P 813 - Design Example on Composite Steel Deck Floor Slabs

7/22/2019 P 813 - Design Example on Composite Steel Deck Floor Slabs

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DESIGN EX MPLE ON COMPOSITESTEEL DECK FLOOR SLABS

byThomas J . McCabe 1

The en c lo sed example i s p res en t ed to demonst ra t e t h e i n t e n t anduse of the AISI T en t a t i v e Recommendations For The Design o f Composi teS t e e l Deck S l a b s , and h e r e a f t e r w i l l be r e f e r r e d to as the c r i t e r i a .Cal cu l a t i o n s u t i l i z i n g procedures p r i o r to the c r i t e r i a a re p re s en t eda t the end o f the example .

The irst page in t h e Appendix s t a t e s t h e given d a t a namely:spans , l oads , and f i r e r a t i n g . The f i r e r a t i n g d i c t a t e s the minimumdep th o f co n c re t e as p e r Underwri te rs L ab o ra t o r i e s recommendat ions .The span and co n c re t e d i c t a t e t h e s t e e l deck s i z e and t h i ck n es s necessaryto c a r ry the wet co n c re t e and c o n s t ru c t i o n l o ad s . Se lec t ion o f t h e deckf a l l s i n to t h e same procedure a s most des ign problems ; ex p e r i en ce ,whether it be your s o r t h a t o f a s t e e l deck s u p p l i e r .assumed to span t h ree 10 f t . sp an s .

The deck i s

Below the given d a t a , the s ec t i o n p r o p e r t i e s f o r t h e deck s e l ec t eda re given . These p r o p e r t i e s were c a l c u l a t e d in accordance w i t h t h e

S p e c i f i c a t i o n For The Design o f Cold Formed S t e e l S t ru c t u ra l Members1968 E d i t i o n o f the American I ro n and S t e e l I n s t i t u t e . The compos i tep r o p e r t i e s o f the s t e e l deck and co n c re t e a r e a l s o given . They werec a l c u l a t e d w i t h c racked sec t ion t h eo ry u s in g th e f u l l s t e e l a re a o ft h e deck. S+ d e s i g n a t e s the top o f the deck in compress ion and S-

1 s t r u c t u r a l Enginee r , INRYCO I n c . , Milwaukee, Wisconsin8 3


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8 4 THIR SPECI LTY CONFERENCE

means t h e bot tom o f t h e deck i s in compress ion . The AISI p r o p e r t i e sgiven assumed a minimum y ie ld s t r en g th o f 33 k s i , w i th a ba se s t e e lt h i ck n es s o f 0.042 i n ch es .

The l a s t two p r o p e r t i e s given a re m the s lope , and k t h e yi n t e r c e p t o f t h e s t r a i g h t l i n e developed from l a b o ra t o ry t e s t s conduc ted in accordance wi th Chapte r o f the c r i t e r i a .

The irst four s t e p s c a l c u l a t e t h e dead l o ad and the maximumd e f l e c t i o n o f t h e s t e e l deck as a form. The maximum d e f l e c t i o n can -no t exceed 3/4 i n ch o r 2/180 whichever i s sma l l e r ; 2 . 1 . 2 . 3 o f thec r i t e r i a . The ponding f a c t o r and d e f l e c t i o n due to t h e wet co n c re t ea re based upon t h e formulae d es c r i b ed i n t h e A . I .S .C . E n g in ee r in gJourna l , Apri l 1965, by J . Chinn . Any r a t i o n a l method may be used .The c r i t e r i a s t a t e s , A d d i t i o n a l co n c re t e dead load due to d e f l e c t i o no f t h e deck s h a l l be co n s id e red in c a l c u l a t i o n s .

The n ex t f i v e s t e p s c a l c u l a t e the p o s i t i v e moments due to deadl oad and the c o n s t ru c t i o n l o ad s s p ec i f i ed i n t h e c r i t e r i a namely: 20PSF uni form load o r 150 l b . co n cen t r a t ed load on one fo o t o f deckwidth . The uni form l oad moment c o e f f i c i e n t s assumed in the c a l c u l a -t i o n s a r e t aken from the A . c . I . Stan d a rd 318-71, P ar t 4. The concen-t r a t e d l oad moment c o e f f i c i e n t s a re fo r t h e l o ad in the c e n t e r o f theirst span . The n ex t two s t ep s check the a c t u a l f i b r e s t r e s s in t he

deck fo r t h e moments c a l c u l a t e d . The c r i t e r i a s t a t e s t h a t t h e s t r e s s e ssh a l l n o t exceed those p e rm i t ted i n t h e AISI s p e c i f i c a t i o n fo r thedes ign o f co ld formed s t e e l .

