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Structural Sandwich Components in Building
Ser TH]. Nztt2 nc. 267 e . 2 BLDG
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NATIONAL RESEARCH COUNCIL OT' CANADA DIVISION OF BUILDING RESEARCH
STRUCTURAL SANDWICH COMPONENTS IN BUILDING
by E. Platts
A N A L Y Z E D
R . T e c h n i c a l P a p e r N o . 2 6 7 of theDivision of Building Research
OTTAWA
TABLE OT' CONTENTS P a r t I - P a s t a n d P r e s e n t L . Z H i s t o r y I. 3 Irnplications in Building Page I
2
7
P a r t I I -2 . -2 2 . 3 2 . 4 2 . 5 2 . 6 2 . 7 2 . 8 2 . 9 P a r t I I I -3 . 2 3 . 3 3 . 4 3 . 5 3 . 6 3 . 6 . L 3 . 6 . 2 3 . 5 . 3 3 . 6 . 4 3 . 6 . 5 3 . 6 . 6 3 . 6 . 7 3 . 6 . 9 3 . 6 . 9 3 . 7 3 . 7 . I Engineering Design Bending Irnpact Colurnn Loading Concentrated Load Racking or Diaphragrn,Action Bowing T e s t sAdvanced Sandwich Theory and Optirnurn Material Properties and Effects
Design Exarnples: The Effects of Core
9 l 0
r 5
r 6
L 7r 8
r 9
I 9 D e s i g n 2 02 2
? ?
P r o p e r t i e sCore Shear, Extensibility and Stabilizing Effects 23
Therrnal and Moisture Effects 24
Creep and Stress-Rupture 26
Skin Materials 28
Steel ?9
Alurninurn ?9
Glass Fibre Reinforced Plastic (FRP) 30
P a p e r - P l a s t i c s 3 l
P l y w o o d 3 1
Hardboard 32
Particleboard 33
A s b e s t o s - C e r n e n t 3 4
Rigid Polyvinyl Chlorides 34
C o r e M a t e r i a l s 3 5
3 . 7 . 2 H o n e y c o r n b C o r e s 3 . 7 . 3 E x t r u d e d P a r t i c l e b o a r d 3 . 7 . 4 D e f o r r n e d P a r t i c l e b o a r d a n d H a r d b o a r d 3 . 7 . 5 E x t r u d e d r f f o a m t ' P o l y s t y r e n e 3 " 7 . 6 B e a d F o a r n P o l y s t y r e n e 3 . 7 . 7 F o a r n e d R i g i d P o l y v i n y l C h l o r i d e 3 . 7 . 8 F o a r n e d P o l y u r e t h a n e 3 . 7 . 9 I n o r g a n i c C o r e M a t e r i a l 3 . 8 A d h e s i v e s 3 . 9 S p a n s Page 3 6 3 7 3 8 3 9 3 9 4 0 4 0 4 0 4 T 4 Z 4 3 4 3 4 6 4 7 5 0 5 2 Part IV: 4 . 2 4 . 3 4 . 4 4 . 5
Systerns, Lirnitations, Potentials
F i r e Sound Joints Potentials
STRUCTURAL SANDWICH COMPONENTS IN BUILDING b y
R . E . P l a t t s
PART I - PAST AND PRESENT
Structural sandwich construction can give rnaxirnurn structure
with rninirnurn rnaterial. Thin sheet rnaterials are bonded as strong
Itskinstt on a light "corert rnaterial, which is thus sandwiched between
t h e r n . S t r e s s e d - s k i n s t r u c t u r e i s a c h i e v e d . T h e s k i n s t a k e t h e d i r e c t s t r e s s e s a s t h e c o r n p o n e n t i s l o a d e d a s c o l u r n n , b e a r n o r diaphragrn; the core positions the skins away from the neutral axis
to provide over-all rigidity, stabilizes thern against local buckling,
t a k e s t h e s h e a r s t r e s s e s b e t w e e n t h e r n , a n d o f t e n p r o v i d e s t h e r r n a l i n s u l a t i o n a s n e e d e d .
With todayrs ernphasis on developrnent of low-rnaintenance s h e e t r n a t e r i a l s , o n p r e f i n i s h e d l a r g e - p a n e l b u i l d i n g s y s t e r n s , o n
better therrnal control, speed of erection, utilization of space and
over-all productivity, the sandwich idea is attractive to rnany.
An increasing nurnber of inquiries and a significant nurnber of
requests for assistance with feasibility studies have been received
by the Division of Building Research, irdicatirg a rapidly growing
i n t e r e s t . T h i s p a p e r r e v i e w s t h e e n g i n e e r i n g b a s i s o f s a n d w i c h
construction and its developrnent needs, relating particularly to
Canadian rnaterials and conditions"
Questions are Sust as irnportant as the prornises of the
structural sandwich concept. The inherent lirnitations are those
of skin structures generally. \{ith the structural elernents
-the skins - positioned at -the surfaces, sensitivity to high
ternperat u r e s a n d e s p e c i a l l y ternperat o f i r e i s a n o b v i o u s d r a w b a c k w h e r e l o a d -b e a r i n g u s e s a r e i n v o l v e d . D e e p l y - s h a p e d f o r r n s c a n i r n p r o v e t h e
fire safety perforfirance in such uses. Ternperature or rnoisture
differentials between the skins can cause srnooth bowing of
sand-wich panels, but this effect is readily calculable and need not be c r i t i c a l . R e s i s t a n c e t o s o u n d t r a n s r n i s s i o n i s a n i n h e r e n t
lirnitation of sandwich space separations! weight, cornplete
separation of layers, and pliability are all irnportant in reducing
sound transrnission, whereas the sandwich strives for rninirnurn
rnaterial and weight, complete bonding together of elernents, and high stiffne s s.
z
-Other lirnitations are not inherent but are brought to the
fore by the capabilities of the structural sandwich. Several thin
s h e e t r n a t e r i a l s a p p e a r p r o r n i s i n g a s s a n d w i c h s k i n s , r n a t e r i a l s r a r e l y c o n s i d e r e d b e f o r e i n s t r u c t u r a l t e r r n s . W h a t i s t h e l o n g -t e r r n s u s -t a i n e d s -t r e n g -t h o f h a r d b o a r d s a n d p a r -t i c l e b o a r d s ? C a n creep deflection be kept within acceptable lirnits with such skins; w i t h p a p e r - p l a s t i c s o r g l a s s f i b r e r e i n f o r c e d p l a s t i c s ; w i t h p l a s t i c f o a r n s o r d e f o r r n e d o r e x t r u d e d p a r t i c l e b o a r d s a s c o r e s ? H o w
can the durability of a new adhesive be assessed without waiting
t e n y e a r s ? M u s t n e w s y s t e r n s b e r e s t r i c t e d o r r n o d i f i e d t o r n e e t
traditional building rules that evolved around older structural
s h a p e s ? T h e s e a n d o t h e r q u e s t i o n s a r e c o n s i d e r e d i n t h i s P a P e r i n s o f a r a s p r e s e n t k n o w l e d g e p e r r n i t s .
B a s i c d e s i g n c o n c e p t s a r e f o l l o w e d f a r e n o u g h t o b e
usable in feasibility studies, or even to the point of prototype
designs with sorne rnaterials. The rigorous rnathernatical
treatrnents of cornplex sandwich design (developed so thoroughly b y o r f o r t h e a e r o s p a c e i n t e r e s t s s i n c e t h e e a r l y 1 9 4 0 1 s ) a r e n e g l e c t e d , e x c e p t i n r e f e r e n c i n g t h e l i t e r a t u r e f o r t h o s e w h o
want to go further. An atternpt will be rnade to define sandwich
design and exarnple capabilities within present knowledge of
rnaterials in order to allow consideration of the developrnent
a r e a s o f a p p a r e n t p r o r n i s e . I . Z H I S T O R Y
T h e r i g o r o u s e n g i n e e r i n g d e s i g n r e q u i r e d o f s a n d w i d r c o r n p o s i t e s h a d s c a r c e l y d e v e l o p e d b e f o r e L 9 4 0 . A s i t s u s e
before and since has been prirnarily in aircraf.t, it could be
a r g u e d t h a t e f f o r t s t o t r a c e t h e p r o g r e s s o f s a n d w i c h d e s i g n a r e w o r t h l e s s i n t e r r n s o f p r e s e n t b u i l d i n g i n t e r e s t s . R e l e
-vant lessons rnay be found, however, and perhaps they will
be better applied in tirne. In any case the story is fascinating.
