1、拱桥拱轴系数的优选# E# a2 K* Q1 e9 S, r& F* s5 X
在做拱桥时,一般基于无铰拱的恒载压力线即悬链线进行在恒载下的必选拱轴系数,参考相关文献,认为主要控制以下几点,可确定较为合理的拱轴系数:(1)拱顶预留一定的负弯矩(2)拱脚预留一定的正弯矩(3)跨径四分点的偏心距较小。为了实现这几个参数,必须在选定跨径、矢高后,进行不同的拱轴系数下的计算,计算出上述的3个关心参数。一般通过有限元软件实现。这就需要变更有限元单元节点的坐标,如何根据选定的跨径、矢高、拱轴系数的区间,输出不同拱轴系数下的各关键点的坐标,这是个需要解决的问题。& |' [4 g9 c3 R
2、主拱圈施工参数的计算
# P& y1 ^9 ` L5 Y9 ]在施工图阶段,选定了拱桥的跨径、矢高、拱轴系数、拱圈高度(在此认为等高),需要输出不同关键节点的拱轴坐标、对应拱圈上下点的坐标及其倾角余弦值。2 `( A2 a m3 C2 @8 g( Q
3、程序实现
4 [6 x8 c- h6 @) c3 b ]为了实现上面两个问题的快速求解,编制小程序。程序的功能是(1)计算不同拱轴系数下的拱轴关键点坐标,方便更新有限元中节点坐标,可快速求解关心的参数,方便拱轴系数的必选(2)选定拱轴系数后,可输出拱圈的施工图数据。程序的代码如下:
8 S# n3 w; s1 y }( Kprogram gzzb, t" c9 v: X$ U! H
implicit none
$ x) Q3 [8 ?" B$ o q j& I3 hinteger i,j,k,n,nm,count,kc0 q. Y) p" e% `4 G, m+ M. L
real l,f,ms,me,detm,x,kk,cosi,m,y0,y1,y2,h,w,cosb
4 R& ?* A, B7 b& w \real,allocatable:: y(:),mi(:)
! N! I/ m) G. i: p. L! Mcharacter*24 fname,dat,out
4 a- h2 ^- S" h4 f! ~+ S; n* K1 Cread(*,'(a\)')fname
5 ^8 j5 m+ W( L" {8 M+ Wk=len_trim(fname) b% [9 m7 A8 h$ R& B3 a4 R' u( p
dat=fname(1:k)//'.txt'4 I5 g N+ x, {. M7 u
out=fname(1:k)//'.out'
, B" ]/ B) @' V, r% E8 iopen(10,file=dat,status='old')( P+ \1 T% g+ S# T& n
read(10,*)kc
; v5 G9 R% Q1 H; ~if(kc==1)then !进行拱轴系数优选,计算不同拱轴系数下的拱轴坐标# \: ?2 U5 p0 o' [
read(10,*)n,l,f,ms,me,detm7 b& P5 Q4 g2 ?! y! {
else$ M8 C# F' `0 q" o# q% D/ r
read(10,*)n,l,f,m,h) j3 z- W& V+ v5 j
endif+ ?* y9 z% j1 @4 T
close(10): D7 Y" J5 l+ M
open(11,file=out)
9 w1 A, i8 p8 Q1 h4 g6 }7 Eif(kc==1)then$ P# L. G( I7 C% V
write(11,'(12x,a)')'不同拱轴系数下拱轴线坐标计算程序') [2 [# z! j, H4 p7 o0 |6 i
else
+ [4 x4 V5 u1 {0 i1 Kwrite(11,'(12x,a)')'等截面拱圈坐标输出程序(可作施工图数据)'
+ \) [2 \, Q/ Q- Uendif8 j3 S, _9 S% Z
write(11,'(a)')'If you have any problem, you can contact with me! E_mail:yzbuilder@163.com'& i& C8 l/ f0 ?" |
if(kc==1)then !不同拱轴系数下拱轴坐标的计算8 G4 Y) @. F2 @3 y1 v9 [- l: w
nm=int((me-ms)/detm)+1
; x$ b W/ Q$ A+ \2 jallocate(y(nm+1),mi(nm+1))
z7 @% F; `0 I- v2 ^) ddo i=1,nm+18 x6 V% Q" A% z. |9 d5 b
mi(i)=ms+(i-1)*detm3 o1 |- I3 k: ]7 h' w
enddo
- O8 J* z5 M0 V, M* e7 c5 Lwrite(11,'(a8,1x,a8,1x,100(f7.3,1x))')'SEC NO.','X cor',(mi(i),i=1,nm+1)/ e9 g2 ]4 m8 s* j8 z+ B. W
