Snow load on buildings

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PREFACE

I n Canada t h e l o a d of snow r e p r e s e n t s u s u a l l y t h e h e a v i e s t l o a d t h a t r o o f s have t o c a r r y . It i s t h e r e f o r e obvious t h a t t h e magnitude of t h e snow l o a d s used i n d e s i g n h a s c o n s i d e r a b l e

i n f l i ~ e n c e on t h e c o s t of c o n s t r u c t i o n .

The d e s i g n snow l o a d s s p e c i f i e d by t h e N a t i o n a l B u i l d i n g Code of Canada (1953) a r e based d i r e c t l y on snow depth measurements made on t h e ground. It i s known t h a t i n many c a s e s t h e a v e r a g e d e p t h of t h e snow on r o o f s i s a p p r e c i a b l y l e s s t h a n t h a t on t h e ground. A t t h e same t i m e c e r t a i n s h a p e s of r o o f s t e n d t o

accumulate snow, due t o d r i f t i n g under wind a c t i o n , t o a depth which i s much g r e a t e r t h a n t h e a v e r a g e depth on t h e ground.

R e a l i z i n g t h i s s i t u a t i o n t h e Advisory S t r u c t u r a l Group of t h e A s s o c i a t e Committee on t h e N a t i o n a l B u i l d i n g Code asked t h e

D i v i s i o n o f B u i l d i n g Research t o u n d e r t a k e a country-wide s u r v e y of a c t u a l snow l o a d s on r o o f s . The f i r s t o b j e c t i v e was t h e deter- mination of t h e r e l a t i o n s h i p between t h e snow l o a d on t h e ground and t h e a c t u a l snow l o a d on v a r i o u s t y p e s of r o o f s .

The second o b j e c t i v e was t h e s t u d y of t h e v a r i o u s f a c t o r s a f f e c t i n g snow l o a d s on r o o f s . For example, t o what e x t e n t do wind, t e m p e r a t u r e , i n s o l a t i o n and h e a t l o s s a f f e c t snow accum~xla- t i o n on r o o f s ? What i s t h e i n f l u e n c e of o r i e n t a t i o n , shape and s i z e of r o o f s ? With answers t o q u e s t i o n s l i k e t h e s e i t i s hoped t h a t magnitudes and p a t t e r n s o f snow l o a d s can be e s t a b l i s h e d which a r e more a c c u r a t e t h a n t h o s e used now,

The s u r v e y was s t a r t e d d u r i n g t h e w i n t e r of 1957-58 w i t h o b s e r v a t i o n s of depth and d e n s i t y b e i n g made a t o v e r 6 0 s t a t i o n s a c r o s s Canada. These o b s e r v a t i o n s have a l r e a d y i n d i c a t e d t e n t a t i v e answers t o some of t h e q u e s t i o n s , b u t b e f o r e any d e f i n i t e conclu-

s i o n can be drawn, t h e r e s u l t s of s e v e r a l w i n t e r s w i l l be r e q u i r e d . I n o r d e r t o g a i n f u r t h e r i n f o r m a t i o n on snow l o a d s it was

t h o u g h t a d v i s a b l e t o review t h e work o f o t h e r c o u n t r i e s on t h i s s u b j e c t , e s p e c i a l l y t h o s e c o u n t r i e s w i t h w i n t e r c o n d i t i o n s similar t o Canada's. To t h i s end a number of R u s s i a n p u b l i c a t i o n s d e a l i n g w i t h snow l o a d s have been t r a n s l a t e d and a r e p r e s e n t e d here. The

s i m i l a r i t y of R u s s i a n and Canadian w i n t e r s makes t h e s e t r a n s l a t i o n s p a r t i c u l a r l y p e r t i n e n t

.

The t r a n s l a t i o n s were made by M r .

D.E.

A l l e n who w a s a member of t h e B u i l d i n g S t r u c t u r e s S e c t i o n of t h e D i v i s i o n u n t i l September 1958 b u t i s now a g r a d u a t e s t u d e n t a t t h e U n i v e r s i t y of B r i t i s h Columbia. The v a l u a b l e a s s i s t a n c e of M r . G. Belkov of t h e

N a t i o n a l Research C o u n c i l ' s T r a n s l a t i o n s S e c t i o n i n checking a l l

t h e t r a n s l a t i o n s Is g r a t e f u l l y acknowledged.

O t t a w a

TAHLX

OF CONTENTS

----

SNOlJ

LOADS

ON F31JIIlDINGS

A o F o

Nikolaev (of the Research Institute of Industrial

construction).

Stroitelt (The Auilder),

8 (10):

18-26,

1 9 3 5 . . . o . . . . o ~ * * * * * * * ~ * ~ * * * ~ ~ ~ ~ ~ ~ o ~ . ~ ~ o ~ o ~ 3

SNOW

IIOADS

SPECIFIED

BY THE RUSSIAN RU1LT)INCr CODE

Stroltel'nye Nor~ny

i Pravila (Constructlon Standards

and Regulations), Part 11, Section

R ,

Chapter 1,

Para.

4, pp. 46-48 (Loads

and Load Coefficients for

Hulldings and Industrial Structures)...

25

UNSOLVED PROBLEMS IN RFTiI(?NS

OF

INTENSE SNOWFAL:.

V.P. Abovskli,

A.M.

Veksman, V.M. Volkov and

G o V o

Matysek. Stroitel'nnia Promyshlennostl (Constructlon

Industry), (11): 30-31,

1954............................

29

THE PROBLEM

OF

SNOW LOAD SPECIFICATION

Y.D. Kan-Khut. Stroltel'naia Promyshlennost'

(construction ~ndustry), (12): 22-23, 1954...

35

SNOW LOADS ACCORDING TO STRUCTURAL STANDARDS AND REGULATIONS

1.1. Cdldenlblat,

R.G. Korenev and A.M.

Sizov (of the

Central Resenrch Institute of Industrial Construction

-

TsNIPs).

Stroitel'nala Promyshlennost' (Constructlon

Industry),

(6): 25-27, 1956... 40

SNOW LOADS

EoD. Kan-Kkut. Stroitel'nala Promyshlennost'

(Construction Industry), (1):

50,

1957...

50

LESSONS FROM TWO ROOF COLLAPSES

A.M. Korablinov and L.S. Krauze. Stroltel'nala

Promyshlennost' (Construction ~ndustry),

(7):

SNOW LOADS ON BUILDINGS

by Eng. A . F, N i k o l a e v ( o f t h e R o s e a r c h I n s t i t u t e of I n d u s t r i a l c o n s t r u c t i o n )

T r a n s l a t e d f r o m " S t r o i t e l ' (The ~ u i l d e r ) " , 1935, v o l ,

8,

no. 10, p a g e s 18-26

The problem of s p e c i f i e d snow l o a d s on b u i l d i n g s , e s p e c i a l l y on i n d u s t r i a l b u i l d i n ~ s , i s e x t r e m e l y i m p o r t a n t i n o u r c o u n t r y d u r i n g t h i s e x t e n s i v e growth i n c o n s t r u c t i o n ,

However i t s a c c u r a t e s o l u t i o n p r e s e n t s g r e a t d i f f i c u l t i e s , When snow f a l l s w i t h o u t any wind, i t must b e e v e n l y d i s t r i b u t e d o v e r t h e r o o f s u r f a c e , But t h i s i s o n l y a t t h e b e g i n n i n g ,

Because of i n a d e q u a t e r o o f i n s u l a t i o n t h e b u i l d i n g t e m p e r a t u r e b e g i n s t o m e l t t h e snow u n e v e n l y , Where t h e snow i s i n c o n t a c t w i t h heat-conduc t i v o m a t e r i a l s , e,g. g l a s s ( s i n g l e g l a z i n g ) , t h e snow w i l l m e l t more q u i c k l y t h a n o v e r wooden s p a n s , T h i s w i l l a l s o o c c u r p a r t l y on warm r o o f s ,

D u r i n g s n o w f a l l w i t h wind, snow w i l l a c c u m u l a t e on r o o f s , b u t u n e v e n l y , Snow a c c u m u l a t e s i n p r o t e c t e d

p l a c e s of low wind s p e e d , However, i f a t a g i v e n wind f l o w d i r e c t i o n a n d a t a g i v e n s p e e d snow a c c u m u l a t e s i n p l a c e s of calm, a t a n i n c r e a s e of wind f l o w speed w i t h o u t a change i n d i r e c t i o n a p l a c e of c a l m i s n o lonrger c a l m and snow w i l l n o t f a l l i n t h i s p l a c e . I n p l a c e s where snow a c c u m u l a t e s a t

a l l wind s p o e d s ( i . e . i n c a l m p l a c e s ) t h e snow a c c u m u l a t i o n w i l l b e t h e g r e a t e r t h e h i g h e r t h e wind s p e e d s f o r a g i v e n

a s q u a r e u n i t per u n i t of t i m e w i l l be g r e a t e r w i t h h i ~ h wind s p c c d t h a n w i t h low wind speed.

