Allowable bearing capacity (q all ) ح م يقس و عهى ان ساحة ك ا تتح ه انتشبة بذ حذ ث Shear failure

Transcription

1 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Ultimat baring apaity ( ) أقم ح م يقس و عهى ان ساحة ؤدي نحذ ث Shar failr ف انتشبة Allowabl baring apaity ( ) ح م يقس و عهى ان ساحة ك ا تتح ه انتشبة بذ حذ ث Shar failr shold b adat to prvnt xssiv sttlmnt and shar failr. Typs of shar failr: - Gnral shar failr: or Dns sand. - oal shar failr: or Mdim ompation soil. - nhing shar failr: or loos soil

2 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Cation of Ultimat aring Capaity of Show ondations withot Entriity:. Trzaghi s thory: Assmption for Trzaghi s thory: i. Th fondation is onsidrd to b show if D f, in rnt stdis th fondation is onsidrd to b show if / 4. Othrwis it is onsidrd to b dp fondation. ii. ondation is onsidrd to b strip if / iii. Th soil from grond srfa األزض انطث ع ح) (سطح to th bottom of th fondation. D is rplad by strss (سطح انتأس س) f D f or Gnral shar failr: Typ of fondation Strip ooting Sar footing Cirlar footing Ultimat baring apaity N N N.N N 0. 4N.N N 0. N : Cohsiv. D f : ondation width (Diamtr if irlar). N N, N, : aring apaity fators givn from Tabl..9 as fntion of angl of frition

3 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 or oal shar failr: Typ of fondation Strip ooting Ultimat baring apaity N N N Sar footing Cirlar footing 0.87N N 0.4N 0.87N N 0.N N, N, N : ators for baring apaity givn from Tabl..40. Myrhof s ations (Gnral baring apaity ation): Trzagi ations nglt: i. Rtanglar footings. ii. Inlination of loads. iii. Shar strngth of soil abov th fondation. Myrhof s ation taks in onsidration thss variabls: N s d i N s d i 0.5N s d i N N, N, : Tabl..44 s d i,,, s d i,,, s d i Shap fators. Dpth fators. Shown blow Inlination fators.

4 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Shap ators: s s s 0.4 N N tan Dpth ators: Cas I: / D f d d d D f 0.4 tan sin D f Dpth ators: Cas II: / D f d d d 0.4 tan D f tan sin tan D f Th Trm radian D f tan is in Inlination ators i i i 90 شا ح ي م انح م ع ان ح ز انسأس هصو أ ك انح م يائم ف ي تصف انقاعدج 4

5 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Efft of watr tabl in baring apaity ations Cas I) Watr tabl is loatd at dpth D w so that 0 D w D f : D D D w f w (انحد انثا ي ان عادنح) sat w (انحد األخ س ي ان عادنح) Cas II) Watr tabl is loatd at dpth D w blow th fondation so that 0 D w : D f.(انحد انثا ي ان عادنح) D w ) انحد األخ س ي ان عادنح ) Cas III) Watr tabl is loatd at dpth D w blow th fondation so that D w > : No hangs in ations. 5

6 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 ator of safty: ي خالل ان عادالت انسابقة حسب ا Ultimat baring apaity ز انق ة ت ثم االج اد انزي ارا أثش عهى انتشبة ت اس ع ذ ن زا ال جب استخذاي ع ذ انتص ى بم ستخذو ق ة أقم ي زا ي خالل قس ة ز انق ة عهى يعايم أيا. Q Gross ltimat baring apaity nt Gross Ultimat load. Nt ltimat baring apaity Gross owabl baring apaity nt Nt owabl baring apaity S nt S nt S S = ( 4) for baring apaity S

7 Df=.00 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl : Dtrmin th siz of sar footings to arry gross owabl load(95kn) givn that: S D.00 f 8.5KN 5. C Us Trzagi ations assming gnral shar failr. 95KN C=0.00 =5 =8.5KN/m Soltion Q Q 95. A S. or sar footing :.N Ara N At 5 N 0.4 N 57.75, N 4.44, N y trialand rror : 9m 7

8 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl : Dtrmin th nt owabl load that fondation an arry (no inlination), Us Myrhof ation givn that: S 4 D w f.00 0KN 5. C 50KN.. Soltion: N s d i N s d i 0.5N s d i At 5 N 0.7, N 0., N 0.88 Th watr tabl is at dpth = m <D f :.8 (9.4 0).KN KN Shap fators: s s s N 0..4 N 0.7 tan tan

9 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Dpth fators: D f d d d / / Inlination fators: tan 5 sin 5. D to absn of inlind load, th inlination fator is vrywhr KN KN S 9.5KN Q A KN nt nt nt nt nt

