E4

ES

E5

E6

E4 1

E4

1 I

i

E5

!

E5 E6

E6

E7

E7

E8

/

1

1 ;

l

E6

E7

E8

E7

! E8

E8

E8

E8

E8 E8

' i

E8

1

E8

, l

1

LOADS ENTERING

I N T O THE

D E S I G N OF S T R U C T U R E S

The s t r u c t u r a l c a l c u l a t i o n s s h a l l be conducted by d e t e r m i n i n g t h e s t r e s s e s developed i n an a p p l i a n c e d u r i n g i t s o p e r a t i o n . These s t r e s s e s s h a l l be c a l c u l a t e d on t h e b a s i s o f t h e l o a d s d e f i n e d below : a ) The p r i n c i p a l l o a d s e x e r t e d on t h e s t r u c t u r e o f t h e a p p l i a n c e , assumed t o be s t a t i o n a r y , i n t h e most u n f a v o u r a b l e s t a t e o f l o a d i n g ; b ) Loads due t o v e r t i c a l m o t i o n s ; C ) Loads due t o h o r i z o n t a l m o t i o n s ; d ) Loads due t o c l i m a t i c e f f e c t s . The v a r i o u s l o a d s , t h e f a c t o r s t o be a p p l i e d , and t h e p r a c t i c a 1 method o f c o n d u c t i n g t h e c a l c u l a t i o n s a r e examined below. I n what f o l l o w s ,

t h e d e f i n i t i o n s g i v e n below a r e used :

Working l o a d :

Weight o f t h e u s e f u l l o a d l i f t e d , p l u s t h e w e i g h t o f t h e a c c e s s o r i e s (sheave b l o c k ~ , hooks, l i f t i n g beams, grab, e t c . )

Dead - - - - - -l o- a- -d

Dead w e i g h t o f components a c t i n g on a g i v e n member, e x c l u d i n g t h e working load.

------------

:

PRINCIPAL

LOADS

The p r i n c i p a l l o a d s i n c l u d e

- t h e l o a d s due t o t h e dead w e i g h t o f t h e c m p o n e n t s : SG

-

t h e l o a d s due t o t h e w o r k i n g l o a d : SL

a l 1 movable p a r t s b e i n g assumed t o be i n t h e i r most u n f a v o u r a b l e p o s i t i o n . Each s t r u c t u r a l member s h a l l be d e s i g n e d f o r t h e p o s i t i o n o f t h e a p p l i a n c e and magnitude o f t h e w o r k i n g l o a d (between z e r o and t h e s a f e w o r k i n g l o a d ) which g i v e s r i s e t o t h e maximum s t r e s s e s ( 1 ) i n t h e mernber i n q u e s t i o n .

L OADS DUE

T O VERTICAL

MOTIONS

These l o a d s stem from p i c k i n g up t h e w o r k i n g l o a d more o r l e s s suddenly, from a c c e l e r a t i o n s ( o r d e c e l e r a t i o n s ) o f t h e h o i s t i n g m o t i o n , and from v e r t i c a l shock l o a d i n g s due t o t r a v e l l i n g a l o n g r a i l t r a c k s .

(1

I n c e r t a i n cases, t h e maximum s t r e s s may be o b t a i n e d w i t h no w o r k i n g l o a d .

2.2.2.1.

LOADS DUE T O H O I S T I N G OF THE YORKIMG LDAD . k m t s k l l bc tekcr. c f t h c o ; c i l l a t i m s

eauzed wPer, l i f t i n g tSEti l a a d by i r r ~ l t f p l y i n g t h e l o a d s due t o t h e working l o a d by a f a c t o r c a l l e d t h e "dynarnic c o e f f i c i e n t Y".

2.2.2.1.1,

VALUES DF THE DYNAMIC COEFFICIENT

y

The v a l u e o f t h e dynamic c o e f f i c i e n t '? t o be a p p l i e d t o t h e l o a d a r i s i n g f r m t h e working l o a d i s g i v e n by t h e e x p r e s s i o n :

kdhere VL i s t h e h o i s t i n g speed i n rn/s. and

C

an e x p e r i m e n t a l l y d e t e r m i n e d c w f f i c i e n t ( 1 ) .

The f o l l a i i n g v a l u e s s h a l l be a d o p t e d :

C C

= 0 , 6 f o r overhead t r a v e l l i n g c r a n e s and b r i d g e c r a n e s = 0,3

for j i b cranes.

The rnaximum f i g u r e t o be t a k e n f o r t h e h o i s t i n g speed when a p p l y i n g t h i s formula i s 1 mís. For h i g h e r s p e e d s , t h e dynamic c o e f f i c i e n t '? i s n o t f u r t h e r i n c r e a s e d . The v a l u e t o be a p p l i e d f o r t h e c o e f f i c i e n t y i n t h e c a l c u l a t i o n s s h a l l i n no c a s e be l e s s than 1,15. The v a l u e s o f '? a r e g i v e n i n t h e c u r v e s of f i g u r e 2.2.2.1.1. speeds VL.

i n terms o f h o i s t i n g

F i g u r e 2.2.2.1.1. Values of dynarnic c o e f f i c i e n t y

Y'

Ovrrhead mrelling v l n t r Bridge c n n e s

-

(i)

The f i g u r e g i v e n f o r t h i s c o e f f i c i e n t 5 i s t h e r e s u l t o f a l a r g e nunber o f measurements made on d i f f e r e n t t y p e s o f a p p l i a n c e s .

Note - The above mentioned c o e f f i c i e n t 6 i s n o t t h e same f o r "overhead t r a v e l l i n g c r a n e s and b r i d g e c r a n e q " 2nd f n r " j i b c r a n e c " , The d i f f e r e n c e a r i s e s from t h e f a c t t h a t t h e dynamic c o e f f i c i e n t y i s , o t h e r t h i n g s being e q u a l , srnaller when t h e h o i s t i n g load i s c a r r i e d by a mmber having some f l e x i b i l i t y , a s i n j i b c r a n e s where t h e j i b i s never r i g i d . In a s i m i l a r way, u s e of t h e c o e f f i c i e n t y a s i n d i c a t e d f o r j i b c r a n e s may be extended t o c e r t a i n o t h e r a p p l i a n c e s such a s , f o r example, t r a n s p o r t e r s f o r t h e d e s i g n c a s e c o r r e s p o n d i n g t o load on t h e c a n t i l e v e r boom ; t h e value o f y i n d i c a t e d f o r overhead t r a v e l l i n g c r a n e s s h o u l d , o f c o u r s e , be used f o r t h e d e s i g n c a s e s where t h e load i s a p p l i e d between t h e l e g s o f t h e machine a s t h e r i g i d i t y o f t h e s t r u c t u r e a t t h i s p o i n t i s comparable w i t h t h a t one o f an overhead t r a v e l l i n g c r a n e g i r d e r .

LOAOS QUE T 0 ACCELERATION (OR D E C E L E R A T I O N ) OF THE H O I S T I N G M O T I O N AND TO V E R T I C A L SHOCK LOAOINGS WHEN T R A V E L L I N G ALONG R A I L TRACKS

S i n c e t h e c o e f f i c i e n t y t a k e s account o f t h e degree o f s n a t c h on t h e working l o a d which i s t h e l a r g e s t shock l o a d i n g , l o a d s due t o a c c e l e r a t i o n ( o r d e c e l e r a t i o n ) o f t h e h o i s t i n g motion and t h e v e r t i c a l r e a c t i o n s due t o t r a v e l l i n g a l o n g t r a c k s , a s s m e d t o be p r o p e r l y l a i d , s h a l l be n e g l e c t e d ( 1 ) .

SPECIAL

CASE

In t h e c a s e o f c e r t a i n a p p l i a n c e s , t h e l o a d s due t o t h e dead l o a d s a r e o f o p p o s i t e s i g n t o t n o s e due t o t h e working l o a d , i n which c a s e a comparison must be made between t h e l o a d i n g f i g u r e o b t a i n e d i n t h e "appliance under load" c o n d i t i o n , w i t h t h e dynarnic c o e f f i c i e n t y a p p l i e d t o t h e working l o a d , and t h e l o a d i n g f i g u r e obt a i n e d i n t h e "no-load" c o n d i t i o n , t a k i n g i n t o account t h e o s c i l l a t i o n s r e s u l t i n g from s e t t i n g down t h e l o a d , a s f o l l o w s : Let be t h e a l g e b r a i c v a l u e o f t h e l o a d s due t o t h e dead load

SL

be t h e a l g e b r a i c v a l u e o f t h e l o a d s due t o t h e working load.

The a m p l i f i e d t o t a l l o a d , when s e t t i n g down t h e load i s o b t a i n e d by t h e e x p r e s s i o n

Which i s compared w i t h t h e load f o r t h e " a p p l i a n c e under load" c o n d i t i o n determined by t h e e x p r e s s i o n :

5,

+

Y 5L

t h e c m p o n e n t being f i n a l l y designed on t h e b a s i s o f t h e more unfavourable o f t h e s e two v a l u e s .

(1

T h i s assumes t h a t t h e r a i l j o i n t s a r e i n good c o n d i t i o n . The d e t r i m e n t a l e f f e c t on h o i s t i n g a p p l i a n c e s o f r a i l t r a c k s i n poor c o n d i t i o n i s so g r e a t , both f o r t h e s t r u c t u r e and t h e machinery, t h a t i t i s necessary t o s t i p u l a t e t h a t t h e r a i l j o i n t s must be maintained i n good c o n d i t i o n : no shock l o a d i n g c o e f f i c i e n t can allow f o r t h e damage caused by f a u l t y j o i n t s . In s o f a r a s high speed a p p l i a n c e s a r e concerned, t h e b e s t s o l u t i o n i s t o butt-weld t h e r a i l s , i n o r d e r t o e l i m i n a t e e n t i r e l y t h e shock l o a d i n g s which occur when an a p p l i a n c e runs over j o i n t s .

- This formula is based on the fact that the dynamic coefficient determines the maximun amplitude of the oscillations set up in the structure when the load is picked up. The amplitude of the oscillation is given by :

It is assumed that the amplitude of the oscillation set up in the structure when the load is set down is half that of the oscillation caused when hoisting takes olace. The ultimate state of loading is therefore

:

Which must be compared with the state of loading given by :

Hoistino and lowerino curve when SI and Sr are of oooosite sion

L D A D S DUE

T O HORIZONTAL MOTIONS SH

The l o a d s due t o h o r i z o n t a l rnotions a r e a s f o l l o w s : 1 ) The i n e r t i a e f f e c t s due t o a c c e l e r a t i o n ( o r d e c e l e r a t i o n ) o f t h e t r a v e r s e , t r a v e l , s l e w i n g o r l u f f i n g motions. These e f f e c t s can be c a l c u l a t e d i n terms o f t h e v a l u e of t h e a c c e l e r a t i o n ( o r d e c e l e r a t i o n ) . 2 ) The e f f e c t s o f c e v t r i f u g a l f o r c e . 3 ) T r a n s v e r s e h o r i z o n t a l r e a c t i o n s r e s u l t i n g from r o l l i n g a c t i o n . 4 ) Buffer e f f e c t s .

HORIZONTAL EFFECTS DUE T 0 ACCELERATION (OR DECELERATION) The l o a d s due t o t h e a c c e l e r a t i o n s ( o r d e c e l e r a t i o n s ) irnparted t o t h e rnovable e l e rnents when s t a r t i n g o r b r a k i n g a r e c a l c u l a t e d f o r t h e v a r i o u s s t r u c t u r a l members.

. . . l .

TRAVERSE A N O TRAVEL MOTIONS For t h e s e motions t h e c a l c u l a t i o n i s rnade by c o n s i d e r i n g a h o r i z o n t a l f o r c e a p p l i e d a t t h e t r e a d of t h e d r i v e n wheels p a r a l l e l t o t h e r a i l . The l o a d s s h a l l be c a l c u l a t e d i n terrns o f t h e a c c e l e r a t i o n ( o r d e c e l e r a t i o n ) time assumed a c c o r d i n g t o t h e working c o n d i t i o n s and t h e speeds t o be a t t a i n e d . From i t i s deduced t h e v a l u e ( i n rn/sL) o f t h e a c c e l e r a t i o n t o be used f o r c a l c u l a t i n g t h e h o r i z o n t a l f o r c e a c c o r d i n g t o t h e rnasses t o be s e t i n motion. Nste - í f t h e speed and a c c e l e r a t i o n v a l u e s a r e n o t s p e c i f i e d by t h e u s e r , a c c e l e r a t i o n t i m e s c o r r e s p o n d i n g t o t h e s p e e d s t o be reached rnay be chosen a c c o r d i n g t o t h e t h r e e f o l l o w i n g working c o n d i t i o n s : a ) Appliances o f low and moderate speed w i t h a g r e a t l e n g t h of t r a v e l ; b ) Appliances of moderate and h i g h speed f o r normal a p p l i c a t i o n s ; c ) High speed a p p l i a n c e s with h i g h a c c e l e r a t i o n . In t h e l a t t e r c a s e , i t i s a l m o s t always n e c e s s a r y t o d r i v e a l 1 t h e r a i l wheels. Table 1 . 2 . 2 . 3 . 1 . 1 . g i v e s t h e v a l u e s of a c c e l e r a t i o n t i m e s and a c c e l e r a t i o n s f o r the three conditions.