Even i f only two f a c t o r s a r e kaken i n t o a c c o u n t , t o m p e r a t u ~ e and wind speed f o r a g i v e n d i r e c t i o n , t h o

accumulation of snow i s e x t r e m e l y complex. I f a l l f a c t o r s a f f e c t i n g snow accumulation on r o o f s a r e t a k e n i n t o a c c o u n t , i . e . t h e shape of t h o r o o f , t h e roughness of t h e r o o f , t h e speed and d i r e c t i o n of t h e wind, p h y s i c a l p r o p e l B t i e s of t h e snowflakes e t c . , i t i s n o t p o s s i b l e t o s o l v e t h i s problem i n t o t a l . I t i s onl-1 p o s s i b l e t o t a k e i n t o account

a

g i v e n f a c t o r i n f l u e n c i n g t h e i r r e g u l a r i t y of l o a d s i f we can

s t u d y one f a c t o r by e l i m i n a t i n g a l l t h e r e s t . This

c o n d i t i o n f o r c e s t h e r e s e a r c h e r t o make use of models s e t up under a r t i f i c i a l c o n d i t i o n s ,

Theref o r e t h e problem of d e t e r m i n i n g accumulation of snow on r o o f s i s t o be s o l v e d a p p r o x i m t e l y w i t h s u f f i c i e n t a c c u r a c y f o r p r a c t i c a l r e q u i r e m e n t s .

Snow l o a d s p e c i f i c a t i o n s e x i s t i n g up t o J u l y 1933, were much t o o l a r g e , w i t h i n s u f f i c i e n t b a s i s and n o t

r e f l e c t i n g t h e r e a l snow l o a d s ,

The new s p e c i f i c a t i o n OST 7626 ( w i t h a new e d i t i o n OST

4535/3

b e i n g p p i n t e d ) c a n be r e g a r d e d a s a f i r s t

approximation t o t h e t r u t h , a l t h o u g h t h e y s u f f e r f r o m a

number of ahortcornin;.;s and r e q u i r e more p r e p a r a t i o n p a r t i c u l a r l y f o r complicated r o o f s h a p e s ,

The aim of t h i s a r t i c l e i s t o e x p l a i n s t a n d a r d 7626, p o i n t i n g o u t t h i s problem of t h e b u i l d e r , and i t s e s t i m a t i o n

from t h e p o i n t of vlew of observations a n ? experiments conducted a t t h e Research I n s t i t u t e of I n d u s t r i a l C o n s t r u c t i o n .

1. B a s i c C a l c u l a t i o n Formula

" U n l f l e d S t a n d a r d s " d e t e r m i n e snow l o a d s from t h e mean of t h e rnaxirn~im snow d e p t h s on t h e ground*.

"1. Snow l o a d s i n kg/m2 of h o r i z o n t a l roof p r o J e o t i o n a r e determined from t h e mean of t h e y e a r l y max1mr.m observed snow d e p t h s on t h e ground i n a c c o r d a n c e w i t h T a b l e I.

The ground snow depth h , i n c e n t i m s t r e s , i s t a k e n from t h e n e a r e s t m e t e o r o l o g i c a l s t a t i o n a s t h e mean of t h e maximum observa- t i o n s from t h e l a s t t e n y e a r s . Where t h e r e are no such r e c o r d s h i s

t a k e n from t h e accolnpanylng c h a r t , ' a n d f o r mountain a r e a s

-

from the accompanying t a b l e .

A s a b a s i s f o r snow l o a d c a l c u l a t i o n t h e formula Ps = l.6h 2

e x p r e s ~ s s t h a t t h e l a r g e s t snow l o a d (Ps kg/m h o r l z o n t a l roof pro- j e c t i o n a t a p i t c h of 20° t o 30°) depend l a r g e l y on t h e ground snow c o v e r depth (h i n em)." I f h i s e x p r e s s e d I n cm., t h e n t h e dimensions of t h e co- 2 e f f i c i e n t 1 . 6 must be kg/m x cm. E x p r e s s i n g t h e l e n g t h i n m e t r e s , f o r a c o e f f i c i e n t of 1.5, we o b t a i n

ka=

kg = I 0 0

2

m2 crn

m2

m/100 m Thus t h e c o e f f i c i e n t 1.6 = 160

2

m2 crn m

g i v e s t h e weight of snow p e r u n i t volume (1.4 p e r m").

-

By ~ ; i v i n g t h e u n i t weight of snow a v a l u e of 160 kg/tn3 a t t h e end of w i n t e r ( i . e . i n March) and n o t 240 t o 250 kC/m3, which i s t h e a c t u a l u n i t weight, s i g n i f i e s t h a t only 64-67 p e r c e n t of t h e snow on t h e ground accumulates on t h e r o o f .

The Research I n s t i t u t e of I n d u s t r i a l C o n s t r u c t i o n , engaged i n i n v e s t i g a t i o n s of snow l o a d s on b u i l d i n g s , have c a r r i e d o u t measurements of snow accumulation on t h e r o o f s of i n d u s t r i a l b u i l d i n g s . Such measurements were a l s o c a r r i e d o u t on r o o f s of t h e second s t a g e of c o n s t r u c t i o n of 1 GPZ

(Feb. 9, 1933). The b u i l d i n g was n o t m a i n t a i n e d and was heated very l i t t l e d u r i n g t h e 1932-33 w i n t e r , and t h e r e f o r e t h e i n f l u e n c e of i n s i d e t e m p e r a t m e on snow melt c a n b e n e g l e c t e d .

F i g . 1 shows a snow l o a d p r o f i l e on a c r o s s - s e c t i o n of t h e second s t a g e of t h e GPZ shop. The h o r i z o n t a l a x i s shows t h e h o r i z o n t a l p r o j e c t i o n of t h e c l e r e s t o r e y e d r o o f c r o s s - s e c t i o n and t h e v e r t i c a l a x i s shows t h e t o t a l snow

l o a d on a l l f o u r elements of each c l e r e s t o r e y span ( t h e f o u r t h p a r t b e i n g t h e s p a c e between t h e c l e r e s t o r e y s )

expressed i n cm2 of t h e snow accumulation c r o s s - s e c t i o n . If t h e l o a d on a l l of t h e b u i l d i n g was evenly d i s t r i b u t e d over i t s h o r i z o n t a l p r o j e c t i o n , t h e d e p t h of

snow c o v e r would b e 1 9 cm. If t h i s i s compared t o t h e snow d e p t h on t h e ground which, a c c o r d i n g t o t h e r e c o r d s of Tirniriazev A g r i c u l t u r ~ l Academy was 27.5 cm. on

March 9, i t a p p e a r s t h a t snow l o a d s f o r r o o f s of t r a p e z o i d a l c l e r e s t o r o y s of t y p e 1

GPZ

i n Moscow a r e 69% of t h e ground

l o a d , which i s 2-4$ g r e a t e r t h a n t h e c a l c u l a t e d ( t h e r o o f and growid snow d e n s i t i e s a c c o r d i n g t o our measurements were t h e same a t 0.24 t o 0.25). To g e t r o o f and ground l o a d s , we m u l t i p l y t h e d e p t h i n m e t r e s b y t h e u n i t weight. 0.275

x

240 = 66 kg/m2 f o r d e n s i t y of 0.24 o r 0.275

x

2 5 0

=

68.75

kg/m2 f o r d e n s i t y of 0.25 on t h e ground. On h o r i z o n t a l p r o j e c t i o n of r o o f we have 0.19

x

240 = 45.6 kg/m2 o r 0.19 x 250 =

47.5

kg/m2 According t o t h e c a l c u l a t i o n f o r m u l a t h e e v e n l y d i s t r i b u t e d l o a d on t h e h o r i z o n t a l p r o j e c t i o n of t h e r o o f i s

P,

= l6Oh

=

1 6 0

x

0.275

=

44

kg/m2 1.e. 1.6

-

3.5

kg/m2 l e s s t h a n t h e a c t u a l , which i s 3.6% f o r a d e n s i t y of 0.24 and

8%

f o r a d e n s i t y of 0.25. Although t h e c a l c u l a t i o n i s somewhat u n d e r e s t i m a t e d , i t meets t h e a c t u a l v a l u e c l o s e enough. 2. D e t e r m i n a t i o n of snow l o a d on a b u i l d i n g

o or

c o m p l i c a t e d r o o f p r o f i l e s : w i t h t r a p e z o i d a l o r r e c t a n g u l a r c l e r e s t o r e y s ( l e n g t h w i s e and t r a n s v e r s e ) , w i t h unequal h e i g h t s of t h e d i f f e r e n t p a r t s , multi-bayed

c y l i n d r i c a l r o o f s e t c

.

