1

TNH TON CC MM CHU LC NGANG C XT NH HNG CA LC DC TRC BNG PHNG PHP MA TRN CHUYN TIPTs. Phan Dng

1. Gii thiu1.1 Trong tnh ton mng cc, cc chu lc ngang l mt bi ton va mang tnh l thuyt c bn va mang tnh thc hnh thc t. Nhng nt chnh pht trin cc nghin cu v bi ton un ngang-dc ca cc c th xem trong [2] v [4]. 1.2 i tng ca bi vit ny s l cc cc mm chu tc dng ca t hp ti trng (thng ng, nm ngang v momen) ng trong nn bin dng n hi cc b nhiu lp (xem hnh 1a). Bi ton nh th c th c gii theo hai s : 1. S dm - gi: tng tc gia cc nn khi chu lc ngang c ri rc ha vi nn bi cc gi chng chuyn v ngang v chng chuyn v xoay t ti trung im ca mi on cc. Bng cch nh th, cc chu lc ngang trong nn n hi c chuyn v dm lin tc nhiu nhp trn cc gi n hi nh hnh 1b. S dm - nn: tng tc gia cc nn khi chu lc ngang vn gi c tnh lin tc nhng trong mi on cc, gi tr c trng cho h s nn l mt hng s. Bng cch nh th, cc chu lc ngang trong nn n hi l mt dm trn nn n hi vi h s nn c dng bc nh hnh 1c.

2.

Trong qu trnh tnh ton, cn phn bit cc tham s c trng cho s tng tc gia cc nn sau y: H s t l ca h s nn, k (kN/m4); H s phn lc nn, kz (kN/m3); M un phn lc nn, Esz (kN/m2); H s cng chng chuyn v ngang ca gi n hi, Cnz (kN/m); H s cng chng chuyn v xoay ca gi n hi, Cqz (kNm/rad.).

1.3 Cc chu un ngang-dc theo s dm -gi c nghin cu k trong [2] i vi nn bin dng tuyn tnh cng nh lm vic trong giai on n hi do nh thut ton ma trn chuyn tip (MTCT). Bi ton un ngang dc ca cc theo s dm nn c gii bng phng php phn t hu hn (PTHH) [5] [6].

2 Bi bo ny gii thiu kt qu ca vic ng dng phng php MTCT kho st cc bi ton c bn ca cc chu lc ngang c xt nh hng ca lc ng theo s dm nn.

Es1 Es2 Es3 Es4 Es5Hnh 1: Cc s tnh ton ca cc chu lc ngang. a. S cc t chu t hp ti trng; b. S dm gi; c. S dm-nn.

2. Ni dung c bn2.1 Ni dung c bn ca phng php MTCT i vi s dm nn [1]: 1. Cc ma trn c bn. Xt mt nhp dm th i, bi ton ny ta lm quen vi ma trn ct biu th trng thi chuyn v ni lc ti tit din bt k ca dm, gi tt l vect trng thi. Ti hai tit din u mt thanh th i l 0 v 1, vec t ny c dng:

0i = {u y 0i

x 0i

M x 0i

Q y 0 u 1}

(1) (2)

1i = {u y 0i

x1i

M x1i

Q y1u 1}

Trong mt nhp dm, quan h gia hai vec t trng thi nu trn c xc nh bng biu thc sau:1i = L i 0i

(3)

y, L i l ma trn chuyn nhp, thc hin php bin i tuyn tnh vec t trng thi 0i thnh vec t trng thi 1i .