Table T.2.2.3.1.1. A c c e l e r a t i o n t i m e and a c c e l e r a t i o n v a l u e

with long travel t o be r e a c h e d

m/s

Acceleration time

Acceleration

(normal a p p l i c a t i o n s ) Acceleration

Í

time

/

Acceleration

(c) h i g h speed w i t h h i g h accelerations Acceleration time

Acceleration

The h o r i z o n t a l f o r c e t o be t a k e n i n t o account s h a l l be n o t l e s s t h a n 1 / 3 0 t h n o r more t h a n 1 / 4 o f t h e l o a d on t h e d r i v e n o r b r a k e d wheels.

2.2.3.1.2.

SLEWING AND L U F F I N G ( O E R R I C K I N G ) MOTIONS F o r s l e w i n g and l u f f i n g m o t i o n s t h e c a l c u l a t i o n s s h a l l be based o n t h e a c c e l e r a t i n g ( o r d e c e l e r a t i n g ) t o r q u e a p p l i e d t o t h e m o t o r s h a f t o f t h e mechanisrns. The r a t e s o f a c c e l e r a t i o n w i l l depend upon t h e a p p l i a n c e ; f o r a n o r m a l c r a n e a v a l u e between 0 . 1 m/s2 ana 0 . 6 rn/s2, a c c o r d i n g t o t h e spoed ano r a d i u s , may be chosen f o r t h e a c c e l e r a t i o n a t t h e j i b head so t h a t a n a c c e l e r a t i o n t i m e o f frorn 5 t o 10 s i s achieved. Note - A method f o r c a l c u l a t i n g t h e e f f e c t s o f a c c e l e r a t i o n o f h o r i z o n t a l m o t i o n s i s g i v e n i n appendix A.2.2.3.

2.2.3.2,

E F F E C T S OF C E N T R I F U G A L FORCE I n t h e case o f j i b c r a n e s , a c c o u n t s h a l l b e t a k e n o f t h e c e n t r i f u g a l f o r c e due t o slewing. I n p r a c t i c e , i t i s s u f f i c i e n t t o determine the h o r i z o n t a l force e x e r t e d a t t h e j i b head as a r e s u l t o f t h e i n c l i n a t i o n o f t h e r o p e c a r r y i n g t h e l o a d and i n gen e r a l t o n e g l e c t t h e e f f e c t s o f c e n t r i f u g a l f o r c e on t h e o t h e r e l e m e n t s o f t h e crane.

2.2.3.3*

TRANSVERSE R E A C T I O N S DUE TO R O L L I N G A C T I O N When two w h e e l s ( o r two b o g i e s ) r o l 1 a l o n g a r a i l , t h e c o u p l e formed b y t h e h o r i z o n t a l f o r c e s n o r m a l t o t h e r a i l s h a l l be t a k e n i n t o c o n s i d e r a t i o n . The components o f t h i s couple are obtained by m u l t i p l y i n g the v e r t i c a l l o a d exerted on the wheels ( o r bogies) by a c o e f f i c i e n t w h i c h depends upon t h e r a t i o o f t h e span p t o t h e wheel base a ( 1 ) .

(1

By "wheelbase" i s u n d e r s t o o d t h e c e n t r e d i s t a n c e between t h e o u t e r m o s t p a i r s o f wheels, o r , i n t h e case o f b o g i e s , t h e c e n t r e d i s t a n c e between t h e f u l c r u m p i n s o n t h e c r a n e s t r u c t u r e o f t h e two b o g i e s o r b o g i e systems. Where h o r i z o n t a l g u i l d i n g w h e e l s a r e p r o v i d e d , t h e wheelbase s h a l l be t h e d i s t a n c e between t h e r a i l c o n t a c t p o i n t s o f two h o r i z o n t a l wheels.

As shown i n t h e graph, t h i s c o e f f i c i e n t l i e s between 0.05 and 0 . 2 f o r r a t i o s between 2 and 8.

9' qos O O 2.2,3.4.

2

4

6

8

BUFFER EFFECTS S T The case rnust be c o n s i d e r e d when t h e irnpact due t o c o l l i s i o n w i t h b u f f e r s i s a p p l i e d t o t h e s t r u c t u r e , and t h e case when i t i s a p p l i e d t o t h e suspended l o a d .

2.2.3.4.1.

BUFFER EFFECTS ON THE STRUCTURE A d i s t i n c t i o n rnust be drawn between : 1) t h e case i n which t h e suspended l o a d can swing. 2 ) t h a t i n which r i g i d guides p r e v e n t swing.

I n t h e f i r s t case t h e f o l l o w i n g r u l e s s h a l l be a p p l i e d : F o r horizontal speeds below 0.7 rn/sec,

no account s h a l l be taken o f b u f f e r e f f e c t s .

F o r speeds i n excess o f 0 . 7 m/sec, account rnust be t a k e n o f t h e r e a c t i o n s s e t up i n t h e s t r u c t u r e by c o l l i s i o n s w i t h b u f f e i s . I t s h a l l be a s s m e d t h a t a b u f f e r i s capable o f a b s o r b i n g t h e k i n e t i c energy of t h e a p p l i a n c e ( w i t h o u t t h e w o r k i n g l o a d ) a t a f r a c t i o n o f t h e r a t e d speed V t f i x e d a t 0.7 V t . The r e s u l t i n g l o a d s s e t up i n t h e s t r u c t u r e s h a l l be c a l c u l a t e d on t h e b a s i s o f t h e r e t a r d a t i o n i m p a r t e d t c t h e a p p l i a n c e by t h e b u f f e r i n use. However, f o r h i g h e r speeds ( g r e a t e r t h a n 1 m/sec), t h e use o f d e c e l e r a t i n g d e v i c e s which a c t upon approach t o t h e ends o f t h e t r a c k i s p e n i t t e d p r o v i d e d t h e a c t i o n o f these d e v i c e s i s a u t m a t i c and t h e y produce an e f f e c t i v e d e c e l e r a t i o n o f t h e a p p l i a n c e which always reduces t h e speed t o t h e p r e d e t e n i n e d lower v a l u e b e f o r e t h e b u f f e r s a r e reached. I n t h i s case t h e reduced speed o b t a i n e d a f t e r s l o w i n g down i s used f o r t h e v a l u e o f V t when c a l c u l a t i n g t h e b u f f e r e f f e c t ( 1 ) . I n t h e second case where t h e l o a d cannot swing t h e b u f f e r e f f e c t i s c a l c u l a t e d i n t h e same manner b u t t a k i n g account of t h e value o f t h e w o r k i n g l o a d .

(1,

I t must be emphasised t h a t a sure and e f f e c t i v e d e v i c e rnust be f i t t e d . A m e r ~en$o f - t r a v e l l i m i t S h i t c h c u t t i n g o f f t h power ~ supply t o t h motor ~ i s not s u f f i c i e n t reason t o a s s m e reduced speed f o r t h e b u f f e r e f f e c t .

2.2.3.4.2.

BUFFER EFFECTS O N T H E SUSPENDED L O A D Impacts due t o c o l l i s i o n between t h p l o a d and f i x e d o b s t r u c t i o n s a r e t a k e n i n t o account o n l y f o r a p p l i a n c e s where t h e l o a d i s r i g i d l y guided. I n t h a t c a s e , t h e l o a d s g e n e r a t e d by s u c h a c o l l i s i o n a r e t o be t a k e n i n t o c o n s i d e r a t i o n . The l o a d s can be computed by c o n s i d e r i n g t h a t h o r i z o n t a l f o r c e a p p l i e d a t t h i l e v e 1 of t h e l o a d which i s c a p a b i e o f c a u s i n g two of t h e c r a b wheels t o l i f t .

LOADS DUE TO C L I M A T I C EFFECTS The l o a d s due t o c l i m a t i c e f f e c t s a r e t h o s e r e s u l t i n g f r m t h e a c t i o n o f t h e wind, f r m snow l o a d s and f r m t w n p e r a t u r e v a r i a t i o n s .

WIND ACTION

This c l a u s e r e l a t e s t o wind l o a d s on c r a n e s t r u c t u r e . I t g i v e s a s i m p i i f i e d method o f c a l c u l a t i o n and a s s u n e s t h a t t h e wind can b l w h o r i z o n t a l l y f r m any d i r e c l i o n , t h a t t h e wind blows a t a c o n s t a n t v e l o c i t y and t h a t t h e r e i s a s t a t i c r e a c t i o n t o t h e loadings i t a p p l i e s t o the crane s t r u c t u r e .

2.2,b.l.l.

WIND PRESSURE The dynamic wind p r e s s u r e i s g i v e n by : q = 0 . 6 1 3 V:

Where q i s t h e dynarnic p r e s s u r e

~ / r n ~

Vs i s t h e d e s i g v wind speed i n m / s .

2.2.4.1,2.

DESIGN HIND CONDITIDNS TWO d e s i g n wind c o n d i t i o n s a r e t a k e n i n t o account i n c a l c u l a t i n g wind l o a d s on cranes.

2.2,4,1.2.1. I n - s e r v i c e

wind

This i s t h e maximm wind i n which t h e c r a n e i s designed t o o p e r a t e . The wind l o a d s a r e a s s m e d t o be a p p l i e d ir! t h e l e a s t f a v o u r a b l e d i r e c t i o n i n combination w i t h t h e a p p r o p r i a t e s e r v i c e l o a d s . I n - s e r v i c e d e s i g n wind p r e s s u r e s and c o r r e s p o n d i n g speeds a r e g i v e n i n t a b l f T.2.2.4.1.2.1. They a r e a s s m e d t o be c o n s t a n t o v e r t h e h e i g h t of t h e a p p l i a n c e ( : l . I t i s a s s m e d t h a t t h o~ p e r a t i n g speeds anü nomina? a c z e l e r a t i o n s a r e n o t n e c e s s a i l i ) reached under extreme h,ind c o n d i t i o n s .

(1)

Miere a wind speed measuring d e v i c e i s t o be a t t a c h e d t o an a p p l i a n c e i t s h a l l norrnally be p l a c e d a t t h e maximm h e i g h t of t h e a p p l i a n c e . In c a s e s where t h e wind speed a t a d i f f e r e n t l e v e 1 i s more s i g n i f i c a n t t o t h e s a f e t y o f t h e a p p l i a n c e , t h e rnanufacturer s h a l l s t a t e t h e h e i g h t a t which t h e d e v i c e s h a l l be p l a c e d .

Wind speed i n service m/s

Wind p r e s s u r e in service

Type o f a p p l i a n c e

~/m*

1

Lifting appliance e a s i l y p r o t e c t e d a g a i n s t wind a c t i o n o r designed f o r u s e e x c l u s i v e l y i n l i g h t wind. Erection operations.

A l 1 normal t y p e s o f c r a n e i n s t a l l e d i n t h e open Appliances n h i c h must c o n t i n u e t o work i n h i a h winds -

-

* For exarnple a p p l i a n c e s of t y p e 12a i n t a b l e T.2.1.2.5. Action of wind on t h e l o z d The a c t i o n o f t h e wind on t h e hook l o a d f o r a c r a n e which handles rniscellaneous l o a d s s h a l l be deterrnined f r m t h e r e l a t i o n s h i p : F = 2 . 5 A x q where F

i s t h e f o r c e e x e r t e d by t h e wind on t h e hook l o a d i n N ,

q

i s t h e i n - s e r v i c e wind p r e s s u r e f r m t a b l e 2.1.4.1.2.1.

A

i s t h e maximun a r e a o f t h e s o l i d p a r t s of t h e hook load i n m i ( 1 ) . Where t h i s a r e a 2 i s n o t known, a minimm v a l u e o f 0.5 m p e r tonne o f s a f e working l o a d s h a l l be csed.

i n N/rnL,

Where a c r a n e i s d e s i g n e d t o h a n d l e l o a d s of a s p e c i f i c s i z e and s h a p e o n l y , t h e wind l o a d i n g s h a l l be c a l c u l a t e d f o r t h e a p p r o p r i a t e dimensions and c o n f i g u r a t i o n s .

2.2.4.1.2.2.

Hind o u t o f s e r v i c e This i s a maximun ( s t o r m ) wind f o r which t h e l i f t i n g machine i s d e s i g n e d t o remain s t a b l e i n o u t o f s e r v i c e c o n d i t i o n s , a s i n d i c a t e d , by t h e rnanufacturer. The speed v a r i e s w i t h t h e h e i g h t o f t h e a p p a r a t u s above t h e surrounding ground l e v e l , t h e g e o g r a p h i c a l l o c a t i o n and t h e d e g r e e o f exposure t o t h e p r e v a i l i n g winds. For l i f t i n g a p p l i a n c e s used i n t h e open a i r , t h e normal t h e o r e t i c a l wind p r e s s u r e and t h e c o r r e s p o n d i n g s p e e d , f o r "out o f s e r v i c e " c o n d i t i o n s a r e i n d i c a t e d i n t h e t a b l e T.2.2.b.1.2.2.

