CHAPTER 4 COMPARISON OF PUSH-OUT TEST RESULTS WITH EXISTING STRENGTH PREDICTION METHODS

Transcription

1 CHAPTER 4 COMPARISON OF PUSH-OUT TEST RESULTS WITH EXISTING STRENGTH PREDICTION METHODS 4.1 General Several tud trength rediction method have been develoed ince the Three o thee method are art o the eciication ued in the US, in Canada, and in Euroe. Thee are the AISC eciication (Load 1993), the Canadian eciication (Steel 1994), and the Eurocode 4 eciication (EN 2001). Other method that have been rooed include Lloyd and Wright (1990), Mottram and Johnon (1990), Lawon (1992), and Johnon and Yuan (1997). Lyon et al (1994) comared their uh-out tet data with rediction rom all o the above method, excet or Johnon and Yuan (1997), and howed that thee method are generally unconervative. The uh-out tet reult in thi tudy conirm that mot o thee method give unconervative rediction or the trength o tud in comoite lab. Below, the olid lab tet reult are comared to the redicted trength rom the AISC eciication equation (Load 1993). The reult rom the comoite lab tet are comared to the redicted trength rom the AISC eciication (Load 1993), the Canadian eciication (Steel 1994), the Eurocode 4 eciication (EN 2001), and a method recently rooed by Johnon and Yuan (1997). Thee method are reented in detail in Section 1.2. Prediction were all made uing meaured material roertie. 78

2 4.2 Solid Slab Ultimate Strength Comarion The reult o the olid lab uh-out tet are comared to the trength ound rom the trength rediction equation in the AISC eciication (Load 1993). The develoment o thi equation i dicued in Section 1.2. The equation wa develoed by Ollgaard et al (1971), and i reeated below. The trength o a tud in a olid lab i a unction o the concrete trength and the area o the tud, and ha an uer limit equal to the tenile trength o the tud. Q = 0.5A E 1. 0A F (4.1) SOL ' c c u where Q SOL = trength o tud in a olid lab A = cro-ectional area o tud c = comreive trength o concrete E c = modulu o elaticity o concrete = 33 w 1.5 ' c w = unit weight o concrete F u = tenile trength o tud The AISC redicted trength are comared to the exerimental trength in Table 4.1 and Fig. 4.1, and aear to be adequate. The rediction are conervative or tandard tet, where heet metal wa not laced between the teel beam and concrete lab and 10% normal load wa alied. For Tet 1-12 and 19-21, which were tandard uh-out tet, the average o Q e /Q AISC i 1.11, with a tandard deviation o and a coeicient o variation o 7.0%. For Tet 22-24, which had no normal load alied, the 79

3 average o Q e /Q AISC i 0.9, with a tandard deviation o and a coeicient o variation o 7.1%. 80

4 For Tet 13-18, which had lat heet metal laced between the teel beam and concrete lab, the average o Q e /Q AISC i 0.85, with a tandard deviation o and a coeicient o variation o 4.2%. The tet erormed by Lyon et al (1994) howed that the AISC equation were lightly unconervative (the ratio o Q e /Q AISC were le than 1.0). When the AISC redicted trength wa governed by the concrete trength, the average ratio wa 0.92, and when the trength wa governed by the tenile trength o the tud, A F u, the average ratio wa The reaon that Lyon tet exhibited maller trength than mot o the one in thi tet rogram i that the author did not ue normal load on the olid lab ecimen. The trength o their tet were cloe to the trength o Tet in thi tet rogram, where no normal load wa ued. 81

5 4.3 Comoite Slab Ultimate Strength Comarion AISC Seciication Proviion The reult o the comoite lab uh-out tet are comared to the redicted trength baed on the AISC eciication (Load 1993). The develoment o thee equation i dicued in Section 1.2. The equation wa develoed by Ollgaard et al (1971), and i reeated below or convenience. The trength o a tud in a olid lab, Q SOL, i a unction o the concrete trength and the area o the tud, and ha an uer limit equal to the tenile trength o the tud. A trength reduction actor, SRF, i multilied by the olid lab tud trength to obtain the trength o a tud in a comoite lab. The SRF, which hould not be taken greater than 1.0, i a unction o the deck geometry and the number o tud in a rib. Q = 0.5A E 1. 0A F (4.1) SOL ' c c u 0.85 H S hr wr SRF = 1.0 (4.2) N R hr hr Q = SRF 0.5A E 1. 0A F (4.3) AISC ' c c u where Q SOL = trength o tud in a olid lab A = cro-ectional area o tud c = comreive trength o concrete E c = modulu o elaticity o concrete = 33 w 1.5 ' c w = unit weight o concrete F u = tenile trength o tud 82