3 ng thc (3) v thc cht l cng thc ca phng php thng s ban u trong mn Sc bn vt liu c vit di dng ma trn. 2. Xc nh cc thng n s ban u: T (1) ta thy bi ton cc chu lc ngang c 04 thng s ban u. Ph thuc vo iu kin lin kt ti u cc (tit din O), thng c 02 thng s cha bit c gi l thng n s. Vn ct li ca gii thut MTCT l xc nh gi tr cc thng n s ny. Cch lm nh sau. Tm ma trn tch nh hng tng th Wn : Nu p dng (3) vo s hnh 1c vi n nhp th nhn c: 1n = L n L n 1 ...L i L i 1 ...L 2 L 1 01 = Wn 01

(4) (5)

Vi:

Wn = L n L n 1 ...L i L i 1 ...L 2 L 1

Ma trn Wn c cp ging ma trn L i Theo iu kin lin kt chn cc C, lp ma trn tuyn iu kin T1 v tnh:* Wn = T1Wn

(6)

Theo iu kin lin kt ti u cc, lp ma trn tuyn cc thng n s T2 v tm ma trn cha cc phn t l h s ca phng trnh xc nh cc thng n s:* K = Wn T2

(7)

Theo cc thng s bit ti u cc, lp ma trn tuyn cc s hng t do ng vi ma trn K, k hiu T3 v tm ma trn ct cha cc s hng t do:* W0 = Wn T3 01

(8)

Trong : 01 l ma trn ct cha cc thng s ban u bit ti u cc. Tm ma trn ct cha cc thng n s ban u cn bit:01 = K 1W0

(9)

Sau khi c kt qu t (9), b sung cc gi tr tm c vo (1) xc nh vec t trng thi ban u 0i ca ton h. 2.2 Cc ma trn chuyn nhp 1. i vi phn cc thuc chiu cao t do: Trng hp un ngang:

4 1 h i 0 1 Li = 0 0 0 0 0 0 h i2 2EI hi EI 1 0 0 h3 i u* y 3EI h i2 * x 2EI h i M* x 1 Q* y 0 1

(10)

Trng hp un nn: sin hi 1 a cos a 0 Li = 0 Nh sin a i a 0 0 0 0 h i2 1 cos a EI a 2 h i sin a EI a cos a 0 0 h 3 a sin a i EI a 3 h i2 1 cos a EI a 2 sin a hi a 1 0 u* y * x * Mx * Qy 1

(11)

Trng hp un ko: sha 1 h i a cha 0 Li = 0 Nh sha i a 0 0 0 0 h i2 cha 1 h 3 sha a i u* y EI a 2 EI a 3 h i sha h i2 cha 1 * x EI a EI a 2 sha * cha hi Mx a * 0 1 Qy 0 0 1

(12)

Trong : ct cui ca cc ma trn cha cc phn t chuyn v ni lc do ti trng ngoi gy ra; hi: chiu di nhp th i;a N = h i EI 0,5

;

2. i vi phn cc nm trong t: Dng chung ca ma trn chuyn nhp nh sau:

5 L 11 L 21 L i = L 31 L 41 0 L 12 L 22 L 32 L 42 0 L 13 L 23 L 33 L 43 0 L 14 L 24 L 34 L 44 0 u* y * x M* x * Qx 1

(14)

T kt qu trong [3] ta c cc cng thc c th sau y: Trng hp un ngang:L11 = L 22 = L 33 = L 44 = f 1 1 (f 2 + f 3 ) 2 1 L13 = L 24 = 2 f 4 2 EI 1 L14 = 3 (f 3 f 2 ) 4 EI 1 L 23 = (f 2 + f 3 ) 2EI L12 = L 31 = 2 2 EIf 4 L 32 = EI(f 2 f 3 ) L 34 = 1 (f 2 + f 3 ) 2

L 41 = 2 3 EI(f 2 + f 3 ) L 42 = 2 2 EIf 4 L 43 = (f 2 f 3 )

Trong :E = si 4 EI 0 , 25

(15)

(16)

ESi : modun phn lc nn c th nguyn kN / m 2 .

f 1 = chh i cos h i f 2 = shh i cos h i f 3 = chh i sin h i f 4 = shh i sin h i

(17)