(1)

ühere, e x c e p t i o n a l l y , a c r a n e i s r e q i i r e d t o handle l o a d s o f l a r g e s u r f a c e a r e a , i t i s a d n i s s i b l e f o r t h e rnanufacturer t o determine a wind speed l e s s t h a n t h a t s p e c i f i e d i n t a b l e T.2.2.A.1.2.1. above which such l o a d s s h a l l n o t be handled.

T a b l e T.2.2.4.1.2.2. Cut o f s e r v i c e wind

1

HeiQht above ground l e v e 1

1

O t o 20 20 t o 100 & r e t h a n 100

Cut o f s e r v i c e d e s i g n wind p r e s s u r e

1

Approximate equivalent out of s e r v i c e d e s i g n wind speed

1 100 1 300

When c a l c u l a t i n g wind l o a d s f o r o u t o f s e r v i c e c o n d i t i o n s t h e wind p r e s s u r e may be t a k e n a s c o n s t a n t o v e r t h e v e r t i c a l h e i g h t i n t e r v a l s i n t a b l e T.2.2.4.1.2.2. A l t e r n a t i v e l y , t h e d e s i g n wind p r e s s u r e a t t h e t o p of t h e c r a n e may be a s s m e d constant over i t s e n t i r e height. Miere c r a n e s a r e t o be permanently i n s t a l l e d o r used f o r extended p e r i o d s i n a r e a s where wind c o n d i t i o n s a r e e x c e p t i o n a l l y s e v e r e , t h e above f i g u r e s may be m o d i f i e d by agreement between t h e rnanufacturer and p u r c h a s e r i n t h e l i g h t o f l o c a l metereological data. For c e r t a i n t y p e s of a p p l i a n c e o f which t h e j i b can be q u i c k l y lowered, ( s u c h a s a tower c r a n e which can be e a s i l y lowered by a b u i i t - i n mechanism) t h e o u t o f s e r v i c e wind need n o t be taken i n t n c o n s i d e r i t i o n p r ~ v i d o it h e machine i s i?tendeU fs: l o w e r i n g a f t e r each working day.

2.2.4.1.3.

LI'IND L O A D CALCULATIONS

For rnost complete and p a r t s t r u c t u r e s , and i n d i v i d u a l members used i n c r a n e s t r u c t u r e s t h e wind l o a d i s c a l c u l a t e d f r m :

F

i s t h e wind l o a d i n N ,

A

i s t h e e f f e c t i v e f r o n t a l a r e a o f t h e p a r t under c o n s i d e r a t i o n i n m2,

q

i s t h e wind p r e s s u r e c o r r e s p o n d i n g t o t h e a p p r o p r i a t e d e s i g n c o n d i t i o n i n N/m

Cf

i s t h e shape c o e f f i c i e n t i n t h e d i r e c t i o n o f t h e wind f o r t h e p a r t under consideration.

2

,

The t o t a l wind l o a d on t h e s t r u c t u r e i s t a k e n a s t h e svm o f t h e l o a d s on i t s romponent parts. In d e t e r m i n i n g s t r e n g t h and s t a b i l i t y r e q u i r e m e n t s of t h e a p p l i a n c e t h e t o t a l wind l o a d s h a l l be c o n s i d e r e d . The magnitude o f t h e wind l o a d t o be a l l m e d f o r i n t h e d e s i g n of a rnechanisrn, i n d e t e r m i n i n g t h e motor and b r a k e r e q u i r e m e n t s f o r t h e rnechanism and t o p r o v i d e f o r the s a f e t y of the appliance i n t h e wind,are given i n t h e chapter dealing with t h e d e s i g n o f mechanisms.

1

. s ~ u y o dapou JC s a l J u a 3 a q j u a a q s c usye? a l e slaqwsu TenpTATpuy j o s q ~ f i u a : aqq p a p j ~ o l d' X ~ e s s a s a u sy s a ~ e ~a qd l Aq paJuasald e a l e TeuoyJTppe aqJ l o 4 e3ueMoT -1e ou ~ o y ~ z ~ n ~ ~ a3yJJeT s u o s papTaa u! pasn a l e az;s Teulou j o s a ~ e ~~ ads s n f ialaqM . s e a l e T e J u o l j 6 u ~ p u o d s a l l o 3a q l OJ p a r ~ d d ea l e s J u a y 3 ! j j a o 3 adeqs a ~ e ~ l d o l d daqJ e (s/,u 9 2 5 h . a pue s/,w 9 > S h . 0 ) sawy6al MOTJ qqoq UJ SuOJJJaS l e T n a l T 3 40 l o L s i ~ o ~ ~ s a s - ~ epue T n 3p a~p~y i3- l e y 4 j o dn apew SJ a w e l j asJJJeT e alaqM .pasn aq Aeu aTqeJ a q j 40 J l e d a T p p j u a q j UJ u a ~ j 6SuoJJJas l e T n 3 l T 3 pue papTs J e T j 40 p a J s n q s u o s s a w e l j asyqqeT l o j s j u a j 3 J j j a o s TTelaAo a q AT~ATJ~UI~JTW 'Junosse OJUJ uayeJ aq TTeqs laqwaw qsea j o ssaulapuaTs 3 ~ w e u A p o l a ea q j ase3 S T ~ u1 J - ~ - p - ~ - t , - z ' aTqeJ z ' ~ 40 J l e d do7 aqJ u ? uaAJ6 slaqwau T e n p j A j p u J a q j l o j s J u a J s T j - j a o s a q l 40 s j s e q aqq uo paJeTnaTe3 aq Apu s a w e l j a3TJJPT a ~ 6 u ~u os peoT P U ~ M a q l - 1 ' t , * ~ ' p ' z - za ~ n 6 ~ 4 UJ p a u j j a p a l e o q e l uo:Jsas pue s s a u l a p u a l s 3 ~ w e u A p o l a b ' o T j e l u o T j 3 a s a q j ~ J J M ' s u o ~ ~ ~xoq a s a 6 1 e ~j o ase3 a q j u T 6 p u e ssaulapuaTs s ~ w e u A p o ~ aaeq j OJ 6 u ~ p l o 3 s e A J ~ A slaqwau TenpjhTpuT l o 4 sanTeA a q l ' 1 . p ' ~ - p . z ' z - 1 a T q q UJ u a ~ a~ l e6 sasnoq A~au'qaew pue s a u e l j a3TJjeT a ~ 6 u ~' ssl a q u a u TenpyAypuT 104 s J u a T s T j j a o 3 a d e q ~

T.2.2.4.1.4.1.

Force coef f i c i e n t s

(1) See f i g u r e 2 . 2 . 4 . 1 . 4 . 1 .

(1)

Aerodynamic s l e n d e r n e s s :

l e n q t h o f member = Y b r e a d t h o f s e c t i o n a c r o s s wind f r o n t b

O,

I* D

I n l a t t i c e c o n s t r u c t i o n t h e l e n g t h s o f i n d i v i d u a l rnembers a r e t a k e n between t h e c e n t r e s o f a d j a c e n t node p o i n t s . See diagram below soiiaity

ratio

(Iii) Spacino r a t i o =

=

area of s o l i d p a r t s = enclosed area A,

=

? ii

x

bi

' , x E7

d i s t a n c e between Facinq s i d e s - 2 0 ~ a S r o a d t h o f members a c r o s s winc f r o n t b 8

f o r " a " t a k e t h ? s n a i l ~ s tp o s s i b l e v a l u e i n t 3 e geometry o f t h e exposed f a c e . (1'4)

Sectlon r a t i o = S'eadtb o í s e c t i o ~a c r o s s h i n d ' r o n t d e o t t o f s e c t i 3 n 3arailei t 3 ~ 1 r dC

i

- b ~ d

F i g u r e 2.2.u.l.L.i D e f l n i t i o n s : Aerodynamic S l e n d e r n e s s , S o l i d i t y R a t i o , S p a c i n q R a t i o , and S e c t i o n R a t i o

~

Where p a r a l l e l frames o r rnernbers a r e p o s i t i o n e d so t h a t s h i e l d i n g t a k e s p l a c e , t h e w i n d l o a d s on t h e windward frame o r member and on t h e u n s h e l t e r e d p a r t s o f t h o s e b e h i r i d i t a r e c a l c u l a t e 5 u s i h g t h e a p p r o p r i a t e shape c o e f f i c i e n t s . The w i n d l o a d ori t h e s h e l t e r e d p a r t s i s m u l t i p l i e d by a s h i e l d i n g f a c t o r T l g i v e n i n t a b l e T.2.2.4.1.4.2. Values o f 11v a r y w i t h t h e s o l i d i t y and s p a c i r i g r a t i o s as d e f i n e d i n f i g u r e 2.2.4.1.4.1.

T a b l e T.2.2.b.1.4.2. Shieldinq coefficients

r

S o l i d i t y r a t i o A/Ae

Spacing r a t i o I

l

N

Where a number o f i d e n t i c a l frarnes o r rnembers a r e spaced e q u i d i s t a n t l y b e h i n d each o t h e r i n such a way t h a t each frarne s h i e l d s those b e h i n d i t , t h e s h i e l d i n g e f f e c t i s assumed t o i n c r e a s e up t o t h e n i n t h frame and Lo r e m a i n c o n s t a n t t h e r e a f t e r . The w i n d l o a d s a r e c a l c u l a t e d as f o l l o w s : On t h e 1 s t . frarne

F1

=

A.q,Cf

in N

Dn t h e 2nd.

F2

=

p.A-q-Cf

i n N

Fn

=

,-(n-l)

frarne

Dn t h e n t h frame (where n i s from 3 t c Fi)

.A.q.if

Dn t h e 9 t h and subsequent f rarnes The t o t a l w i n d l o a d i s t h u s : Wñere t h e r e a r e u p t o 9 frames

Ftotal

= [l+ 7 + q2 + P

Where t h e r e a r e more t h a n 9 frames

F total

= [l

Note

-

q + qi

a

3

v3

+

.. .

+

.. .

(n-1)

-

1 ~ ~ q . c ~

~7' + ( ~ - ~ ) Q ' ] A . ~ . C ~

The t e r m nX used i n t h e above formula i s assumed t o have a l o w e r l i m i t o f 0.10. I t i s t a k e n as 0.10 whenever nX < 0.10.

2.2.4.1.4.3.

La t t i c e t o w e r s In c a l c u l a t i n g t h e "face-on" wind l o a d on s q u a r e t o w e r s , i n t h e a b s e n c e o f a d e t a i l e d c a l c u l a t i o n , t h e s o l i d a r e a o f t h e windward f a c e is r n u l t i p l i e d by t h e f o l l o w i n g overall force coefficient : For t o w e r s composed o f f l a t s i d e d s e c t i o n s

1,7*(1

+

rl)

For t o w e r s composed o f c i r c u l a r s e c t i o n s where D.VS

<

6 m

2

/S

where D-VS >, 6 m2/s

1,4

The v a l u e o f n i s t a k e n from t a b l e 2 . 2 . 4 . 1 . 4 . 2 . r a t i o o f t h e windward f a c e .

f o r a/b = 1 according t e t h e s o l i d i t y

The maxirnum wind l o a d on a s q u a r e t o w e r o c c u r s when t h e wind blows on t o a c o r n e r . In t h e a b s e n c e o f a d e t a i l e d c a l c u l a t i o n , t h i s l o a 6 c a n b e c o n s i d e r e d a s 1 . 2 t i m e s t h a t d e v e l o ~ e dw i t h " f a c e - o n " wind on one s i d e .

7.2,4,1.4.4.

Farts inclined

i n r e l a t i o n t o t h e wind d i r e c t i o n

I n d i v i d u a l members, f r a m e s , e t c . Where t h e wind blows a t an a n g l e t o t h e l o n g i t u d i n a l a x i s o f a member o r t o t h e s u r f a c e o f a f r a m e , t h e wind l o a d i n t h e d i r e c t i o n o f t h e wind i s o b t a i n e d from :

where F , A , q and Cf a r e a s d e f i n e d i n 2 . 2 . 4 . 1 . 3 . and O i s t h e a n g l e o f t h e wind (8< 9 0 ° ) t e t h e l o n g i t u d i n a l a x i s o r f a c e .

L a t t i c e t r u s s e s and t o w e r s Where t h e wind blows a t a n a n g l e t o t h e l o n g i t u d i n a l a x i s o f a l a t t i c e t r u s s t o w e r , t h e wind l o a d i n t h e d i r e c t i o n o f t h c wind is o b t a i n e d from :

O where F , 0 , q and C f a r e a s d e f i n e d i n 2 . 2 . 4 . 1 . 3 . arld K2 = which c a n n o t b e l e s s t h a n D,35 o r g r e a t e r t h a n 1 . 50 ( 1 , 7 -

01

2) S

Where O i s t h e a n g l e o f t h e wind i n d e g r e e s l o n g i t u d i n a l a x i s of t h e t r u s s o r tower.

( 2 < 90°) t o t h e

Sp i s t h e a r e a i n m' o f t h e b r a c i n g members o f t h e t r u s s o r t o w e r p r o j e c t e d on t o i t s windward p l a n e . 2

S i s t h e a r e a i n m o f a l 1 ( b r a c i n g and main) members o f t h e t r u s s o r tower p r o j e c t e d on t o i t s windward p l a n e . The v a l u e o f K2 i s assumed t o have l o w e r and upper limits o f 0.35 and 1 . 0 r e s p e c t i v e l y I t i s t a k e n a s 0.35 whenever t h e c a l c u l a t e d v a l u e < 0 . 3 5 and a s 1 . 0 whenever t h e c a l c u l a t e d value > 1.0.