,

t h e possibility of snow accuinulati,on i n lowered r o o f p a r t s blown away from t h e h i z h e r p a r t s

should b e t a k e n i n t o a c c o u n t . T h e r e f o r e snow l o a d s ta!cen from t h e maxima of T a b l e 1 ( c o r r e s p o n d i n g t o a p i t c h of

2 0 - 3 0 ° ) R r u rerillcod 50 p e r c e n t f o r h.ip;her b a r t s , but a r e t a k e n

n o t l e s s t h a n 25 lct:/mL. Thia 50 p e r c e n t i n t r a n r r f e r r e d i l a a n e v e n l y ( I l s t r i b ~ l t e d a d d i t i o n a l l o a d on one s i d e of t h e a x i s of t h e lower p a r t of t h e r o o f ,

I f t h e h i g h e r r o o f p a r t h a s a concave p r o f i l e , no r e d u c t l o n of l o a d on t h e hi.zhor p a r t i s made, b u t lower p a r t s t a k e an a d d i t i o n a l l o a d of 50 p e r c e n t .

For r o o f s w i t h o u t a t t i c s , which a r e planned f o r m e l t - i n g o f snow, t h e l o a d i s reduced t o conform w i t h t h e c a l c u l a t e d h e a t c o n d i t i o n s , namely:

( a ) For r o o f s which have moderate h e a t l o s s ( w i t h a

t h e r m a l r e s i s t a n c e from 1.10 t o 0 . 7 5 ) a t i n g i d e t e m p e r a t u r e of

15'

( c )

and h a v i n g 2 / 3 t h e r o o f a r e a o v e r h e a t e d a i r s p a c e , snow l o a d s a r e reduced 50 p e r c e n t . ( b ) F o r r o o f s w i t h g r e a t h e a t l o s s ( w i t h a t h e r m a l r e s i s - t a n c e l e s s t h a n 0.75) and h e a t f l o w o v e r 8 ~ 0 cal./hour/m2 of h o r i - z o n t a l r o o f p r o j e c t i o n , t h e snow l o a d s a r e reduced

75

p e r c e n t . ( c ) I n a d d i t i o n , i n t h e above c a s e s , s t r e s s e s a r e t o be checked f o r t h e f u l l snow l o a d ( w i t h no r e d u c t i o n f o r m e l t - i n g ) and t h e p e r m i t t e d s t r e s s e s i n t h e r o o f e l e m e n t s s h o u l d be i n c r e a s e d by

35

p e r c e n t . " C o n s e q u e n t l y , a c c o r d f n g t o " U n i f i e d s t a n d a r d s " t h e l o a d s on t h e p r o f i l e GPZ c a n be c a l c u l a t e d a s f o l l o w s :

The ground snow d e p t h i s d e t e r m i n e d from t h e t a b l e and c h a r t ; ? g i v e n i n t h e s t a n d a r d s . F o r Moscow t h i s d e p t h i s 1;8 cm. From T a b l e I ( i n b o l d p r i n t ) f o r h = 60 cin. 2 o r l e s s , t h e g r e a t e s t l o a d i s 100 kc/m ( c o r r e s p o n d i n g t o a -x- T a b l e s and c h a r t s a r e n o t g i v e n i n t h i s p a p e r . . .

0!i Set l; L c > n I ( Il'i r;. 2 ) t h o l o a d 1.3 On S o c t i o n 11, t h e l o a d tnlccn i s Ps 0.sL2 p l u s h d f t h e l o a d on t h e higtlor s e c t i o n , o r 0.5 PsTtl, o r a l a d T h i s , l o a d must b o e v e n l y d i s t r i b u t e d on l e n ~ t h L2. T h e r e f o r e , t h e l o a d p e r rn2 of p r o j e c t i o n of S e c t i o n I1 i s e x p r e s s e d a s : On S o c t i o n I11 of F i g . 2 t h e l o a d i s

Q3

= 0.5 PsL2 ke/lin.m. = 0.5 x 1 0 0

"

= 100 kg/*?

S i n c e t h e r o o f of

GPZ

has modorata h e a t l o s s and an i r i s i d e t e m p e r a t u r e of

+

1S0(c) accordirig t o "Tlnif i ed S t a n d r r d s " t h e snow l o a d s are r e d u c e d 5 0 p e r c e n t . T h e r e f o r e , f i n a l l y , t h e l o a d on S e c t i o n

I,

Q1 =

25

lq;/rn 2 Secl;ion

I?,

Q?

=

76

kG/m2 S e c t i o n 111,

e3

= 50 kC/1n2 F i g w e

3

s k i o r ~ s a cor!:pn~-l-(-m of a c t u a l snow l o a d i n lcg/in2 of h o r i z o n t a l . r o o f p r o j e c t i o n from o b s e r v a t i o n s by t h e R e s e a r c h I n x t i t u t e w i t h l o a d s a c c o r d . i n ~ t o s t a r l d a r d @ST 7026

.

T h e ;jar:!-l,crl l i n e : ; st-tow t h e r ' c a l :;now lolrds on S e c t i o n 1, 11 and I11 and t h e ! - ~ . o r L ~ o n t a l 13.n~:: show .th.c s p e c j . f i e d . l o a d or1

c l e r e s t o r s y (> (1l'i.c;. 11) a r o l a r < q e r only i n some c a s e s and t h e n f o ~ s h o r t periocis, n o t more t h a n t t r e e t o s i x days, t h a n t h e s p e c i f i e d . TTowever, i n ~ : e n e r a l t h e a c t u a l snow l o a d s a r e l e s s t h a n t h e s p e c i f i e d .

Such a s t a t e z ~ e n t , however, c a n b e made only f o r t h e w i n t e r of 193Lk-35 when s n o w f a l l was l i g h t . According t o t h e weathel- r e c o r d s , t h e g r e a t e s t snow d e p t h i n t h e I;oscow r i v e r b a s i n i n t h e 1934-35 w i n t e r was 39 cm. on t h e second t e n - d q p e r i o d of February. Consequently, f o r w i n t e r s w i t h g r e a t s n o w f a l l s , much g r e a t e r a c t u a l snow l o a d s t h a n t h o s e specified and over l o n g e r p e r i o d s of t i m e a r e t o b e expected.

For r o o f s having two s l o p i n g s u r f a c e s o r having

a curved shape, "Unified Standards'' recommend two c a l c u l a t i o n s of snow l o a d (1) f u l l uniform l o a d over t h e whole s u r f a c e and ( 2 ) one-sided l o a d on h a l f t h e span.

Where a r o o f a d j o i n s a h i g h v e r t i c a l s u r f a c e t h e p o s s i b l e f o r m a t i o n of snow accumulation should b e c o n s i d e r e d e q u a l t o t h e w a l l h e i g h t , b u t n o t g r e a t e r t h a n f o u r t i m e s t h e ground snow d e p t h

(kh).

The u n i t weight of l o o s o snow i s t a k e n as 100 k c ~ m 3 .

Consequently, i n t h i s c a s e t h e l o a d

Q = 2 h 1 100 = 1.25 P s l i n k g / l i n . m. ( F i g .

5 ) .

The s t a n d a r d ,c:ives no i n d i c a t i o n a s t o t h e l e n g t h of t r i a n g u l a r accumulation. However, from t h e aerodynamic c o n s i d e r a t i o n a s g i v e n i n a s s i s t a n t Prof. E. I. R e t t e r l s ; : -

11

a l - t i c l e d e a l 3 . n ~ w i t h t h e irif l uonce of h c i f h t s New s t a n d a r d s f o r wind l o a d s on b u i l d i n g s " , t h i s l e n ~ t h c a n be approximated by 20 h.

The ~ m i t weight of l o o s e snow i s recommended a t

100 1cg/m3 by "Standards". O b s e r v a t i o n s , s p e c i a l l y t a k e n by t h e Hesearch I n s t i t u t e , have shown t h e u n i t weight of f r e s h l y f a l l e n snow t o vary between

85

and 190

ki.,/m3.