It is built on the contributions of rrlany of the great figures
of elastic stability theory; their findings have rnade possible
all rnodern aircraft, and rnay affect ground environrnent rnore
t h a n c a n b e p r e d i c t e d .
Structural sandwich history can Properly be traced only
i n t h e c o n t e x t o f g e n e r a l s t r e s s e d s k i n d e v e l o p r n e n t s . T h e t e r r n i n o -logy should be noted briefly:
3
-coverings are rnaJor contributors to structural perforrnance. o t h e r r n e r n b e r s a r e u s e d t o t r a n s f e r s t r e s s e s and stabilize the c o m p r e s s i o n p o r t i o n s o f t h e s k i n s . T h e t e r r n h a s c o r n e into p a r t i c u l a r u s e f o r c o r n p o n e n t s s u c h a s f l a t p a n e l s w h e r e stabi-r i z i n g a n d s h e a stabi-r - stabi-r e s i s t i n g r n e r n b e r s a r e s p a c e d s o r n e d i s t a n c e a p a r t .
Monocoque is rnore or less the sarne thing. It rnay refer to s t r e s s e d s k i n e n c l o s u r e s w h e r e t h e s i d e w a l l s t h e r n s e l v e s a r e a r r a n g e d a s t h e s o l e s h e a r w e b s , a s i n a i r c r a f t f u s e l a g e s , b u t the terrn is equally applicable to aircra{.t wings where sorne
s h e a r w e b s a r e e n c l o s e d .
Structural sandwich refers to thin skin larninates where the shear and stabilizing functions are given to a continuous or n e a r - c o n t i n u o u s l r c o r e r r bonded to the entire area of both skins.
T h e t e r r n q u a s i - s t r e s s e d s k i n i s u s e d i n t h e s e d i s c u s s i o n s t o denote structures where the skins add to the bearn strength of the whole, but where longitudinal frarning still plays a large p a r t , o r i s t h o u g h t t o d o s o .
T h e t h e o r y b e g a n l o n g b e f o r e t h e t e r r n s w e r e c o i n e d , a n d rernarkable applications antedated the rnore cornplete design s c i e n c e b y s o r n e n i n e t y y e a r s . I t b e g a n w i t h t h e b r i d g e b u i l d e r s , even before Whipple published apparently the first treatise on s t r e s s a n a l y s i s o f s i r n p l e b r i d g e f r a r n e s i n 1 8 4 7 . W i t h w r o u g h t iron plate just recently cornpeting with cast iron in bridge
b u i l d i n g , R o b e r t S t e p h e n s o n t o y e d w i t h i d e a s t o s t r e s s such p l a t e t o a c h i e v e t h e h i g h - c l e a r a n c e , s t i f f , I o n g s p a n n e e d e d f o r t h e f i r s t r a i l r o a d b r i d g e a c r o s s t h e M e n a i S t r a i t s i n W a l e s . Apparently it was he who first conceived of a trthrough-tubularrl
s t r u c t u r e : t w i n r e c t a n g u l a r t u b e s o f I 5 - f t w i d t h , Z 7 - f . t d e p t h , a n d l , 5 l I - f t l e n g t h , t h e c e n t r a l s p a n 4 6 0 f . t , w i t h t h e t r a i n d e c k ( l o w e r d e c k ) , s i d e s a n d t o p r r s k i n s r r a l l s h a r i n g i n t h e d e e p b e a r n a c t i o n ( l ) . T h i s i s t h e B r i t a n n i a B r i d g e , b u i l t b e t w e e n l B 4 5 a n d 1 8 5 0 a n d s t i l l i n u s e ( F i g u r e l ) . W i l l i a r n F a i r b a i r n , w h o s e s h o p s h a d r e c e n t l y p i o n e e r e d wrought iron plate rnanufacture and use in srnall girder bridges and large ship hulls (which thus becarne and have rernained q u a s i - s t r e s s e d s k i n s t r u c t u r e s ) s h a r e s c r e d i t f o r t h e B r i t a n n i a d e s i g n . F a i r b a i r n c o n d u c t e d a n d a s s e s s e d e x t e n s i v e r n o d e l t e s t s , s t i f f e n e r r e f i n e r n e n t s , a n d e v e n f u l l - s c a l e t e s t i n g f o r Stephenson, while Professor Hodgkinson, a rnathernatician,
4
-h e l p e d d e d u c e e r n p i r i c a l f o r r n u l a e f r o r n t -h e t e s t s " F a i r b a i r n secured patents on the tubular girder and published his noted engineering rnilestone rrAn Account of the Construction of the Britannia and Conway Tubular Bridgesr " London, IB49 Ql.
F a i r b a i r n w a s r e r n a r k a b l e . G o u g h ( 3 ) a t t r i U u t e s t h e first sandwich-like thinking to hirn, noting that in one of his t e s t s o n a r r a n g e r n e n t s f o r t h e B r i t a n n i a h e u s e d w o o d b a c k i n g planks to stabilize ttre wrought iron plates. The ternptation to dwell on the Britannia Bridge and all its supporting tests
and works is strong indeedr In this one triurnph civil engineering c a n p e r h a p s c l a i r n t h e f i r s t t r u e s t r e s s e d s k i n o r r n o n o c o q u e d e s i g n , a l t h o u g h i t h a s s c a r c e l y u s e d i t a g a i n a s a c o m p l e t e s t r u c t u r e i n t h e i n t e r v e n i n g c e n t u r y . P l a t e g i r d e r s a n d e v e n tubular colurnns can also be dated frorn this one programr and t h e s e h a v e b e e n e n g i n e e r i n g t o o l s e v e r s i n c e .
Perhaps the first truly successful - if ernpirical -sandwich sheet rnaterial carne a little later, with the advent o f c o p r u g a t e d c a r d b o a r d i n t h e l 8 7 0 r s . T h e f u r t h e r d e v e l o p r n e n t of new sheet rnaterials and rnants efforts to fly worked together to push the evolution of stressed skin. The rnost irnportant of' these rnaterials was plywood, in which the ability to turn wood into large dirnensionally-controlled sheets opened the door to e a s y e x p l o i t a t i o n o f s t r e s s e d s k i n a p p l i c a t i o n s . T h e t h i c k n e s s of plywood gives very high bending stiffness corrrpared to rnetals of sirnilar weight, so that high stressing of cornpression skins i s r e a d i l y a c h i e v e d .
O n e e a r l y r e v i e w e r ( 4 ) i r n p l i e s t h a t r e l i a b l e w a t e r - r e s i s t a n t p l y w o o d s w e r e f i r s t i n u s e i n R u s s i a r t r n a n y y e a r s t t b e f o r e 1 9 0 0 . R u s s i a n a i r c r a f t b e g a n t o u s e i t i n a q u a s i - s t r e s s e d s k i n s e n s e i n t h e e a r l y l 9 0 0 r s , w i t h S t e g l a u i n 1 9 1 2 b u i l d i n g t h e f i r s t c o r n p l e t e l y p l y -wood aircraft, including the wing covering. In the sarrre year
Bechereau in France used plywood in the first true |trnonocoquerl
fuselage. The Gerrnans rnade extensive use of glued-on plywood as rran integral part of the structureil in their World War I aircraft (4).