do i=0,n/2,1 !section number3 F1 b# _) L/ f+ K. I
cosi=i*(l/n)/(0.5*l)
8 Y$ A; Y' `+ Q( f! Cdo j=1,nm+1,1
J6 G; U) I$ M3 p2 f% Lm=ms+(j-1)*detm
* ~7 A1 x7 h- Z) k5 zkk=log(m+sqrt(m**2-1))
0 T2 N! |% Q5 m( t+ X g( uy(j)=1-(cosh(kk*(1-cosi))-1)/(m-1)! G4 U( T* ^' \" T, t
y(j)=y(j)*f
5 @' s8 x' Q/ R0 ? D' Yenddo
/ l2 A2 ?+ T' f5 ^6 Awrite(11,'(i8,1x,f8.3,1x,100(f7.3,1x))')i,i*l/n,(y(k),k=1,nm+1)
8 S% ?" O. K: l3 [+ X! ?# }enddo# x+ A' C& N/ D# `8 @2 Q
count=0
; c- A7 s! l; M- g+ odo i=n/2-1,0,-1' F3 y1 M7 k6 v `
count=count+1
3 C* R8 G2 u1 Ccosi=i*(l/n)/(0.5*l)
+ C/ m# z* ?1 g cdo j=1,nm+1,1
; \; o2 r" U6 x8 x, b$ m Mm=ms+(j-1)*detm( `5 W7 O6 B8 _4 Z9 W- m
kk=log(m+sqrt(m**2-1))( Q) X; K U! M1 g; K9 x) S0 L
y(j)=1-(cosh(kk*(1-cosi))-1)/(m-1)* y8 h1 B% M( N& a) p8 ?+ ~5 h
y(j)=y(j)*f- o5 k9 y# a: I/ R0 a1 z
enddo* Q/ ^2 ?( k4 N( Y9 i
write(11,'(i8,1x,f8.3,1x,100(f7.3,1x))')i+2*count,l/2+count*l/n,(y(k),k=1,nm+1)
6 u" U( t, R w5 [6 P5 q; Tenddo
) c! m2 d& B+ q( @1 H2 oelse !选定拱轴系数后,计算拱轴坐标及拱圈上下点的坐标,方便施工图相关数据的输出
- U3 J! H" s8 N2 y1 `. e9 z write(11,'(a8,1x,a8,1x,4(a7,1x))')'SEC NO.','X cor','y0','y1','y2','cosB'2 z' _& h0 t, B- q9 _/ \5 u: u* {* w
do i=0,n/2,1 !section number
' t$ J6 ^6 a& R% q% jcosi=i*(l/n)/(0.5*l)# X7 w0 \+ j. k+ P( x% l8 i- ^8 b2 |: C
kk=log(m+sqrt(m**2-1))$ ~* J$ ?8 w/ t* K6 t
y0=1-(cosh(kk*(1-cosi))-1)/(m-1)
) [ t; s" A; B+ @# a% I2 Qy0=y0*f
4 w- P/ h: w! k6 h! Cw=f*kk/(0.5*l*(m-1))*sinh(kk*(1-cosi))
5 J' D9 Y) f' m; Z0 I5 _cosb=1/sqrt(w**2+1), L; S4 z5 L0 x$ l
y1=y0+h/2/cosb% {3 e1 ~5 x2 Y* l5 t/ v
y2=y0-h/2/cosb
) W1 j0 [2 c5 U9 _0 uwrite(11,'(i8,1x,f8.3,1x,4(f7.4,1x))')i,i*l/n,y0,y1,y2,cosB- A z. @( }7 h
enddo# @% v3 @2 u) C
count=00 u( Z9 d, L) G; z
do i=n/2-1,0,-1% b2 E" r+ x3 O% e
count=count+1
) H7 |: R* d8 ^cosi=i*(l/n)/(0.5*l)
7 }/ u. u$ {1 j3 |9 S8 f, rkk=log(m+sqrt(m**2-1))6 o+ h9 N$ `5 x4 c9 H7 l4 S
y0=1-(cosh(kk*(1-cosi))-1)/(m-1)
/ |3 ~0 v% F& t) _y0=y0*f
6 _" v2 Y3 m: i7 [4 Pw=f*kk/(0.5*l*(m-1))*sinh(kk*(1-cosi))
& y' {' j- N" e9 O+ r+ A" ycosb=1/sqrt(w**2+1)3 d6 c) j' K& W6 U2 }) M" ~
y1=y0+h/2/cosb