T a b l e 2 g i v e s some u n i t w e i g h t s of f r e s h l y f a l l e n snow. From t h e t a b l e i t i s s e e n t h a t t h e u n f t weight of new snow a v e r a e e s

135

lce/m3.

3.

The I n f l u e n c e of' Wind on Snow

_-

I q o n d

_{-- -}

The i n f l u e n c e of wind on snow l o a d i s t a k e n i n t o account by t h e s t a n d a r d s a s f o l l o w s :

"For u n s h e l t e r e d l o c a l i t i e s , s u b j e c t t o s t r o n g

*

and f r e q u e n t w f n t e r winds ( s p e e d s of 1 2 m/sec. o r more) which p r e v e n t s snow accumulation on r o o f s , t h e l o a d s g i v e n

i n S e c t i o n 1 ( T a b l e 1 ) a r e reduced

50

per c e n t , b u t n o t l e s s t h a n 25 kg/m2."

Thus " u n i f i e d S t a n d a r d s " do n o t g i v e any

i n d i c a t i o n of t h e snow d i s t r i b u t i o n a c c o r d i n g t o t h e roof s u r f a c e ancl depending on t h e wind d i r e c t i o n , They t a k e

i n t o a c c o u n t only t h e p o s s i b l e f o r m a t i o n of snow accumulation i n d e p r e s s e d r o o f p a r t s c a l c u l a t e d from t h e snow blown away from t h e h i g h e r p a r t s , The d i r e c t i o n of t h e wind, p r e v a i l i n g

.*

5.-

The wind s p e e d s a r c talcen a s t h e mean of t h e rr~xima ( s e a s o n a l ) f r o n t h e recol7ds of t h e n o a r e s t m e t e o r o l o g i c a l s t a t i o n s , A speed of 12 in/sec, c o r r e s p o n d s t o

7

on t h e B e a u f o r t s c a l e ; a speecl wbLtch swzys t r e e b r n n c h e s o r t h i n t r u n k s . 11

d w i n c s n o w f a l l , a r e n o t c o n s i d e r e d by "Unified S-tandards" a t a l l . However, t h e s i g n i f i c a n c e of t h i s f a c t o r i s enormous. To l o o k a t t h e i n f l u e n c e of wind d i r e c t i o n , t h e Research I n s t i t u t e made f i e l d o b s e r v a t i o n s on b u i l d i n g s d u r i n g t h e s p r i n g of 1934 ( A p r i l 1 4 ) . On t h i s d a y , t h e snow accompanied w i t h a n o r t h - west wind f e l l on t h e roof which was p r e v i o u s l y f r e e of snow. The wind speed determined f r o m a V i l ' d weather vane r e a c h e d

14

m/sec. ( p l a t e d e f l e c t e d t o t h e h o r i z o n t a l

p o s i t i o n ) . The C A G I anemometer a t t h i s time r e g i s t e r e d a speed of a p p r o x i m a t e l y 24 m/sec. The t e m p e r a t u r e was -0.5O ( C ) .

During t h i s t i m e on t h e I s e c t i o n of t h e

GPZ

r o o f , snow d e p t h s were measured on f i v e of t h e c l e r e s t o r e y s :

13,

11, 6 ,

3

and. 1 a t t h e i r mid-section, p e r p e n d i c u l a r t o t h e a x i s of t h e c l e r e s t o r e y (Fig.

4 ) .

The f o l l o w i n g photographs of snow a c c u m u l a t i o n were t a k e n a t t h e time of o b s e r v a t i o n . F i g u r e 6 shows a g e n e r a l view of c l e r e s t o r e y 1 3 a f t e r t h e A p r i l s n o w f a l l . The sloped. p a r t of t h e c l e r e s t o r e y w i t h windows i s snowless. I n t h e i n t e r - c l e r e s t o r e y s p a c e t h e snow d e p t h I s minimum. C r o s s i n g t o t h e o t h e r c l e r e s t o r o y s t h e snow d e p t h i n c r e a s e s a p p r e c i a b l y . F i g u r e

7

shows t h e leeward s i d e of c l e r e s t o r e y

3

and t h e windward s i d e of c l e r e s t o r e y 2. The snow accumulated

on t h e leeward s i d e , whereas t h e windward s i d e 1 ~ 1 1 3 snowless.

Comparing t h e s e c l e r e s t o r e y s w i t h t h e former,

i t

i s seen t h a t i n c r o s s i n g t h e c l e r e s t o r e y s ( i n t h e d i r e c t i o n of t h e wind), t h e amount of p r e c i p a t e d snow i s i n c r e a s e d ,

F i g u r e 8 g i v e s t h e change of snow load, t o t a l l e d over each c l e r e s t o r e y , according t o t h e wind d i r e c t i o n , The a b s c i s s a g i v e s t h e accumulated p r o j e c t i o n of c l e r e s t o r e y c r o s s - s e c t i o n , and t h e o r d i n a t e g i v e s t h e a m ~ u n t of snow d e t a i n e d by t h e s e p a r a t e c l e r e s t o r e y s , expressed i n cm 2

of snow accumulation on each c r o s s - s e c t i o n , I n t h i s form t h e c u r v e d i s t i n c t l y shows, a c c o r d i n g t o t h e a b l a t i o n of t h e c l e r e s t o r e y depending on t h e wind d i r e c t i o n , s t a r t i n g from c l e r e s t o r e y

13,

t h e amount of snow p r e c i p i t a t e d on t h e c l e r e s t o r e y i n c r e a s e s . This i n c r e a s e i s observed t o c l e r e s t o r e y 2, and then t h e load b e g i n s t o d e c r e a s e .

Thus t h e magnitude of snow load on c l e r e s t o r e y 3

i s

7.7

t i m e s t h e l o a d on c l e r e s t o r e y 13.

F i g u r e

9

shows t h e change of snow load on t h e S e c t i o n s I, 11, 111, I V . From t h e graph, it i s s e e n t h a t , t h e snow load on S e c t i o n s I11 and I V , l y i n g i n t h e leeward of t h e c l e r e s t o r e y s , i n c r e a s e s t o c l e r e s t o r e y

3

and t h e n s h a r p l y d e c r e a s e s ; t h e snow load on S e c t i o n s I and 11, l y i n g i n t h e windward of t h e c l e r e s t o r e y s , i n c r e a s e s t o

c l e r e s t o r e y

6 ,

and t h e n g r a d u a l l y d e c r e a s e s t o c l e r e s t o r e y 1, Thus, i f t h e r e i s snowfall w i t h win4 whose

d i r e c t i o n i s p e r p e n d i c u l a r t o t h e c l e r e s t o r e y a x i s , t h e f o l l o w i n g c o n c l u s i o n s can be made of t h e accumulation of

snow on c l e r e s t o r e y s u r f a c e s .

1. Tho g r e a t e r p a r t of snow accumulates on t h e leeward p a r t of t h e c l e r e s t o r e y ( S e c t i o n s 111 and I V ) .

2, The amount of snow accumulatfne on each c l e r e s t o r e y , and on e a c h s e c t i o n of each c l e r e s t o r e y ,

i n c r e a s e s ( u p t o c e r t a i n l i m i t s ) i n c r o s s i n g from c l e r e s t o r e y t o c l e r e s t o r e y i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e c l e r e s t o r e y

axis and i n t h e d i r e c t i o n of t h e wind.

In t h e c a s e of t h e snowstorm of A p r i l

14,

t h e d i f f e r e n c e i n t h o amount of snow a c c u m u l a t i n g on two c l e r e s t o r e y s w a s such t h a t t h e l o a d on c l e r e s t o r e y

3

w a s

a l m o s t e i g h t t i m e s

(7.7)

t h e l o a d on c l e r e s t o r e y

13,

l o c a t e d 120 m. a p a r t . We s h a l l t r y t o e x p l a i n t h e c a u s e of uneven snow accumulation a c c o r d i n g t o t h e r o o f p r o f i l e .

I f t h e problem of t h e motion of a snow p a r t i c l e

i n

a i r i s approached m a t h e m a t i c a l l y ,

i t

l e a d s t o t h e

i n t e g r a t i o n of d i f f e r e n t i a l e q u a t i o n s of t h e motion of t h e p a r t i c l e , which i n t h e end a r e n o t always p o s s i b l e t o

e v a l u a t e . Attempts a t a mathematical a p p r o a c h t o t h e s t u d y of t h e motion of a snow p a r t i c l e i n a i r , which i s t i e d t o t h e problem of snow accumulation a t o b s t a c l e s , has been

4:-

made by d i f f e r e n t a u t h o r s

.