O l d e r i d e a s w e r e s t i l l i n a d v a n c e o f p r a c t i c e : t h e f i r s t U . S . p a t e n t o n p l y w o o d , N o . 5 1 7 3 4 , i n 1 8 6 5 , i s c r e d i t e d t o J o h n K . M a y o
of N4airre; in a re-issue of 1868 the inventor includes drawings of l a r g e t u b u l a r b r i d g e s o f b o t h c i r c u l a r a n d r e c t 4 n g u l a r c r o s s - s e c t i o n
5
-T h e d r i v e f o r I ' c l e a n e r r ' r f a s t a i r c r a f t l e d p r o f e s s o r H u g o J u n k e r s t o d e v e l o p t h e f i r s t cantilever wings, in which he utilized r n e t a l s h e e t s t r e s s e d s k i n a c t i o n , laboriously stabilizing flat steel s h e e t b y w e l d i n g c o r r u g a t e d s t e e l s h e e t b e h i n d it. His srnall J u n k e r s J - I u s e d t h e i d e a s u c c e s s f u l l y i n I 9 1 6 , a n d r e d t o q u i t e l a r g e r n u l t i - e n g i n e r n a c h i n e s ( 6 ) . T h e approach was tedious and
s o r n e w h a t h e a v y , a n d t h e B r i t i s h a n d o t h e r s p r e f e r r e d to direct all efforts to developing the necessary forrns with light alloy s p a r s a n d r i b s w i t h f a b r i c c o v e r s , o r u n s t r e s s e d r n e t a l sheet
covers' paralleling the traditional wood craft. In the rneantirne,
F o k k e r u s e d t h i c k c a n t i l e v e r w i n g s of quasi-stressed skin ply-w o o d c o n s t r u c t i o n t h r o u g h t h e I 9 2 0 r s . P l y ply-w o o d stressed skin panels later went into building through the design and test work o f t h e U . S . F o r e s t P r o d u c t s i n t h e r n i d - 1 9 3 0 , s , a n d t h e y h a v e rernained a sound (if conservative) design choice in srnall buildings since that tirne.
The plastics were allowing new choices of forrnable, high-s t r e n g t h high-s h e e t r n a t e r i a l high-s b y t h e e a r l y 1 9 0 0 t high-s . I n 1 9 1 8 W e high-s t i n g h o u high-s e o b t a i n e d B r i t i s h P a t e n t l z 0 7 o I o n h i g h - p r e s s u r e p a p e r - p l a s t i c and o t h e r f i b r e - p l a s t i c l a r n i n a t e s , w i t h d r a w i n g s s h o w i n g o n e - p i e c e
rrronocoque fuselage construction. It is rernarkable that in 1886 Jules
V e r n e v i s u a l i z e d t h e r n y t h i c a l A l b a t r o s s giant aircraft, describing i t s c o n s t r u c t i o n a s e n t i r e l y o f h i g t r - p r e s s u r e p a p e r - p l a s t i c larninates,
with rernarkable properties indeed, all in his novel The clipper of
t h e C l o u d s .
The paper-plastic larninates apparently excited rnuch
thought, and were rnuch in rnind in what rnay have been the first e n g i n e e r i n g c o n c e p t i o n o f t h e t r u e s t r u c t u r a l s a n d w i c h . L o n g interested in full sheet stabilization for optirnurn strength-to-w e i g h t f o r a i r c r a f t , v o n K a r r n a n d e s c r i b e d h i s s t r u c t u r a l s a n d w i c h r t f o r l i g h t s t r u c t u r e s o t i n G e r r n a n y in t924 (British Patent ?35883, 1925]'. Von Karrnan suggested kraft paper a n d o t h e r f i b r e - p l a s t i c s k i n s b o n d e d t o b o t h s i d e s o f c o r k o r b a l s a w o o d c o r e s , a n d i n c l u d e d s t i f f e n e d j o i n t details connected.
by the glue-lapped larninate skins. All this antedated the first
noted use of sandwich aircraft by over ten years, while f o r e c a s t i n g i t s d e s i g n a l r n o s t e x a c t l y .
A b r e a k t h r o u g h i n s i n g l e - s k i n r r r o n o c o q u e d e s i g n s a t i s f i e d t h e n e e d s o f l o w - s p e e d a i r c r a f t f o r s e v e r a l y e a r s , a n d i d e a s o f s a n d w i c h c o n s t r u c t i o n w e r e s e t a s i d e . I n 1 9 3 0 t h e U . S . N a t i o n a l
6
B u r e a u o f S t a n d a r d s c o n d u c t e d extensive tests of edge compression o f t h i n s h e e t s w i t h t h e i r u n l o a d e d e d g e s s t i f f e n e d o r restrained to v a r i o u s d e g r e e s ( Z ) . T h i s w o r k c h a n g e d the irnplications of elastic theory of thin plate quite radically: long after the centre area of t h e s h e e t h a s b u c k l e d , t h e r e s t r a i n e d e d g e a r e a s r e r n a i n stable and readily support loads of rnany tirnes the initial buckling load. T h e a c t i o n i s c o n s i s t e n t , r e v e r s i b l e a n d s o u n d , and following von K a r r n a n r s r e s o l u t i o n o f t h e b a s i c equation in 1932, the
post-b u c k l i n g - s t r e s s e d n ' t h i n wall rnonocoquetr becarne the basis for a l l t h e l a r g e t r a n s p o r t a i r c r a f t o f t h e 1 9 3 O t s a n d I i l 4 0 ! s , a n d f o r t h e n o r r n a l s p e e d o n e s o f t o d a y . Y e t a l l s u c h p o s t b u c k t i n g c a p a b i l i -t i e s r e r n a i n r r -t r o " " d in ground-based cons-truc-tion engineering.
The structural sandwich was next forced frorn theory into p r a c t i c e t o p r o v i d e t h e s r n o o t h n e s s and strength required in h i g h - p e r f o r r n a n c e a i r c r a f t . A t d e H a v i l l a n d i n E n g l a n d , A . E . H " g g t s d e s i g n g r o u p b u i l t t h e r a d i c a l and successful Albatross r n a i l - c a r r i e r i n 1 9 3 7 ( 7 ) , f o l l o w i n g v o n K a r r n a n r s I 9 Z 4 p r o p o -s i t i o n -s q u i t e c l o -s e l y . T h i n c e d a r p l y w o o d w a s b o n d e d t o b o t h s u r f a c e s o f a b a l s a w o o d c o r e t o f o r r n a c o r n p l e t e s a n d w i c h rnonocoque fuselag€, a beautifully curved srnooth tube. The w i n g s u s e d s t r e s s e d s k i n s o f s p r u c e p l a n k i n g . T h e c r a f t f l e w f a s t a n d r e g u l a r c o u r i e r r u n s , c r u i s i n g a t o v e r 2 0 0 r n p h w i t h a r a n g e o f 3 , 0 c 0 r n i l e s . T h e n i n 1 9 4 3 t h e r e r n a r k a b l e d e H a v i l l a n d Mosquito bornber (7) brought decisive attention to sandwich
c o n s t r u c t i o n . D e s i g n e d b y R . E . B i s h o p a n d b u i l t l a r g e l y i n Canada, it used thin birch plywood skins on balsa core and flew 380 mph, 4?5 rnph in later rnodels, taking it far ahead o f i t s c o r n p e t i t o r s ( F i g u r e Z ) .