6 SRF = trength reduction actor or a tud in a comoite lab N R = number o tud er rib H S = height o tud h R = height o deck rib w R = average width o deck rib Q AISC = AISC redicted trength o a tud in a comoite lab The AISC redicted trength are comared to the exerimental trength in Table 4.2 and Fig All o the exerimental trength, excet or ive o the tet, were igniicantly le than the AISC redicted trength, which make the equation unconervative. The trength o the trong oition tud were much cloer to the redicted trength than the trength o the weak oition tud. The average ratio or all tet in Table 4.2 o Q e /Q AISC i 0.709, the minimum i 0.347, and the maximum i 1.183; the tandard deviation i 0.169, and the coeicient o variation i 23.8% CSA Proviion The reult o the comoite lab uh-out tet are comared to the trength rom the trength rediction equation in the Canadian Standard Aociation (CSA) eciication (Steel 1994). The equation or the trength o a tud in a olid lab wa develoed by Ollgaard et al (1971). It i the ame equation a the one in the AISC eciication. The equation or the trength o a tud in a comoite lab were develoed 83

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9 by Jaya and Hoain (1988). The aroach i baed on a concrete ull-out model, develoed by Hawkin and Mitchell (1984), in which the ailure urace i a yramidal cone o concrete which roagate downward rom the underide o the tud head. Jaya and Hoain (1988) develoed earate equation, rom which the tud trength cannot be taken greater than the trength o a tud in a olid lab, or 1.5 in. and 3 in. deck. The develoment o thee equation, which are reeated below, i dicued in Section 1.2. For 2 in. deck, a contant o 6.2 wa ued in the equation or Q CP, intead o 4.2 or 3 in. deck or 7.3 or 1.5 in. deck. The CSA redicted trength, Q CSA, i taken a the minimum o Q SOL and Q CP. 86

10 Q = 0.5A E 1. 0A F (4.1) SOL ' c c u Q = ρa or h R = 3 in. (4.4) CP ' 4.2 c Q = ρa or h R = 1.5 in. (4.5) CP ' 7.3 c where Q SOL = trength o tud in a olid lab A = cro-ectional area o tud c = comreive trength o concrete E c = modulu o elaticity o concrete = 33 w 1.5 ' c w = unit weight o concrete F u = tenile trength o tud or h <w 1 /2, Q CP = concrete ull-out trength o a tud in a comoite lab ρ = 1.0 or normal denity concrete = 0.85 or emi-low denity concrete A = concrete ull-out area. For a ingle tud, the aex o the ull-out area, with our ide loing at 45, i taken a the center o the to urace o the head o the tud. For a air o tud, the ull-out area ha a ridge extending rom tud to tud. h R = height o deck rib ( H wr A ( ) = 2 2 ) (4.6) or h >w 1 /2, A ( d) = 2 2H w + w (4.7) R 2 R 2 ( 2h hrwr A ( ) = ) (4.8) 87

11 2 A ( d) = 2 2( 2h + h w h ) (4.9) R R + where h = H h R H = height o tud w R = average rib width w 1 = over-all trough width To ue thee equation, H /d mut not be le than 4.0, (H -h R ) mut not be le than two tud diameter, and the tranvere acing mut not be le than our tud diameter. The CSA redicted trength, mot o which were governed by the equation or Q SOL, are comared to the exerimental trength in Table 4.3 and Fig Fig. 4.3 how that the CSA method i unconervative or all excet ive tet. The average ratio o Q e /Q CSA i 0.726, the minimum i 0.414, and the maximum i 1.183; the tandard deviation i 0.172, and the coeicient o variation i 23.7% Eurocode 4 Proviion The reult o the comoite lab uh-out tet are comared to the trength ound rom the trength rediction equation in Eurocode 4 (EN 2001). The equation are imilar to the AISC equation, excet the contant 0.5 i changed to 0.37 in the equation or the trength o a tud in a olid lab, and the uer limit on thi trength i 80% o the tenile trength o the tud. The trength reduction actor i alo imilar, excet the 88

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14 contant 0.85 i changed to 0.7. Thee equation are reented below. Q = 0.37α A E 0. 8A F (4.10) SOL ' c c u SRF = 0.7 N R H S h hr R w h R R (4.11) An uer limit i laced on SRF a ollow: For tud welded through deck greater than 1.0 mm (0.039 in.) thick, 1.0 or ingle tud 0.80 or multile tud For tud welded through deck le than 1.0 mm (0.039 in.) thick, 91

15 0.85 or ingle tud 0.70 or multile tud For 19 mm (3/4 in.) or 22 mm (7/8 in.) tud welded through hole in deck, 0.75 or ingle tud 0.60 or multile tud Q = SRF EC 4 Q SOL (4.12) where Q SOL = trength o tud in a olid lab H = 0.2 H α + 1 or 3 4 d d A = cro-ectional area o tud c = comreive trength o concrete E c = modulu o elaticity o concrete = 33 w 1.5 ' c w = unit weight o concrete F u = tenile trength o tud SRF = trength reduction actor or a tud in a comoite lab N R = number o tud er rib 2 H S = height o tud h R = height o deck rib w R = average width o deck rib Q EC4 = Eurocode 4 redicted trength o a tud in a comoite lab 92