Among t h e most i n t e r e s t i n g i s t h e work of P r o f ,

.N.

E.

Zukovskii.

9

Eng. D o ~ ~ o v , N. E. Combatting snow on R u s s i a n r a i l r o a d s ;

P r o f , Rykin, N. A. Tile work of t h e a e r o m e c h a n i c a l l a b o r a t o r i e s , p u b l i c a t i o n of t h e I n s t i t u t e of Communication, P e t r o g r a d , 1 9 4 , No. 11; P r o f . Zukovskii, N. Z . ( 1 ) on s n o w d r i f t s and ( 2 ) on

s n o w d r i f t s and s i l t i n g of r i v e r s , p u b l i c a t i o n of t h e l i s t e d a r t i c l e s of Narkomzem, no. 30 and o t h e r s .

I n h i s f i r s t a r t i c l e

N,

E,

Zukovskii e x p l a i n s t h e f o l l o w i n g phenomenon, When a snows t o r n c a r r y i n g snow

near

t h e ground meets i n

i t s

p a t h m o t i o n l e s s o b s t a c l e s ,

then

in

f r o n t of t h e o b s t a c l e a r e formed snow hollows, m d

BB g e m d i s t a n c e from t h e o b s t a c l e a r e formed snow mounds.

Z u k s v e k i i s i m p l i f i e s t h e problem by supposing t h a t t h e o b s t a c l e i s a l a r g e l o n g round c y l i n d e r whose h o r i z o n t a l axis i s p e r p e n d i c u l a r t o t h e wind d i r e c t i o n ,

By s e l e c t i n g a combination of flow p a t h s whose t o t a l r e s u l t a n t f l o w would p a s s over t h e c y l i n d e r g i v i n g a

complete a s p o s s i b l e d e s c r i p t i o n of snow a c c u m u l a t i o n a c t u a l l y observed and N, E, Zukovskii g i v e s a m a t h e m a t i c a l a c c o u n t of t h i s p r o c e s s which i s q u a l i t a t i v e l y well-known from.

o b s e r v a t i o n s i n t h e n a t u r a l c o n d i t i o n s , The b a s i c c a u s e of snow a c c u m u l a t i o n I n s p e c i f i c p l a c e s remains o b s c w e ,

The second a r t i c l e of P r o f , N. E, Zukovskii, "on snow d r i f t s and s i l t i n g of r i v e r s " , i s devoted t o t h e

s o l u t i o n of t h e problem, C o n s i d e r i n g t h e motion of a snow p a r t i c l e on a v e r t i c a l p l a n e o n l y , P r o f , Zukovskii g i v e s t h e f o l l o w i n g e q u a t i o n of motion:

( U

-

u )

and (V - v ) a r e t h e h o r i z o n t a l and v e r t i c a l p r o j e c t i o n of t h e r e s i s t a n c e of t h e a i r t o t h e moving

t h e

x

and y a x i s , which i n g e n e r a l terms a r o f u n c t i o n s of t h e c o - o r d i n a t e s and of time; U and

v

-

t h e speed components 'of t h e snow p a r t i c l e on t h e same axes; .mg

-

t h e weight of %ha

snow p a r t i c l e

.

The e q u a t i o n s show, t h a t i n p l a c e s of calm, i . e . where U and V a r e n e a r l y zero, t h e r e i s always a n i n c r e a s e d snow accumulation. The a c t i o n of g r a v i t y s e t s out t h e

primary motion i n which snow p a r t i c l e s begin t o s e t t l e on t h e ground or r o o f . On t h e o t h e r hand, where t h e wind speeds

U and V a r e l a r g e , we c a n n e g l e c t t h e weight of t h e p a r t i c l e i n t h e above e q u a t i o n s s i n c e

i t s

e f f e c t i s r e l a t i v e l y small. I n t h i s c a s e t h e component of t h e p a r t i c l e speed i s e q u a l t o t h e component of t h e wind speed, and t h e t r a j e c t o r i e s of t h e snow p a r t i c l e s c o i n c i d e w i t h t h e l i n e s of a i r flow.

Regarding t h e f u l l d e t e r m i n a t l o n of t h i s problem, n o t c o n s i d e r i n g i n d e t a i l t h i s very i n t e r e s t i n g a r t i c l e ,

i t

i s n e c e s s a r y t o determine mathematlcally t h e speed i n

each point of space.

Thus t h e unevenness of snow accumulation on t h e p r o f i l e of one of t h e c l e r e s t o r e y s c a n be explained by t h e uneven d i s t r i b u t i o n of wind stream speed a t d i f f e r e n t p o i n t s n e a r t h e c l e r e s t o r e y p r o f i l e .

An anemometer survey, t a k e n on 1 GPZ, confirms t h i s s t a t e m e n t . Fig. 10 g l v e s t h e speeds, measured i n t h e space between t h e c l e r e s t o r e y s .

Measurements were t a k e n by two Fuss anemometers. The speed a t each p o i n t i s e x p r e s s e d a s a p e r c e n t a g e of t h e wind speed a t a h e i g h t of 2 m. f r o m t h e c l e r e s t o r o y s u r f a c e . Measurements were t a k e n a t t h i s p o i n t i n every c a s e and

s i m u l t a n e o u s l y w i t h t h e speed measwemeilts of t h e o t h e r p o i n t s

.

F i g u r e 11 d e p i c t s t h e aerodynamic flow, o b t a i n e d by photographing b l a c k r l b b o n , hanging i n t h e space between t h e c l e r e s t o r e y s , spaced 1 m, a p a r t .

F i g u r e 12 shows a s k e t c h of t h e flow, o b t a i n e d i n a t r a y i n t h e hydrodynamic l a b o r a t o r y of P r o f , N. E, Zukovskii i n MGU. The f l o w was o b t a i n e d by decomposition of water

a c c o r d i n g t o t h e method of P r o f . D. S. V i l t k e r . The t e s t s were done by E. I. R e t t e r ,

B e

V. Gladkov and t h e a u t h o r .

By comparing t h e d i s t r i b u t i o n of wind speed i n t h e i n t e r - c l e r e s t o r e y s p a c e ( F i g , 1 0 ) w i t h t h e snow

a c c u m u l a t i o n on t h e c l e r e s t o r e y p r o f i l e ( F i g .

6

and

71,

i t i s s e e n t h a t snow i s d e t a i n e d i n calm p l a c e s . The d e p o s i t i o n of snow i s f a c i l i t a t e d by t h e f a c t t h a t n e a r p o i n t A of F i g . 11 and 1 2 t h e wind speed v e c t o r forms a n o b t u s e a n g l e w i t h a l l of t h e snow p a r t i c l e v e c t o r s . A t p o i n t B t h i s a n g l e i s a c u t e .

The unevenness of snow accumulation over a l l t h e c l e r e s t o r e y s , t a k e n a t one c r o s s - s e c t i o n , c a n b e s i m i l a r l y e x p l a i n e d , i . e . t h e i n c r e a s e of snow accumulating on a c l e r e s t o r e y i s e x p l a i n e d by t h e d e c r e a s e of wind speed a t t h i s s e c t i o n . T h e snow-wind f l o w strenni which has a f o r c e T upon c o n t a c t w i t h c l e r e s t o r e y

13

(Fig.

8

and

4)

l o s e s

p a r t of

i t s

energy, A s t h e flow passes t o o t h e r c l e r e s t o r e y s t h e l o s s of k i n e t i c energy, owing t o t h e r e t a r d i n g of t h e snow-wind stream becomes even g r e a t e r . However, t h e decrease of speed i s observed only t o c l e r e s t o r e y

3,

whereupon t h e speed again i n c r e a s e s ,

Thus t h e d i r e c t i o n and speed of wind d u r i n g snowfall r e n d e r s enormous i n f l u e n c e on t h e uneven snow load d i s t r i b u t i o n

on b u i l d i n g r o o f s ,

Uneven snow d i s t r ib u t i o n i s observed:

( 1 ) Between s e p a r a t e p a r t s of any one c l e r e s t o r e y

-

c o n s i d e r i n g t h e same c r o s s - s e c t i o n ( 2 ) Between s i m i l a r p a r t s of d i f f e r e n t c l e r e s t o r e y s

-

o o n s i d e r i n g t h e same c r o s s - s e c t i o n .