2.2.4.2.

SNOU LOAD

Cnow loads shall be neglected in the design calculations for overhead travelling cranes, bridge cranes and jib cranes.

2.2.4.3.

TEMPERATURE VARIATIONS Stresses due to temperature variations shall be considered only in special cases such as when members are not free t3 expand. In such cases, the maximum temperature fluctuation shall be taken to be : - 20° C to + 45O C.

MISCELLANEOUS LOADS

2.2.5

7.2.5. L .

L O A D S C A R R I E D BY P L A T F O R M S Access gangways, driver's cabins and platforms shall be designed to carry the following concentrated loads : 3000 N

for maintenance gangways and platforms where materials may be placed,

1500 N

for gangways and platforms intended only for access of personnel,

300 N as the horizontal force which may be exerted on handrails and toe-guards. These loads are not to be used in the calculations for girders.

C A S E S OF L O A D I N G

Three different cases of loading are to be considered for the purpose of the calculations :

- the working case without wind, - the working case with limiting working wind, - the case of exceptional loadings. Having determined the various loads in accordance with section 2.2, account is taken of a certain probability of exceeding the calculated stress, which results from imperfect methods of calculation and unfzrseen contingencies, by applying an amplifying coefficent y,, which varies according to the group classification of the appliance. The values of this coefficient I c are indicated in clause 7.3.a.

CASE

1

:

APPLIANCE WORKING WITHOUT WIND

The f o l l o w i n g s t i a l l be t a k e n i n t o c o n s i d e r a t i o n : t h e s t a t i c l o a d s due t o t h e dead w e i g h t SG, t h e l o a d s due t o t h e w o r k i n g l o a d SL m u l t i p l i e d by t h e dynamic c o e f f i c i e n t y , and t h e two most u n f a v o u r a b l e h o r i z o n t a l e i f e c t s SH among t h o s e d e f i n e d i n clause 2 . 2 . 3 . , e x r l u d i n g buffer forces. A l 1 t h e s e l o a d s must t h e n be m u l t i p l i e d by t h e a m p l i f y i n g c o e f f i c i e n t yc s p e c i f i e d i n c i a u s e 2.3.4., v i z :

I n cases where t r a v e l m o t i o n t a k e s p l a c e o n l y f o r p o s i t i o n i n g t h e a p p l i a n c e and i s n o t n o r m a l l y u s e d f o r moving l o a d s t h e e f f e c t o f t h i s m o t i o n s h a l l n o t be comb i n e d w i t h a n o t h e r h o r i z o n t a l m o t i o n . T h i s i s t h e case f o r example w i t h a d o c k s i d e c r a n e which, once i t has been p o s i t i o n e d , h a n d l . e s a s e r i e s o f l o a d s a t a f i x e d p o i n t .

CASE

11

: APPLIANCE

WORKING W I T H WIND

The l o a d s o f case 1 a r e t a k e n t o w h i c h a r e added t h e e f f e c t s o f t h e l i m i t i n g w o r k i n g ( t a b l e T.2.2.4.1.2.1.) and, where, a p p l i c a b l e w i n d SW d e f i n e d under 2.2.4.1.2.1. t h e l o a d due t o t e m p e r a t u r e v a r i a t i o n , v i z :

Note - The dynamic e f f e c t s o f a c c e l e r a t i o n and r e t a r d a t i o n do n o t have t h e same v a l u e s i n case 11 a s i n case 1, f o r when a w i n d i s b l o w i n g t h e a c c e l e r a t i n g o r b r a k i n g t i m e s a r e n o t t h e same as when s t i l l c o n d i t i o n s p r e v a i l .

2.3.3.

CASE

111

:

APPLIANCE

SUBJECTED

TO E X C E P T I O N A L

LOADINGS

E x c e p t i o n a l l o a d i n g s o c c u r i n t h e f o l l o w i n g cases :

- a p p l i a n c e o u t o f s e r v i c e w i t h rnaximum w i n d - a p p l i a n c e w o r k i n g and s u b j e c t e d t o a b u f f e r e f f e c t - a p p l i a n c e u n d e r g o i n g t h e t e s t s i n d i c a t e d i n b o o k l e t 8. The h i g h e s t o f t h e f o l l o w i n g c o m b i n a t i o n s s h a l l be c o n s i d e r e d : a ) The l o a d s SG due t o t h e dead w e i g h t , p l u s t h e l o a d SWmaXdue t o t h e maximurn [ i n c l u d i n ~t h e r e a c t i o n s o f t h e w i n d as m e n t i o n e d under c l a u s e 2.2.4.1.2.2. anchorages) b ) t h e l o a d s SG due tr :he dead W i g h t and SL due t o t h e w o r k i n g l o a d p l u s t h e g r e a t e s t b u f f e r e f f e c t ST a s e n v i s a g e d i n c l a u s e 2.2.3.4. C ) t h e l o a d s SG due t o t h e dead w e i g h t p l u s t h e h i g h e s t o f t h e two l o a d s ? ' P1 SL and P2 SL ; P1 and p2 b e i n g t h e c o e f f i c i e n t s by w h i c h t h e s a f e w o r k i n g l o a d i s m u l t i p l i e d f o r t h e dynamic t e s t (P1) and f o r t h e s t a t i c t e s t ( ~ 2 as ) i n clauses 9 . 1 . 1 . and 8.1.2.

These t h r e e c a s e s a r e e x p r e s s e d by t h e f o r m u l a e :

Note 1 - I t s h o u l d b e n o t e d t h a t t h e c h e c k s under ( c ) a r e o n l y t o b e made i n c a s e s w h e r e t h e working l o a d , when assumed t o a c t a l o n e , p r o d u c e s s t r e s s e s opposed i n d i r e c t i o n t o t h o s e c a u s e d by t h e dead w e i g h t u p t o t h e p o i n t a t which t h e s t a t i c t e s t l o a d d o e s n o t e x c e e d 1 , 5 t i m e s t h e s a f e working l o a d . Note 2

-

When u s i n g d e c e l e r a t i n g d e v i c e s i n a d v a n c e o f b u f f e r irnpact u n d e r t h e c o n d i t i o n s rnentioned i n c l a u s e 2.2.3.4.1. ST w i l l be t a k e n t o b e t h e h i g h e s t l o a d r e s u l t i n g e i t h e r from t h e r e t a r d a t i o n p r e v i o u s l y c a u s e d by t h e d e c e l e r a t i n g d e v i c e o r frorn t h a t f i n a l l y c a u s e d by t h e b u f f e r .

CHOOSING

THE

AMPLIFYIYG

COEFFICIENT

yc

The v a l u e o f t h e a m p l i f y i n g c o e f f i c i e n t yc depends upon t h e g r o u p c l a s s i f i c a t i o n of the appliance. Table T.2.3.4. Values o f amplifyinq c o e f f i c i e n t y c Appliance group

YC

1.00

A2

A3

A4

1.02

1.05

1.08

A6

A5

i 1.11 8

1

,

1.14

1

A7

,

A8

1.17

!

1.20

i

1 l

2

SEISMIC EFFECTS In g e n e r a l t h e s t r u c t u r e s o f l i f t i n g a p p l i a n c e s do n o t have t o be checked f o r European seismic effects. However, i f o f f i c i a l r e g u l a t i o n s o r p a r t i c u l a r s p e c i f i c a t i o n s s o p r e s c r i b e , s p e c i a l r u l e s o r r e c o m n e n d a t i o n s can be a p p l i e d i n a r e a s s u b j e c t t o e a r t h q u a k e s . T h i s r e q u i r e m e n t s h a l l b e a d v i s e d t o t h e s u p p l i e r by t h e u s e r o f t h e i n s t a l l a t i o n who s h a l l a l s o p r o v i d e t h e c o r r e s p o n d i n g s e i s m i c s p e c t r a .

(1

Loadings r e s u l t i n g from t h e working l o a d a r e t a k e n i n t o a c c o u n t b u t t h e e f f e c t s o f l o a d swing r e s u l t i n g from t h e s h o c k a r e n e g l e c t e d b e c a u s e t h i s swing o n l y l o a d s t h e s t r u c t u r e when t h e o t h e r e f f e c t s have been p r a c t i c a l l y a b s o r b e d . T h i s comment d o e s n o t a p p l y t o r i g i d l y g u i d e d l o a d s which c a n n o t swing.

L O A D S E N T E R I N G I N T D THE D E S I G N OF MECHANICMS Mechanisrns a r e s u b j e c t e d t o two k i n d s o f l o a d i n g : a ) The l o a d s , r e p r e s e n t e d by t h e symbol SM, which a r e d i r e c t l y d e p e n d e n t upon t h e t o r q u e s e x e r t e d on t h e mechanisms by t h e m o t o r s o r t h e b r a k e s . b ) The l o a d s , r e p r e s e n t e d by t h e syrnbol SR, which a r e i n d e p e n d e n t o f motor o r b r a k e

a c t i o n b u t which a r e d e t e r m i n e d by t h e r e a c t i o n s which a c t upon t h e m e c h a n i c a l p a r t s and which a r e n o t b a l a n c e d by a t o r q u e a c t i n g on t h e d r i v e s h a f t s ( 1 ) .

TYPE

Srq L D A D S

The l o a d s o f t h i s t y p e t o b e c o n s i d e r e d a r e : a ) SMG l o a d s , c o r r e s p o n d i n g t o a v e r t i c a l d i s p l a c e m e n t o f t h e c e n t r e o f g r a v i t y o f moving p a r t s o f t h e a p p l i a n c e o t h e r t h a n t h e working l o a d . b ) SML l o a d s , c o r r e s p o n d i n g t o a v e r t i c a l d i s p l a c e r n e n t o f t h e working l o a d a s d e f i n e d i n c l a u s e 2.2. f o r s t r u c t u r e s . c j SM l o a d s , c o r r e s p o n d i n g t o f r i c t i o n a l f o r c e s which have n o t been a l l o w e d f o r i n c a l c u l a t i n g t h e e f f i c i e n c y o f t h e rnechanism ( s e e c l a u s e 4 . 2 . 6 . 1 . 1 . , b o o k l e t 4 ) d j SMn l o a d s , a s s o c i a t e d w i t h a c c e l e r a t i o n ( o r b r a k i n o ) o f t h e m o t i o n . e ) SMhll o a d s , c o r r r s p o n d i n g t o t h e e f f e c t o f t h e working wind assurned f o r t h e appliance.

TYPE

SR L O A D S

The l o a a s o f t h i s t y p e t o be c o n s i d e r e d a r e : a ) SRG l o a d s due t o t h e w e i g h t s o f cornponents which a c t on t h e p a r t u n d e r c o n s i d e ration ; b ) SRL l o a d s due t o t h e w o r k i n g l o a d a s d e f i n e d i n c l a u s e 2 . 2 . , C)

for structures.

SRA l o a d s due t o t h e a c c e l e r a t i o n s o r d e c e l e r a t i o n s o f t h e v a r i o u s m o t i o n s o f the a p p l i a n c e o r its p a r t s , a s c a l c u l a t e d according t o c l a u s e 2.2.3.1. f o r s t r u ~ t u r e s ~ i n s o f aa rs t h e o r d e r o f rnagnitude o f t h e s e l o a d s i s n o t n e g l i g i b l e compared t o t h e SRG and SRL l o a d s .

d j SRw l o a d s duo t o t h e l i m i t i n g w o r k i n g wind SW o r t o t h e maxirnum wind SWmax ( s e e c l a u s e 2 . 2 . b . l . j , i n s o f a r a s t h e o r d e r o f magnitude of t h e s e l o a d s i s n o t negligible.

(1)

I n a t r a v e l m o t i o n , f o r i n s t a n c e , t h e l o a d s due t o t h e v e r t i c a l r e a c t i o n on t h e r a i l w h e e l s and t h e t r a n s v e r s e l o a d s t h a t s t r e s s t h e wheel a x l e b u t a r e n o t t r a n s m i t t e d t o t h e components o f t h e d r i v i n g mechanism.

C A S E S OF L O A D I N G Three c a s e s of l o a d i n g a r e t o be c o n s i d e r e d i n t h e c a l c u l a t i o n s : Case 1. : Mrmal s e r v i c e w i t h o u t wind Case 11 : Nsrmal s e r v i c e w i t h wind Case 111 : E x c e p t i o n a l l o a d i n g s . A maximum l o a d must be d e t e r m i n e d f o r each c a s e of l o a d i n g which s e r v e s a s t h e basis for the calculations.

Nste

-

C l e a r l y , c a s e 1 and 11 a r e one and t h e same i n t h e c a s e of a p p l i a n c e s which a r e n o t exposed t o wind.