16 The Eurocode 4 redicted trength, mot o which are unconervative, are comared to the exerimental trength in Table 4.4 and Fig The trength o trong oition tud are adequately redicted, but the trength o weak oition tud are not. The average ratio o Q e /Q EC4 i 1.150, the minimum i 0.535, and the maximum i 2.082; the tandard deviation i 0.313, and the coeicient o variation i 27.2% Johnon and Yuan Model The reult o the comoite lab uh-out tet are comared to the trength ound rom the trength rediction equation rom Johnon and Yuan (1997). Five mode o ailure are conidered or tranvere heeting: hank hearing (SS), rib unching (RP), rib unching with hank hearing (RPSS), rib unching with concrete ull-out (RPCP), and concrete ull-out (CPT). Theoretical model or each ailure mode are given below. For hank hearing ailure o tud in lab that are reinorced o that litting cannot read, the hear trength i ound rom Eurocode 4: r 0.5 ( cecm ) 0. A u P = 0.37A 8 (4.13) where P r = hear trength o tud in a olid lab A = cro-ectional area o tud c = cylinder trength o concrete E cm = modulu o elaticity o concrete u = ultimate trength o tud 93

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19 For other ailure mode, the hear trength i deined by P = k P r t r (4.14) where P r = hear trength o tud k t = reduction actor or mode o ailure other than SS For concrete ull-out ailure o tud in lab with one tud er trough, in a central or avorable oition, the trength i P = k r c P r (4.15) 96

20 k c = [ ηc + λc ( 1+ λc ηc ) ] 2 ( 1+ λ ) c 1.0 (4.16) 2 h 0.56ν tuh bo 4 η = c 1.0 (4.17) h N P r r erty λ c = (4.18) h P r T 0. 8A y ν tu 0.8 u 0.5 = cu (4.19) 5 (4.20) where k c = reduction actor or CPT ailure mode η c = non-dimenional grou or CPT ailure mode λ c = non-dimenional grou or CPT ailure mode ν tu = hear trength o concrete h = height o tud b o = average width o deck trough h = height o teel deck N r = number o tud er rib e r = ditance rom center o tud to nearer wall o rib or avorable oition tud T y = yield tenile trength o tud cu = cube trength o concrete I h>2h, ue h=2h. I η c 1.0, it hould be taken a 1.0. Thi indicate ailure tye SS rather than CPT. 97

21 For rib unching ailure o tud laced in the unavorable oition, the trength i P = k r k r = r P r [ ηr + λr ( 1+ λr ηr ) ] 2 ( 1+ λ ) r ( e + h h ) r 1.0 (4.21) (4.22) t y η r= 1. 8 (4.23) P e Ty λ r = (4.24) 2h P r T 0. 8A y u (4.25) where k r = reduction actor or RP ailure mode η r = non-dimenional grou or RP ailure mode λ r = non-dimenional grou or RP ailure mode e = ditance rom center o tud to nearer rib wall or unavorable oition tud t = thickne o teel deck y = yield trength o teel deck For combined rib unching and concrete ull-out ailure o tud in lab with two tud laced in erie or diagonally in a trough, the tud laced on the unavorable ide i aumed to ail by rib unching. The tud laced on the avorable ide i aumed to ail by concrete ull-out. The reitance o the two tud are added to get the combined reitance. For the rib unching ailure mode, the equation are a ollow: P = k r u P r (4.26) 98

22 k u = [ ηu + λu ( 1+ λu ηu ) ] 2 ( 1+ λ ) ( e + h h ) r u 1.0 (4.27) t y η u = (4.28) P ety λ u = (4.29) 2h P r where k u = reduction actor or rib unching in RPCP ailure mode η u = non-dimenional grou or rib unching in RPCP ailure mode λ u = non-dimenional grou or rib unching in RPCP ailure mode e = ditance rom center o tud to nearer wall o rib For the concrete ull-out ailure mode, the equation are a ollow: P = k r k = P r [ η + λ ( 1+ λ η ) ] 2 ( 1+ λ ) 1.0 (4.30) (4.31) 2 h 0.56ν tuh e + t 4 η = i 0. 75h ( e + t ) (4.32) h P r r ( e ) 2 + t ν tu ( e + t ) 0.75h 3 η = i 0. 75h > ( e + t ) (4.33) h P ety λ = (4.34) h P r T 0. 8A y u (4.35) 99

23 ν tu = 0.8 cu (4.36) where k = reduction actor or concrete ull-out in RPCP ailure mode η = non-dimenional grou or concrete ull-out in RPCP ailure mode λ = non-dimenional grou or concrete ull-out in RPCP ailure mode t = acing o tud When h>2h, aume h=2h. I η 1.0, k i taken a 1.0 and the ailure mode i RPSS. The Johnon and Yuan redicted trength are comared to the exerimental trength in Table 4.5 and Fig The equation aear to adequately redict the trength o both trong and weak oition tud. The average ratio o the exerimental trength to the redicted trength i 1.01, the minimum i 0.57, and the maximum i 1.60; the tandard deviation i 0.23, and the coeicient o variation i 23%. On average, the Johnon and Yuan equation rovide good rediction o tud trength and ailure mode. However, the minimum and maximum ratio are not a cloe to 1.0 a deired. Although baed uon a ound undertanding o the behavior o tud, the method i tediou and omewhat diicult to ue, and the uer mut irt redict the ailure mode o the tud o that the aroriate model can be ued. 100

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