Designing A Concrete Arch Bridge

Transcription

1 This is th mous Shwnh ri in Switzrln, sin y Rort Millrt in It spns 37.4 mtrs (122 t) n ws sin usin th sm rphil mths tht will monstrt in this lsson. To pro with this lsson, lik on th Nxt utton hr or t th top o ny p. Whn you r on with this lsson, lik on th Contnts utton hr or t th top o ny p to rturn to th list o lssons.

2 7 99 t t 11 t Th Prolm: This is prtilly inish orm irm o ri tht will spn 99 t. Th rwy slops t 7%. Eiht wlls sp 11 t prt rin totl ls o 120 h rom th sti k to onrt rh low. Th rh is onrt sl tht is 8 inhs thik n 16 t wi throuhout th spn. Th llowl xil strss in th rh is 800 l/in 2. Shp th rh in suh wy tht smnt is prlll to th ri k s shown.

3 7 99 t t 11 t Stp 1: Wht is th mximum llowl xil or in th rh Th ivn prmtrs r n rh thiknss o 8 inhs, n rh with o 16 t, n n llowl strss o 800 l/in 2. Th ross stionl r o th rh is its with tims its thiknss: Ar = (with)(thiknss) = (16 t)(12 in./t)(8 in.) = 1536 in 2 Th llowl xil or in th rh is th r o th rh tims th llowl strss: For = (Ar)(llowl strss) = (1536 in 2 )(800 l/in 2 ) = 1,228,800 l = 1229

4 A B Stp 2: Construt lin irm n pply intrvl nottion. Workin lokwis rom th uppr lt, pl xtrnl rvity ls on th orm irm. Th sps or intrvls twn ors r ll with th upprs lttrs o th lpht. In this irm, th irst ip l is pl ovr th ltmost rh wll. Lttrs A n B r ssin to th intrvls on ithr si o th l. This is l AB.

5 A B C Th son l is pl ovr th nxt rh wll. Lttr C is to th irm, n this oms l BC. With h l, vrtil lin o tion is xtn own throuh th r o th orm irm whr th rh will onstrut.

6 A B C D Th pross ontinus until ll th ls on th rh hv n onstrut n ll. This is l CD.

7 A B C D E This is l DE.

8 A B C D E F This is l EF.

9 A B C D E F G This is l FG.

10 A B C D E F G H This is l GH.

11 This is l HI. Th lin irm is now omplt. All o th xtrnl rvity ls tin on th rh hv n pl on th lin irm. Vrtil lins o tion hv n rwn or h l, xtnin own throuh th r o th orm irm whr th rh will onstrut.

12 Stp 3: Construt l lin to ny onvnint sl. Th L Lin is rphil summtion o th ls tin on th strutur. On th L Lin, th mnitu o th ors rom th lin irm r rwn to sl. Binnin with or AB, w plot smnt o th l lin, prlll to AB, ll. Th lnth o sls to 120, th mnitu o th or. 120 L Lin 400

13 On in, w work lokwis roun th Form Dirm, plottin h l onto th L Lin in tip-totil shion. Althouh th L Lin is ompos o vtors, th ns o th or smnts r mrk with horizontl tik mrks rthr thn rrow hs. This hlps to kp th irm lil n urt. Vtors rrn tip-to-til L Lin 400

14 Sin ll o th ls on our rh r o qul mnitu, h smnt o th L Lin will qul in lnth. Whn th ls on strutur vry in mnitu, or r not ll stritly vrtil in irtion, th smnts o th L Lin will vry in lnth n irtion s wll. L Lin 400

15 W ontinu ross th, plottin ll th ls on th rh onto th L Lin. Noti how intrvls on th orrspon to points on th L Lin. L Lin 400

16 W ontinu ross th... L Lin 400

17 W ontinu ross th... L Lin 400

18 W ontinu ross th... h L Lin 400

19 Th L Lin is now omplt. Th totl lnth o th L Lin is qul to th totl l on th rh, in this s L Lin 960 h i 400

20 Stp 4: Construt ry o known irtion ut unknown lnth. Ry is vtor whos lnth is qul to th mnitu o th or in rh smnt, n whos irtion is prlll to tht or. Construt ry throuh point on th l lin, prlll to rh smnt. Althouh w on t yt know th lotion o point o, th lt n o ry, it must our somwhr lon this lin. h i L Lin 400

21 A B C D E Hr is th qution w us in Stp 1 to in th mximum llowl or in th rh: For = (Ar)(llowl strss) = (1536 in 2 )(800 l/in 2 ) = 1,228,800 l = 1229 F G H I Stp 5: Construt th lonst ry n in point o. Evn or w know th lotion o point o, w n skth th nrl lyout o th rys o th For Polyon. W n s rom this skth tht, or ny point o tht lis on ry, ry o will th lonst ry, orrsponin to th rtst or in th rh. Thus w must limit ry o to lnth o Ry o is th lonst ry L Lin o o o o o oh h i 400

22 From point, w us ompss to strik n r o rius 1229, th mximum or llowl in th rh. Whr this r intrsts with ry is point o. Th L Lin hs now om prt o For Polyon. Point o is th Pol o th irm. Hr is th qution w us in Stp 1 to in th mximum llowl or in th rh: For = (Ar)(llowl strss) = (1536 in 2 )(800 l/in 2 ) = 1,228,800 l = 1229 Pol o h i For Polyon 400 rius = 1229 ry o

23 By slin th lnth o ry on th For Polyon, w n now trmin th mnitu o th or in smnt o th rh o h i For Polyon 400 rius = o

24 Stp 6: Throuh th Pol o, onstrut th rminin rys o th For Polyon, innin t th ntr n workin towr th ns. As h ry is rwn, onstrut prlll to it th orrsponin smnt o th onrt rh on th Form Dirm. Sl th lnth o h ry to in th mnitu o th or in th orrsponin smnt o th rh. o h i For Polyon o

25 This is ry o. o o h i For Polyon o o

26 This is ry o. o 1180 o o 1180 h i For Polyon 400 o o o

27 This is ry o o o 1180 o o 1229 h i For Polyon 400 o o o

28 This is ry o o o 1180 o o 1097 o h i For Polyon o o o o

29 This is ry o o o 1180 o o 1097 o 1108 o h i For Polyon o o o o o

30 This is ry oh o o 1180 o o 1097 o 1108 oh 1132 o 1132 o o o o o oh h For Polyon 400

31 This is ry oi o o 1180 o o 1097 o 1108 oh 1132 oi 1168 o h i For Polyon o o o o o oh oi

32 A B C D E F G H I This is th ri tht you hv sin. Th or polyon is rphil tool tht llows you to in th ors in strutur, n to in simultnously th pproprit orm or th strutur o o 1180 o o 1097 o 1108 oh 1132 oi 1168 o h i For Polyon 400 Mximum or in rh o oi o o o o oh

33 A o 1168 B o 1132 C o 1108 D 1097 E 1098 F o 1113 G o 1141 H oi 1229 oh 1180 I Usin th sm mth tht w us to in th orm n ors or th rh, w n in th orm o suspnsion ri whos l n sly rry ivn mximum or. Th pol o th For Polyon lis to th riht o th l lin, rthr thn to th lt. Th ors in th l r tnsil, rthr thn omprssiv. Clik on th Contnts utton to in nw lsson. Clik on th im o th Shwnh Bri to rturn to th innin o this lsson. h i o o o o o oh oi o For Polyon 400