: M3 R4 k, R6 Xy2=y0-h/2/cosb
: Y' y/ l! ?/ F" M+ w" l( S0 Xwrite(11,'(i8,1x,f8.3,1x,4(f7.4,1x))')i+2*count,l/2+count*l/n,y0,y1,y2,cosB
/ L3 }, F$ s& @' k0 \9 T6 ? Denddo
5 e- F5 q0 g, b" X+ E6 ~" [2 z; s/ mendif; `+ M" @' i! O' \4 y
end program gzzb; o+ G2 S J e! c* f
4、实例计算
) W/ C" O9 E: j+ Z U8 ?(1)不同拱轴系数下的拱轴坐标的输出+ C; p7 y' H# I- d) m9 t/ j: o
某钢筋混凝土拱桥,计算跨径为140m,矢高17.5m。试进行拱轴系数介于1.5和2.3之间的拱轴坐标的计算,沿拱桥跨径方向等分48等份。
3 h5 v9 o+ Y. Z6 Q6 T9 N4 t数据文件gq.txt的文件内容如下:$ q9 ^3 `- @/ ]/ ~. a( c. w4 u5 d
19 T$ f7 z3 n; `6 S4 y8 L* }. Y
48,140,17.5,2.0,2.3,0.05
% H1 k e4 [& x; J& U运行程序后结果文件内容如下:
, D: I9 l5 h( T* F E" a" C, z不同拱轴系数下拱轴线坐标计算程序
" W0 B6 ?) X- T: TIf you have any problem, you can contact with me! E_mail:yzbuilder@163.com! f9 ?: h0 N L- v3 h4 v2 `
SEC NO. X cor 2.000 2.050 2.100 2.150 2.200 2.250 2.300
: Y5 {9 f7 T# N 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000! f- m8 o! c# y& ]- f
1 2.917 1.611 1.619 1.627 1.634 1.642 1.649 1.656# l5 g6 J" [) m) o! W! I: }
2 5.833 3.122 3.136 3.149 3.163 3.176 3.189 3.202/ s1 N' Y6 {$ L% U$ } j+ Z/ c6 E
3 8.750 4.537 4.555 4.573 4.591 4.608 4.625 4.642; l1 E3 _3 v( s0 ]9 E; s
4 11.667 5.860 5.881 5.902 5.923 5.944 5.964 5.983
% M+ G3 {; ~0 q' x4 J7 g1 @ 5 14.583 7.095 7.119 7.142 7.164 7.187 7.209 7.230
" ?; U$ n' |9 N 6 17.500 8.247 8.271 8.295 8.319 8.342 8.365 8.387
; l$ |6 l' \8 m+ V 7 20.417 9.317 9.342 9.366 9.390 9.413 9.436 9.459
2 y6 Z; \: Q B9 [2 e; J 8 23.333 10.311 10.335 10.358 10.382 10.405 10.427 10.450
* }5 M* w- p$ g. b" k& ^: F) E0 e 9 26.250 11.230 11.253 11.275 11.298 11.320 11.341 11.363, [+ c9 `: W2 i* n( H! l3 d8 E
10 29.167 12.077 12.099 12.120 12.141 12.161 12.182 12.202
9 T7 \+ m( v/ L- J5 m 11 32.083 12.855 12.875 12.895 12.914 12.933 12.951 12.970
. T' ?6 l5 P& n, D& T 12 35.000 13.567 13.585 13.602 13.620 13.637 13.653 13.670
* f2 r/ b$ D+ G$ I3 j 13 37.917 14.214 14.230 14.245 14.261 14.275 14.290 14.305- S% {7 X3 ]& ]4 C- M
14 40.833 14.799 14.812 14.825 14.839 14.851 14.864 14.877
! N( Z' f9 e& w! A/ u 15 43.750 15.322 15.334 15.345 15.356 15.367 15.377 15.388