( 3 )

A t s t r e a m flow d i r e c t i o n s n o t perpendicular t o t h e c l e r e s t o r e y a x i s , d i f f e r e n t l o a d s a r e observed a l s o on t h e same p a r t of a c l e r e s t o r e y b u t a t d i f f e r e n t c r o s s - s e c t i o n s ,

-

Q)

S

8

0 d U 0 Q

-

0 k I& d d -P d 0 N d

8

-

'Yi

_\

2

V PC I 4

g

d V) UI '4-4 0 0

4

u d 0 4 MJ

2

k 0 m 0 4 -P va 4

Id

-P

8

9

d U U Q ~ ~ O U 'ON

8

$

a'

0 f!

ii

0 0 0 : . d o \O 0 o - P c r \ f d \ O cl

2 P g

a

9

E: -P - d o cd & d - P c r \ - P -P 0 d 4'

3 : k i l s

a a - P

03

d 3 g 4' d d m 0 -P w s t p

b

S Z d d d

A d

d 2

d -P a ol \o\ Q ) U d

k z $

Z E b

83

m -Pa \ \ a a d m m d a) & d m m o o c\l c \ l a m 0 0 0 cU w a r n 0 0 0 0 m m o o cU c \ l a m 0 0 0 cU c r \ \ O r n u\ 0 0 0 cu 3 C O cU rl u\ 0 0 0 N m o m u\ 0 0 0 cy m 0 d

3

m m 0 cu 3 r n 3 d m N C0 0O c\l 0 *PPd d 0 -P

2

= ' a

,o

k

5

m

%

Q, d

= j F

_{g 4}

0 0 m 0 w 3 0

s

0

2

0 0 cr\ 0 0 cU 0 0 d 0 0

TABLE

I1

, 1935 Date

5

Feb.

7

Feb* 10 Feb. 1 0 Feb. 20 Feb. 22 March Depth of F a l l e n Snow ( c m ) 2 1

5

1 0

13

13

1 2 Temperature -2.6

-7.7

-5

-5.3

-5.1

+1.8

-5.3

-5.4

U n i t Weight of Sn3w (kg/m )

85

11 0

156

170 190 100 Wind Speed (m/sec.) 6.0

3.5

3

.6

5.0 5.0 3.0 Snowfall D u r a t i o n ours) 9 1 0

3

3

3

3

Fig. 1

Change of total clerestorey snow loads in crn2 of cross-section

( G P Z on March, 1933)

Fig. 3

Comparison of actual and speclfled snow loads in kg/tn2 hcrizontel roof projection on clerestorey 6 of GPZ during February and March

F i g . 4

Plan showing clerestoreys on 1 GPZ of the Kaganovitch works

; * L

F i g . 7

Change of t o t 2 1 c l e r e s t o r e y snow load according

t o

t h e wind d i r e c t i o n on A p r i l 1 4 , 1934. 1 GPZ

Fig. 9

Change of snow load according t o wind d i r e c t i o n on 4 s e c t i o n s of t h e c l e r e s t o r e y s April 1 4 , 1934. 1 GPZ

W i n d Fig. 10 D i s t r i b u t i o n

of

wind speeds i n t h e i n t e r - c l e r e s t o r e y space, 1 GPZ, June 1 6 , 1934 Fig. 11 Aerodynamic f l o w I n t h e I n t e r - c l e r e s t o r e y space, Jan. 8 , 1934. Wind speed 6-7 m/sec

SNOW

LOADS

SPECIFIED BY THE RTJSSIAN B U I L D I N G CODE

T r a n s l a t e d f r o m t h e R u s s i a n " S t r o i t e l l n y e Normy 5. _{P r a v i l a}

( C o n s t r u c t i o n S t a n d a r d s and Re u l a t i o n s ) " P a r t 11, S e c t i o n B, C h a p t e r 1, Para.

4,

pp. 46-48 ?Loads and Load Coefficients

f o r B u i l d i n g s and I n d u s t r i a l S t r u c t u r e s ) . Snow Loads

The snow l o a d p e r s q u a r e m e t e r a r e a of h o r i z o n t a l p r o j e c t i o n of roof i s determined a c c o r d i n g t o t h e f o r m u l a

PC

=

PC ( 1

.lc)

wh.ere p = weight of snow c o v e r i n kg/m 2

depending on t h e r e g f o n of t h e USSR a c c o r d i n g t o T a b l e

4

c = c o e f f i - c i e n t depending on t h e p r o f i l e of t h e r o o f a c c o r d i n g t o T a b l e

5.

The l o a d f a c t o r "n" f o r snow l o a d s h a l l be t a k e n e q u a l t o

1.4.

The. Weight of Snow Cover P T a b l e

4

Note: I n mountain d i s t r i c t s , as w e l l a s i n t h e r e g i o n s

-

of extreme n o r t t i and f a r e a s t t h e wefght of snow c o v e r p i n kg/& s h a l l b e t a k e n n u m s r i c a l l y e q u a l t o 2t1, where h = d e p t h of snow c o v e r i n cm, t a k e n from r n c t e o r o l o ~ . , i c a l o b s e r v a t i . o n s :LS tllc tiican of t h e maximum y e a r l y d e p t h a t a s k : c ? l l , c ? r c c l l o c a t i o n f o r t h e No. I 2

3

4

5

Region of USSR ( S e e F i g . 2) I I1 I11 I V

v

Weight of Snow Cover i n kg/m2 ( psf

.

)

50

( 1 0 ) 70 ( 1 4 ) 100 ( 2 0 ) 150 ( 3 1 ) 200

(41)

p a s t 10 y e a r s , I n t h e mountain d i s t r i c t s t h e weight of snow cover s h a l l be taken not l e s s

t h a n 60 kg/m2 ( 1 2 p.s.f.)." Value of C o e f f i c i e n t c Table

5

No 1

2

3

Shape of roof Simple r o o f , Pentroof and Gable roof

s l o p e

a

4 _2s0

a

>, 60°

Simple arched roof

Complex roof w i t h t r a n s v e r s a l or l o n g i t u - d i n a l c l e r e s t o r e y s , w i t h unequal h e i g h t s of s o p a r a t e p a r t s , e t c .

I

c 1.0 0.0 4 /10f I n accord w i t h Fie;.

3

Note A t i n t e r m e d i a t e a n g l e s of roof p i t c h t h e c o e f f i c i e n t c i s found by i n t e r p o l a t i o n where4

=

span of a r c h f = r i s e of a r c h The c o e f f i c i e n t c s h a l l n o t be g r e a t e r t h a n 1.0 nor l e s s t h a n 0.3 The d i f f e r e n c e i n h e i g h t H

i s

given

i n

metres

0 Y /.\ w P c C rl 0 a h .A h 0 tL 0 0 h o a d Ql a s k . S O F

:

"i.4

0 I/) a d 0

.

p u m c ( d cd2

:

3 b 0 c e V) O)e A d m IH Y O E : 0 r l r l 'H Ti Y O

g2

5

b7 a " N rl o m K a 4 a 5 k*" w d 0 4 - a _c k o 5 m o a 4 El 5 4 4 0 ,Q k d rl d rl Y a d 2 (d Y c o d d 2 4 3 4 O c d C m m o rl

P = 2OOH. but n o t

<

s

c and not 2 4q

b u t n o t < 5.0m. and not 7 10.0 m.

Fig. 3

UNSOLVED PROBLIXS I N REGIOl\TS OF INTENSE SIJO~C,'!I?,T.

by V.

P,

Abovskii, A , M a V e k s m , V.

M a

Volkov, G o

V,

Matysek

( E h g i n e e r s )

T r a n s l a t e d from t h e Russian " S t r o i t e l t n a i a Promyshlennostf ( C o n s t r u c t i o n ~ n d u s t r y ) ' ; 1954, no. 11, pp, 30-31

Observations d u r i n g more t h a n 20 y e a r s of m a i n t a i n i n g r o o f s of i n d u s t r i a l b u i l d i n g s i n S i b e r i a show t h a t t h o s e

r e s p o n s i b l e f o r d e s i g n of p r o j e c t s do n o t , t o a c o n s i d e r a b l e e x t e n t , t a k e account of f a c t u a l m e t e o r o l o g i c a l f e a t u r e s

which d e t e r m i n e t h e mechanism and magnitude of snow cover on r o o f s ,

For many p a r t s of S i b e r i a , wind r e c o r d s show t h a t most s t r o n g winds d u r i n g snowstorms come from t h e s o u t h w e s t ,

T h i s i s confirmed f r o m t h e b a s i c m e t e o r o l o g i c a l o b s e r v a t i o n s d u r i n g 1931-1952 g i v e n i n Table I, The c o i n c i d e n c e of maximum m e t e o r o l o g i c a l f a c t o r s given i n T a b l e I c r e a t e s s t a b l e c o n d i t i o n s f o r snow d e p o s i t i o n behind o b s t a c l e s . O f s i g n i f i c a n c e i s snow a c c u m u l a t i o n when t h e r e i s no s n o w f a l l , i , e . w i n d - d r i f t i n g of s m a l l snow g r a i n s from t h e ground o r r o o f b r i n g s a b o u t a r a p i d s h i f t of snow and

v o r t i c a l accumulation w i t h compression behind o b s t a c l e s , T h i s r e s u l t s , f o r t h o s e c a s e s where t h e r o o f c o n f i g u r a t i o n d o e s n o t a l l o w a f r e e sweep-past of snow,

i n i n t e n s i v e a c c u m u l a t i o n of snow d r i f t s a t t h e r a t e of

1 metre i n

24

hours.