The n ex t n i n e s t e p s r e p e a t t h e p reced in g procedure to check t h edeck s t r e s s e s a t t h e s u p p o r t , only us ing the a p p l i c a b l e moment co e f f i c i e n t s and S - .


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DESICN EX MPLE ON SL BS 8 5

The n e x t c a l c u l a t i o n dete rmines the a l l o wab le load per web o fthe deck us ing 3 . 5 a ) 2) of the AISI S p e c i f i c a t i o n . The subsequen tt h ree s t e p s c a l c u l a t e the maximum a c t u a l l oad per web due to deadand c o n s t r u c t i o n l o a d s . This comple t es the check o f the s t e e l deckas a form t o ca r ry the c o n s t r u c t i o n loads and t he wet c o n c r e t e .

The n e x t phase i s to dete rmine t h e a l lowab le load on t he com-p o s i t e s l a b . Since adequate r e in fo rcem en t to a l low the composi tes l a b to a c t as a con t inuous beam i s no t p r e s e n t ; t he s l ab i s cons ide red as s imple spans of t en f e e t . The u l t i m a t e shear in L b . / F t .i s dete rmined us ing formula 7) o f t he c r i t e r i a f o r shear -bond capa-c i t y . The a l lowab le l i v e load i s t hen ob ta ined us ing the load f a c t o r so f 1 .7 f o r l i v e l oad and 1 .4 f o r dead load . The l i v e load becomes 104PSF wi th 28 PSF dead load app l i ed t o t he s l a b . The n e x t s t e p checksthe a l lowab le l i v e l oad fo r a de f l e c t i on o f /360 and i s 338.5 PSF.The c r i t e r i a s t a t e s t h a t the moment o f i n e r t i a used s ha l l be t heaverage o f the f u l l composi te i n e r t i a and t he i n e r t i a ob ta ined f romcracked se c t i o n t heo ry . I f t he ne u t r a l a x i s f a l l s wi th in the deck,on ly t he conc re te above the deck i s cons ide red .

The c r i t e r i a s t a t e s t h a t s h r in k ag e r e in fo rcem en t s ha l l be pro vided equa l to 0.001 o f t he a r e a o f concre t e above the s t e e l deck.This amounts to x 6, No. 8 wire . This comple t es the d es ig n exampleper the c r i t e r i a .

The l a s t c a l c u l a t i ons show the a l lowab le l i v e l oad on t h e s l a busing t he composi te s e c t i o n p r o p e r t i e s cracked t heo ry . The a l lowab les t e e l s t r e s s i s dete rmined by d ed u c t i n g the dead load s t r e s s from t heminimum y i e l d and mul t ip ly ing by 0 .6 . The dead load s t r e s s i s found


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8 6 THIR SPECI LTY CONFERENCE

by us ing the se c t i o n modulus to the bot tom o f t he s t e e l deck whenthe top o f the deck i s in compression o f Sb. The a l lowab le conc re tes t r e s s i s 0.45 The a l lowable load i s 157.5 PSF as opposed tot h a t o f 104 28 o r 132 PSF in the c r i t e r i a . Genera l ly speakingthe c r i t e r i a g ives lower l oads fo r long spans and higher loads fo rsh o r t spans than those computed by a l lowab le s t r e s s . This i s becausethe u l t i m a t e load va r i e s l i n e a r l y w i t h the shea r span which i s i n d e -pendent o f the se c t i o n p r o p e r t i e s .


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DESIGN EX MPLE ON SL BS 8 7

APPENDIX

GIVEN: 1) 30 ' Bays , 10 ' Beam Cente r s(2 ) Super imposed Loads

A. Off i c e Live so PSFP a r t i t i o n 20 PSFC e i l i n g R PSF

B. C o r r i d o r Live 100 PSFC e i l i n g 8 PSF

(3) 2 l our u n p r o t e c t e d f i r e r: : t t ingUSE: 5 - 1 / 4 t o t a l dep th l i g h t H e i g h t c o n c r e t e

We 110 1 b . / f t 3 l 14 : = 3000 p s i

P r o p e r t i e s Per foo t of_Wicl th :

As 0.687 in 2 +.')I 0 . 503 in 4 shST =43. 443 in 3 l f

m - 3438 k

Oo4l7 in3

-s0.453 i l 3 sc' lo632 in4 Tc0 0 :ss

. a ~ ~d=4.112 0=5-1 /4

+--Y-s_b_= 1 3 8 l. .'(

0 0 12 7. 3l l

I . 7 3 i n350 8 5 ' l in 4


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818

CRITERIAFind a c t u a l s t r e s sdu-=- to de.:ld l o a dplt.:s 150. c o n c e n t r a t e d l o a d rnoment

Find pond.ingraoment n e g a t i y e

Find dead loadnegat . ive moment

T ota l n e g a t i v ed . ad l oa d moment

Find 20 f uni formload nega t ivemoment

Find 1 5 0 1 conc e n l : r a t e d l o a dnega t ive moment

f i n d a c t u a l s t r e s sdue to dead l o a dp lus 20/J uni formlo3.d mornent

Find a c t u a l s t r e s sdue to d ead l o a dplus 1501 concent r a t ed load moment

Find a l l o w a b l eweb r e a c t i o n

Find loadrer foo t

Find number o fcbs per foot.