T2 I c; e% o 16 46.667 15.787 15.796 15.805 15.814 15.823 15.831 15.840
& R) V( h" i1 K) O 17 49.583 16.193 16.200 16.207 16.215 16.221 16.228 16.235
/ H" r: N5 H$ U8 m 18 52.500 16.543 16.548 16.554 16.559 16.564 16.569 16.574
/ u3 F" f s0 m- e' z3 k 19 55.417 16.837 16.841 16.845 16.849 16.852 16.856 16.859$ Q6 @4 z9 G; m) i
20 58.333 17.077 17.079 17.082 17.084 17.087 17.089 17.091
9 [6 Y/ y x' r% V2 b 21 61.250 17.262 17.264 17.265 17.267 17.268 17.269 17.271
& q7 t& y1 l0 ]- S2 _- X+ S. ] 22 64.167 17.395 17.395 17.396 17.396 17.397 17.398 17.398) u9 A2 H% C# s* C5 }1 c
23 67.083 17.474 17.474 17.474 17.474 17.474 17.474 17.475$ `# r, O! F, h6 t
24 70.000 17.500 17.500 17.500 17.500 17.500 17.500 17.500$ R7 V: J8 Z i: W, ~8 C
25 72.917 17.474 17.474 17.474 17.474 17.474 17.474 17.475
+ M( l' d6 {. B K 26 75.833 17.395 17.395 17.396 17.396 17.397 17.398 17.398
7 X7 Z: @& d6 E$ @. w2 } 27 78.750 17.262 17.264 17.265 17.267 17.268 17.269 17.271
& d" l( z& ^- Q0 u2 ` 28 81.667 17.077 17.079 17.082 17.084 17.087 17.089 17.091
; p& P$ E) E7 A' O* K 29 84.583 16.837 16.841 16.845 16.849 16.852 16.856 16.859. T# I6 y0 p/ B$ T8 h, n
30 87.500 16.543 16.548 16.554 16.559 16.564 16.569 16.574
/ a+ t% f1 H) n# I" W 31 90.417 16.193 16.200 16.207 16.215 16.221 16.228 16.235% e0 n" |$ |6 h; j& I+ L
32 93.333 15.787 15.796 15.805 15.814 15.823 15.831 15.840
) \8 c( `/ \+ h" Q! a0 a5 t8 _1 @ 33 96.250 15.322 15.334 15.345 15.356 15.367 15.377 15.388
- D" V! y2 V- d, o3 c+ P 34 99.167 14.799 14.812 14.825 14.839 14.851 14.864 14.8774 D, J1 }+ O! z. [
35 102.083 14.214 14.230 14.245 14.261 14.275 14.290 14.305 @* j# v6 u1 j5 d1 f+ J P4 ?' v
36 105.000 13.567 13.585 13.602 13.620 13.637 13.653 13.670
, U5 U& l7 G7 l; i) V 37 107.917 12.855 12.875 12.895 12.914 12.933 12.951 12.970" d: }6 a6 X" \% R
38 110.833 12.077 12.099 12.120 12.141 12.161 12.182 12.202' M$ C/ D2 I6 b& o( ~- O
39 113.750 11.230 11.253 11.275 11.298 11.320 11.341 11.363
7 {( b- \: z3 c0 x9 x7 S 40 116.667 10.311 10.335 10.358 10.382 10.405 10.427 10.450- {8 Z& _5 T$ m; \5 Y* @! g$ W
41 119.583 9.317 9.342 9.366 9.390 9.413 9.436 9.459