The u n i t weight of snow, from f i e l d measurements d u r i n g January-February, i s 300-350 kg/m3 and i n v n r c h i n c r e a s e s t o 450 kg/rn3.

F i g u r e a 1, 2 and

3

show I n s t a n c e s of i n t e n s i v e snow accumulation.

The d i r e c t consequences of t h e described. phenomena were i n a number of c a s e s , t h e q u i c k development of

s t r u c t u r a l d e f o r m a t i o n of l o a d b e a r i n g s t r u c t u r a l e l e m e n t s of t h e r o o f which l e d t o t h e f a i l u r e of p u r l i n s and t r u s s e s ,

Snow l o a d s a r e e s p e c i a l l y s i g n i f i c a n t f o r r o o f s w i t h l a r g e a r e a s ,

4-8

h e c t a r e s , which a r e now b e i n g e n c o u n t e r e d more o f t e n , e s p e c i a l l y because a s a t i s f a c t o r y mechanized method of snow removal on r o o f s h a s n o t y e t been d e v i s e d . Of i n t e r e s t i s t h e c o n s t r u c t i o n of a n i n d u s t r i a l b u i l d i n g i n S i b e r i a , whose r o o f i s shown i n F i g . 1.

Sudden o v e r l o a d s of snow on a r o o f under

c o n s t r u c t i o n b r o u g h t a b o u t d e f o r m a t i o n f a i l u r e of t h e t r u s s e d beam s u p p o r t l n g t h e r o o f , I n one c a s e , one f o r m a t i o n of

p u r l i n s had a s a g of 1 7 t o 24 cm, which i s

3

-

4

t i m e s l a r g e r t h a n t h e a l l o w a b l e ; i n o t h e r c a s e s t h e f a i l u r e of s u p p o r t i n g s l a n t members of m e t a l t r u s s e s brought a b o u t s a g g i n g i n t h e ctiords on t h e a v e r a g e of a b o u t

60

cm. ( F i g *

41,

However, t h e r e w a s no f a i l u r e of t h e r o o f s u p p o r t i n g beams o r t h e r o o f i n g s l a b s , T h i s i s e x p l a i n e d by t h e c o n t i n u o u s w i r e t i e s between c o n c r e t e r o o f i n g s l a b s and t h e bond of t h e cement j o i n t - f i l l e r , r e s u l t i n g i n a r o o f t h a t i s t o some

e x t e n t monolytt-lic and t h u s a b l e t o c a r r y a l o a d i n d e p e n d e n t l y o v e r a c o n s i d e r a b l e span w i t h o u t c o l l a p s e ,

In

t h e above c a s e of p u r l i n deformation, o f t r ~ removal of t h e snow l o a d , t h e s l a b b a s e s h i f t e d because of

t h e r e s i d u a l d e f o r m a t i o n of t h e p u r l i n and assumed a mean l o c a t i o n between t h e d e s i g n e d and maximum sag i n p l a c e s of overload.

To sum up, i t i s n e c e s s a r y :

( 1 ) t o q u i c k l y b r i n g i n t o r e a l i t y t h e d e c i s i o n of t h e

T e c h n i c a l O f f i c e of t h e M i n i s t r y of C o n s t r u c t i o n d e a l i n g w i t h t h e problem mentioned here. The d e c i s i o n n o t e d

" t h a t t h e Research I n s t i t u t e (TsNIPS) and H y p r o t i s up t o now have n o t been g i v i n g proper a t t e n t i o n t o t h e h i g h l y s e r i o u s problem of f i n d i n g a s p e c i f i c a t i o n f o r snow d e p o s i t i o n on r o o f s of i n d u s t r i a l b u i l d i n g s and t h a t a method of p r o t e c t i o n a g a i n s t snow l o a d s on i n d u s t r i a l b u i l d i n g s must be a n i n d i s p e n s a b l e p a r t of t h e p r o j e c t " .

(2)

t o r e f r a i n from a f o r m a l a t t i t u d e toward t h e d e s i g n of r o o f s of i n d u s t r i a l b u i l d i n g s

i n

S i b e r i a and t h e Far E a s t b u t t o t a k e i n t o account t h e i n f l u e n c e of l o c a l m e t e o r o l o g i c a l c o n d i t i o n s .

(3)

t o d e s i g n r o o f s of a shape which p r o v i d e f o r a

maximum sweep away of snow; i n p a r t i c u l a r

it

i s

d e s i r a b l e t o a r r a n g e r o o f s w i t h o u t v e r t i c a l p r o j e c t i o n s i n t h e d i r e c t i o n of t h e p r e v a i l i n g wind, w i t h c l e r e s t o r e y s a r r a n g e d p a r a l l e l t o wfnd d i r e c t i o n w i t h a s t r e a m l i n e

shape of t h e c l e r e s t o r e y ends; i n c a s e s where it i s p o s s i b l e , t o s u b s t i t u t e f o r r o o f s w i t h c l e r e s t o r e y s ones w i t h o u t c l e r e = t o r e y s .

(4)

For r o o f s of l a r g e s i z e , h a v i n g more t h a n two s l o p e s , t h e p o s s i b i l i t y of mechanized snow c l e a r i n g s h o u l d n o t b e o v e r - r a t e d e s p e c i a l l y s i n c e d u r i n g a snowstorm, c l e ~ n i n 3 i s n o t p o s s i b l e , On t h e b a s i s of t h e f o r e g o i n g , one c a n c o n c l u d e t h a t i n t h o s e c a s e s where on a r o o f p a r t t h e r e i s observed i n t e n s i v e snow accumulation, t h e s t r u c t u r a l c a l c u l a t i o n of r o o f t r u s s e s f o r t h i s p a r t must b e based on a c t u a l

a c c u m u l a t i o n , i.e. s t r u c t u r e s must t a k e t h e snow l o a d even i f a minimum c o e f f i c i e n t of r e s e a r c h i s used.

The s c i e n t i f i c i n v e s t i g a t i o n and p l a n n i n g

o r g a n i z a t i o n s must soon g e n e r a l i z e a v a i l a b l e methods of r o o f maintenance i n S i b e r i a , t h e F a r E a s t and o t h e r r e g i o n s

of t h e Union. Along w i t h t h i s t h e problem should b e t h o r o u g h l y s t u d i e d i n l a b o r a t o r y c o n d i t i o n s , s i n c e t h e d a t a used a t p r e s e n t , t h o s e on which t h e s t a n d a r d s a r e b a s e d , and t h o s e used i n t e c h n i c a l l i t e r a t u r e have become

o b s o l e t e . T a b l e I

3

2.8 0.4 Wind D i r e c t i o n Wind Frequency

$

Mean Wind Speed m/sec.

Snow Storm Wind

d Frequency ,o 1 0 4.8 1LO E E S S S W W N W 2 5

5.l4

29.0

7

2,6

0.5

32

6.2

56.0 1 3 3.6 3.0 N

4

2.6 0.1 NE 6 3.0 0.1

Fig. 1

Snow on a roof between t h e south ends of t h e c l e r e s t o r e y s and t h e w a l l p r o t r u d i n g above the r o o f . The snow depth i s 2.3

m

Fig. 2

Snow d r i f t s between t h e ends of t h e c l e r e s t o r e y s .

F i g . 3

Snow d r i f t s on a r o o f along t h e n o r t h e n d s of the c l e r e s t o r e y s

Fig. 4

Metal r o o f s t r u c t u r e a f t e r removal o f r o o f slabs ( v i e w o f the

THE PROBLEM OF SNOI-J LOAD SPECIF'ICATION

_-

by

E m

D.

