HOW TO CHECK STEEL-CONCRETE COMPOSITE BEAM? worked examples for CO001

Transcription

1 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 HOW TO CHECK STEEL-CONCRETE COPOSTE BEA? ored exmples or CO001 WORKED EXAPLE 1: BEA WTH TRAPEZODAL SHEET Seodr em s omposed o PE seto (S5) d orete (C5/0) sl o 50 hgh o trpezodl sheet SŽ 1100 hh s oreted perpedulr to the PE em. Sher ore s trserred usg sher studs Köo 19/75. Geometr L = 000 l = 1800 h = 50 h p = 50 h = 00 seodr em sp seodr em spg orete sl hgh trpezodl sheet hgh PE em hgh h h p h 1/9

2 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 Lods Ded lods PE eght g A 78, ,50 0, N/m Trpezodl sheet eght g 0, trp N/m Corete sl eght g h eq 5 l 0,085 51,8,70 N/m equvlet orete sl hgh h eq s ostt hgh o orete sl o ross seto re equl to ross seto re o orete sl oreted to trpezodl sheet ordg to the gure elo. Overll ded lod g g g trp g 0, 0,,7,1 N/m mposed lods Serve lod o elg q serv,0 N/m q q serv l,0 1,8 5,0 N/m Lods omtos For SLS g q,1 5, 9,5 N/m For ULS d 1,5 g 1,5 q 1,5,1 1,5 5, 1,9 N/m terl ores 1 1 d L 1,9 1,1 Nm 8 8 edg momet 1 1 d L 1,9 8 N sher ore /9

3 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 Altertve : Elst soluto Sher resste Sher resste o omposte em s the sme s or steel PE seto sher resste o orete sl s egleted. Sher stress PE e should ot exeed sher stregth o steel. S t , ,.10 5, 9,57 P t S s e thess s seod momet o re s rst momet o re or horzotl ut the etrodl xs Rellt rtero 0 9,57 5 0,9 => odto s stsed Bedg resste Norml stress PE lges should ot exeed eld stregth o steel d orml stress orete sl should ot exeed ompressve stregth o orete. The lulto s rred out th eetve dth o orete sl e due to sher lug. e 0 e e1 e l l0 L or smple em The omposte seto s susttuted ll-steel seto th redued sl dth usg rto. E E 10 1,0 15 /9

4 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 E 10 GP Youg's modulus o steel m 0 E E 15 GP ool used smplto to te to out log term eets del (equvlet) ll-steel seto: Cross seto re o equvlet (del) ll-steel seto A A A A e h s ross seto re o orete sl A 88 s ross seto re o PE em Frst momet o re o equvlet ll-steel seto S S S ,.10 70,5.10 S A z ,.10 s rst momet o steel prt to the upper res o sl S A z rst momet o orete prt to the upper res o sl /9

5 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 Posto o etrod xs o equvlet ll-steel seto z A S 70, , top 85,7 Seod momet o re (momet o ert) o equvlet ll-steel seto,, 9, , ,50.10 s momet o ert o steel prt, A z 19, , 5,1.10 s momet o ert o orete prt, A z 15, ,7 9,.10 19,.10 momet o ert o PE to the o etrod ,.10 xs (te rom stt tles) e h momet o ert o orete sl to the o etrod xs 1, z1 1, 170, P 77, ,1.10 z 1, 77, , P 1 1 1,1.10 z 1 77, ,7,0 P 1 1 1,1.10 z 1 77, ,7,87 P 5/9

6 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 Crtero or steel prt 1 170, 0,7 5 0 Crtero or orete prt,87 0,7 0 1,5 Sher studs Wll e dded => odto s stsed => odto s stsed Deleto servelt lmt stte Overll deleto o omposte em depeds o the o eretog. the se o eretog thout termedte supports some lod ses t o steel PE seto th o omposte to d other lod ses t o omposte seto. Lod ses tg o steel PE seto: eght o orete mxture, trpezodl sheet eght d PE eght,1 g g trp g 0, 0,,7 L,1 N/m 5,1 5, E ,.10 Lod ses tg o omposte seto: mposed lods, q 5,0 N/m L 5, 5 5, E ,50.10 Overll deleto: 1 17,1, Lmt vlue o deleto: 1, 17,1, lm L Crtero or deleto lm 1, 0,89 => odto s stsed /9

7 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 Altertve : Plst soluto Sher resste Sher resste o omposte em s the sme s or steel PE seto sher resste o orete sl s egleted. pl, Rd A v ,07 N A v s sher eted re o PE = e re Rellt rtero pl,rd 8 19,07 0,0 => odto s stsed Bedg resste Eetve dth o orete sl due to sher lug e 0 e e1 e l l0 L or smple em Hgh o ompressed prt o orete sl s lulted rom equto orml ore PE seto s equl to orml ore orete sl or ssumpto tht eutrl xs psses through orete sl. F A d A 0, 85 d A x F rom there e x A d 0,85 e d , , 7/9

8 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 d d C 0 1,5 5 1, P 5 P x 9 h 50 => ssumpto s stsed Plst edg resste pl, Rd F r F r 9,8 0,11 107,75 Nm r h h hp x ,11 m F A d ,8.10 N 9,8 N F A 0,85 d ,85 1, 9,8.10 N 9,8 N Rellt rtero pl,rd 1,1 107,75 0, 57 => odto s stsed Sher studs d = 19 h s = 75 dmeter o sher stud legth o sher stud Chrterst erg resste o oe sher stud th dmeter rom 1 to 5 P r π d 0,8 u m 0,9 d E m π 19 0,8 00 m 0,9 0, ,7 m 80, N 80, E m = 0 GP orete Youg's modulus or short lod durto 8/9

9 Desg o omposte ems - BUT FCE KDK Odřej Peše Drt 017 hs 75 hs 75 0, 1 0, 1 0,99 or,9 d 19 d 19 Desg erg resste or trpezodl sheet oreted perpedulr to the PE em P rd P r t 80, 0,85 5,5 N 1,5 t s tor or orete sls oreted to trpezodl sheet oreted perpedulr to the PE em 0,7 0 hs 0, t 1 0,90 t,mx 0,85 => t 0, 85 r h p hp Overll sher ore etee PE seto d orete sl N A d m A 0,85 d A s sd ,8 m m 9,8 N ,85 1, 0 9,8 mum umer o sher studs or ull omposte to P N Rd 9,8 5,5 1, Numer o sher studs hh s possle (mxml relzle umer) to put oto em s lueed shpe o trpezodl sheet. The ve legth o SŽ 1100 s 00, thus sher studs spg s 00 too. L 000 mx 15 => ull omposte to l 00 ve Other xml spg o sher studs or ull omposte to L 000 mx,9 lve 00 => ull omposte to 1, Deleto servelt lmt stte The sme s or elst soluto lm 1, 0,89 => odto s stsed 9/9