THIRD SPECIALTY CONFERENCE

FOR. HH..A

f = (TPM + POf) / +S

DLM Wd L 2 (l_:J10

TNM = PH + DLM

CLM (W) (L2) ( 12) /10

PCM 150 L ( 12) /10

f = (TNM CLM)/-s

f = (TNM + PO ) / -s

A. I .S . I. 3. 5

V ' 1 .1 WLV = 1 .1 WuL _ 150

~ L U L ~ T I O S

( 4 7 1 7 . 3 6 0 0 ) / . 4 1 719945 < 20000 OK( 2 . 1 . 2 . 2 )

PH ( . 8 ) (110) ( .411) Ci fYP;\f 366 In . Lb.

DLM ( 4 0 . 1 9 ) (10) 2 ( 1 2 ) / 1 04823 In . Lb.

TNM ' 366 48235189 I n . Lb.

CLM ZO) (10) 2 ( 1 2 ) / 1 02400 In . Lb.

PCM (150) (10) ( 1 2 ) / 1 01800 ln . L ;).

(5189 + 2400) / . 4277772 Lbs /lnz < 20000

f (5189 + 1 8 0 0 ) / . 4 2 716368 < 20000

N = 2 .1 2 5 5 0 . 6tPmax::. ( . 042) 2 [ 30S ( 2 .3 ) ( 5 0 . 6

- 2.022 ( 5 0 . 6 ) - . O i l (50 .62Pmax 643 .b.

v I. 1 ) (60 . 19) ( 0) . 662 Lb.v I. I ) ( 40 . 19) (10) + ISO , 592

Nw 24 = 1 . 5n;


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DESIGN EXAMPLE ON SLABS 819

CRITERIA I F O R ~ f U L C L C U L T I O ~Find dead l oad I wd 3 . 4 As wd (3 . 4) ( . 68 7)I + ~ + d1 w< CsJ] 110 [s.2s + 2. 12S (7 9116 -12 Cs rr ~. 2. 34 + 37. 85

40. 19 Lbs/Ftz

Find pending f ac tor PF Wc 4 (144) PF = 110 I OJ 4 (144)

IJ. Chinn AISC El iT 4 29. s X ro 6 ( . S03JiT 4Eng. JournalApril - 196S PF . 110

4s ( 40 . 19 ~ _ _ 1 _ 7 _ 2 ' 1ind de f l e c t i on due s = 3 w ~ ~ ~ J = ( 3)to uniform load ( 384) ( 29. s X 10 6 ) ( . SD3)s = . 366 In .

-Find t o ta l 6T =6 5 (- 1 6T - 366 ( ~ )ef l ec t ion 1=--1 1(2 .l. z . 3) T = 0. 41 I in . Ll180 . . 667 In .Find pending PM = h- we 6-r L2 P = 8 (110) (. 4111) ( r ~ Yr omen t pos i t i v e ' TZ IT

PM 333 l n . Lb.

rind dead load DLM . DLM ., ( 4 0. 19) (1 D) 2 (12 )111moment pos i t i v e 11 4 384 In. Lb.

Tota l pOS l t l .Ye TPM = PM + DLM TPM 333 + 4 384dead loadmoment . 4717 In . Lb .Find 20 I con- CLM (ZO) L z (12) I 11 CLM (ZO) ( l OJ 2 (12)111s t ruc t ion loadpos i t i v e moment . Z1BZ l n . Lb.Find 150 con- PCM ISO L (1Z) PCM ,. (1 SO) (1 0) (12) IScent rated lo:1 d ---,----pos i t i v e moment PCM .. 3600 l n . Lb.

Find actual s t r e s s f - (TPM + CLM) I ( +S) f = ( 4 717 + Z18Z) I .417d u ~ to dead loJ.dpI us 20 construe f . 16S44 < zoooo OKt l l ) l lo d :::d:nent oI (2. 1. 2 2


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820 THIRD SPECIALTY CONFERENCE

CRITERIA FOR.'fULA CALC ULAT1 ONFind load pe r p v p 662 . 441 Lb. < 643 OKweb f[ 1.5Find u l t ima t e Yu [ mA 5 + 12K YTe ] vu . ( . 8) (4 . 112) ~ 3 4 3 8 ( . 687)shea r 31 . , 3 ) (10)

+ (12) ( . 38) VToOo]vu . 1080.6 Lb . /F t .