Kan-Xhut

T r a n s l a t i o n from t h o Russian " S t r o i t e l f n a i a Promyshlennost C o n s t r u c t i o n ~ n d u s t r y " 19511, No. 12, pp. 22-23

I n t h e r e g i o n s of t h e USSR where t h e r e a r e f r e q u e n t and s t r o n g winds ( f o r example, i n most of Kazakstan) snow n e v e r accumulates on f l a t r o o f s b u t d o e s accumulate a s g r e a t d r i f t s behind r o o f p r o j e c t i o n s .

U p t o now, s t a n d a r d s on snow l o a d s (OST 90/058-40) and b u i l d i n g s t a n d a r d s and r e g u l a t i o n s do n o t talce i n t o account t h e s e l o c a l f e a t u r e s of c l i m a t e i n s u f f i c i e n t measure. I n Fig, 1 i s an i l l u s t r a t e d c o n t r a d i c t i o n between t h e s p e c i f i e d s t a n d a r d and t h e a c t u a l l o a d ( t a k e n i n Karaganda P r o v i n c e ) . ( a ) For f l a t r o o f s w i t h s l i g h t s l o p e , t h e e s t a b l i s h e d s t a n d a r d l o a d i s 70 kg/rn2

(14

p.s.f.) Snow on f l a t r o o f s a s t h e above i s n o t r e t a i n e d , Even i n t h e c a s e of s n o w f a l l w i t h o u t wind, which i s extremely uncommon i n Karaganda, t h e l o a d on f l a t r o o f s n e v e r comes n e a r t o t h e s t a n d a r d s p e c i f i e d . Only once i n

8

y e a r s (1933-1940) was t h e monthly s n o w f a l l more t h a n 1 0 cm.

( 4

i n . ) which i s , w i t h a d e n s i t y of 200 kg/m3 of l o o s e snow ( n o t packed by t h e wind), a l o a d of n o more t h a n 20 kg/m2

(4

p.s.f .). It should be t a k e n i n t o a c c o u n t t h a t t h e r e a r e no l o n g p e r i o d s i n Karaganda w i t h o u t s t r o n g winds, which sweep a l l t h e snow from f l a t r o o f s .

T h e r e f o r e f o r f l a t r o o f s w i t h s m a l l s l o p e ( u p

t o

10') a maximum l o a d of 20 kg/m2

(4

p a s .f .) c a n b e used.

-

36

-

The t h i c k n e s s of

i c e

d e p o s i t on r o o f s i s u s u a l l y s m a l l and i c e f o r m a t i o n i s l o c a t e d f o r t h e most p a r t n e a r c o r n i c e s . Because of t h i s , one c a n assume t h a t

i c e does n o t a f f e c t t h e d e s i g n l o a d f o r r o o f s v e r y much, ( b ) For a r o o f n e a r t h e w a l l s of a roof p r o j e c t i n g h i g h e r t h e OST 90/058-40 s t a n d a r d s p e c i f i e s a l o a d of

93

ke/m2 ( 1 9 p.s.f,), and t h e b u i l d i n g s t a n d a r d s and r e g u l a t i o n s 2 a snow l o a d of 112 kg/m ( 2 3 p . s . f , ) , I f t h e c o e f f i c i e n t of o v e r l o a d of

1.4

i s t a k e n i n t o a c c o u n t , t h e s t a n d a r d l o a d becomes 112 kg/mc x

1.4

=

157

kg/tn2 (32 p . s . f . ) .

The a c t u a l snow load depends f i r s t o f a l l on t h e h e l g h t of t h e p r o j e c t i o n

H.

Up t o a c e r t a i n v a l u e of H

(which w i l l d i f f e r f o r d i f f e r e n t l o c a l i t i e s ) , a

maximum

h e i g h t of snow d r i f t of

O,9H,

and a n a v e r a g e of

O.7H

can

be assumed ( F i g , 1).

From measurements on b u i l d i n g c o n s t r u c t i o n s i n t h e Karaganda i t w a s determined t h a t t h e d e n s i t y o f

snow d r i f t e d behind a p r o j e c t i o n r e a c h e s

350

ke/m3. For example, t a k i n g a h e i g h t of p r o j e c t i o n H

=

2.0

m.

which i s n o t very l a r g e , we o b t a i n a l o a d which i n t h i s c a s e i s t h e a c t u a l load

p

=

0.7I-I = 0.7

x

2.0

x

350 = 490 kg/m2 ( 9 8 p.s.f.), o r a p p r o x i m a t e l y t h r e e t i m e s t h e s t a n d a r d s p e c i f i e d ,

P e r i o d i c snow removal f r o m r o o f s does n o t p r e v e n t l a r g e snow accumulations behind p r o j e c t i o n s ,

s i n c e snow removal from behind p r o j e c t i o n s i s out of t h e q u e s t i o n d u r i n g snowstorms w i t h wind speeds from

15

t o

4~

m e t r e s p e r second.

-

37

-

( c ) For i n c l i n e d r o o f s t h e s p e c i f l e d snow l o a d d e c r e a s e s from 70 kg/rn2 (15 p.s.f.) t o 0 kg/m2 w i t h t h e f o l l o w i n g i n c r e a s e i n s l o p e s : a c c o r d i n g t o OST 90/058-1+0 from 2 s 0 t o

so0,

a c c o r d i n g t o t h e b u i l d i n g s t a n d a r d s and r e g u l a t i o n s from 250 t o 60'. A c t u a l l y on t h e leeward s i d e of r o o f s w i t h a s l o p o of

35'

-

45'

snow a c c u m u l a t i o n s up t o 1.0 m e t r e high have been observed ( F i g . 2 ) , t h a t i s a l o a d r e a c h i n e

350

lcg/m2 ( 7 0 p.s.f.).

The r e a s o n f o r t h e c o n t r a d i c t i o n between s p e c i f i e d and a c t u a l snow l o a d s i n p l a c e s where t h e r e a r e h i g h and f r e q u e n t winds, i s t h a t i n d e r i v i n g t h e d a t a only t h e amount of s n o w f a l l was c o n s i d e r e d , whereas d i s t r i b u t i o n

of snow i s a l s o a f u n c t i o n of t h e wind speedg. Both

OST 90/058-40 and t h e s t r u c t u r a l s t a n d a r d s g i v e t h e same snow l o a d s f o r Minsk and Kara~;anda, whereas snow i s

d i s t r i b u t e d on r o o f s d i f f e r e n t l y i n Kazakstan where t h e r e a r e h i g h e r winds t h a n i n B y e l o r u s s i a . The i n c o r r e c t c o n s i d e r a t i o n of snow l o a d s l e a d s t o t h e f o l l o w i n g e r r o r s : (1) A l l r o o f s w i t h a s l o p e l e s s t h a n 10' and w i t h o u t p r o j e c t i o n s have s p e c i f i e d l o a d s which a r e t o o l a r g e and a r e never encounteyed i n p r a c t i c e .

A d e c r e a s e of t h e s p e c i f i e d l o a d ( f r o m 70 t o 20 kg/m2 i n Karaganda) p r o v i d e s a s a v i n g of about

8

r u b l e s / s q . m. The i n t r o d u c t i o n of a supplement t o t h e e x i s t i n g s t a n d a r d snow l o a d s f o r some r e g i o n s of t h e

USSR would p o v i d e a n econotny of many m i l l i o n s of r u b l e s every y e a r .

( 2 ) All- r o o f s having s t e e p s l o p e s or pro j e c t i o n s have s p e c i f i e d snow l o a d s which a r e much l e s s than t h e a c t r ~ a l l o a d s . Because of t h i s i n one of t h e r e g i o n s d e f o r m a t i o n s and even c o l l a p s e s occur o f t e n ,

I n c o n n e c t i o n w i t h t h e use of l i g h t constrtlc t i o n s , t h e r a t i o of silow l o a d t o t o t a l l o a d becomes more

irnpox*t~nt; therefore t h e problem of c o r r e c t e s t i m a t i o n of snow 1o:id a c q t ~ i r o s s p e c i a l importance,

I n our o p i n i o n , i t i s a b s o l u t e l y n e c e s s a r y t h a t t h e C e n t r a l Committee (Ts.N.1

.P.S.

) as soon a s p o s s i b l e o r g a n i z e f i e l d o b s e r v a t i o n s and work o u t s p e c i f i c a t i o n p r o p o s a l s f o r snow l o a d s which t a k e i n t o a c c o u n t t h e a c t u a l a c c u m u l a t i o n s of snoM

i n

r e l a t i o n t o t h e v e l o c i t y of t h e wind.

*ind direction

--L

F i g * 1

Shape of snow-drift on a

roof

ledge

F i g * 2