6 Trng hp un nn: f3 f2 1 L 12 = L 34 = + 2 a b L 13 = L 24 = 3 f 4 f3 f2 L 14 = 4 b a 2 2 2 2 a +b a +b L 21 = L 43 = f2 f3 2a 2b 2 2 b a L 22 = L 33 = f 1 + f4 2ab L 23 = 3 (af 2 + bf 3 ) (a 2 + b 2 ) 2 L 31 = L 41 = EIf 4 2ab b 2 3a 2 a 2 3b 2 L 32 = f3 f 2 EI 2a 2b 2 2 2 2 2 2 2 2 L 41 = b(b 3a ) + a (a 3b )1 f 2 + a (a 3b ) b(b 3a )1 f 3 EI + 2 2 2 2 a +b a +b f2 + N f3 2b 2a Trong cng thc ny: L 11 = L 44 = f 1 1 f 4

(18)

{[

] [

] }

E 0,5 N a = si + 4EI 4EI E 0,5 N b = si 4EI 4EI 1 = b2 a 2 2ab

0,5

(19)

0,5

(20) (21) (22)

3 =4 =

1 2abEI1 2(a + b 2 )EI2

(23)

f1 = chbh i cos ah i f 2 = shbh i cos ah i f3 = chbh i sin ah i f 4 = shbh i sin ah i

(24)

7 Trng hp un ko: f2 f3 L 12 = L 34 = 0,5 + b a L 13 = L 24 = 3 f 4 f3 f2 L 14 = 4 b a 2 2 2 2 a +b a +b L 21 = L 43 = f2 f3 2a 2b 2 2 a b L 22 = L 33 = f 1 + f4 2ab L 23 = 3 (bf 2 + af 3 ) (a 2 + b 2 ) 2 L 31 = L 42 = EIf 4 2ab a 2 3b 2 b 2 3a 2 L 32 = f3 f 2 EI 2b 2a 2 2 2 2 2 2 2 2 L 41 = a (a 3b ) + b(b 3a ) 6 f 2 + b(b 3a ) a (a 3b ) 6 f 3 EI + 2 2 2 2 a +b a +b f2 f3 + N 2a 2b L 11 = L 44 = f 1 6 f 4

(25)

{[

] [

] }

Trong trng hp ny, cc h s: a, b, 3 v 4 ging nh un nn. Cc i lng cn li tnh nh sau:6 = a 2 b2 2ab f 1 = chah i cos bh i f 2 = shah i cos bh i f 3 = chah i sin bh i f 4 = shah i sin bh i

(26)

(27)

2.3

Li gii ca MTCT i vi ba bi ton cc mm chu lc ngang:

Da vo nhng ni dung c bn v cc ma trn chuyn nhp trnh by trn gii ba bi ton sau y: 1. Bi ton th nht: xc nh trng thi chuyn v ni lc ca cc chu lc ngang c xt nh hng ca lc dc trc. ngha: Ti mt tit din bt k z, trng thi chuyn v ni lc bao gm: chuyn v ngang yz, chuyn v xoay Z , momen un Mz, lc ct Qz, v phn lc t pz. Nhng i lng ny c dng kim tra cc trng thi gii hn ca cc.

8 iu kin tnh: Lin kt u cc: t do. T hp ti trng u cc: lc ngang Q, momen M v lc dc N (nn hoc ko). Lin kt chn cc: ty thuc iu kin thit k. Ma trn tuyn iu kin T1 c cu trc ph thuc vo iu kin lin kt chn cc. Ma trn tuyn n T2 ph thuc vo iu kin lin kt u cc: t do, c cu trc: 1 0 0 1 (28) T2 = 0 0 0 0 0 0 Ma trn tuyn cc s hng t do T3 ph thuc hai thng s bit u cc l M v Q, c cu trc: 0 0 0 0 (29) T3 = 1 0 0 1 0 0

Cc ma trn:

2. Bi ton th hai: Xc nh cng chng chuyn v ngang v chuyn v xoay ca u cc c xt nh hng ca lc dc trc. ngha: cng chng chuyn v ngang v chuyn v xoay l cc phn lc momen v lc ct xut hin trong lin kt ngm ti u cc khi chu chuyn v cng bc n v. Nhng i lng ny l tham s u vo tnh ton mng cc theo s khung vi tr cc trong t. iu kin tnh Lin kt u cc: ngm cng. T hp ti trng u cc: lc dc N (nn hoc ko). Lin kt chn cc: ty thuc iu kin thit k. Ma trn tuyn iu kin T1: ging bi ton th nht. Ma trn tuyn n T2

Cc ma trn tuyn:

90 0 T2 = 1 0 0 0 0 0 1 0

(30)

Ma trn tuyn cc s hng t do T3: 1 0 0 1 T3 = 0 0 0 0 0 0

(31)

3. Bi ton th ba: Xc nh chiu di tng ng ca cc khi chu lc ngang, cn gi l chiu di tnh ton chu un ca cc hay l chiu di chu un ca cc c xt nh hng ca lc dc trc. ngha: Chiu di chu un ca cc l chiu di mt thanh tng ng hai u ngm cng c cng chng chuyn v ngang (nu bi ton th hai) bng ca cc thc. i lng ny l tham s u vo tnh mng cc theo s khung c tr tng ng. iu kin tnh: Lin kt u cc: ngm trt T hp ti trng u cc: lc ngang v dc trc N (nn hoc ko). Lin kt chn cc: ty thuc iu kin thit k.

Cc ma trn tuyn:

Ma trn iu kin T1: ging bi ton th nht. Ma trn tuyn n T2: 1 0 T2 = 0 0 0 0 0 1 0 0

(32)

Ma trn tuyn cc s hng t do T3: 0 0 1 0 T3 = 0 0 0 1 0 0

(33)

10 Ghi ch: bo m kt qu chnh xc, chiu di on cc trong t phi tha mn iu kin ca Babanov v Perov [6].

3. V d:3.1 V d 1: Kho st nh hng ca lc dc trc N n chuyn v-ni lc ca cc chu lc ngang. u bi Cho mt cc ng thp ng trong nn t st ng nht vi cc s liu xut pht nh trn hnh 2a. Yu cu xc nh chuyn v ni lc trong cc chu lc ngang vi ba trng hp: un ngang di tc dng ca Q= 50kN v M=50kNm, un-nn: thm lc nn dc trc N=1000kN v un ko: thm lc ko dc trc N=1000kN.

z

Hnh 2: Cc s tnh ton ca v d 1. a. S liu cho trc ca v d; b. Phn chia cc thnh nhiu on vi biu mo un phn lc nn; c. S dm-nn tnh cc chu lc ngang. Gii 1. S dm nn: Trong trng hp chung, t kch thc cc v biu phn b h s nn theo chiu su cho (H.2a) ta tm c biu phn b m un phn lc nn tng ng (H.2b). Nu chia phn cc ngp trong t thnh nhiu on nh th s xc nh c gi tr E SZ ti hai u mi on. Hnh 2c m t s dm nn ca v d cho vi

11E Si l gi tr trung bnh cng ca E SZ trong mi on. Cch chia on nh th s

c nh gi mc chnh xc theo iu kin (30) trong [6] nh bng 1. Bng 1: Kt qu kim tra iu kin (30) trong [6]. S th t phn t2 3 4 5 6 7 8 9hi E si