Find l i ve l oad LL 1 [ ~ 1 .4 LL . l ~ 2 ) (1080. 6) 1 .4 2 8 ~f o r o f f i c e C T 1.1 10Cor r ido r no t LL . 104 .0 Lb . / F t . 2 > soc r i t i c a lFind al lowable wr.i v e load fo r L X 12 . ( 5) (1 728) w . (43704) Cic + I f ):: . L 300 3841 (10) 3DO"

w 43704 I w . ~ 6 ~ - t r - - 9 . 6 3 2 )-;:r--I . ( l c + I f ) / 2 w . 338. 5 PSF

Check by e x i s t i n g w ::r__:_oLf) .6 Sc w = -s3ooo 4 717 ) . 6 1. 743)en . t e r i a r s [ : z ~ -:4TI1 . s (10) 2

w . 3 f ST w . 157 .5 PSFc~ I. w . ( . 3) (3000) [4 3. 443)100w . 391 .0 PSF


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dd l

D L f

E

f c

DESIGN EX MPLE ON SL BS

Sn BOLS USED

Ful l a re a o f s t e e l deck ( i n . 2/ft.C e l l sp a c i n g ( i n . )Bending d e f l e c t i o n due to wet c o n c re t e ( i n . )Tota l d e f l e c t i o n o f deck due to wet c onc re t e andponding ( i n . )Capac i ty r e d u c t i o n f a c t o rE f f e c t i v e dep th o f composi te s l a b ( i n . )Depth o f s t e e l deck ( i n . )Dead l oad bend ing s t r e s s in s t e e l deck a t thbo t t om f i b e r ( L b . / i n . 2 ).Modulus o f e l a s t i c i t y o f s t e e l = 29. S x 10 6( L b . / i n . 2 Minimum y i e l d s t r e n g t h o f deck ( L b . / i n . 2 )Bending s t r e s s (Lb . / i n . Z )28 day c onc re t e compress ive t e s t c y l i n d e r s t r e n g t h( L b . / i n . 2 ).Moment o f i n e r t i a o f compos i t e s e c t i o n based oncracked s e c t i o n ( I n . 4 / f t . o f wid th )Ful l moment o i n e r t i a o f composi te s e c t i o n( l n . 4 / f t . o f wid th )

I Moment o f i n e r t i a used in d e f l e c t i o n c a l c u l a t i o n s( I n . 4 / f t . o f width )k I n t e r c e p t o f r e g r e s s i o n l i n eL Length o f span f t .

82

LL Allowable super imposed 1 i v e load for s e r v i c e c o n d i t i o n sCUI' 1-loment due to a 20 'SF uni fo rm c o n s t r u c ~ t i o n load in Lbs.IJL 1 ~ i n p ~ ~ . . _ n l c u


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822

PC M

TPI>I

TP

mN

pPF

THIRD SPECI LTY ONFEREN E

/>lament o f 150 Lb. c o n c e n t r a t e d l o a d in Lbs.T o t a l p o s i t i v e c o n s t r u c t i o n l oad and dead l o a d

moments in Lbs.T o t a l n e g a t i v e c o n s t r u c t i o n l o a d and dead l o a dmoments in Lbs.Slope o f r e g r e s s i o n l i n eA c t u a l l e n g t h o f b e a r i n g f o r a maximum va lueo f web d e p t hNumber o f webs p e r ft.

Load p e r web (Lbs . )Pund ing Fa c t o r

Prnax Al loHab le l o a d p e r \vcb (Lbs . ) / \ lSI 3 .5Se c t i on modulus o f deck ( T n . 3 / f t . )

t S t e e l deck t h i c k n e s s e x c l u s i v e o f c o a t i n g s ( l n . )Vu C a l c u l a t e d u l t i m a t e s h e a r ( L h s . / f t . o f wid th )

W Live LoadConc re te \vcight ( J . h s . / f t . 3 Weight o f s t e e l deck p l u s c o n c r e t e ( L h s . / H . 2 Average Rib lv id th ( l n . )

Sc Compos i t e s e c t i o n moLlulus to bo t tom o f deck Tn. 3/ft.ST Compos i t e s e c t i o n modulus to top o f c o n c r e t e ( T n . 3 / f t . )

Dead l o a d ~ p l i e d to s l a b e x c l u s i v e o f s l a b \ve ightcLb s . f t -

l Nominal o u t to o u t Llcpth o f s l a b ( l n . )D i s t a n c e f rom c c n t ro i d : l l a x i s o f o; tecl deck to bo t tomo f s tcL l deck (Tn . )

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P 813 - Design Example on Composite Steel Deck Floor Slabs