T h e i n c e n t i v e s o f w a r a n d t h e c o n s e q u e n t n e e d f o r f a s t f l i g h t q u i c k l y d i r e c t e d r n a n y r e s o u r c e s t o w o r k o n s a n d w i c h theorr,r and developrnent - feLr more than are usually focussed o n c i v i l p r o . ; e c t s . S p e e d s n e a r a n d b e y o n d the supersonic r e g u i r e v e r y t h i n l a r n i n a r - f l o w w i n g s w i t h h i g h l y s t r e s s e d s k i n s f r e e f r o r n p r o t r u d i n g r i v e t s o r a n y r i p p l i n g e f f e c t s . B y t h e l a t e l 9 4 0 t s e n g i n e e r i n g t h e o r y and practice rnoved b e y o n d t h e b a s i c s t a g e s o f r e l e v a n c e to rnost building develop-rnent, now or in the near future. While rnissing rnany
7
-irnportant contributors, a few will be noted: at Carnbridge U n i v e r s i t y i n 1 9 3 9 , G o u g h , E l a r n and de Bruyne pioneered the theory of edge corrlpression and local buckling of sand-wich larninates, checking by rigorous testing prograrns that becarne the rule in all following work (3). They began f r o r n t h e o v e r - a l l s t a b i l i t y t h e o r y o f T i r n o s h e n k o ( 1 9 1 3 ) and B i o t , R e i s s n e r a n d o t h e r s ( 2 ) . S u c h b u c k l i n g w a s reduced to forrnulae within useful engineering lirnits by Hoff and Mautner, while williarns, Leggett and Hopkins developed sandwich bearn theory and noted the function of shear deforrnations. Other notable work of the pioneering L940t s was carried out under M a r c h , E r i c k s e n , L i b o v e , B a t d o r f , V a n d e N e u t , C o x , B i j l a a r d , G o o d i e r , S t e i n a n d M a y e r s . H a b i p ( B ) h a s
recently surveyed the thread of the rnathernatics of sandwich analysis in the forrn of a concise review and bibliography. 1 . 3 I M P L I C A T I O N S I N B U I L D I N G
Perhaps the rnore notable institutions in early sandwich d e s i g n w o r k w e r e t h e R o y a l A i r c r a f t E s t a b l i s h r n e n t i n t h e U . K . , a n d t h e u . s . F o r e s t P r o d u c t s L a b o r a t o r y i n M a d i s o n , w i s c o n s i n . The latter group had been intensively involved in the engineering analysis and test developrnent of plywoods, and their resulting cornpetence in orthotropic structure analysis and adhesives technology was well adapted to I'sandwich thinkingrr and, later, t h e e n g i n e e r i n g d e v e l o p r n e n t o f g l a s s - f i b r e - r e i n f o r c e d p l a s t i c s . A l t h o u g h a i r c r a f t - i n s p i r e d s a n d w i c h e n g i n e e r i n g s o o n p r o g r e s s e d beyond the requirernents of building, the work of such groups in material developrnents has rernained relevant indeed. Reliable p l y w o o d s , p a p e r - p l a s t i c s ( c o u n t e r t o p s a n d s u r f a c i n g s ) , reinforced p l a s t i c s , w o o d a d h e s i v e s and especially rnetal adhesives, honey-cornb and plastic foarn cores and insulations, elastorner sealants for curtain walls and sealed double windows, plastic skylights, all are to sorne extent by-products of aircraft developrnent and its dernand for ideal sandwich structure.
Perforrnance criteria and attitudes in the aircraft and other young industries should have even trrore relevance to hopes for a viable building production industryr 3s it strains t o k e e p a b r e a s t o f r n o u n t i n g n e e d s . T e c h n i c a l p e r f o r r n a n c e c o d e s , p r e p a r e d s o l e l y b y a n d f o r t e c h n i c a l p e o p l e , are the
8
-rule in governing the evolution of aircraft, and requirernents are s e l d o r n i r r a t i o n a l .
Structural sandwich developrnents have rnade progress in building applications. The Jicwood House in Great Britain
followed on the heels of the Mosquito bornber in L944 with plywood-h o n e y c o r n b s a n d w i c plywood-h d e s i g n . T h e u . s . F o r e s t P r o d u c t s L a b o r a -tory erected a plywood-honeycornb sandwich house in L947 that is still p e r f o r r n i n g w e l l , a n d t h e i r c o n c u r r e n t w o r k o n h o l l o w - c o r e flush doors resulted in the only true sandwich rrcornrnodityrr in the building field (9). Koch and Bernist notable Acorn plywood-honeycornb
sandwich house of 1948 (I0) was far rnore advanced as a folding, Iightweight unit than the folding rnilitary houses of today. In C a n a d a , s t r e s s e d - s k i n p l y w o o d a n d l a t e r s a n d w i c h u n i t s h a v e satisfied rnuch of our Far North housing needs since the late l 9 + O t s , b u t t h e i r c o s t s s c a r c e l y c o r n p e t e w i t h the fast-produced w o o d f r a r n e h o u s i n g i n t h e p o p u l a t e d a r e a s ( l l ) . C u r t a i n - w a l l developrnents have been fairly steady, with sorne difficulties.
There are real lirnitations on the use of sandwich in
t o t a l s t r u c t u r e , a s w i l l b e d i s c u s s e d , b u t t h e c r i t i c a l l y e x p a n d i n g needs for housing and building production dernand a rational
systern approach (IZl, and in this the structural sandwich wilt probably play a larger role. While stretching the use of rnaterial to the ultirnate, the sandwich concept is also arnenable to optimurn rnachine production that rnay becorne critically irnportant (lt). Its real lirnitations represent a challenge; irnposed lirnitations on building \rses rnust be accorded rnuch rnore basic thought in terrns of the whole building job.
9
-PART U - ENGINEERING DESIGN
W h e n s t r u c t u r a l s a n d w i c h t h e o r y t a k e s a c c o u n t o f p l a t e a c t i o n , c o r n e r e f f e c t s , s k i n s t a b i l i t y , s h e a r d e f o r r n a t i o n s , d i r e c t i o n a l r i g i -dity variations and cornbined load conditions, it becorrres unusually corrl-p l e x . U s i n g s t r a i n - e n e r g y r e l a t i o n s r n a d e s o l v a b l e o n l y b y a s s u r n p t i o n s of edge conditions and elastic actions, solutions have been derived that c o r r e l a t e r e a s o n a b l y w e l l w i t h l o a d t e s t s . G i v e n t h e v a r i a t i o n s b e -tween assurned and actual conditions, as well as those in the norrnal p r o p e r t i e s o f r n a t e r i a l s , e v e n r i g o r o u s r n a t h e r n a t i c a l a n a l y s e s d o n o t predict perforrnance rnuch rnore accurately than do sirnple approxi-rnate rnethods.
This paper confines itself to engineering approxirnations, which can be rnore than adequate for feasibility studies where a proponent requires a rrfirst lookt' at where a sandwich cornposite rnight be used, for exarnple, finding the spans for given loads and deflections. Approxirnations can be adequate for prototype designs t h a t a r e t o b e f a b r i c a t e d f o r p r o o f - t e s t i n g o r d e v e l o p r n e n t - t e s t i n g , and such testing is desirable even if onerous design rnethods have been followed. Sirnple load and environrnental testing is alrnost always of value in such developrnent work. Overdesign can be r e d u c e d , l o a d - f a c t o r s d e r i v e d r n o r e c l o s e l y , a n d t h e u s u a l
r t u n e x p e c t e d l l stress or other weakness corrected. T h e l l o n p a p e r l t design should not be considered fully adequate without such supporting e v i d e n c e .
D e s i g n a n d t e s t p r o p e r t i e s a r e d e t e r r n i n a b l e , b u t i n building construction the perforrnance criteria are often ill-d e f i n e ill-d i n t h e o r y a n ill-d p r a c t i c e . T h e s e a r e d i s c u s s e d f o r
certain applications in Part IV.
The notation used is as follows, except where otherwise noted:
span
distributed load per unit area total distributed load
total concentrated load at a point or along a line bending rnornent
s h e a r l o a d
Youngrs rnodulus of elasticity of the skin rnaterial in the span direction
rnornent of inertia
shear rnodulus of rigidity of core relating to span d i r e c t i o n
s t r e s s , u s u a l l y i n s k i n i n s p a n d i r e c t i o n strain in axial extension or corrlpression defle ction s h e a r s t r e s s P o i s s o n r s r a t i o n b -w =
w
-P _ M = V -E = g A -V = I = Q =A b h t c d NA 1 0 -c r o s s - s e -c t i o n a t e a a s d e s i g n a t e d sandwich width full thickne s s skin thickne s s c o r e t h i c k n e s s d i s t a n c e b e t w e e n c e n t r o i d s o f s k i n s neutral axis 2. 2 BENDING A s t r u c t u r a l s a n d w i c h i s , i n e f f e c t , a n I - b e a r n a n d c a n be designed as such: the skins are the flanges and the core the w e b . F i g u r e 3 s h o w s t h e s t r a i n a n d s t r e s s a c t i o n t h r o u g h a syrnrnetrical sandwich spanning the page under bending load. Syrnrnetrical here Ineans that the skins are equal in E as weII
a s i n t h i c k n e s s . T h e f i r s t a s s u r n p t i o n w i t h s u c h b o n d e d c o r n p o s i t e s is that transverse sections plane before bending rernain plane
after bending, and that all rnaterials are elastic under norrnal c o n d i t i o n s ; h e n c e t h e s t r a i g h t - l i n e s t r a i n d i a g r a r n . T h e s t r e s s e s are then o = eE at any point.
