5 Allwabl barg aaity and ttlmnt Vrtial tr ra il - du t nntratd lad: 3 5 r r x y - du t irularly ladd ara lad:. G t tabl 5..6 Fd / by dtrmg th trm: r/(/) /(/) 3- blw rtangular ladd ara: th t i at th rnr th rtangl: G t tabl 5..8-9,d, by dtrmg th trm: m Z L n Z th t i th ntr th rtangl: G t tabl 5.3.30 t d by dtrmg th trm: m L n 4- Arximat Mthd ( V : H).. L ( )( L ) ng. Haytham ai
5- Avrag vrtial tr ra blw th rnr rtangular ladd ara: Avrag vrtial tr ra a layr il ha dth rm =0 t =H a G t igur 5.7.34 t d a by dtrmg th trm: m n H L H Avrag vrtial tr ra ii layr that tart rm dth =H t dth =H, u th llwg rmula: a( H ) a( H) ; ; H a( H ) H H H rm 0 H H / H a a rm 0 H a( H) ttlmnt alulat. lati ttlmnt vr aturatd lay: A A, A = ( H/, L/), A = (D /) and = β. u H : Dth lay layr undr th bttm undat. igur 5.4 t bta A, A tabl 5.7 t gt a tyial valu β = (OR, ). alulat lati ttlmnt bad n latiity thry: ( Flxibl) ( Rigid) 0.93 ( Flxibl, ntr ). 3. mrvd uat r lati ttlmnt = G F / ng. Haytham ai
4. lati ttlmnt andy il ug tra lun atr: 0 0. 5 Tim yar 0. lg 0. D tiv tr at th lvl undat. Q lumn. Lad = Nt undat rur ra. A FundatAra. : tra lun atr, it i givn a hwn blw: ( m) 0.5 0. () Fr uar r irular undat Z 0 0. Z =0.5 (m) Z = 0 Fr undat with L/ 0 Z 0 0. Z = (m) Z =4 0 U tn / t t / t.5 3.5 95.7854 KN / m 4.4484 b N Fr irular r uar tg Fr tri tg 000 b / t ng. Haytham ai 3
5. ttlmnt undat n and bad n T Myrh thry t i dirnt rm th nt all all D dit nt all rntd hatr3 N 60 Fr 4 t... 4 nt N 60 Fr 4 t... 6 Myrh thught h wa t nrvativ whn h alulatd th nt allwabl barg aaity that h ha rad it valu by 50%:. 5 nt ( all) nt ( all) ud alulatd wl thry: F d : Dth atr D Fd 0. 33 nt ( all) N 60 Fd.m 0.05 5 N 60 0.3 Fd.m 0.08 5.64 r rlat nglih unit (U) 6. Ttal rimary nlidat ttlmnt : Fr nrmally nlidatd il: H lg : mr dx 0.009(LL-0) H : Thikn layr undr nidrat. : nitial vid rati. : Ovr burnd rur(tivtr). : Addd vrtial rur. ng. Haytham ai 4
ng. Haytham ai 5 Fr vrnlidatd lay with <= lg H Fr vrnlidatd lay with 0 < < lg lg H H Fild lad tt (lat lad tt) Fr lay il: u u Fr and il: u u Fr lay: Fr and: xaml A ntuu undat n a dit and layr il, Aum 3 / 5 t b and tim yar r = 0yr. U th tra lun atr t d th lati ttlmnt.