10 .5 m h ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl : ind th ltimat baring apaity of sar footing (.5m x.5m) whih is plad.5m blow th grond srfa of soil having th shown proprtis: d=8kn/m C=0.00 =0.5 m Th watr tabl is loatd at distan (h) blow th grond srfa; if sat=9kn/m ind th ltimat baring apaity sing Trzagi ation for th following ass: h = 7m. h = 4m. h = m. h = 0m. Commnt on th rslts. Soltion as I) h=7m d = 4.5m> No fft of watr tabl on baring apaity KN 0 N o.4, N.N N KN 0.4N. 0

11 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Cas II) h = 4m d=.5m< KN.N N KN N. 4.4KN Cas III) h = m D = m, D =.5m 8.N 880.KN KN 9 0 9KN N 0.4N Cas IV) h = 0.00 D = 0m, D =.5m.N KN 9 0 9KN N KN 0.4N. Commnt; as th watr tabl is bing nar to th fondation, th baring apaity drass.

12 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Entriy loadd fondation: ع ديا تتعسض انقاعدج نح م يسكص تد ا حساف فإ ضغط انتستح ك ي تظ ا ك ا ي ضح تانشكم انتان : x =/(x) ع د ج د ا حساف ف ح م انقاعدج ع ان سكص تسثة ذنك ف ت ن د ضغط غ س ي تظى أسفم انقاعدج ذنك حسة ق ح اال حساف. On way ntriity

13 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 M= max min. or </: I M A I M A / / عهضنا تسي ف اك دن ت نا وصعنا لأ جز صنا ر ت ءاج اقنا : عهضنا اجتا ف وصعنا اك ن ا ت min max. or = /: max Rmmbr, for irlar fondation, th momnt of inrtia is givn by: 4 4 D I, D is diamtr of th irl. min max

14 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00. or > /: Thr will b tnsion strsss on th fondation whih is prohibitd in dsign, so w will nglt th tnsion strss and at max as follow: (/ - ) max max max 4 ( ) ج د ا حساف ف األح ال جعم يساحح انقاعدج انت تتح م األح ال أقم ي ان ساحح األصه ح حت حصم عه يساحح أخس ك انح م ف ا ف ان تصف ك ا ي ضح ف ا ه : - A min., sd If th momnt is in th plan of () : / - / - Th ation sd to at th baring apaity is Myrhofs or Trzagis ation: N N N s d i s d i 5 To find shap fators: s, To find dpth fators: s, 0. in last trm is rlatd to soil blow th fondation. To find th gross ltimat load Q : Q A s d i 4

15 4 ft ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Q S (Against baring apaity) Q Chk that S max fator of safty is adat for max : Exampl 4: Dtrmin th siz of sar footing ( x ) that sbjtd to vrtial load (00,000Ib) and momnt (5,000Ib.ft), th soil profil is givn blow: Us S=, w=.4 Ib/ft d=00ib/ft C=0.00 =0 Q=00,000Ib M=5,000Ib.ft sat=0ib/ft C=0.00 =0 Soltion: - ind th ntriity (): M 5, ft 00, ind th fftiv ara A : A 0.5 sd. A min.(, )

16 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 - ind : N N N s d i s d i 5 0. s d i At 0 N 8.4, N Ib / ft Ib /. ft. s s Shap fators: tan Dpth fators: Assm D d d f / tan0( sin 0) Inlination fators: 4.54 D to absn of inlind load, th inlination fator is vrywhr. Q Q 00,000Ib Q Q A S 00,000 00,000Ib 00, Aftr arrangmnt of ation: 00, ft

17 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl 5: An ntriy loadd fondation is shown in th figr; dtrmin th ltimat load Q that fondation an arry sing Myrhof s ation. Soltion: N N N s d i s d i 5 At N.5, N ft 0..85, N 8 ft Shap fators: N s N 8.5 s s D f d d d.7 tan tan Dpth fators: /.5/ tan sin s d.54 i 7

18 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Inlination fators: D to absn of inlind load, th inlination fator is vrywhr Ib / ft Ib / ft A ft Q Ib / ft Ib

19 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl : or th sar fondation shown in th igr, find th gross owabl load that fondation an arry for th following ass: A- No watr tabl is obsrvd. - Watr tabl at dpth 0.5m blow th ottom of th fondation. Us S = with Myrhof ation. Soltion: Cas A: No Watr Tabl At 5 N 4., N., N 48.0 A m.5m..5.8m Shap fators:. s tan tan s Dpth fators: D / /.5 f d d tan5 sin