T h e u n s c a l e d s t r e s s d i a g r a r n o f F i g u r e 3 s u g g e s t s t h a t in this case the E of the core is about one-sixth the E of the
s k i n , s o t h a t t h e c o r e i s s t r e s s e d o n l y o n e - s i x t h a s
rnuch as the skins and contributes little to the bending resistance o f t h e w h o l e . I n p r a c t i c e t h e c o r e r n a t e r i a l u s u a l l y h a s I e s s than one-hundredth the E of the skin, so that the "approxirnate
s t r e s s r r d i a g r a m s h o w n i s v e r y c l o s e t o t h e a c t u a l o n e . T h u s t h e b e n d i n g s t i f f n e s s o f t h e c o r e c a n b e n e g l e c t e d i n r n o s t
c a s e s . F u r t h e r , t h e s e p a r a t e b e n d i n g r e s i s t a n c e s o f t h e t h i n s k i n s a r e u s u a l l y s r n a l l a n d c a n b e n e g l e c t e d , s o t h a t t h e i r axial forces produce the only resisting couple or rnornent that n e e d b e c o n s i d e r e d . T h a t i s M = s k i n f o r c e x d = o t b d ( l ) ( a s d e t e r r n i n e d f o r e i t h e r o f t w o i d e n t i c a l s k i n s ) . T h e s h e a r f o r c e s i n a t h i n - s k i n s a n d w i c h a r e c a r r i e d a l r n o s t e n t i r e l y b y t h e c o r e , g i v i n g f a i r l y u n i f o r r n s t r e s s i n t e n s i t y t h r o u g h -o u t , s -o t h a t
Thicker skins t h e c o r e s h e a r s t r e s s
l
I t
-pick up more of the shear load so that rnay be better approximated as
V b ( c + t ) V V f - - - b c w h i c h i s s o r n e t i r n e s e x p r e s s e d f o r c o n v e n i e n c e as
( z l
( 3 ) ( 4 ) ( 5 ) This surrrs up norlnal bending strength considerations for p r e s e n t p u r p o s e s . r n b u i l d i n g a p p l i c a t i o n s d e f l e c t i o n s r a t h e r t h a n s t r e n g t h u s u a l l y r u l e s a n d w i c h design or use. Unfortunately, bending stiffness is rrrore difficult to calculate even in sirnplified forrn.The stiffness factor EI is again deterrnined frorn the skins a l o n e . T h e g e n e r a l e x p r e s s i o n I = { ( I o + A t < Z ) r e a d i l y g i v e s t h e rnornent of inertia of this sirnplified section, where ro is the rnornent of inertia of each skin about its own axis, A the area of each skin, and k (its distance frorn the neutral axis of the section) equals a/z nr a syrnrnetrical sandwich. with thin skins the Io can be neglected so that I = dA t*l'. Surnrned for the two skins this becornes
) , A d " I = - = 2 b t d 2 and E u t d Z ' o L = z
for a syrnmetrical sandwich strip with thin skins.
Where the skins have appreciable thickrless the EI rnay be rnade to include the Io for each skin by the rnore exact expre s sion
I -_ L Z -_ b ( h 3 - " 3 ) I Z
t 6 )
H e n c e E I = E b ( h 3 - " 3 ) ( 7 ) for a syrnrnetrical sandwich strip with thick skins.Where a sandwich or any larninate includes skins differing i n t h i c k n e s s a n d r / o r E n o r t h e c o r e i t s e l f h a s a p p r e c i a b l e b e n d i n g s t i f f n e s s ( e . 8 . , a s o l i d p l y w o o d c o r e w i t h t h i n r n e t a l s k i n s ) , o r when any nurnber of layers are involved, the rnethod of trtransforrned
s e c t i o n ' r i s u s e f u l . A s s h o w n f o r a s i r n p l e c a s e i n F i g u r e 4 , t h e e l e r n e n t s a r e t r a n s f o r r n e d i n t o a n e q u i v a l e n t h o r n o g e n e o u s c r o s s -section of the sarne E throughout. It is rnost convenient to conceive of this ad;ustrnent as affecting the widths, b, of the elernents of t h e c r o s s - s e c t i o n o n l y , t h e s e b e i n g r n a d e i n p r o p o r t i o n t o t h e r a t i o o f t h e E f o r t h e e l e r n e n t t o t h e r e f e r e n c e E s e l e c t e d . I t i s f u r t h e r c o n v e n i e n t t o s e l e c t t h e E f o r o n e o f t h e e l e r n e n t s a s t h e r e f e r e n c e E , e . g . E i n F i g u r e 2 . T h e w i d t h o f t h i s e l e r n e n t then rernains as before, S*t the other elernent widths rnust be transforrned to "J o, .la o as shown. AII other dirnensions
o r
o r
s u c h a s t , c , h a n d d , a n d t h u s t h e c e n t r o i d a l d i s t a n c e s b e t w e e n e l e r n e n t s , r e r n a i n a s b e f o r e .
Calculation of I and EI rnay now be made for the transforrned s e c t i o n , u s i n g t h e r e f e r e n c e E ( E 1 i n F i g u r e 4 ) . T h e v a l u e o f E I so obtained will apply directly to the original section without further adjustrnent.
The transforrned section technique is also applicable and u s e f u l f o r c a l c u l a t i o n s o f s t r e s s e s a n d s t r a i n s i n s u c h u n b a l a n c e d
s e c t i o n s . W h e n c a r r i e d o u t a s d e s c r i b e d a b o v e t h e I f o r t h e transforrned section rrray be calculated and used in calculating
strains at various points in the section under a given applied bending rnornent M. These wiII also be the strains in the c o r r e s p o n d i n g p a r t s o f t h e r e a l s e c t i o n , t h e n e u t r a l a x i s b e i n g i n t h e s a r n e r e l a t i v e p o s i t i o n f o r b o t h c a s e s . T h e s t r e s s e s i n the real section rnay be found frorn the strains by using the real E for the rnaterial at the point in question. Thus the s t r e s s e s a t a n y p o i n t i n t h e o r i g i n a l s e c t i o n w i l l b e r e l a t e d
1 3
-to those calculated for the transforrned section in the ratio of the real E to the reference E for the rnaterial at that point.
When using the transforrned section approach for the calculation of EI, and recalling that the contributions of the individual elernents to I are given approxirnately by AkZ in e a c h c a s e , i t c a n b e r e a s o n e d t h a t t h e r e s p e c t i v e a r e a s o f elernents only need to be transforrned, by rnultiplying the real e l e r n e n t a r e a i n e a c h c a s e b y i t s E r a t h e r t h a n b y a r a t i o o f E . Thus when the deterrnination is carried out by surnrning the values of AkZ for each elernent the result obtained yields EI since the transforrnation has already introduced E.
In the norrnal sandwich the core stiffness does not contribute appreciably and the above procedure yields
6 ( E r , t E z t ' l d z
E I =
E l t t * E z t z
for an asyrnrnetrical sandwich strip with thin skins.