lut 0 D 55 575b / t 575 0.5 0.5 4000 575. 0.96 Tim yar 0 0.lg 0. lg 0. 0. = 5 x 3 = 495 b / t () ( m) 0.5 0. = 0.5 + 0. 0.96.4 () 4000 575 495.4 = 0.65 4000 575 439. 0 0 t b / t t t th ntr ah art at th ntr ah art t 3 / b 6 6,000 3 0.369 5.757 0 50,560 7 0.595 6 4.749 0 50,560 4 0.488 5.337 0 08,800 6 0.63 6 9.368 0 5 5.506 0 b / b / t i givn by trlat. 5 439.5.5060 0.4t 73. 7mm xaml Fd th i th uar tg that arry allwabl lad 000 KN givn that: N 60 0 mm 5 all U wl thry. ng. Haytham ai 6
ttlmnt (mm) lut A th lad i rlativly larg, w will lv aumg >.m nt ( all) nt ( all) N60 0.08 0.3 N 60 0.3 0.08 Fd 5 000 0 0.3.5 0.33 0.08 y trial and rrr, =.3m Fd 5 5 5 xaml3 Frm lat lad tt th llwg rult wr givn: uar lat (305mm x 305mm) Allwabl lad n undat = 500KN. all = 5mm and il. Dtrm th i uar undat. Rlat btwn ttlmnt and tr 0 0 0 30 40 50 60 70 tr (KN/m) 0 00 400 600 800 lut Q 500 A :tr n lat. (m) KN / m (Trial and rrr) mm givn mm givn hk 5mm rm urv rm uat.5 400 4 44 Nt OK 3. 60 7 3. OK that th arriat width undat i 3.m ng. Haytham ai 7
xaml4 Rr t th llwg igur,dtrm th avrag tr ra th lay layr blw th ntr th undat du t th nt undat lad 50 tn. Atr that, dtrm th rimary nlidat ttlmnt r th lay layr. lut: H ah H a H H H `T d blw th ntr th undat, w hav t ubdivid th ara a hwn th igur. 4 r 50 t / t 4409. b / t 55 T d ah :.5 m 0.3.5 n 0.3 = 0. a H T d ah :.5 m 0.83 3.5 n 0.83 3 = 0. a H 0. 3 0. 4409. 4 78.67b / t 3 000 00 4.5 H lg 6.4 3 40 6.4 37.87 0 H 0 lg 859. 0.068 000 0.58 37.87 lg lg 0.37 t.65 0.7 859. 0.7 000 aly at 0, 0.06, 000 and 00 at 0.7, 0.5 ng. Haytham ai 8
xaml5 Rr t th llwg igur,th nt lad r unit ara at th lvl undat i 300 b/t. Aum that th undat i rigid, dtrm th lati ttlmnt that th undat will undrg bad n th thry latiity. 300 0.3 300i artial lut : lv it by yurl and gt n mark bnu ( Rigid) ( Flxibl ) 0.93 ( Flxibl, ntr ). F = 0.5874 F = 0.047 = 0.605 =0.88 ( Rigid ). 0.457 xaml 6 Rr t th llwg igur, dtrm ttlmnt th undat. lut: A A H 3.5 A 0.66 L 3.5 600KN / m aturatdlay D. 0.8 A 0.93.5 50.5 0.66 0.96 0.4m 4m 600 50KN / m ng. Haytham ai 9
xaml 7 Rr t igur 5.6 yur txt bk, th tr n th lvl undat i 300,r th and. = 0.3, =300 b/, D =.95 t, H=3 t,u a tim 5 yar r th r and 0.Aum that th undat i uar 6.5 x 6.5 t,dtrm th lati ttlmnt that th undat will undrg ug lun l atr. lut : 300 D 0.95 34. 5 0 34.5 0.5 0.5 300 34.5 5 0. lg.34 0. = 0 x (3.5+.95) = 68 () ( m) 0.5 0. = 0.705 () Z( t) Z(t) t th ntr layr 0.943 ( ) Z at th ntr th layr 3.5.65 460800(300* ) 0.405 6.839 0 9.75 8.5 460800 0.355 6 7.458 0 5.03 0 5 34.5.030 0.0374t 0. 0.943.34 300 449 xaml 8 Tw lat lad tt with uar lat wr ndutd th ild. At. ttlmnt, th rult wr :- Width lat () Lad (b) 8,070 4 5800 What i uar tg i ruird t arry a nt lad 50,000 b at a ttlmnt. ng. Haytham ai 0
ng. Haytham ai lut: t n m A Q b n i m n m n m A Q n m n A m Q A A 5. 63 4 67.5 33.54 50000 / 67.5 33.54 96 576 5800 48 44 8070 96 4 4 576 4 4 48 4 44