i (m 1 ) 0.259 0.366 0.435 0.481 0.517 0.557 0.605 0.64

(m)1.2 2.4 2.4 2.4 24 4.2 6 3

(kPa)5766 23064 46128 69192 92256 123616 179980 216225

h i

nh gi Tha Tha Tha Tha Tha Khng tha Khng tha Khng tha

0.31 0.878 1.044 1.155 1.241 2.337 3.631 1.92

2. Trng hp un ngang (ch trnh by ma trn kt qu): Cc ma trn chuyn nhp1 14,8 0,00034 0,00168 0 0 1 0,00005 0,00034 0 L1 = 0 0 1 14,8 0 0 0 0 1 0 0 0 1 0 0 2.35256 0.00000887 0.00000713 0.90124 0.16437 0.90124 0.0000073 0.0000089 65986.552 52989.339 L2 = 0.90124 2.35256 0.90124 54259.525 65986.552 0.16437 0 0 0 0 1.19963 0.00000223 0.00000089 0.99845 0.00515 0.99845 0.0000037 0.0000022 4151.092 1660.535 L3 = 0.99845 1.19963 0.99845 6917.061 4151.092 0.00515 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

2.30520 0.00000882 0.00000711 0.80275 0.32782 0.80275 0.0000072 0.0000088 131098.394 105678.622 L4 = 0.80275 2.30520 0.80275 106334.335 131098.394 0.32782 0 0 0 0

122.25791 0.00000879 0.00000709 0.70455 0.49033 0.70455 0.0000070 0.0000088 195336.762 158068.120 L5 = 0.70455 2.25791 0.70455 156229.583 195336.762 0.49033 0 0 0 0 2.21070 0.00000870 0.00000707 0.60662 0.65191 0.60662 0.0000069 0.0000087 258702.894 210158.104 L6 = 0.60662 2.21070 0.60662 203950.419 258702.894 0.65191 0 0 0 0 0 0 0 0 1 0 0 0 0 1

0.17642 0.00001848 0.00003293 0 3.63433 4.08221 3.63433 0.0000005 0.0000185 0 738551.977 1315987.500 3.63433 L7 = 0.17642 0 3.63433 0 21871.020 738551.977 4.08221 0 0 0 0 1 21.09484 0.00003757 0.00002717 0 16.67252 4.69954 16.67252 0.0000654 0.0000376 0 2094913.772 1514994.807 16.67252 L8 = 21.09484 0 4.69954 16.67252 0 3648985.736 2094913.772 0 0 0 0 1 1.66609 0.00001188 0.00001306 0 1.19085 2.82442 1.19085 0.0000052 0.0000119 0 827749.631 910511.116 1.19085 L9 = 1.66609 0 1.19085 0 360250.270 827749.631 2.82442 0 0 0 0 1 673653.6804 17.2142244 92.89576767 40459.45311 33873.40471 622967.5525 17.7272925 107.8820448 3267369280 Wn = 78673148905 2754607.455 19893471.77 4725091697 63115362308 1135765.885 2905918.644 0 0 0 0

0 0 0 0 1

Bn phn t u ca ct cui cng tt c cc ma trn ny u bng khng do khng c ti trng ngoi tc ng trn nhp. V chn cc lin kt t do nn ma trn tuyn iu kin T1 c dng:0 0 1 0 0 T1 = 0 0 0 1 0 7867314890 2754607.455 19893471.77 0 3267369280 * Wn = T1 Wn = 4725091697 6311536230 1135765.885 2905918.644 0 78673148905 3267369280 * K = Wn T2 = 4725091697 62115362308 1132403961.250 * Q = Wn T3 = 4041684.529

13 0.33576 X = K 1Q = 0.02834

Vec t trng thi ti cc tit din c chia: 01 = {0.33576 0.02834 50 50 1} 02 = L1 01 = {0.01714 0.00906 790 50 1} 03 = L 2 02 = {0.00806 0.00608 792.6443 35.120 1} 04 = L 3 03 = { 0.00025 0.00133 422.0203 198.1350 1} 05 = L 4 04 = { 0.00096 0.00029 55.7750 96.0994 1} 06 = L 5 05 = { 0.00022 0.00022 35.8538 1.3136 1} 07 = L 6 06 = {3.0454E 05 2.064E 05 13.5046 10.9109 1} 08 = L 7 07 = {2.6794E 06 5.08462E 0 1.3513 0.4349 1} 09 = L 8 08 = {4.66648E 09 9.43176E 08 0.03915 0.02588 1}