The v a r i o u s l o a d i n g s b e i n g determined a s i n d i c a t e d i n paragraph 2 . 5 . , a c c o u n t i s taken o f a c e r t a i n p r o b a b l l i t y o f exceeding t h e c s i c u l a t e d s t r e s s , which r e s u l t s f r m i m p e r f e c t methods o f c a l c u l a t i o n and uriforseeri c o n t i n g e n c i e s , by a p p l y i n g an a m p l i f y i n g c o e f f i c i e n t y, depending on t h e grouD i n wbich t h e mechanism i s c l a s s i f i e d . The v a l u e s of t h i s c o e f f i c i e n t Y, a r e i n d i c a t e d i n t a b l e T.2.6.

Values o f a m p l i f v i n o c o e f f i c i e n t y,

CASE

2,6.1

2.6.1.1.

1 - KORMAL

d I T H O U T WlND

TYPE S M LOADS The maximum l o a d S p , , , , ~ t h e l o a d s SMG, S m , S,+, the relation :

o f t h e SM t y p e ( s e e c l a u s e 2 . 5 . ) i s determined by combining and SMAd e f i n e d i n c l a u s o 2.5.1. which can be e x o r e s s e d by

Sp,max: = (%G Note

2.6.1-2,

SERVICE

-

+

-%

+

SM-

+

%A)

Ym

I t must be p o i n t e d o u t t h a t i t i s n o t t h e combination of t h e maximum v a l u e s o f e a c h o f t h e t e r m s i n t h i s r e l a t i o n t h a t must be c o n s i d e r e d , but t h e v a l u e r e s u l t i n g from t h e most u n f a v o u r a b l f combination t h a t could a c t u a l l y o c c u r i n prac:I~e.

TYPE S R LOA05 Tho maxinu% l o a 3 SE &,, c f t h e Sq t y 3 ~( s e ? c l a u s ? 2 . 5 . ) i s determined by combining t h e l ~ a d cSR,, SRi, Ssa, d e ~ i n " i n c l a J s e 2 . 5 . 2 . w q i c l can be e x p r e s s e d by t h e relatloi : S;,sx1

' (SRi

+

sRL

+

SRA) 'yr

CASE

2.6.2.

2.6.2.

L.

11 - NORMAL SER\!ICI

W I T H WIND

T Y P E SM LOADS

'[he maximum l o a d SM 11 o f t h e SM t y p c (see c l a u s e 2.5. ) i s d e t e r m i n e d by comb i n i n g t h e l o a d s SMG, SML and Sw- d e f i n e d i n c l a u s e 2.5.1. w i t h one o f t h e f o l l o w i n g two c o m b i n a t i o n s : a ) t h e l o a d Sm and t h e l o a d SMW8 c o r r e s p o n d i n g t o a 80 N/m2 wind.

b ) t h e l o a d S w z 5 c o r r e s p o n d i n g t o a 250 N/m2 wind. The h i g h e r o f t h e two v a l u e s expressed by t h e r e l a t i o n s s e t o u t below i s t a k e n :

Fne n o t e i n c l a u s e 2.6.1.1.

2.6.2.2.

a p p l i e s here also.

T Y P E SR LOADS

The maximum l o a d SRmax 11 o f t h e SR t y p e (see c l a u s e 2.5.) t h e l o a d s SR,-, SRL and SRA d e f i n e d i n c l a u s e 2.5.2. w i t h t o 3 250 N/m wind, as expressed by t h e r e i a t i o n :

The n o t e i n c l a u s e 2.6.1.1.

CASE

%,5,3.

2,6.3.1,

i s d e t e r m i n e d by combining w h i c h corresponds

applies here also.

111 - E X C E P T I O N A L LOADS

T Y P E SH LOADS

The maxirnm l o a d SMrnax111 o f t h e SM t y p e d e f i n e d under c l a u s e 2.5. i s d e t e r m i n e d by c o n s i d e r i n g t h e maximum l o a d t h a t t h e motor can a c t u a l l y t r a n s r n i t t o t h e mechanism, a l l o w i n g f o r l i m i t a t i o n s due t o p r a c t i c a 1 o p e r a t i n g c o n d i t i o n s . The v a l u e s o f SMmaX111 a r e s p e c i f i e d i n c l a u s e 2.6.4.

2.6.3.2.

TYPE S R LOADS S i n c e t h e consequences o f an o v e r l o a d &e t o c o l l i s i o n w i t h a b u f f e r o r f o u l i n g a r e f a r l e s s s e r i o u s f o r a rnechanism t h a n f o r t h e s t r u c t u r e , t h e e x c e p t i o n a l l o a d i n g t o be taken i s t h a t g i v e n under paragraph a ) o f c l a u s e 2.3.3. i n t h e s t r u c t u r e s chapter . This g i v e s :

-

SR rnax 11i = S~~

+

rnax

In c a s e s where a d d i t i o n a l mooring o r guying rneans a r e used t o e n s u r e i m o b i l i t y o r s t a b i l i t y under rnaximum wind, t h e e f f e c t of t h e s e d e v i c e s on t h e rnechanisrn rnust be taken i n t o account where a p p l i c a b l e .

A P P L I C A T I O N OF THE ABOVE C O N S I D E R A T I O N S F O R C A L C U L A T I N G SM The mechanisms of h o i s t i n g a p p l i a n c e s perform one of t h e f o l l o w i n g f u n c t i o n s :

- P u r e l y v e r t i c a l d i s p l a c e m e n t s of t h e c e n t r e of g r a v i t y of moving masses ( e . g . h o i s t i n g rnotions).

- P u r e l y h o r i z o n t a l d i s p l a c e m e n t s i n which t h e c e n t r e of g r a v i t y of t h e rnoving rnasses a s a whole s h i f t s h o r i z o n t a l l y (e.g. t r a v e r s e , t r a v e l , slewing o r c o u n t e r balanced l u f f i n g m o t i o n s ) .

- Movernents c m b i n i n g an e l e v a t i o n of t h e c e n t r e of g r a v i t y o f t h e rnoving masses w i t h a h o r i z o n t a l displacernent ( e . g . non-counterbalanced l u f f i n g ) .

2.6.4.1.

HOISTING HOTIONS For t y p e SM l o a d s , t h e formula r e d u c e s t o t h e following : Case 1 and 1 1 : In t h i s c a s e t h e l o a d due t o t h e h o i s t i n g a c c e l e r a t i o n i s n e g l e c t e d because i t i s m a l 1 ccunpared t o S*. Case 111 : Bearing i n mind t h e g e n e r a l r u l e s o f c l a u s e 2 . 6 . 3 . 1 . , i t i s assumed t h a t t h e maximun l o a d s t h a t can be t r a n s r n i t t e d t o h o i s t i n g rnechanisms a r e l i m i t e d i n p r a c t i c e t o 1 , 6 times t h e SMrnax1 l o a d ( 1 ) .

(1)

In a h o i s t i n g rnotion i t i s irnpossible under normal working c o n d i t i o n s t o t r a n s r n i t t o t h e rnechanism l o a d s g r e a t e r t h a n t h o s e due t o t h e h o i s t i n g of t h e working l o a d , a s t h e e f f e c t s of a c c e l e r a t i o n a r e n e g l i g i b l e . A g r e a t e r load c o u l d r e s u l t only from rnishandling (poor judgernent o f t h e l o a d , e t c . ) .

t h e b a s i s of e x p e r i e n c e gained over rnany y e a r s of p r a c t i c e w i t h widely d i f f e r i n g h o i s t i n g a p p l i a n c e s i t i s now a c c e p t e d t h a t a c o e f f i c e n t of 1 , 6 g i v e s a d e q u a t e s a f e t y . I t must be s t r e s s e d t h a t t h e use o f e x c e s s i v e l y powerful rnotors s h o u l d be avoided.

On

2.6.4.2.

HORIZONTAL MOTIONS Case 1

- The f o r m u l a r e d u c e s t o :

Case 1 1 - The h i q h e r o f t h e f o l l o w i n g two v a l u e s i s t a k e n :

Case 111 - For S M m a x1 1 t~h e l o a d c o r r e s p o n d i n g t o t h e rnaximum t o r q u e o f t h e motor (01t h e b r a k e ) i s t a k e n u n l e s s o p e r a t i n g c o n d i t i o n s limit t h e t o r q u e a c t u a l l y t r a n s m i t t e d , t h r o u g h wheel s l i p on t h e r a i l s , o r t h r o u g h t h e u s e o f s u i t a b l e l i m i t i n g means ( e . g . h y d r a u l i c c o u p l i n g , t o r q u e l i m i t e r , e t c . ) . In t h i s c a s e t h e v a l u e a c t u a l l y t r a n s m i t t e d must be t a k e n (1).

COMBINE0 HOTIONS Case 1 and 1 1 : For c a s e s 1 a n d 1 1 , t h e o a d SM formula d e f i n e d i n c l a u s e s 2 . 6 . 1 . 1 .

11 i z ! i s d e t e r m i n e d by a p p l y i n g t h e g e n e r a l and 2 . 6 . 2 . 1 .

Case 1 1 1 : The l o a d c a u s e d by a p p l y i n g t h e maximum motor t o r q u e SMCnax c a n b e t a k e n f o r t h e maxirnum v a l u e SMmax111. T h i s o f t e n unduly h i g h v a l u e i s a l w a y s a c c e p t a b l e s i n c e i t enhances s a f e t y . I t must b e u s e d when t h e power i n v o l v e d f o r r a i s i n g t h e c e n t r e s o f g r a v i t y of t h e rnoving masses i s n e g l i g i b l e cornpared t o t h e power needed t o overcome a c c e l e r a t i o n s o r wind e f f e c t s . C o n v e r s e l y , when t h e e f f e c t o f t h e a c c e l e r a t i o n s o r t h e wind i s n e g l i g i b l e i n compar i s o n w i t h t h e e f f e c t o f d i s p l a c i n g t h e c e n t r e s o f g r a v i t y o f t h e moving m a s s e s v e r t i c a l l y , t h i s v a l u e is t o o h i g h and SMmax111 c a n b e c a l c u l a t e d from t h e f o r m u l a :

Between t h e s e two l i m i t i n g v a l u e s , e a c h i n d i v i d u a l c a s e s h o u l d b e examined a c c o r d i n g t o t h e motor c h o s e n , t h e method o f s t a r t i n g and t h e r e l a t i v e m a g n i t u d e s o f t h e l o a d s due t o i n e r t i a a n d wind e f f e c t s on t h e one hand and t h o s e due t o r a i s i n g o f t h e c e n t r e s of g r a v i t y on t h e o t h e r . Without e x c e p t i o n , when o p e r a t i n g c o n d i t i o n s l i m i t t h e t o r q u e a c t u a l l y t r a n s m i t t e d t o the mechanim ( s e e c l a u s e 2.6.4.2.1, t h i s l i m i t i n g torque w i l l be taken a s t h e v a l u e o f SMCmax i f i t i s l e s s t h a n t h e v a l u e s d e f i n e d above.

(1)

Whereas i n t h e c a s e of h o i s t i n g m o t i o n s t h e l o a d s normally t r a n v n i t t e d t o t h e mechanism a r e l i m i t e d by t h e l o a d l i f t e d , i n h o r i z o n t a l m o t i o n s t h e maximum t o r q u e o f t h e motor c a n a l w a y s b e t r a n s m i t t e d t o t h e mechanism i f no m e c h a n i c a l l i m i t a t i o n e x i s t s . T h i s is why a d i f f e r e n t way o f e v a l u a t i n g SMmaX111 h a s been s p e c i f i e d a c c o r d i n g t o whether a h o i s t m o t i o n o r o t h e r motion is b e i n g c o n s i d e r e d . o r SMrnax i n t h e c a s e o f a p p l i a n c e s n o t s u b j e c t e d t o wind.

A P P E N D I X A - 2.1.1.

H A R M O N I S A T I O N OF THE C L A S S E S OF U T I L I Z A T I O N OF A P P L I A N C E S AND M E C H A N I S M S

The p r e s e n t appendix s e t s o u t t o demonstrate a rnethod by w h i c h i t i s p o s s i b l e i n many cases t o d e r i v e t h e c l a s s o f u t i l i z a t i o n o f mechanisms from t h a t o f a p p l i a n c e s as a whole and f r o m c e r t a i n parameters c h a r á c t e r i z i n g t h e d u t y t o be performed. The s t a r t i n g p o i n t i s t h e average d u r a t i o n tmc( i n seconds) o f a h o i s t i n g c y c l e T h i s i s t h e r e f o r e t h e t i m e necessary t o p e r f o r m a l 1 as d e f i n e d i n c l a u s e 2.1.2.2. t h e o p e r a t i o n s i n such a c y c l e . The t o t a l d u r a t i o n o f use T o f t h e a p p l i a n c e , expressed i n h o u r s , i s t h e n g i v e n by the r e l a t i o n : T = -N . tmc - 3600 Where N r e p r e s e n t s t h e number o f h o i s t i n g c y c l e s d e t e r m i n i n g t h e c l a s s of u t i l i z a t i o n o f the appliance. Table T.A.2.1.1.1. g i v e s t h e v a l u e s o f T f o r c y c l e d u r a t i o n s o f 30 - 480 S i n accordance w i t h t h e c l a s s o f u t i l i z a t i o n o f t h e a p p l i a n c e . The number o f h o i s t i n g c y c l e s i s t h e maximum number f o r t h i s c l a s s o f u t i l i z a t i o n ; t h e s e v a l u e s a r e , however, a d j u s t e d t o 15 625, 31 250 and 62 500 r e s p e c t i v e l y f o r c l a s s UO, U1 and U2, i n o r d e r t o reduce t h e number o f d i f f e r e n t v a l u e s f o r T. The n e x t s t e p i s t o d e t e r m i n e f o r each mechanism t h e r a t i o C L i between t h e d u r a t i o n o f use o f t h e mechanism d u r i n g a h o i s t i n g c y c l e and t h e average d u r a t i o n tmco f the cycle. Table T.A.2.1.1.2. g i v e s t h e t o t a l d u r a t i o n s o f use Ti o f t h e mechanism depending on t h e t o t a l d u r a t i o n o f use o f t h e a p p l i a n c e , and f o r v a r i o u s c o n v e n t i o n a l v a l u e s o f t h e r a t i o C L i . T h i s t a b l e a l s o shows t h e c l a s s of u t i l i z a t i o n o f t h e rnechanism. The v a r i o u s c l a s s e s a r e r e p r e s e n t e d by t h e stepped areas. I t i s t h u s s u f f i c i e n t t o d e t e r m i n e t h e c l a s s o f u t i l i z a t i o n o f t h e a p p l i a n c e by referente t o t a b l e T.2.1.2.2., t h e average d u r a t i o n o f t h e h o i s t i n g c y c l e and t h e v a l u e s o f Cxi i n o r d e r t o o b t a i n t h e c l a s s e s o f u t i l i z a t i o n o f t h e mechanisms.