20 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Inlination fators: i i N 0 s d i N s d i 0.5 N kN/ m Q kN Q 59.5/ 8. 5kN s d i Cas : At watr tabl at dpth 0.5m blow th bottom of fondation: D w = 0.5m < ( =.5m) = x = kn/m d KN.5 N s d i N s d i 0.5 N kN/ m Q kN Q 7.7 / 7. 9kN s d i أخز ن س انج اب ي طق تأ انح م انر أصثحت تتح ه انقاعدج ف ج د Watrأصثح tabl أقم ي انح م انر تتح ه ف حال غ ات. 0

21 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl 7: for th rtanglar fondation shown blow: a) Compt th nt owabl baring apaity sing gnral baring apaity ation (S=). b) If th watr tabl is lowrd by m. What fft on baring apaity wold or d to watr lowring? Givn data: Dimnsions of fondation ( m x m) = 5 o C = 0.00 Soltion: D to inlind load in th ntr of olmn, w hav to translat it to th Cntr of th footing, and so thr will b momnt xrtd and so ntriity dvlops. M 700 os(0).5 55KN. m M m 700 Th momnt in th dirtion of : (0.75).5m m.5m, m sd الحظ انفشق ب زا انسؤال سابق ف را انسؤال نى عط ا اال حساف يثاشسج نك ق ح انح م ان ائم شا ح ان م تح ث ك انح م يائم ع د انع د تانتان حسة انعصو ان اشئ ع قم انح م نهقاعدج ك اال حساف حاصم قس ح انعصو عه ان سكثح انسأس ح

22 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Cas I) KN At 5 0., N N 0 0KN N N 0.88 N s d i s d i 5 Shap fators:.5 s tan s Dpth fators: D /.5/ f d d tan 5( sin 5) Inlination fators: i i KN Cas II) d = m<m.58 7KN y similar ations: KN nt s d i 4.KN. nt KN.

23 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl 8: or th shown sar footing (.5m x.5m) if th owabl load =800 KN, s S= to dtrmin th owabl rsisting momnt (M). Us Trzagi ations ( =5 o ) Soltion:.N N 0. 4N.5.5m At 5 N KN, N m KN S A min or 0.5m 0.5m M KN. m

24 4 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 X Y X Y Mx My Two way ntriity y x M M i d s i d s i d s N N N 5 0. How to find A? Cas I) & ), max(.5.5 A A

25 5 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Cas II) & 0 Cas III) & 0 Throgh th graph. : & : x - axis : y - axis look at igr.8 and Tofind A A Throgh th graph. : & : axis x - : axis y - look at igr..7. and Tofind ), max( A A

26 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Cas IV) A A Tofind & and y - axis : x - axis : & : Throgh th graph. look at igr. 9.

27 m ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl 9: Rtanglar footing is sbjtd to two way ntriity. Dtrmin th gross ltimat load that fondation an arry givn that:.5m, m D f 0.m 0.4m m Mx d=8kn/m sand =5 Q=?? My d=8kn/m sand =5 Soltion: - Stdy th as of ntriity: Cas I.5.5 (0.) A A.5 (0.8).5m.908m max(, ).908m N m m N s d i s d i 5 o sand: C= N s d i At 5 N., N

28 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Shap fators: s s 0.75 tan Dpth fators: D f d d / /.5 0. tan5( sin 5) Inlination fators:.5.7 D to absn of inlind load, th inlination fator is vrywhr. Q.KN. lt KN 8

29 ft ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl 0: Rfr to th following figr. Th show fondation masring 4 ft ft is sbjtd to a ntri load and a momnt. If = 0.4,ft =. ft and th dpth of th fondation is ft. Dtrmin th owabl load th fondation an arry. Us a fator of safty of 4.Soil proprtis ar: =5 Ib/ft³, = 5⁰, = 0.0. Soltion: Stdy th as of ntriity: & 0 CasII A max(, ) A Tofind ft A and look at figr ft. ft ft.48 ft 4 ft Q N N N s d i s d i Ib / ft N N Ib / Ib 94Kips s d i ft 9

30 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Exampl : Rfr to th following figr dtrmin th gross ltimat baring apaity Soltion: / 0.5/.5 0. / 0./.5 0. Cas I m m A m max(, ).5 A m.5 At = 0: N = 8.4, =.4 Shap fators: s s 0.75 tan tan Dpth fators: D f d d / 0.7 /.5 tan0 sin

31 ondation Enginring ECIV 45 Chaptr () aring Capaity of Show ondation irst trm 00 Inlination fators: D to absn of inlind load, th inlination fator is vrywhr. N s d i N s d i 0.5 N s kN d i