( 8 )
Again, where the contribution arnounts to and can be added directly
skins have appr.eciable thickness, their
b ( E r t l + E z t ; l
T
(e)
to equation (8) to obtain the full EI. In rnany bearns the sole property governing deflection under load is the EI value. Unfortunately this is the case in
sandwich cornposites only when the span is very long in relation to the thickness, or when the rnodulus of rigidity G of the core is quite high. For rnany building applications and rnany core rnaterials the shear deflection becornes significant and rnust be considered in addition to the usual bending deflection, which relates only to the extension and cornpression of the skins. The shear stiffness = bcG (for thin skins). The approxirnate relations for rnaxirTrurTr deflection for a sirnply supported bearn then becorne
5 W ! , 3
w!,
3 8 4 E I B b c G f o r a s a n d w i c h s t r i p u n d e r u n i f o r r n l o a d s a n dt 4 -c f o r c e n t r e - p o i n t l o a d . P i 3 4 8 E T P!, 4 b c G
( r l )
T h e s e a p p l y p a r t i c u l a r l y f o r t h i n - s k i n s a n d w i c h s t r i p s , but the approxirnations are rough so that further adjustrnents f o r n o r r n a l s k i n s a r e s e l d o r n w a r r a n t e d . T y p i c a l e f f e c t s o f s h e a r s t i f f n e s s w i l l b e s h o w n l a t e r . T h e f o r e g o i n g s t i f f n e s s r e l a t i o n s a l l r e f e r , a s n o t e d , t o s a n d w i c h n s t r i p s r " d e n o t i n g n a r r o w b e a r n s . T h e w i d t h o f r n o s t s a n d w i c h p a n e l s i n t r o d u c e s ' r p l a t e a c t i o n t r t o t h e b e n d i n g s t i f f n e s s p o r t i o n o f t h e t o t a l d e f l e c t i o n . T h i s i s t h e s t i f f e n i n g d u e t o r e s t r a i n t a g a i n s t w i d e n i n g a n d n a r r o w i n g o f t h e c o r r r p r e s s i o n a n d t e n s i o n s k i n s , r e s p e c t i v e l y . T h e t e n d e n c y t o e x t e n d o r c o n -t r a c -t l a -t e r a l l y w i -t h s -t r e s s i s -t h e P o i s s o n e f f e c -t , a n d -t h e r e s -t r a i n -t f o r c e s i n t u r n s e t u p c o u n t e r a c t i n g s t r e s s e s i n a c c o r d a n c e w i t h P o i s s o n r s r a t i o , v . T h e r e s u l t i s t h a t t h e s k i n w i l l d e f o r r n o n l y ( t - v ' ) a s r n u c h a s i t w o u l d i n a n a r r o w s t r i p u n d e r e q u a l a x i a l s t r e s s . T h e b e n d i n g s t i f f n e s s E I o f a s a n d w i c h p a n e l i s t h u s r n o r e a c c u r a t e l v s t a t e d a s E I ( p l a t e ) = E I ( s t r i p ) / ( r - v z )( 1 z )
a n d e q u a t i o n s ( 5 ) , ( 7 ) , ( 8 ) , ( 9 ) c o u l d b e s o r n o d i f i e d t o r e p r e s e n t rrlore accurately a panel in sirnple bending or in colurnn loading, a s w i l l b e n o t e d .A s v f o r r n o s t i s o t r o p i c r n a t e r i a l s i s i n t h e o r d e r o f 0 . 3 , ( 1 - v Z ) b e c o r n e s a b o u t 0 . 9 . T h u s t h e b e n d i n g s t i f f n e s s o f a s a n d w i c h p a n e l w i l l b e a b o u t I 0 p e r c e n t g r e a t e r t h a n t h a t c a l c u -lated for a strip bearn. This applies only to the pure bending p o r t i o n o f s a n d w i c h d e f l e c t i o n s ( t h e f i r s t p a r t s o f e q u a t i o n s ( I 0 ) a n d ( l I ) ) , n o t t o t h e s h e a r p o r t i o n , s o t h a t t h e f i n a l e f f e c t w i l l b e s o r n e t h i n g l e s s t h a n 1 0 p e r c e n t i n r n o s t c a s e s , S u c h p l a t e action of panels is often neglected in the usual approxirnate c a l c u l a t i o n s .
When a sandwich panel or any plate is supported on aII e d g e s t h e a d d e d b e n d i n g s t r e n g t h a n d s t i f f n e s s i s r n a r k e d . T o d a t e d e r i v e d s o l u t i o n s f o r s a n d w i c h p l a t e s a r e c o r n p l e x a n d s t i l l approxirnate. Very roughly, the deflection of such a plate rnay
1 5
-be about 50 per cent of the deflection calculated for a narrow strip running the short woy, when the panel is nearly square. As the geornetry changes so that the length approaches twice the width, this factor increases to about 90 per cent, becorning the sarne as if only two sides were supported. Such sirnple factors are not reliable and are useful only for prelirninary feasibility studies.
The above cornpletes the appcoxirnate assessrnent of sandwich bending stiffness and strength, except for the often-irnportant aspect of ripple-instability of. the cornpression skin. This is introduced rnore readily in the discussion of sandwich colurnns.
2 . 3 I M P A C T
The irnpact resistance in bending of a sandwich panel can be approxirnated by assuming that the deflection at failure under static load equals the deflection at failure under dynarnic irnpact load, and that the rnaterials behave elastically to
failure under such fast loading. For sirnplicity it is also assurned that a given width of panel acts fully in resisting the point load. With the ultirnate bending resistance M calculated as in equation (l), the ultirnate point load is calculated to produce M at the point in question. Considering both norrnal bending and shear, the ultimate deflection is then calculated e l a s t i c a l l y a s i n e q u a t i o n ( 1 1 ) . T h e w o r k d o n e i s , t h e n , i n t h e o r d e r o f
w o r k - t o - f a i l u r e = j e O = i r n p a c t r e s i s t a n c e ( 1 3 ) in load x distance units.
A g a i n , t e s t i n g i s n e c e s s a r y w h e r e i r n p a c t r e s i s t a n c e is irnportant in a particular application. The lower the bending stiffness the higher the irnpact strength; the structural sandwich often exhibits remarkable irnpact properties because of its high strength and thickness ratio and its low shear rnodulus.
1 6
-2.4 COLUMN LOADING
The structural sandwich is seldorn used as yet for load-bearing walls in buildings, the few exceptions being in low houses where alrnost any sandwich configuration is excessively strong in colurnn action. Again, the exhaustive mathernatical deri-vations are onerous and still approxirnate in relation to practical conditions. Given that the usual situation is one of over-design, and that a sirnple load test would be done in any case, the following approxirnations should be adequate. Plate action
e f f e c t s a r e o p e r a t i v e a s i n b e n d i n g , b u t t h e i r i n c l u s i o n i s s c a r c e l y warranted unless vertical edge stiffeners are included in the p a n e l s y s t e r n .
Where the skins are sufficiently stabilized by the core (discussed a little later) a flat sandwich panel colurnn may fail in over-all buckling of the Euler type. lf the colurnn length-to-thickness ratio is very high (perhaps about ?0 or rnore) the c l a s s i c E u l e r e q u a t i o n h o l d s :
P e = ,,2 EI
( t 4 )
L L Z
for sle4der colurnns. Pe = Euler load - ultirnate (buckling) load; Ll = effective vertical length of the panel colurnn = full height where the top and bottorn edges are free to rotate.
For the less slender panels norrnally encountered in building the buckling load is influenced by the low shear rnodulus of sandwich cores in sornething like the following rnanner:
P e s = P e G b c ( l 5 )
P e * G b c
for stubby colurnns with thin skins. Pes = ultirnate (buckling) load = Euler load rnodified for shear; Pe = Euler load as before. This equation gives only a rough idea of the order of P e s w h e r e t h e s k i n s h a v e a p p r e c i a b l e t h i c k n e s s .
1 7
-Local buckling (rippling) of the skins may occur at less load than over-all or Euler buckling if the core is too low in s t i f f n e s s . F o r t u n a t e l y , H o f f a n d M a u t n e r r s c o n s e r v a t i v e approxirnation for rnost sandwich constructions is sirnple:
^ l
" " " - z
o " , i s t h e c r i t i c a l s t r e s s i n skin and core properties as
t h e s k i n a n d E " , E . , G " r e f e r t o indicated.
( 1 6 )
Note the independence of such rippling frorn skin or c o r e t h i c k n e s s e s . W a v e - s t a b i l i t y r n a t h e r n a t i c s f i n a l l y r e s o l v e d that only the elastic properties of the rnaterials are operative, and that both the theoretical work and supporting test prograrns w e r e r e r n a r k a b l e i n d e e d . T h e c r i t i c a l s t r e s " o . , a l s o a p p l i e s without change as the ultirnate stress in the colnpression skin of a sandwich in bending. This is especially irnportant in assessing a sandwich bearn strength under point load. 2 . 5 C O N C E N T R A T E D L O A D
The buffeting of supersonic airstrearns rnay be the prirne factor in aircraft, dernanding cores with high strength and stiffness perpendicular to the skins. Buildings are free of such unusual problerns, but the sirnple question of denting abuse can dernand sirnilar core properties. Whether the expected load ranges from a bicycle leaning against a wall to a stiletto heel placed on a floor, the support of thin skins (e. g., rnetal) against perrnanent denting is often the sole reason for using a hard core rather than a soft one. With such skins, a reasonable first assurnption rnay be that the resistance to visible denting under concentrated load testing (tested with a l-in. diarneter disc) is about twice the flat cornpressive strength of the usual core rnaterial or greater. This should be checked by actual test wherever dent resistance is irnportant. The plate action effect of even thin skins on an elastic support can be substantial in local load resistance. W h e r e t h e s k i n s a r e t h i c k e r ( e . g . , h a r d b o a r d , p l y w o o d ) the dent and puncture resistances increase sharply and soft cores are often adequate - except sornetirnes in shipping where puncture loads rnay be very high indeed.