, ^! s# ^1 T! i* {. r) C$ p 42 122.500 8.247 8.271 8.295 8.319 8.342 8.365 8.387
' } N r! i5 _: Q& X2 d 43 125.417 7.095 7.119 7.142 7.164 7.187 7.209 7.2300 F Q- p8 S4 J$ K% ]4 z
44 128.333 5.860 5.881 5.902 5.923 5.944 5.964 5.983 s1 E( F4 W+ C; c( u5 H
45 131.250 4.537 4.555 4.573 4.591 4.608 4.625 4.642
4 K9 E. G4 l4 G3 E U( S. V1 E 46 134.167 3.122 3.136 3.149 3.163 3.176 3.189 3.202
" a3 N% o8 w$ x: P. ` 47 137.083 1.611 1.619 1.627 1.634 1.642 1.649 1.656
; m# s* ]$ k& r/ u1 V0 ^) ] 48 140.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0009 Z; O' v, O2 _! Y
2、选定拱轴系数后,拱轴坐标及拱圈上下点坐标,及余弦值/ R* g0 n& H# |! @7 X8 ]+ S- R
仍以上个例题为算例,选定拱轴系数为2.24,拱圈高度3m,沿跨径方向48等分。/ i. Q4 r+ p, c' l, z# j. }+ U6 c+ G; D
数据文件内容如下:! d# }* Z# T8 t# g& D4 M- `2 j
2% D+ s1 \: D2 i2 P
48,140,17.5,2.24,3
6 n; F% h( ?; e; {( M9 g运行程序后结果文件如下:, N0 y8 E% i4 ^% F9 b( N
等截面拱圈坐标输出程序(可作施工图数据)' A1 o2 R# b: h- B5 |& U3 {# Y
If you have any problem, you can contact with me! E_mail:yzbuilder@163.com
, N8 q. ]6 t' _+ |SEC NO. X cor y0 y1 y2 cosB2 v7 ^& A% a9 P: N A7 H: B
0 0.000 0.0000 1.7372 -1.7372 0.8635
* ?- v J- y4 {. H5 j7 R* { 1 2.917 1.6475 3.3565 -0.0614 0.8777/ F1 s/ C0 z2 b/ d- ~; _- W& Q# F" B9 J
2 5.833 3.1863 4.8699 1.5028 0.8910
5 [/ ~( d. |6 Z 3 8.750 4.6219 6.2827 2.9612 0.90324 h8 U3 v: l# P( c- Y( I
4 11.667 5.9596 7.5999 4.3194 0.9145
! |, |2 w6 F; s Y 5 14.583 7.2042 8.8261 5.5823 0.9248
9 Y' o9 f: |+ E# r2 P 6 17.500 8.3602 9.9657 6.7546 0.9343
' |, t& S- }! O9 [ 7 20.417 9.4318 11.0227 7.8409 0.9429
: Y4 o7 R5 V2 R- _- p7 D V 8 23.333 10.4229 12.0008 8.8450 0.9506
, K6 z) c4 U( S* n* N; u4 O 9 26.250 11.3371 12.9034 9.7707 0.9577
/ L9 R# o( J; `8 ] 10 29.167 12.1777 13.7338 10.6216 0.9640+ W/ I5 {7 C5 B9 F
11 32.083 12.9478 14.4948 11.4008 0.9696
! {8 M; N& E1 d. O! L: g 12 35.000 13.6501 15.1891 12.1111 0.9747
+ W7 V. B8 Y6 n) Q! f: j 13 37.917 14.2873 15.8192 12.7553 0.97910 p0 t7 v6 H. {* x9 w
14 40.833 14.8615 16.3874 13.3357 0.9831
* T# O! r+ g6 K 15 43.750 15.3750 16.8955 13.8545 0.9865. L6 o9 B0 ]/ ^# b, a/ G( X