From t h e c u r v e s o f t h e nomogram T.A.2.1.1.3. the classes of u t i l i z a t i o n f o r the mechanisms i n terms o f t h e s e t h r e e parameters can be found d i r e c t l y .

Table T.A.2.1.1.1. Total d u r a t i o n o f use ( T ) of l i f t i n q a p p l i a n c e s i n h o u r s

E X A W L E OF APPLICATION Docksido cargo crane. Tho class of utilization for the appliance will be ü5. A hoisting cycle comprises the following operations

- hoisting of load - travelling ; - slewing ;

;

- lowering ;

- unhooking of load

-

-

;

hoisting empty ; slewing ; travelling ; lowering empty ; hooking on of new load.

The average time for completion of the cycle will be estimated at 150 s. The ratios cxi will be estimated as follows : - hoisting (hoisting and lowering)

: CLi = 0.63

- slewing (2 directions)

: CLi = 0.25

- travelling (do. )

: C Y ~=

Table T.A.2.1.1.1.

0.10

gives us for class U5 and tmc = 150 S :

For the various mechanisms, table T.A.2.1.1.2. gives us, for T = 2 0 835 h, the following total durations Ti and classes of utilization :

- hoisting

(ai= 0.63)

:

- slewing

(ai= 0.25)

: Ti =

5 209 h

T5

- travelling

(vli = 0.10) : Ti =

2 084 h

T4

T~ = 13 126 h

T7

Frorn the curves in table T.A.2.1.1.3. the same conclusions are drawn on the basis of the ordinate t., = 150 s (broken line).

APPENDIX A

-

2.2.3.

C A L C U L A T I O N OF L O A D S D U E T O A C C E L E R A T I O N S OF

HORIZONTAL MOTIONS

PART 1 - METHOD

B A S I C DATA Let v

be t h e s t e a d y h o r i z o n t a l v e l o c i t y o f t h e p o i n t o f s u s p e n s i o n o f t h e l o a d , e i t h e r a t t h e end o f t h e a c c e l e r a t i o n p e r i o d , o r a t t h e b e g i n n i n g o f t h e b r a k i n g p e r i o d , a c c o r d i n g t o w h e t h e r an a c c e l e r a t i o n o r a b r a k i n g p r o c e s s i s b e i n g c o n s i d e r e d , and

F

a n i m a g i n a r y h o r i z o n t a l f o r c e i n t h e same d i r e c t i o n a s v , a p p l i e d a t t h e p o i n t o f s u s p e n s i o n o f t h e l o a d and p r o d u c i n g t h e same e f f e c t on t h e motion under c o n s i d e r a t i o n a s t h e a c c e l e r a t i n g o r d e c e l e r a t i n g t o r q u e a p p l i e d by t h e motor o r t h e brake.

PROCEDURE The d i f f e r e n t ~ u a n t i t i e ss e t o u t below must be c a l c u l a t e d i n s u c c e s s i o n . E q u i v a l e n t mass (m) The i n e r t i a o f a l 1 moving p a r t s o t h e r t h a n t h e l o a d , i r i t h e motion under c o n s i d e r a t i o n , is r e p l a c e d by a s i n g l e e q u i v a l e n t rnass m a s s m e d t o be c o n c e n t r a t e d a t t h e p o i n t o f s u s p e n s i o n o f t h e l o a d and g i v e n by t h e r e l a t i o n :

Where :

m,

= i s t h e t o t a l mass o f a l 1 e l e m e n t s , o t h e r than t h e l o a d , u n d e r g o i n g t h e same

p u r e l i n e a r motion a s t h e p o i n t o f s u s p e n s i o n of t h e l o a d ; Ii

= t h e moment o f i n e r t i a o f a p a r t u n d e r g o i n g a r o t a t i o n d u r i n g t h e rnotion under

c o n s i d e r a t i o n , t h i s rnoment o f i n e r t i a b e i n g c o n s i d e r e d a b o u t t h e a x i s o f r o t a t i o n , and wi

=

t h e angular v e l o c i t y of t h e p a r t r e f e r r e d t o , about i t s a x i s of r o t a t i o n , corresponding t o t h e l i n e a r v e l o c i t y v of the point of suspension of t h e load.

The sum L c o v e r s a l 1 p a r t s i n r o t a t i o n ( s t r u c t u r e , mechanisms, m o t o r ) d u r i n g t h e motion c o n s i d e r e d . However, i n t h e c a s e o f mechanisms, t h e i n e r t i a o f components o t h e r t h a n t h o s e d i r e c t l y c o u p l e d t o t h e motor s h a f t can be i n g o r e d .

Mean a c c e l e r a t i o n o r d e c e l e r a t i o n ( h j :

wiiere m1. i s Khe mass o f t h e l o a d .

Mean d u r a t i o n o f a c c e l e r a t i o n o r d e c e l e r a t i o n (T,)

:

Vean i n e r t i a f o r c e s : The a c c e l e r a t i o n c o r r e s p o n d i n g t o t h e a c c e l e r a t i o n j, a t t h e p o i n t o f s u s p e n s i o n o f t h e l o a d i s c a l c u l a t e d f o r e a c h component p a r t i n n o t i o n . k l t i p l y i n g t h i s a c c e l e r a t i o n by t h e mass o f t h e component c o n s i d e r e d g i v e s t h e rnean i n e r t i a f o r c e i t sustains. I n t h e p a r t i c u l a r c a s e o f t h e l o a d i t s e l f , t h i s f o r c e o f i n e r t i a Fcm w i l l b e g i v e n by : F ~ m= m i jm

P e r i o d o f o s c i l l a t i o n T1 :

Tl = 2

~

f l 9

= t h e l e n g t h o f s u s p e n s i o n o f t h e l o a d wher i t i s i n i t s uppermosi p o s i t i o n ( v a l u e s of below 2,00 m need n o t be t a k e n i n t o c o n s i d e r a t i o n j a n d ,

g = t h e a c c e l e r a t i o n due t o g r a v i t y .

Value o f p When t h e system d r i v i n g t h e motion c o n t r o l s t h e a c c e l e r a t i o n and t h e d e c e l e r a t i o n and r n a i n t a i n s i t a t a c o n s t a n t v a l u e , U i s t a k e n e q u a l t o O i r r e s p e c t i v e o f t h e rnasses m and rnl.

Value o f

B

:

Value o f Y;, : With t h e v a l u e s o b t a i n e d f o r and t h e c o r r e s p o n d i n g v a l u e o f ih.

3,

t h e g r a p h i n f i g u r e A.2.2.1.

i s used t o f i n d

l n e r t i a f o r c e s t o be c o n s i d e r e d i n t h e d e s i q n o f t h e s t r u c t u r e : The f o r c e s o f i n e r t i a which t a k e a c c o u n t o f dynarnic e f f e c t s and which rnust t h e r e f o r e be considered i n t h e s t r u c t u r a l ca!culations a r e obtained a s follows :

vh

-

I n e r t i a f o r c e due t o t h e l o a d :

-

I n e r t i a f o r c e on moving p a r t s o t h e r t h a n t h e l o a d : t w i c e t h e mean i n e r t i a f o r c e s .

F,,

JUST I F ICAT I O N A

j u s t i f i c a t i o n o f t h e rnethod g i v e n above f o l l o w s i n p a r t 2 o f t h i s a p p e n d i x .

P A R T 2 - E X P L A N A T I O N OF T H E M E T H O D

STATEMENT Of

THE PROBLEM

A h o i s t i n g a p p l i a n c e is a physical system c o n s i s t i n g e s s e n t i a l l y of :

- c o n c e n t r a t e d m a s s e s (hook l o a d , c o u n t e r w e i g h t s , (girders, ropes, 1,

...

...

and d i s t r i b u t e d m a s s e s

- e l a s t i c c o n n e c t i o n s between t h e s e m a s s e s ( g i r d e r s , r o p e s ,

... 1.

I f such a s y s t e m , o r i g i n a l l y i n a s t a t e o f e q u i l i b r i u m , i s s u b j e c t e d t o a v a r y i n g l o a d , i t d o e s n o t t e n d p r o g r e s s i v e l y t o w a r d s a new s t a t e of e q u i l i b r i u m e v e n i f t h e new l o a d a p p l i e d i s i t s e l f c o n s t a n t . On t h e c o n t r a r y , i t is s e t i n a more o r l e s s complex o s c i l l a t i n g motion a b o u t t h i s new s t a t e o f e q u i l i b r i u m . h r i n g t h i s m o t i o n , t h e v a r i o u s i n t e r n a l l o a d s and s t r e s s e s o f t h e system c a n e x c e e d - sometimes t o a marked e x t e n t - t h e v a l u e s t h e y would have asswned had t h e s y s t e m b e e n i n s t a t i c e q u i l i b r i u m u n d e r t h e i n f l u e n c e o f t h e new l o a d . Such a s i t u a t i o n a r i s e s d u r i n g a c c e l e r a t i o n o r d e c e l e r a t i o n ( b r a k i n g ) o f a h o r i z o n t a l motion o f a h o i s t i n g a p p l i a n c e . Thus i f , s t a r t i n g from a p o s i t i o n o f r e s t , a n a p p l i a n c e o r p a r t o f an a p p l i a n c e b e g i n s a motion o f t r a n s l a t i o n o r r o t a t i o n , t h e component p a r t s o f t h e s y s t e m undergo a c c e l e r a t i o n s and a r e t h e r e f o r e s u b j e c t e d t o i n e r t i a f o r c e s . Once a s t e a d y s p e e d i s a t t a i n e d , t h e a c c e l e r a t i o n c e a s e s , t h e i n e r t i a f o r c e s d i s a p p e a r and t h e e x t e r n a 1 l o a d u n d e r g o e s a new v a r i a t i o n . The a n g l e t h r c u g h which a r o t a t i n g s y s t e m t ü r n s i e . 9 . i h e r o t a t i n g p a r t o f a c r a n e j d u r i n g t h e timo f o r which i n e r t i a f o r c e s a r e a p p l i e d i s g e n e r a l l y r e l a t i v e l y s m a l l . T h i s b e i n g s o , no a p p r e c i a b l e e r r o r w i l l be i n v o l v e d i f one assumes t h a t e a c h p o i n t i n t h e svstem follows a s t r a i g h t path during t h i s time. Since, moreover, t h e r e i s no d i f f e r e n c e o f principie between t h e t r e a t m e n t u s e d f o r l i n e a r m o t i o n s and m o t i o n s o f r o t a t i o n , i n what f o l l o w s t h e l i n e a r motion w i l l b e c o n s i d e r e d i n g r e a t e r d e t a i l ( c h a p t e r 2!, whereas o n l y a s h o r t n o t e ( c h a p t e r 3 ) w i l l c o v e r r o t a t i o n .

CALCULATING THE LOADS I N THE CASE OF A LINEAR MOTION

GENERAL DATA I t i s now p r o p o s e d t o examine t h e p a r t i c u l a r c a s e o f b r a k i n g o f t h e t r a v e l motion o f a c o m p l e t e o v e r h e a d t r a v e l l i n g c r a n e when i t i s c a r r y i n g a l o a d s u s p e n d e d from i t s h o i s t i n g r o p e . O t h e r c a s e s e n c o u n t e r e d i n p r a c t i c e can be d e a l t w i t h i n s i m i l a r fashion. C o n s i d e r i n g f i g l ~ r eA.2.1.

let :

ml

be t h e mass o f t h e suspended l o a d ,

m

t h e t o t a l mass o f t h e o v e r h e a d t r a v e l l i n g c r a n e i n c l u d i n g t h e c r a b ( s e e n o t e below c o n c e r n i n g t h e i n e r t i a o f t h e motor and o f t h e machinery d r i v i n g t h e motion),

x

a c o o r d i n a t e d e f i n i n g t h e p o s i t i o n o f t h e c r a n e a l o n g i t s t r a c k (more p r e c i s e l y , x represents t h e coordinate of the point of suspension of t h e hoisting rope along an a x i s p a r a l l e l t o t h e d i r e c t i o n of t r a v e l ) ,

a c o o r d i n a t e d e f i n i n g t h e p o s i t i o n of t h e c e n t r e of g r a v i t y of t h e suspended l o a d a l o n g an a x i s of t h e sarne d i r e c t i o n , s e n s e and o r i g i n a s t h e a x i s of x ,

1

z = x1

-

x

a c o o r d i n a t e e x p r e s s i n g t h e h o r i z o n t a l dicplacernent o f t h e l o a d r e l a t i v e t o the crane.