Trng hp un ngang-dc: Cch tnh cc chu un-nn, un-ko cng ging nh i vi un ngang. Mt s kt qu chnh yu v chuyn v-ni lc khi cc chu un ngang dc ghi bng 2 v c v thnh cc biu trn hnh 3. Nhng con s t v d ny cho thy rt r nh hng ca lc dc trc n trng thi chuyn v-ni lc ca cc nh nu trong [2], [5] v [6]. Bng 2: Chuyn v-ni lc khi cc chu un Trng hp chu un Chuyn v ni lc v v Un ko Ung ngang Un-nn tr xut hin N=1000Kn N=0kN N=1000kN u y (m) 0.23869 0.33576 0.56702 u cc x (rad) -0.01999 -0.02834 -0.04832 u y (m) 0.0128 0.0174 0.02723 Mt t x (rad) -0.00664 -0.00906 -0.01772M z (kNm) p z (kN / m 2 )

Mt t Z=-1,2m Z=-1,2m Z=-6,0m

564.11 574.44 45.458 -26.04

790 792.64 59.966 -35.712

1329.79 1313.8 93.372 -59.892

3.2

V d 2: Kho st nh hng ca lc dc trc N n cng chng chuyn v ngang ca u cc: u bi

14 S dng li s liu v cc v t nn cho trn hnh 2 xc nh gi tr cc cng chng chuyn v ngang ca u cc c xt n lc dc trc cc N theo nguyn l nu trong [7]. Gi tr ca lc dc trc N khng vt qu sc chu ti nn cho php Pan = 3000kN v sc chu ti ko cho php Pak = 1300kN .a) b)

c)

d)

Hnh 3: Biu chuyn v ni lc ca cc chu lc ngang c xt nh hng lc dc. a_ Chuyn v ngang; b_ Phn lc nn*; c_ Momen un; d_ Lc ct. : un ko, : un ngang, : un ko.

*: gi tr th tng 1,55 ln.

15

Hnh 4: S xc nh cng chng chuyn v u cc c xt nh hng lc dc trc.

a. S dm nn; b. S xc nh Mu v Qu; c. S xc nh M v Q. Gii 1. Hnh 4 m t s dm-nn gii bi ton th hai cng vi hai s nguyn tc xc nh mt b gm 04 phn lc trong lin kt ngm u cc do cc chuyn v cng bc n v gy ra di tc dng ca lc dc trc; tm tt nh sau: Khi u=1 v = 0 th thu c cc phn lc lin kt, k hiu: Mu v Qu (H.4b) Khi u=0 va = 1 th thu c cc phn lc lin kt, k hiu M v Q (H.4c). 2. kho st nh hng ca lc dc trc N n gi tr cc cng chng chuyn v u cc Mu, Qu, M v Q, ta chia ra ba trng hp chu un. Un ngang: N=0 Un-nn:lc dc trc N bin thin trong khong t 0 n 3000kN.

16 Un-ko: lc dc trc N bin thin trong khong t 0 n 1300kN.

Kt qu tnh ton ghi bng 3 v v nn th hnh 5: tt c cho thy, i vi cc chu lc ngang c xt, lc dc trc nh hng rt ng k n cng chng chuyn v u cc.Bng 3: Gi tr cc cng chng chuyn v u cc c xt nh hng ca lc dc trc N.N (kN) 0 200 400 600 800 Mu (kN.m/m) Ko Nn -5792.05 -5792.05 -5811.09 -5774.83 -5830.08 -5757.55 -5849.02 -5740.21 -5867.9 -5722.82 -5679.1 -5652.71 -5635.04 -5617.32 -5599.55 -5581.71 -5563.82 -5545.87 -5527.87 Qu (kN/m) Ko Nn

