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MC LC

I. MC CH.......................................................................................................................- 3 -

II. C S L THUYT.......................................................................................................- 3 -

1. Phng trnh tnh cng !"t #$ h%&! !"t '() ngh%*n.................................................- 3 -

+. Phng trnh ,%-! %/n 0n 2 3h4n 3h5% 6ch th7c 05% #7% h8t nh!)/n.................- 4 -

9. Cng !"t #$ h%&! !"t r4)..............................................................................................- 5 -

:. Phng trnh tr;n............................................................................................................- 5 -

III. TI< T=>

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2 1

2 1

1 119

i

p p

P P P WD D

= =

- OPi > l" nUng /ut. ]ng /ut nghin > tn vt liu t< H1$n H2

2 1

2 1

1 119 i

p p

P P P W TD D

= =

I#TK

1 2,

p pD D

l" #h th ^! ngu)n liu v" /&n hMm, mm

- N$u nghin #h thF D C nh(n vi

4

3

- ]ng /ut tiu th ho ng E ^! m+) nghin

_ o/P U I =

>'ong =V `V in th$, a

bV Ang dcng in,

o/

V th

- eiu /ut ^! m+) nghin

100L_

PH

P=

+. Phng trnh ,%-! %/n 0n 2 3h4n 3h5% 6ch th7c 05% #7% h8t nh!)/n

b

p

p

dKD

dD

=

>'ong =V

V #hi lCng th l;) t'n '()

HV #h th ht

Y1, ZV h[ng / Zi?u th f tnh h(n hi ^! #hi ht

- ) th h(n vi + gi+ t' tEng ng, t! =

( )1 2

1 1

2 11

b b

p p

KD D

b

+ + = +

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- >ng %u+t t! *jt giX! '() th n v" n-1 v" gi& /k /k dng '() tiu huMn =

1n

n

p

p

Dr const

D

= =

.

( )1

1 1

11 n n

b b

n n n p p

KD D

b

+ + = = +

W!u = t! th!)1n np p

D rD

=v"o t! C

( )11 1

1_

1 n n

b

b b

n p p

K rD K D

b

+

+ +

= =+

vi

( )1 1_

1

bK rK

b

+

=+

eof( )log 1 log log _

nn pb D K = + +

- Y v" Z C *+ nh Z[ng +h vn

thBonp

D

t'n : th log log v" /u) '! h / g=

1K+v" tung g=

_ v"K K b.

9. Cng !"t #$ h%&! !"t r4)

100J

EFa

=

>'ong =V V #hi lCng vt liu Z!n Gu ho v"o '(), g

pV #hi lCng vt liu di '(), g

!V t@ / ht = th? lPt %u! '(), L

- >h /F a

t'ong th nghim C tnh nh /!uV

qBm '() mt #hi lCng ^! vt liu, #h&o /+t *+ nh1J

. ) vt liu cn li t'n '()

1F J v" '() li *+ nh C2J, ti$ t l) vt liu cn li t'n '() ( )

1 2F J J +v"

'() ti$ t.

>ng / + gi+ t'1 2 3 ...J J J+ + +

/ tim n $nF a

8

eiu /ut '() l" 100L n$u1

J F a=

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:. Phng trnh tr;n- Yhi t'n mt #hi lCng ! ht vi mt #hi lCng Z ht \, to th"nh hrn hC :ng

nht. >h"nh hGn ^! ht v" \ t'ong hrn hC ls tngV

qi vi ht V

A

aC

a b

=

+

qi vi ht \V

B

bC

a b=

+

- >h"nh hGn + ht / nh nh!u mPi #hng gi!n th? th ^! hrn hC t'n. Nhng hrn

hC ls tng n") h@ t ti #hi thAi gi!n t'n l" v v" #hng *ut hin nhXng )$u t

hng li %u+ t'Fnh t'n.- >'n th t$, thAi gi!n #hng th ti$n ti v C nn th"nh hGn + ht v" \ /

#h+ nh!u mri hGn th? th.- q? +nh gi+ m :ng u ^! hrn hC, t! f t'ng Zi + gi+ t' /!i Zit ZFnh

hEng t'ung ZFnh.

- N$u t'ong hGn th? th1V

^! hrn hC th = th"nh hGn th th ^! v" \ lGn lCt l"

1 1,

A BC C

, gi+ t' /!i Zit ZFnh hEng t'ung ZFnh ^! hrn hC th = / l"

( )

( )

2

1

2

1

1

1

N

A iA

iA

N

B iB

iB

C C

s N

C C

sN

=

=

=

=

- ai,A BC C

l" th"nh hGn ^! ht , \ t'ong hrn hC, t! th),A Bs s

"ng nh #hi hrn

hC = "ng gGn vi hrn hC l tng.