_ 1 8 _
2. 6 RACKING OR DIAPHRAGM ACTION
S a n d w i c h p a n e l h o u s e s t r u c t u r e s o f t e n u s e t h e p a n e l s as t h e s o l e l n e a n s o f r e s i s t i n g w i n d r a c k i n g f o r c e s . R a c k i n g s t r e s s e s a r e r a r e l y a n a l y s e d f o r t h e a c t u a l d e s i g n o r c o n s t r u c t i o n . T h e s t r e s s e s a r e l o w i n r e l a t i o n t o t h e r a c k i n g s t i f f n e s s a n d strength o f a k n o s t a n y s h e e t r n a t e r i a l u s e d i n b u i l d i n g . N e v e r t h e l e s s t h e r a c k i n g q u e s t i o n i s u s u a l l y r a i s e d f o r n e w s y s t e r n s . T h e forces o n f a s t e n e r s d o d e s e r v e t h o u g h t , b u t e v e n t h e s e are usually
s r n a l l b e c a u s e o f t h e l a r g e s i z e o f r n o s t p a n e l s and their corresponding r r l e v e r a g e .
" T h e s e f o r c e s c a n b e c o n s e r v a t i v e l y a s s e s s e d f o r p a n e l wall, roof or floor diaphragrns by considering the panels as
un-yielding rectangles of fixed geornetry that rack by rotation only. s u c c e s s i v e g r o u p s o f f a s t e n e r s r r r a y be elirninated to allow deter-rninant rnornent couples, or the load sharing between all fasteners rnay be assurned to be proportional to the relative rnovernent at each point with an incrernent of rotation.
S u c h a s s e s s r n e n t s s h o u l d b e a d e q u a t e f o r r n o s t low
buildings, even industrial buildings where a long roof diaphragrn r n u s t c a r r y c r o s s - w i n d l o a d s t o s h o r t e n d w a l l s . S i n c e t h e e a r l y atternpts at rrengineering analysistt of srnall house structures i n t h e U . S . A . i n t h e l 9 3 0 t s , a u t h o r i t i e s h a v e continued to require a t r a d i t i o n a l r a c k i n g t e s t o f a n B - b y 8 - f t w a l l section for acceptance of new constructions. This rnay have been useful for an understanding of the lirnits of traditional walls with horizontal boards, but it
usually has little relevance to rigid sheet and panel walls. rts s i z e a n d t i e - d o w n r n e t h o d a l l o w n o r n e a s u r e of fastener per-forrnance, and alrnost any sandwich or other stabilized. sheet c o n s t r u c t i o n w i l l p a s s t h i s t e s t w i t h ease.
Although these sections are intended to deal with design rnethods rather than application questions, it is awkward to discuss racking analysis without noting that it is often unwarranted..
where the racking efficiency of the structural sandwich may be of irnportancer as in use for high buitdings, the rigorous rnathernatical solutions referenced in Section ?.9 would be u s e f u l .
1 9
-2. 7 BOWING
As the skins and cores of sandwich larninates have little b e n d i n g r e s i s t a n c e , t a k e n s e p a r a t e l y , a n y d i r n e n s i o n a l change of one skin only forces an over-all curvature frorn the plane. rf the change occurs in both directions in the plane, the curvature is cornpound. The bowing is essentially a geometrical effect inversely proportional to the thickness, and may be calculated approxirnately as
K F
8 0 0 h ( 1 7 )
w h e r e
and
ft = percentage change of one skin cornpared to the other
6 = rnax. (centre) deflection frorn the plane. An initially warped core cannot bow a panel originally fabricated flat; only changes in the strong faces can do so. It the panel is fabricated with both skins at equal ternperature and fnoisture content, bowing will only result frorn different environrnents on either side, as will be discussed. The bowing is srnooth and not severe if the thickness is reasonable and the edges free to allow planar expansion. It has been reported that rigidly restrained dirnensions have caused panel skins to tear the core apart, in extrerne conditions, when the core t e n s i l e s t r e n g t h n o r r n a l t o t h e f a c e s w a s l o w .
2 . B T E S T S
Considerable effort has been expended in preparing standard test rnethods for sandwich constructions and building cornponents, and sorrle relevant ones rnay be noted briefly. The test procedures rnay often be sirnplified considerably for parti-cular cases, especially when used for successive developrnental purposes. Irnportant core properties include flat cornpression strength and rnodulus, ASTM C365-57, which relates to denting a b u s e a n d s k i n s t a b i l i z i n g . F l a t t e n s i o n , A S T M C Z 9 7 - 6 1 , a l s o relates to the latter. Shear strength and shear rnodulus are key p r o p e r t i e s , a n d A S T M C ? 7 3 6 1 c o r n p r e s s i o n r n e t h o d i s s t r a i g h t -forward and useful.
z o
-Concerning the perforrnance of the whole panel, ASTM C 4 B 0 - 6 2 g i v e s a s t a b l e s e t - u p t o r n e a s u r e l o n g - t e r r n c r e e p ' w h i c h w i l l b e d i s c u s s e d i n d e t a i l i n P a r t I I I . G e n e r a l d u r a -b i l i t y i s a l w a y s d i f f i c u l t t o a s s e s s ; t h e e x p o s u r e c y c l e s o f ASTM C48l -6? rnay be as good as any, but the effect of edge c l o s u r e s o f a p a n e l c a n r n a k e s u c h s h o r t - t e r r n e x p o s u r e s o f q u e s t i o n a b l e r n e a n i n g . S o r n e s u c h e x p o s u r e s ' c o r r e l a t e d with expected environrnental extrernes, should always be tried when dirnensional changes or forces rnight occur in the
c o r e r n a t e r i a l s , e . 8 , u r e t h a n e f o a m s a n d w o o d f i b r e c o r e s . A S T M E 7 2 - 6 I , s t r e n g t h t e s t s o f p a n e l s f o r b u i l d i n g c o n s t r u c t i o n , c a n b e a p p l i e d a s r e l e v a n t t o d e s i r e d u s e s o f s a n d w i c h p a n e l s . Sirnplification can often be effected responsibly. The ubiquitous
racking test is there. It and the rather difficult axial load (colurnn) test for load-bearing walls often rnay be unnecessary because of the intrinsic overdesign of any stiff sandwich in
such loading and the ability to check by calculation the order of perforrnance. Therrnal transrnission and condensation control can be calculated or tested as for any panel; the latter i s n o t e d i n P a r t I l t . F i r e p r o p e r t i e s r e c e i v e c o n s i d e r a b l e attention in Part lV.