M (kN/rad)Ko 5811.03 Nn

Q (kN.m/rad)Ko Nn

637.769 637.769 5792.048 5792.048 -70390.2 -70390.2 650.738 625.114 676.65 5774.821 -70873.5 -69914.8 5757.53 -71354.3 -69436.8 663.698 612.444 5829.958

599.762 5848.832 5740.186 -71832.4 -68956.3

689.594 587.068 5867.651 5722.788 -72308.1 -68473.3 702.529 574.361 5886.417 5705.336 -72781.3 -67987.6 721.917 555.277 5914.465 5679.057 -73486.5 -67254.2 536.165 523.408 510.638 497.855 485.059 472.251 459.429 446.594 5652.654 5634.983 5617.257 5599.475 5581.637 5563.743 5545.792 5527.748 -66514.7 -66018.3 -65519.2 -65017.2 -64512.4 -64004.7 -63494.1 -62980.5

1000 -5886.72 -5705.37 1300 -5914.85 1600 1800 2000 2200 2400 2600 2800 3000

17 a)-5500 -5550 -5600

un nn-5650Mu (kNm/m)

-5700

un ngang: Mu = -5792.048 kNm/m-5750 -5800 -5850 -5900 -5950 0 500 1000 1500 N (kN) 2000 2500 3000 3500

un ko

b)750

un ko700

un ngang: Qu = 637.769 kN/m650

Qu (kN/ m)

600

550

un nn500

450

400 0 500 1000 1500 N (kN) 2000 2500 3000 3500

Hnh 5: th quan h gi tr cng chng chuyn v ngang u cc ph thuc vo lc dc trc N. a_ Phn lc momen un Mu; b_ Phn lc lc ct Qu.

18 3.3 V d 3: Kho st nh hng ca lc dc trc N n chiu di chu un ca cc: u bi Vn s dng s liu v cc v t nn cho hnh 2 tm gi tr ca chiu di chu un Lu v momen ngm M ng c xt nh hng ca lc dc trc N theo nguyn l nu trong [7]. Gii 1. Hnh 6 m t s dm nn gii bi ton th ba cng vi s nguyn tc xc nh chuyn v ngang ca u cc lin kt ngm trt di tc dng ca lc ngang Q = 50kN c xt nh hng ca lc dc trc N.

Hnh 6: S xc nh chiu di chu un c xt nh hng lc dc trc. a. S dm-nn, b. S xc nh chiu di chu un v momen ngm. 2. Cch kho st nh hng ca lc dc trc n gi tr ca chiu di chu un Lu v momen ngm M ng cng ging nh bi ton th hai. Kt qu tnh ton thu c ghi bng 4 v v nn cc th hnh 7 v 8. Cc con s t v d ny mt ln na cho thy, lc dc trc c nh hng ng k n Lu v M ng .

19 Bng 4: Gi tr ca Lu v M ng c xt nh hng ca lc dc trc N (kN) 0 200 400 600 800 1000 1200 1300 1400 1600 1800 2000 2200 2400 2600 2800 3000 Trng hp chu lc dc trc Nn Lu (m) 18.24 18.36 18.49 18.61 18.75 18.89 19.03 19.1 19.17 19.32 19.48 19.64 19.81 19.98 20.16 20.34 20.54M ng (kN.m)

Ko Lu (m) 18.24 18.12 18 17.88 17.77 17.66 17.55 17.5M ng (kN.m)

-454.09 -461.902 -470.047 -478.541 -487.407 -496.672 -506.362 -511.376 -516.507 -527.142 -538.303 -550.03 -562.367 -575.364 -589.075 -603.562 -618.892

-454.09 -446.5 -439.212 -432.204 -425.46 -418.966 -412.708 -409.663

2021

20.5

un nn20

Chiu di chu un Lu (m)

19.5

19

18.5

un ngang: Lu = 18.24 m

18

un ko

17.5

17 0 500 1000 1500 N (kN) 2000 2500 3000 3500

Hnh 7: th quan h gi tr chiu di chu un ph thuc vo lc dc trc N.-400

un ko un ngang: Mng = -454.09 kNm

-450

M men ngm M ng (kNm)

-500

un nn-550

-600

-650 0 500 1000 1500 N (kN) 2000 2500 3000 3500

Hnh 8: th quan h gi tr momen ngm ph thuc vo lc dc trc N ng vi Q = 50kN.