,A Bs s

h thu v"o nhiu )$u tt nhng %u)$tnh nht l" thAi gi!n t'n.

- >'n th t$, tw) thBo )u Gu ^! / m" t! *+ nh thAi gi!n t'n thh hC. q? +nh gi+

m! t'n mt hrn hC, t! = th? dwng i lCng #h+ l" h@ / t'n v" C nh nghS!V

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esI

s

=

- ai

e

l" lh huMn ls thu)$t

( )

( )2

1

1

A Be

A B

s N

A iA

i

C C

n

C C NI

n C C

=

=

=

n l" / ht t'ong t'Ang hC t'n vt liu 'Ai

III. TI< T=>

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- ]ho vt liu v"o m+) t'n, #hi ng m+), Zm thF #$ *+ nh thAi gi!n t'n. H

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- Y$t %u& h(n th '()V Yhi lCng Bm '()90,1+ !=

Bn! $ K%t &' th( n!hi)m ph>n t(ch r>?

@n r>? K(ch th/c r>? 1mm2 Kh-i ./0n! trn r>? 1!2

1 0,75 2,0

2 0,425 18,7

3 0,315 28,0

4 0,25 1,9

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Bn! L$ K%t &' t(nh to;n cho 4M th< .o! .o!

log np

D lognp

D

0,02220 -1,6537 0,75 -0,1249

0,20755 -0,6829 0,425 -0,37160,31077 -0,5076 0,315 -0,50170,02109 -1,6760 0,25 -0,6021

Bn! O$ K%t &' t(nh to;n hi)' s'=t r>?

@n r>? Th3i !ian ( )iJ ! ( )iJ ! Hi)' s'=t

1 5 33,4 33,4

88,132 10 0,8 34,23 15 0,6 34,84 20 3 37,85 25 0,1 37,9

Bn! $ K%t &' t(nh to;n IstQi th3i 4iRm Fs

+,' N J iAC ( )2

iA AC C ( )2

iA AC C s n e Is1 27 84 0,2432 0,1729

0,2678 0,1956 1020 0,0148 0,0759

2 83 33 0,7155 0,00323 60 59 0,5042 0,02404 95 21 0,8190 0,02565 108 58 0,6506 0,00016 69 43 0,6161 0,00197 96 43 0,6906 0,00108 65 76 0,4610 0,0392

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Bn! #$ K%t &' t(nh to;n IstQi th3i 4iRm #Fs

+,' N J iAC ( )2

iA AC C ( )2

iA AC C s n e Is1 55 56 0,4955 0,0268

0,0753 0,1037 1178 0,0138 0,1332

2 97 39 0,7132 0,00293 78 70 0,5270 0,01744 102 45 0,6939 0,00125 108 79 0,5775 0,00676 89 76 0,5394 0,01437 110 43 0,7190 0,00368 80 51 0,6107 0,0023

Bn! ##$ K%t &' t(nh to;n IstQi th3i 4iRm s

+,' N J iAC ( )2

iA AC C ( )2

iA AC C s n e Is1 71 61 0,5379 0,0147

0,0642 0,0957 1105 0,0143 0,1490

2 103 69 0,5988 0,00363 59 31 0,6556 0,00004 88 73 0,5466 0,01275 100 45 0,6897 0,00096 85 66 0,5629 0,0093

7 101 32 0,7594 0,01018 66 55 0,5455 0,0129

Bn! #9$ K%t &' t(nh to;n IstQi th3i 4iRm s

+,' N J iAC ( )2

iA AC C ( )2

iA AC C s n e Is1 67 112 0,3743 0,0811

0,1900 0,1648 1181 0,0138 0,0837

2 84 121 0,4098 0,06223 84 31 0,7304 0,00514 78 75 0,5098 0,02235 105 56 0,6522 0,00006 97 52 0,6510 0,00017 75 19 0,7979 0,01938 83 42 0,6640 0,0000

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Bn! #$ K%t &' t(nh to;n IstQi th3i 4iRm #9s

+,' N J iAC ( )2

iA AC C ( )2

iA AC C s n e Is1 93 80 0,5376 0,0148

0,1267 0,1345 1257 0,0134 0,0994

2 67 92 0,4214 0,05653 80 96 0,4545 0,04184 94 70 0,5732 0,00745 107 60 0,6407 0,00036 91 43 0,6791 0,00047 107 65 0,6221 0,00148 81 31 0,7232 0,0041