Let us a s s m e t h a t a t t h e i n s t a n t t = O t h e overhead t r a v e l l i n g c r a n e i s rnoving i n t h e p o s i t i v e s e n s e of t h e x a x i s a t a v e l o c i t y v, and t h a t t h e l o a d i s a t r e s t r e l a t i v e t o the crane. ( Z = z 1 = O , with : Z ' = dt

e)

I f t h e braKe i s a p p l i e d t o t h e t r a v e l rnechanisrn a t t h e i n s t a n t t = O , i t w i l l g i v e r i s e from t h a t i n s t a n t t o a h o r i z o n t a l b r a k i n g f o r c e p a r a l l e l t o , b u t o f o p p o s i t e s e n s e t o , t h e x a x i s a t each p o i n t where a d r i v i n g wheel i s i n c o n t a c t w i t h i t s r a i l . To s i r n p l i f y r n a t t e r s , l e t u s assume t h a t t h e c r a b i s l o c a t e d a t mid-span o f t h e main g i r d e r s of t h e overhead t r a v e l l i n g c r a n e . I t f o l l o w s by syrnrnetry t h a t t h e t o t a l f o r c e a t each r a i l i s t h e same. Let u s d e s i g n a t e i t s p r o j e c t i o n on t h e x a x i s by 5 ( w i t h > O ) , s o t h a t t h e t o t a l b r a k i n g f o r c e a c t i n g on t h e systern i n rnotion ( c r a n e p l u s l o a d ) i s equal t o F i n a b s o l u t e v a l u e . I f t h e systern were composed of r i g i d l y i n t e r c o n n e c t e d masses, t h i s would r e s u l i i n a d e c e l e r a t i o n o f a b s o l u t e value j,, given by t h e r e l a t i o n :

f o r g o t t e n however t h a t F o r i g i n a t e s i n t h e b r a k i n g t o r q u e a p p l i e d I t must n o t tr th: t r - i z l meihs?isrn krbicb a u j t í i c t o : - ~ l r u~ i á i i t "Le L i d v e i irle1 ii;iuT t i t e c r a n e and t h e l o a d b u t a l s o t h e r o t a t i o n a l i n e r t i a o f t h e d r i v i n g m o t o r and t h e i n t e r v e n i n g m a c h i n e r y . G e n e r a l l y s p e a k i n g , one can n e g l e c t t h e r o t a t i n g i n e r t i a o f a l 1 components o t h e r t h a n t h o s e i n t e g r a l w i t h t h e motor s h a f t . I n many cases, however, t h e i n e r t i a o f t h e l a t t e r must be t a k e n i n t o account and t h e r e l a t i o n ( 2 . 1 . 1 . ) h o l d s good o n l y p r o v i d e d t h a t m i n c o r p o r a t e s an e q u i v a l e n t mass me g i v e n b y t h e relation : 2 me v = lm N2 (2.1.2.) where Im = i s t h e moment o f i n e r t i a o f a l 1 t h e components i n t e g r a l w i t h t h e m o t o r s h a f t ( i n c l u d i n g t h e m o t o r i t s e l f , o f c o u r s e ) and

q, =

t h e a n g u l a r v e l o c i t y o f t h e m o t o r c o r r e s p o n d i n g t o t h e t r a v e l l i n g speed v o f t h e crane.

i h d e r t h e e f f e c t o f t h e d e c e l e r a t i o n jm,t h e suspension r o p e c a n n o t r e t a i n i t s v e r t i c a l p o s i t i o n . I t s new p o s i t i o n o f e q u i l i b r i m i s i n c l i n e d t o t h e v e r t i c a l a t an a n g l e % g i v e n b y t h e r e l a t i o n : O,,. = a r c t g

Jm 9

(2.1.3.)

where g i s t h e a c c e l e r a t i o n due t o g r a v i t y . I n t h i s case t h e r o p e e x e r t s a h o r i z o n t a l f o r c e on t h e c r a n e whose p r o j e c t i o n Fcm on t h e x a x i s i s g i v e n by :

I n p o i n t o f f a c t , t h e system i s n o t r i g i d , t h e d e c e l e r a t i o n i s n o t c o n s t a n t and t h e l o a d and i t s suspension r o p e adopt an o s c i l l a i s n o t therefore given by (2.1.1.), t i n g m o t i o n , and t h e h o r i z o n t a l f o r c e developed by t h e r o p e on t h e c r a n e can a s s m e v a l u e s d i f f e r i n g g r e a t l y frorn ( 2 . 1 . 4 . ) . By a s i m i l a r r e a s o n i n g , one may c o n c l u d e t h a t t h e d e c e l e r a t i o n o f t h e system g i v e s r i s e t o i n e r t i i f o r c e s w h i c h a c t on each component p a r t of t h e c r a n e and t h e c r a b , b u t t h a t because o f t h e e l a s t i c i t y o f t h e g i r d e r s t h e system w i l l u n d e r g o an o s c i l l a t i n g m o t i o n i n t h e c o u r s e o f w h i c h t h e s t r e s s e s w i l l be s u b j e c t t o f l u c t u a t i o n s w h i c h must be e s t i m a t e d . The n e x t two p a r a g r a p h s d e a l i n s u c c e s s i o n w i t h t h e e f f e c t o f t h e i n e r t i a f o r c e s on t h e l o a d and on t h e g i r d e r s .

E F F E C T OF I N E R T I A F O R C E S O N T H E L O A D I n d e t e r m i n i n g t h e m o t i o n w h i c h t h e l o a d executes a f t e r t h e b r a k e i s a p p l i e d , one can n e g l e c t t h e movement o f t h e p o i n t o f suspension due t o g i r d e r f l e x i b i l i t y i n a h o r i z o n t a l p l a n e . The a m p l i t u d e o f t h i s movement i s , i n f a c t , v e r y s m a l l comp a r e d w i t h t h e a m p l i t u d e o f s w i n g i n g o f t h e l o a d . C a l c u l a t i o n s can t h e r e f o r e be c a r r i e d o u t w i t h t h e c r a n e c o n s i d e r e d as a system which i s n o t s u b j e c t t o d e f o r m a t i o n .

The p r o j e c t i o n Fc on t h e x a x i s o f t h e f o r c e e x e r t e d b y t h e r o p e on t h e c r a n e i s given by the r e l a t i o n :

where

-! i s

t h e s u s p e n s i o n l e n g t h o f t h e l o a d . I t w i l l be n o t e d t h a t F,

is propor-

t i n ~ a lt n t h p d i c p l x c m w t 2 s f thi. loa4 n i t l i itispecl L O i t s p o s l t i o n o t i n i t i a l

e q u i l i b r i m , j u s t a s i f i t were an e l a s t i c r e s t o r i n g f o r c e . The e a u a t i o n s o f motion c a n be w r i t t e n :

X1 - X rnx" = mlg ---

P

-

F

(2.2.3.)

w h i l e , assurning x = 0 , f o r t = 0 , t h e i n i t i a l c o n d i t i o n s a r e a s f o l l o w s : f o r t = O,

xl

= x = O

xo1 = x'= v z

: x l - x = 0

2 '

=

X l 1 -

x':

o

Let :

E q u a t i o n s ( 2 . 2 . 2 . ) and ( 2 . 2 . 3 . ) t h e n become : x" + z" * x"-Y

2

$2

,0

z = - j ,

whence

With t h e i n i t i a l c o n d i t i o n s of ( 2 . 2 . 4 . ) t o ( 2 . 2 . 7 . ) , i s g i v e n by : j z (1 - c o s o , t )

=_o; %

the solution t o these equations (2.2.15. )

The c o m p l e t e e x p r e s s i o n f o r x i s o f no d i r e c t i n t e r e s t t o u s .

i t c a n t h e n b e s r e n w i t h o u t d i f f i c u l t y t h a t zm i s t h e p o s i t i o n o f e q u i l i b r i u m t h a t c a n b e assumed by t h e l o a d d u r i n g a c o n s t a n t d e c e l e r a t i o n o f t h e c r a n e e q u a l t o t h e v a l u e jm d e f i n e d by ( 2 . 1 . 1 . ) , i . e . d u r i n g t h e d e e e l e r a t i o n t h a t would be o b t a i n e d by a p p l y i n g t h e b r a k i n g f o r c e F t o t h e t o t a l mass ( c r a n e p l u s l o a d ) i n m o t i o n , t h i s mass b e i n g assumed t o e o n s t i t u t e a r i g i d system. The v a l u e z = z m d e f i n i n g t h e l o a d d i s p l a c e m e n t c o r r e s p o n d s t o t h e h o r i z o n t a l f o r c i F,,, d e f i n e d by ( 2 . 1 . 4 . ) e x e r t e d by t h e r o p e on t h e c r a n e . Comparison between ( 2 . 2 . 1 . ) , ( 2 . 2 . 1 5 . ) and ( 2 . 2 . 1 7 . ) t h e n shows t h a t :

I f t h e d e c e l e r a t i o n p e r i o d o f t h e c r a n e l a s t s f o r a t i m e td s u c h t h a t :

i t w i l l be s e e n t h a t F, momentarily becomes t w i c e Fcm, o r i n o t h e r w o r d s , t h a t i t s maximum v a l u e F c m a x i s g i v e n by t h e r e l a t i o n : (2.2.20.)

'c max = 2 Fcm

if t t i e c o n d i t i o n ( 2 . 2 . 1 9 . ) i s n o t s a t i s f i e d , t h i s means t h a t t h e c r a n e h a s s t o p p e d b e f o r e t h e l o a d h a s r e a c h e d i t s maximum d i s p l a c e m e n t z = 2 z m . However, a f t e r t h e crane s t o p s , t h e load w i l l usually continue t o o s c i l l a t e , s o t h e rope w i l l continue t o e x e r t a v a r y i n g h o r i z o n t a l f o r c e on t h e c r a n e , and t h e maximum v a l u e which t h i s c a n a t t a i n must be s o u g h t . I t i s e a s y t o v e r i f y t h a t a f t e r t h e c r a n e h a s s t o p p e d , t h e motion o f t h e l o a d i s d e f i n e d by t h e e x p r e s s i o n : z = zd cos

b1

Z ' d s i n u1 ( t - t d ) (t - td) + 01

with

z V d=

q

z m s i n $ td

where td is t h e s m a l l e s t p o s i t i v e v a l u e o f t t h a t makes t h e e x p r e s s i o n ( 2 . 2 . 1 6 . ) f o r x ' e ~ u a lt o z e r o . The maximum v a l u e F c m a x assumed by F,

i s Lhen g i v e n by t h e r e l a t i o n :

(2.2.21.)

G e n e r a l l y s p e a k i n g , we may t a k e : F c -max

-

Fcm The d e t e r m i n a t i o n o f Tm

Jm

n 2T1 = Wl

-

yh

(2.2.25.)

yh is s i m p l i f i e d by i n t r o d u c i n g t h e f o l l o w i n g q u a n t i t i e s

:

t h e t i m e f o r which t h e slowing-down phase o f t h e c r a n e would l a s t i f t h e d e c e l e r a t i o n were c o n s t a n t and t h e system i n motion n o t s u b j e c t t o deformation. t h e p e r i o d o f o s c i l l a t i o n o f t h e pendulum s y s t e m formed by t h e suspended l o a d ( c r a n e s t o p p e d ) .

I t c a n be v e r i f i e d w i t h o u t d i f f i c u l t y t h a t p a r a m e t e r s p and B d e f i n e d by t h e r a t i o s :

yh depends o n l y on two non-dimensional

which c a n be o b t a i n e d v e r y e a s i l y . I t w i l l be n o t e d t h a t ( 2 . 2 . 1 6 . ) c a n be w r i t t e n :

x t = v [ l -

(4t ) + U

-1 sin

(ut j

21íhr'l+;,! and t h e r e f o r e :

t h i s e q u a t i o n makes i t p o s s i b l e t o d e t e r m i n e t h e v a l u e o f i n t o (2.2.24.).

q td

t o be i n t r o d u c e d

The g r a p h i n f i g u r e ( 2 . 2 . 1 . ) p l o t s t h e v a l u e s o f yh a g a i n s t B f o r v a r i o u s v a l u e s o f p. (The c u r v e p = O w i l l be e x p l a i n e d l a t e r i n Chapter 5 ) . I f p < 1 (which i s g e n e r a l l y t h e c a s e w i t h overhead t r a v e l l i n g c r a n e t r a v e l m o t i o n s , s u c h a s t h a t i n t h e exarnple d e a l t w i t h ) , an a n a l y s i s o f t h e problem shows t h a t lh can i n no c a s e exceed 2 . T h i s v a l u e i s r e a c h e d d u r i n g t h e c r a n e d e c e l e r a t i o n phase i f t h e c o n d i t i o n ( 2 . 2 . 1 9 . ) i s s a t i s f i e d o r , which i s t h e same t h i n g , i f 6 r e a c h e s o r e x c e e d s a c e r t a i n c r i t i c a l v a l u e , Bcrit dependent upon p. Above t h i s c r i t i c a l v a l u e , yh t h e r e f o r e r e m a i n s c o n s t a n t and e q u a l t o 2 , whatever t h e v a l u e o f 0.