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4. Kt lun4.1 Bi ton cc chu un tng qut c gii bng phng php MTCT theo s dm nn ch yu da trn nhng ch dn v cc php ton ma trn trong cch s dng ma trn chuyn [1] v cc cng thc ma trn chuyn nhp ca cc phn t cc khng tip t [2] cng nh cc phn t tip t [3]. So snh vi mt s cch gii khc trong [2], [6] v SAP2000, kt qu tnh cc chu un ngang dc bng MTCT theo s dm nn l chnh xc v khi lng tnh ton t hn. 4.2 Da vo th mnh ny, thng qua v d c th, kho st nh hng ca lc dc trc n trng thi chuyn v ni lc ca cc chu lc ngang i vi ba bi ton c bn trong tnh ton thit k mng cc. Kt qu kho st cho php khng nh: trong nhiu trng hp, khi tnh cc v mng cc chu lc ngang khng th b qua nh hng ca lc dc trc. 4.3 Cc chu un ngang-dc c gii bng phng php MTCT theo s dm nn c th tm thy c nhiu ng dng nh: 1. Tnh cc n chu lc ngang phc tp hoc cc kt cu c th chuyn v s cc chu lc ngang trong nn bin dng n hi cc b phn lp. 2. Nu chn dng mt h s nn hp l gii thut ni trn cho php xt c tng tc n hi do phi tuyn gia cc v t. 3. Ba bi ton cc chu lc ngang c xt n nh hng ca lc dc trc s l c s xy dng cch tnh mng cc c xt n lc dc khi chu lc ngang.

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TI LIU THAM KHO[1] Lu Th Trnh, Lu Mc Lan: Cch s dng ngn ng ma trn trong l thuyt h thanh. Nh xut bn Xy dng, H Ni, 2007. [2] Phan Dng: Tnh ton cc mm chu lc ngang c xt nh hng ca ti trng ng bng phng php ma trn chuyn tip. Lun n Ph Tin S Khoa hc K thut, H Ni, 1984. [3] Phan Dng: Gii bi ton un ngang-dc ca dm trn nn n hi bng phng php ma trn chuyn tip. Cc bo co hi ngh kt cu xy dng ln th nht. Tp 4: Kt cu xy dng cng trnh giao thng, H Ni, 1985, tr.202-207. [4] Phan Dng: Tnh ton cc v mng cc trong xy dng giao thng. Nh xut bn Giao thng vn ti, H ni, 1987. [5] Phan Dng: Tnh cc mm chu un ngang-dc trong nn nhiu lp bng phng php phn t hu hn. Tp san: Kho st-Thit k, N0.2, 1986. Vin Thit k Giao thng Vn ti, B Giao thng vn ti, H Ni, tr33-41. [6] Phan Dng: Tnh ton cng trnh bn trn nn cc theo s khung c tr cc trong t bng phng php phn t hu hn. Tp ch Khoa hc Cng ngh Giao thng Vn ti, No.2, 2008, Trng i hc Giao thng Vn ti Tp. H Ch Minh, tr.88-102. [7] Phan Dng: Chuyn v nm ngang v chuyn v xoay ca cc mc y i theo TCXD 205:1998-Mt dng khc ca cng thc tnh v cc ng dng. Tp ch Bin & B, No. 3+4/2009, Hi Cng ng thy-Thm lc a Vit Nam, tr.50-58.