Bn! #E$ K%t &' t(nh to;n IstQi th3i 4iRm s

+,' N J iAC ( )2

iA AC C ( )2

iA AC C s n e Is1 70 88 0,4430 0,0467

0,1206 0,1313 1279 0,0133 0,1010

2 102 65 0,6108 0,00233 79 55 0,5896 0,00484 98 103 0,4876 0,02945 114 83 0,5787 0,00656 88 66 0,5714 0,0077

7 96 50 0,6575 0,00008 99 23 0,8115 0,0232

AI. ?IE< CJ KI TH

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HSnh #

5 10 15 20 25 3032.5

35

37.5

40

$

in 4MiJ t

+. ?%n 0Nlog

thO

lognp

D

Bn! #$ Bn! s- .i)'

log -1,6537 -0,6829 -0,5076 -1,6760

lognp

D-0,1249 -0,3716 -0,5017 -0,6021

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-1.8 -1.6 -1.4 -1.2 -1 -.8 -.6 -.4

-.8

-.6

-.4

-.2

.

HSnh 9$ in 4M

log lognp

D

9. ?%n 0Nnp

D

Bn! #L$ Bn! s- .i)'

npD

0,75 0,425 0,315 0,25

0,02220 0,22974 0,54051 0,56160

log

lognp

D

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.2 .3 .4 .5 .6 .7 .8.

.2

.4

.6

HSnh $ in 4Mnp

D

:. ?%n 0N ,%-! %/n ch 5 tr;n thO thQ% g%Rn

Bn! #O$ Bn! s- .i)'

>hAi gi!n I/K 5 15 30 60 120 300

I 0,0759 0,1332 0,1490 0,0837 0,0994 0,1010

npD

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HSnh E

0 50 100 150 200 250 300 3500

0.05

0.1

0.15

0.2

Chart Title

$

in 4MI t

AII. K< LUhAi gi!n t'nV C *+ nh Z[ng thF #$ IZm t!)K nn / = /!i / nhng /!i /

n") nh, #hng +ng #?.

Yhi lCng 'ing ^! vt liuV vF u *!nh v" u n"nh = #hi lCng 'ing * *@

nh!u nn #hng t+ ng nhiu $n %u+ t'Fnh t'n.

>nh d v~ IgicnKV & 2 loi u u #hng = tnh d v~ vn nn %u+ t'Fnh t'n /

d d"ng hEn.

xu l) ti nhiu v t' nn = tFnh f t'ng, hnh *+ !o hEn.

W!i /=t t'ong %u+ t'Fnh $m u.

AIII. PH LC1. Tnh t(n th ngh%&' ngh%*n

J;c 4h? th ht goV

2 231,5 6 3,375 10,60

4 4

dV h m = = =

Hin th Z mft ht goV

2 221,5

1,5 6 9,5625 30,044 4

d

dh m = + = + =

- q? *+ nh #h th ht ngAi t! dung #h+i nim Ang #nh tEng Eng, = l"

Ang #nh ^! ht Gu = wng t@ / din th Z mft vi th? th. Ho = Ang #nh

tEng Eng ^! ht go t' #hi nghin l"V

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1

3,3756 6 2,12

9,5625p

VD mm

= = =

- |+ nh

2pD

>hBo nh lut \ond, vt liu /!u #hi nghin = 80L %u! '() t l" th l;) li t'n

'() 20L0, 2 =

>hBo gi&n :np

D , t! *+ nh C

0,4np

D mm

T(nh c7n! s'=t n!hi*n

- ]ng /ut ? nghin vt liu Inghin #hK t< #h th

12,12pD mm=

$n #h th

20, 4

pD mm=l"

2 1

3

4 1 1 6019

3 40

4 1 1 319 0, 2 10

3 20, 4 2,12

0, 08836 88, 36

i

p p

i

P W TD D

W

kW W

=

=

= =

T(nh hi)' s'=t m;? n!hi*n

- ]ng /ut tiu th ^! m+)

1 0_ o/ o/

220 5,4 0,8 220 3,6 0,8

316,8

P UI UI

W

=

=

=

- eiu /ut m+) nghin

88,3627,89L

_ 316, 8

PH

P= = =

+. Tnh t(n th ngh%&' r4)

- H! v"o gi&n :iJ t

Ang ong tim n $n Ang thng

37,9iJ =

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