I f U > 1 (which c o u ~ dbe t h e c a s e h i t h t r a v e r s ~m o t i n n s . i n which m ~ s q m n t i ~ i l y r e p r e s e n t s o n l y t h e mass o f t h e c r a b , o r w i t h s l e w i n g m o t i o n s ) , t h e same a n a l y s i s shows t h a t , a g a i n p r o v i d e d 6 r e a c h e s o r e x c e e d s a c e r t a i n c r i t i c a l d a l u e Bcrit d e p e n d e n t upon U, yh c a n exceed 2 a n d r e a c h a maximum g i v e n by :

T h i s maximum c a n a c t u a l l y be r e a c h e d o n l y d u r i n g t h e s w i n g i n g motion o f t h e l o a d s u b s e q u e n t t o t h e b r i n g i n g t o r e s t o f i t s p o i n t o f s u s p e n s i o n . The c r i t i c a l v a l u e Bcrit i s s u c h t h a t t h e c r a n e i s h a l t e d b e f o r e t h e c o n d i t i o n ( 2 . 2 . 1 9 . ) i s s a t i s f i e d , o r b e f o r e Fc r e a c h e s 2 Fcm. However, any v a l u e o f B g r e a t e r t h a n leads t o t h e c o n d i t i o n ( 2 . 2 . 1 9 . ) b e i n g s a t i s f i e d and Fc n e c e s s a r i l y p a s s e s t h e v a l u e 2 Fcm, whence yh > 2. I t w i l l a l s o be n o t e d t h a t i f 2 > Bcrit h a s been c a l c u l a t e d t a k i n g v e q u a l t o t h e maximum s t e a d y s p e e d o f t h e m o t i o n , b r a k i n g a p p l i e d s t a r t i n g from t h e i n i t i a l speed :

ecrit

Bcrit

B w i i l n e c e s s a r i i y ? e a d t o t h e maxirnum v a l u e o f yh g i v e n by ( 2 . 2 . 3 0 . ) . This i s t h e r e a s o n why, i n t h e g r a p h o f f i g u r e A . 2 . 2 . L . , t n e v a i u e s o f 'kh havo bee-i m a i n t a i n e d f o r a l 1 v a l u e s o f B g r e a t e r t h a n Ocrit.

F i q u r e A.2.2.1.

As r e g a r d s t h e c h o i c e o f T1, i t s h o u l d be n o t e d t h a t t h e danger o f r e a c h i n g h i g h v a l i r ~ sn f vh i q 311 t h p g r o s t e r a- t h e r u s p o n s i x l c n g t h f ü f ti-ie lucid i ~ t ~ o r l i e i s h o r t e r , because 6 t h e n a t t a i n s i t s c r i t i c a 1 v a l u e more r a p i d l y . The c a l c u l a t i o n s must t h e r e f o r e be made a s s m i n g t h a t t h e l o a d i s n e a r i t s uppermost p o s i t i o n . I n practice w i l l g e n e r a l l y l i e between 2 and 8 m. The t a b l e below g i v e s t h e v a l u e s o f T1 f o r a few v a l u e s o f

e

e.

I t remains f o r u s t o examine t h e e f f e c t o f t h e h o r i z o n t a l f o r c e F c m a x ov t h e l o a d i n g c o n d i t i o n s s u s t a i n e d by t h e s t r u c t u r e . T h i s f o r c e a c t u a l l y e x i s t s , so t h a t any components such a s t h e c r a b w h i c h t r a n s m i t

i t d i r e c t l y must b e d e s i g n e d t o w i t h s t a n d i t . The c o n f i g u r a t i o n o f t h e l o a 6 a c t i n c j o n t h e g i r d e r as a whole t h e r e f o r e deserves come a t t e n t i o n . L e t us f i r s t c o n s i d e r t h e case where F C m a x o c c u r s b e f o r e t h e c r a n e has come t o h a l t . I t would be i n c o r r e c t t o c o n s i d e r t h e l a t t e f as a beam s u p p o r t e d a t h o t b enos ano s u b j e c t e d a t i t s c e n t r e t o t h e f o r c e F c m a x . One must n o t l o s e s i g h t o f t h e f a c t F t h a t each o f t h e two s u p p o r t i n g p o i n t s can t r a n s m i t o n l y a r e a c t i o n The s u c c e s s i v e 2 . d i a g r a m s i n f i g u r e A.2.2.2. i l l u s t r a t e how t h e p r o b l e m must be c o n s i d e r e d . Diagram "a" r e p r e s e n t s t h e i d e a l s t a t e o f e q u i l i b r i u m , i n w h i c h t h e system as a whole i s s u b j e c t e d t o a d e c e l e r a t i o n jm( o r an a c c e l e r a t i o n x" = - ,)j and i n which t h e r o p e d e v e l o p s a f o r c e FCm. Each m a t e r i a l element dm o f t h e system t h e r e f o r e s u s t a i n s a n i n e r t i a f o r c e jmdm. Diagram "a" i s a s u p e r i m p o s i t i o n o f diagram "b" and diagram "c". Diagram "b" r e l a t e s t o t h e l o a d due t o t h e i n e r t i a f o r c e s on t h e c r a n e p r o p e r ( t h i s i s d e a l t w i t h i n p a r a g r a p h 2.3.1, w h i l e d i a g r a n " c " shows t h e e f f e c t o f t h e l o a d due t o t h e r o p e . I n p o i n t o f f a c t , t h e a c t u a l f o r c e developed by t h e r o p e i s n o t t h e f o r c e Fcm r e p r e s e n t e d i n diagram " c " b u t t h e f o r c e :

-.

'c max ' +h 'cm

(2.2.31.)

Since t h e supporting p o i n t s (braked wheels) a r e n o t capable o f i n c r e a s i n g t h e i r r e a c t i o n , t h e excess f o r c e ( y h - l ) F c m can o n l y r e s u l t i n a supplementary a c c e l e r a t i o n x " expressed b y : x'l

z

( y h - 1)

Fcm

(2.2.32.

w h i c h i s t r a n s l a t e d i n t o a d i s t r i b u t e d l o a d - x " dm on a l 1 m a t e r i a l elernents o f t h e crane. Diagram "d" c o n s e q u e n t l y r e p r e s e n t s t h e l o a d i n g c o n f i g u r a t i o n t o be t a k e n i n t o account when d e s i g n i n g t h e g i r d e r s . L e t us c o n s i d e r t h e case i n w h i c h F c m a x a r i s e s a f t e r t h e crane has h a l t e d . T h i s t i m e , t h e b r a k e d wheels no l o n g e r have t o d e v o t e p a r t o f t h e r e a c t i o n o f which t h e y a r e c a p a b l e t o t a k i n g up t h e i n e r t i a f o r c e s on t h e c r a n e , and i n g e n e r a l ,

rnust be r e g a r d e d a s b e i n g f i x e d . T h i s b e i n g s o , t h e ~ i r d e rrniist h? d e q i q n ~ r lsq i f i t were s u p p o r t e d a t each end and s u b j e c t e d t o t h e f o r c e Fcrnax a t i t s c e n t r e . T h i s l a t t e r c a s e i s i n p o i n t o f f a c t t h e o n l y one which needs t o b e c o n s i d e r e d , b e c a u s e when Fc r e a c h e s i t s rnaxirnwn v a l u e 2 FCm b e f o r e t h e c r a n e c a n e s t o a s t a n d s t i l l - t h i s f o r c e can s t i l l a r i s e i n t h e c o u r s e of t h e pendulurn rnotion which f o l l o w s a f t e r it has stopped. A l 1 t h e p r e c e d i n g c o n s i d e r a t i o n s s t i l l h o l d good i f , i n s t e a d o f c o n s i d e r i n g a b r a k i n g p h a s e , one i s d e a l i n g w i t h an a c c e l e r a t i o n phase of t h e c r a n e , i n t h e c o u r s e o f which i t is speeded up, by a c o n s t a n t d r i v i n g t o r q u e , from r e s t t o a g i v e n s t e a d y s p e e d .

7~

EFFECT OF I N E R T I A FORCES ON THE STRUCTURAL STEELWORK I n t h e p r e v i o u s c h a p t e r , t h e s t r u c t u r e was a s s m e d t o be p e r f e c t l y r i g i d . I n f a c t , however, i t p o s s e s s e s a d e g r e e of e l a s t i c i t y and c o n s e q u e n t l y a l s o assumes an o s c i l l a t i n g rnotion d u r i n g t h e b r a k i n g p e r i o d and a f t e r corning t o r e s t . Because t h e s t r u c t u r e is cornposed e s s e n t i a l l y o f d i s t r i b u t e d r a t h e r t h a n s i m p l e c o n c e n t r a t e d rnasses, i t is u s u a l l y v e r y d i f f i c u l t t o d e t e r m i n e t h e motion t h e o r e t i c a l l y , and such c a l c u l a t i o n s would be j u s t i f i e d o n l y i n t h e case o f very l a r g e a p p l i a n c e s i n which t h e i n e r t i a f o r c e s play an appreciable p a r t . F i q u r e A.2.2.2. LOADlNG

ACCELERATION

111 almvsr a i i c a s e s , l t w i l l s u f f i c e t o r e p r e s e n t a s t r u c t u r e a s b e i n g a s i m p l e o s c i l l a t i n g system having r e s t o r i n g f o r c e s p r o p o r t i o n a l t o t h e e x t e n s i o n and s u b j e c t e d t o t h e o v e r a l l a c c e l e r a t i o n o f t h e r e f e r e n c e system t o which i t i s r e f e r r e d . In view o f t h e n o t e f o l l o w i n g e x p r e s s i o n ( 2 . 2 . 1 . ) t h e c o n s i d e r a t i o n s developed i n para.graph 2 . 2 . can be a p p l i e d h e r e a l s o . Wwever, t h e n a t u r a l p e r i o d of t h e o s c i l l a t i o n s (comparable t o t h e p e r i o d Tl of paragraph 2 . 2 . ) i s always a p p r e c i a b l y s h o r t e r than t h a t o f a suspended l o a d , n o t exceeding a few t e n t h s of a second i n most c a s e s . The r e s u l t o f t h i s i s t h a t t h e parameter corresponding t o B always SO t h a t Yh must always be taken e q u a l t o 2 , t h i s exceeds t h e c r i t i c a 1 v a l u e Bcrit, being t h e c o e f f i c i e n t a p p l i c a b l e t o i n e r t i a l o a d s c a l c u l a t e d w i t h t h e mean d e c e l e r a t i o n jm. The only e x c e p t i o n t h a t could be made t o t h i s r u l e would be f o r extremely b r i e f r e t a r d a t i o n p h a s e s , such a s t h o s e r e s u l t i n g from S r a k i n g a low-speed t r a v e l motion, with t h e wheels s l i p p i n g on t h e r a i l s . Because t h e o s c i l l a t i n g motions of t h e s t r u c t u r e have a h i g h f r e q u e n c y , t h e maximum r e s u l t i n g l o a d i n g s a r e superimposed momentarily upon t h o s e due t o t h e l o a d .

CALCULATING THE LOADS I N THE CASE OF A SLEWING MOTION In t h e c a s e of a slewing motion, c o n s i d e r a t i o n s s i m i l a r t o t h o s e of c h a p t e r 2 can be developed. To c a l c u l a t e t h e e f f e c t s o f t h c i n e r t i a f o r c e s on t h r l o a d , i t i s only necessary t o d e t e r m i n e m from t h e r e l a t i o n :

where v

i s t h e h o r i z o n t a l l i n e a r v e l o c i t y of t h e suspension ~ o i n tof t h r load ;

1 i s t h e moment of i n e r t i a of a l 1 p a r t s i n motion ( s t r u c t u r e , machinery, m o t o r )

referred t o a particular shaft, U

i s t h e a n g u l a r v e l o c i t y o f t h a t s h a f t corresponding t o t h e v e l o c i t y v above

CALCULATING THE LOADS I N THE CACE OF A LUFFING HOTION In t h e c a s e o f a l u f f i n g motion, c o n s i d e r a t i o n s s i m i l a r t o t h o s e o f c h a p t e r 2 can be developed. I t w i l l s u f f i c e t o d e t e r m i n e m frum t h e r e l a t i o n :

where v

i s t h e h o r i z o n t a l l i n e a r v e l o c i t y o f t h r suspensiun p o i n t of t h e l o a a .

T

i s t h e t o t a l k i n e t i c energy o f t h e masses i n motion when t h e h o r i z o n t a l l i n e a r v e l o c i t y of t h e suspension p o i n t o f t h e l o a a i s e ~ u a lt o v.