2.9 ADVANCED SANDWICH THEORY AND OPTIMUM DFSIGN
A brief note with references rnay be useful where engineering interests warrant fuller understanding of sand-wich theory. Habipts review and bibliography (8) should again be cited, particularly in tracing original work. The n o t a b l e w o r k o f t h e U . S . F o r e s t P r o d u c t s L a b o r a t o t y f o r rnilitary sponsors has always atternpted to expedite solutions. such work by Raville defines the bending of sandwich plates (13). Norris, March, Ericksen, Kuenzi, Zahn and Kornlners developed
a n d t e s t e d e x p r e s s i o n s f o r e d g e c o m P r e s s i o n ' e d g e s h e a r ( r a c k i n g ) , c y l i n d e r s u n d e r a x i a l l o a d , e t c . , t h a t a r e c o n c i s e l y stated in a flight vehicle handbook (14). such work has been extended and further refinernents rnade in the last few years. Again, these rigorous derivations lnay often show little
irnprovernent over approxirnate rnethods for practical building c o n d i t i o n s .
z I
-P h y s i c a l e x p r e s s i o n s h a v e b e e n u s e d f u r t h e r t o e s t a b l i s h optirnurn design rules based on rninirnizing either rnaterial
(weight) or cost. Kuenzi (15) derives sirnple rninirnurn weight re-lations for bending stiffness and strength, edge cornpression
( c o l u r n n l o a d i n g ) , e t c . r sssurning that core properties are a
c o n s i s t e n t f u n c t i o n o f d e n s i t y . D a r v a s ( 1 6 ) s i r n i l a r l y d e r i v e s
rninirnurn cost design for bending stiffness and strength, resulting
again in sirnple relations:
_t
r
-?
r
for optirnum stiffness and
for optirnurn strength in bending,
c o r e t h i c k n e s s t o s k i n t h i c k n e s s , a n d price per unit volurne of core to price
volurne of skin.
w h e r e rl = ratio of
r = ratio of per unit
These and other investigators have noted that such optirnurn aPProaches
cannot be followed very often in practice. In building, the core thickness
rnay be dictated by insulation requirernents, bowing, the size of
electri-cal boxes, or sirnply the need to trlook solid.rt The skin thickness rnay
be controlled by denting considerations, or quite often the available
z z
-PART III - MATERIAL PROPERTIES AND ET'F'ECTS
Sandwich skins are, essentially, axially loaded elements. The significance of axial property leve1s is a farniliar part of engineering principle. The significance of core and adhesive actions and sorne other effects, on the other hand, should be introduced by quantitative exarnples to allow rnore rneaningful discussion of sandwich rnaterials. Then the relevant properties of the more prornising rnaterials rnay be described, allowing the capabilities of various structural sandwich cornposites to be dernonstrated and problerns and potentials discussed.
3. 2 DESIGN EXAMPLES: THE EF.FECTS OF CORE PROPERTIES
C o n s i d e r a s t r u c t u r a l s a n d w i c h s t r i p w i t h 2 8 - g a u g e ( 0 . O l a 9 - i n . sheet steel skins bonded to a ?-in. core, in the first instance elirnina-ting any core effects by assurning a very high G value. This is a rather stiff sandwich, but it *ooid be cornparable to one using /e-n. f i r p l y w o o d , c e r t a i n i-itt. asbestos board, or 3/ l6-in. glass-fibre-reinforced plastic on the sarne core. From equation (5), Part II:
E I l Z - i n . s t r i p = 2 9 x L o 6 * l Z x 0 . O I 5 x 2 ? = 1 0 . 4 x 1 0 6
A residential floor load of 40 psf with a live load deflection requirernent of l/360 span (Residential Standards, Canada 1965) can be carried over a considerable span. Frorn the first or pure bending portion of equation (I0)
5w!,4
3 8 4 E I
!, ' 3 6 0 '
-w = 4 0 p s f = 4 0 r c f ] j n rt (plf) on 12-in. strip = 3.33 to/tin. in. (pli)
8 7 i n . , a l l o w a b l e s p a n
= 8 9
= Q .
3 6 0Substituting a core of, say, 2 pcf. G = 400 psi, the shear deflection of this by the second portion of equation (10):
" b 24-in. = pure bending deflection polyurethane floor panel is foarn of approxirnated ^ w!'? A - -- s - S b c G 3 . 3 3 x 8 7 2 ( 5 w ) 3 6 0 8 x 1 2 x Z x 4 0 0 = 0 . 3 3 i n .
2 3
-T h e t o t a l d e f l e c t i o r 6 -T i s t h u s a b o u t 0 . 5 7 - i n . or 2.4 tirnes the pure bending 6o. The ne* allowable span should be close to
?
--7t
tirnes the old span, or about 65 in. (Such a relation
v
7 a
cannot be extended to wide variations of span because the 6" p o r t i o n d o e s n o t v a r y as the cube of the span.) Table r shows the effects of a norrnal range of shear stiffnesses for this .stubbytt exarnple. As norrnal plate action will render the panels sorne I 0 p e r c e n t s t i f f e r t h a n shown in these narrow strip calculations, the shear effect rnay be considered negligible when the calculated
O t / 6 U b e c o r n e s a s l o w as, s?y, I.09. T h i s h a p p e n s w i t h t h i s stubby exarnple, with the core G approaching 8000 psi.
Sirnilarly, Table I shows these effects for a longer span use of the sarne panel, as in curtain wall or sorne roof uses. Now the shear effect neay be considered negligible when G = 3000 o r m o r e . W h e n t h e E I v a l u e i s l e s s a t a g i v e n t h i c k n e s s , a s i s t h e c a s e f o r r n o s t s a n d w i c h s k i n s , t h e n 6 , i s d e c r e a s e d in relation to 6O, and the need for high G values is reduced.
3. 3 CORE SHEAR, EXTENSIBILITY AND STABILIZING ET.FECTS
The preceding examples allow the norrnal range of shear s t r e s s e s t o b e d e r n o n s t r a t e d . T h e s e a r e s u r p r i s i n g l y l o w b e c a u s e the shear irwebtr of the sandwich trr-bearnit covers the entire area. The stubby floor panel yields the rnost severe shear:
r r n a x = #
=
#
= 6 p s i
The longer curtain wall exarnple yields a core shear of 4 . 4 p s i . T h e s e a r e t y p i c a l c o r e s h e a r s t r e s s e s , a l t h o u g h thinner panels under heavy floor loads on shorter spans can a p p r o a c h l 5 p s i c o r e s h e a r . T h e s h e a r s t r e s s e s o n t h e a d h e s i v e between core and skin are practically identical to the core shear" E v e n v e r y l o w d e n s i t y c o r e s a n d i n e x p e n s i v e adhesives can
take such stresses for dynarnic or short terrn loads, but if they are sustained indefinitely there rnay be a creep problern, as w i l l b e d i s c u s s e d .
No rnatter what its strength, the core rnaterial cannot allow full developrnent of sandwich capacity unless it can trgivstr enough to follow the strain in the skins. A few rnaterials of
2 4
-o t h e r w i s e e x c e l l e n t p r -o p e r t i e s a r e e i t h e r t -o -o b r i t t l e -o r friable to suit sandwich composites. The working range of compressibility and extensibility of the skin rnaterials can be deterrnined well enough by dividing the relevant yield stress b y E . T h u s s t e e l w i l l b e s t r a i n e d a b o u t 0 . 1 3 p e r c e n t t o b e fully worked in tension or cornpression, alurninurn about 0. I7 p e r c e n t , w o o d p e r h a p s a b o u t 0 . 2 5 p e r c e n t , h a r d b o a r d s 0 . 5 p e r c e n t o r s o , a n d b o t h p a p e r - p l a s t i c a n d g l a s s f i b r e p l a s t i c l a r n i n a t e s I t o l . 5 p e r c e n t , r e p r e s e n t i n g t h e h i g h e x t r e r n e . Most core rnaterials can follow such skin strains without rupture.
Finally, the cornpression skin in a panel in bending or column loading will fail in local rippling at less than yield stress if the core provides inadequate stabilization. Equation ( I 6 ) o f S e c t i o n 2 . 4 r n a y b e r e w r i t t e n : B o 3 E.G. = -: ' S But l . .
about i E. for isotropic core rnaterials, I 5 o 3
c r
E s t o r l s o t r o P l c c o r e s . G
so that
Using the yield or ultirnate stress of a skin rnaterial and its axial rrrodulus E", the rninimurn cornpression rnodulus E of the core perpendicular to the skin can thus be deterrninedcto prevent skin rippling. As exarnples, carbon steel skins would dernand a core of E. = 4500 psi or tnore if the use required the full yield stress of the steel. Sirnilarly, utility alurninurn
sheet would require a core E. of about 2800 psi, and fir plywood one of about 1800 psi. Generally, the core rnaterials with better
G properties will also have E values rnore than adequate for normal skin stabilization.
3.4 THERMAL AND MOISTURE EFFECTS
Bowing and internal condensation can be unrelated, problerns of sandwich constructions t e m p e r a t u r e o r r n o i s t u r e r e g i r n e s e x i s t a c r o s s The environrnental ranges and effects should be
particular, if
wherever differential the panel thickness.