16 46.667 15.8296 17.3455 14.3137 0.98956 D. T2 |7 O( b+ g* @
17 49.583 16.2268 17.7388 14.7149 0.9921
4 v0 r. \. b7 n 18 52.500 16.5683 18.0769 15.0596 0.9943
' [! H% ^" N: |& n* N' b 19 55.417 16.8551 18.3611 15.3492 0.9961. z' q& x( t! x5 _
20 58.333 17.0884 18.5922 15.5846 0.9975
5 s. b: Z: Y. I0 z" K 21 61.250 17.2690 18.7711 15.7669 0.9986$ x7 }( p/ r: }8 k7 {8 |5 S1 c
22 64.167 17.3975 18.8984 15.8965 0.99947 Q0 V5 `& M/ S7 w3 |) [1 d
23 67.083 17.4744 18.9746 15.9742 0.9998* D/ l$ r1 C, Z
24 70.000 17.5000 19.0000 16.0000 1.0000
4 c* }/ a: R& R$ r2 q6 J3 y 25 72.917 17.4744 18.9746 15.9742 0.9998+ G, j, R# j) j$ Z, s# x
26 75.833 17.3975 18.8984 15.8965 0.9994
" L" ?7 K% M6 _& F; z 27 78.750 17.2690 18.7711 15.7669 0.9986
0 k9 I# U0 P; s) d9 v d4 M 28 81.667 17.0884 18.5922 15.5846 0.9975
! r: I, i( ~+ ^- E$ U; M 29 84.583 16.8551 18.3611 15.3492 0.99619 Z$ v' ?2 P& p4 Z
30 87.500 16.5683 18.0769 15.0596 0.9943
! J) z9 A# j0 ]& l) T- Z1 l 31 90.417 16.2268 17.7388 14.7149 0.9921
8 ]" ?4 A3 p% P8 D 32 93.333 15.8296 17.3455 14.3137 0.9895
1 W. i' [6 g- q 33 96.250 15.3750 16.8955 13.8545 0.9865
' h, D( f" F0 X5 G; d" y 34 99.167 14.8615 16.3874 13.3357 0.9831
4 |4 U9 w& B# s4 v 35 102.083 14.2873 15.8192 12.7553 0.9791
% `. O8 [; z, H2 B3 P# q" [" l1 y 36 105.000 13.6501 15.1891 12.1111 0.9747
- B- B4 c k' n% t/ P8 t# f 37 107.917 12.9478 14.4948 11.4008 0.9696
' k9 Z, ~) Y! p! V& C 38 110.833 12.1777 13.7338 10.6216 0.9640
0 M; n& b3 w. t* n" h2 ] 39 113.750 11.3371 12.9034 9.7707 0.95777 @2 c# A- c! Q3 I0 Y
40 116.667 10.4229 12.0008 8.8450 0.9506* F7 P7 v" o4 u7 N
41 119.583 9.4318 11.0227 7.8409 0.94295 }9 J# S: ?9 S4 U
42 122.500 8.3602 9.9657 6.7546 0.93434 {+ N9 }/ ]( K4 }
43 125.417 7.2042 8.8261 5.5823 0.9248$ N+ C9 X8 R" _' L- S
44 128.333 5.9596 7.5999 4.3194 0.9145$ p4 e# O) y4 M" Q
45 131.250 4.6219 6.2827 2.9612 0.9032
. u# `* E4 {/ n. ] 46 134.167 3.1863 4.8699 1.5028 0.8910
7 c; A! l0 u7 x; Z 47 137.083 1.6475 3.3565 -0.0614 0.8777
; y4 X8 F% i+ m, i- q8 O( R 48 140.000 0.0000 1.7372 -1.7372 0.86352 {9 y( \" ~' O3 W( V: Y5 O! W
. N3 U% l. [6 }% i$ V) ^ |