of 94
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1/94
Chapter 2 Phn b
$ng su't trong )'t2.1 Khi nim
2.2 $ng su't do tr*ng l,-ng b/n thn
2.3 $ng su't do t/i tr*ng ngai
2.4 $ng su't trong n1n khng 23ng nh't
2.5 Phn b45ng su't d,6i 27mng
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2
2
*ng su't
BM,.a C1N2n Mng
2.1 Khi ni5m
TS Nguy6n Minh Tm
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2
3
*ng su't
2.1.1 Cc thnh ph8n $ng su't
[ ]
+
=
p
p
p
p
p
p
zzyzx
yzyyx
xzxyx
00
00
00
3
zyxp
++=
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
4
*ng su't
*ng su't trn m9t ph;ng
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
5
*ng su't
*ng su't chnh
( ) ( )( ) 02 222
22223
=+
+++++
xyzxzyyzxxzyzxyzyx
xzyzxyzxzyyxzyx
0322
1
3 =+ III
zyxI ++=1222
2 xzyzxyzxzyyxI ++=222
3 2 xyzxzyyzxxzyzxyzyxI +=
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
6
*ng su't
2.1.2 *ng su't trn m9t ph;ng
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
7
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
8
*ng su't
Vng trn Mohr
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
9
*ng su't
C=c Vng trn Mohr $ng su't l )i>m n?m trn vng trn Mohr sao chot@)i>m ) vB)%Dng song song vEi m9t ph;ng c8n xc ).nh $ng su't,)%Dng th;ng ny c?t vng trn Mohr tFi gi tr., c8n tm
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
10
*ng su'tTGng qut
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
11
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
12/94
2
12
*ng su't
Th dH
BM,.a C1N2n MngTS Nguy6n Minh Tm
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13/94
13
Solution
2 *ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
14/94
2
14
*ng su't
2.2*ng su't do trJng l%Kng bLn thn
2.2.1 *ng su't theo ph%1ng )$ng
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
15
*ng su't
2.2.2 *ng su't cNa phn t)'t bLo ha
0
BM,.a C1N2n MngTS Nguy6n Minh Tm
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2
16
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
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2
17
*ng su't
Th dH
BM,.a C1N2n MngTS Nguy6n Minh Tm
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18/94
18
Solution
2 *ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
19/94
2
19
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
20/94
7/25/2019 2011 06 Files Ung Suat Chap 2
21/94
21
Solution
2 *ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
22/94
2
22
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
23/94
2
23
*ng su't
L=c th'm
BM,.a C1N2n MngTS Nguy6n Minh Tm
7/25/2019 2011 06 Files Ung Suat Chap 2
24/94
2
24
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 * '
7/25/2019 2011 06 Files Ung Suat Chap 2
25/94
2
25
*ng su't
Th dH
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 * '
7/25/2019 2011 06 Files Ung Suat Chap 2
26/94
26
Solution
2 *ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 * '
7/25/2019 2011 06 Files Ung Suat Chap 2
27/94
2
27
*ng su't
Mao dOn trong )'t
,i vEi n%Ec c't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 * 't
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2
28
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 * 't
7/25/2019 2011 06 Files Ung Suat Chap 2
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2
29
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 * 't
7/25/2019 2011 06 Files Ung Suat Chap 2
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2
30
*ng su't
Th dH
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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31
Solution
2 *ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
32
*ng su't
uhh += '
2.2.3 *ng su't theo ph%1ng ngang
vh K '' =
K #i$u ki'n t)nh: Ko
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
33
*ng su't
2.3*ng su't do tLi trJng ngai
2.3.1 *ng su't do tLi trJng tPp trung
BM,.a C1N2n MngTS Nguy6n Minh Tm
5
2.
.2
.3
r
zypzy = 5
2.
.2
.3
r
zxpzx =
++
=235 )(
).2(..
3
.21..
.2
.3
zRr
zryx
r
zyxpxy
2 *ng su't
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2
34
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
35
*ng su't
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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2
36
*ng su't
L=c tc dHng bn trong khi )'t
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
37
*ng su't
2.3.2 *ng su't do tLi trJng )%Dng th;ng
( )
( )
( )222
2
222
2
222
3
2
2
2
zx
qz
zx
zqx
zx
qz
zx
x
z
+=
+=
+=
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
38
*ng su't
TLi trJng )%Dng th;ng bn trong khi )'t
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
39
*ng su't
2.3.3 *ng su't do tLi trJng ph8n b )2u hnh bQng
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
40
g
[ ])2cos(sin
++= q
z
[ ])2cos(sin
+= q
x
[ ])2sin(sin
+= qzx
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
41
g
!" x!" #!" !" x!" #!" !" x!" #!"
! ! !"# !"# !"$%
!" !"&&'( !")#& ! !"&((# !"'(#%$ !"!$($* !"*&&)& !"*$')' !"$#%
!#$ !" !"*#!( ! !"&!%%$ !"$&%&* !"%)$% !"*&'&% !"$*)% !"%&&'
!%$ !"&!$ !"$%% ! !"($!&( !"%(#&% !"#$(# !"*&%!( !"%&$#( !"%($'
!$ !"(($ !"('& ! !")$*'# !"('( !"#') !"*)&)* !"%%#!& !"%#*'
!&$ !"''(% !"!(!# ! !"'!)!' !"!&))) !"%)$% !"**)&' !"*%$( !"%!$)
" !"#*&( !"!*!#% ! !"#!# !"!##$ !"!() !"*! !"!&!(# !"#&%"!#$ !"*'( !"!%%) ! !"*$'# !"!$$% !"!)%!% !"$)!!# !"!# !"%*%
"!$ !"$( !"!$(# ! !"$)&!& !"!%% !"!##!' !"$$*!( !"!*!%# !"!&)&
"!&$ !"$*#$ !"!!&! ! !"$$$(' !"!*%$ !"!*$!$ !"$!%$) !"!%($ !"!)(*
# !"$!#( !"!!') ! !"%&)' !"!!&&' !"!$*$# !"%)*& !"!%!%' !"!'$)
% !"%!(* !"!!& ! !"%!#'( !"!!$% !"!'#$ !"&)& !"!!'&% !"!$(
' !"#)# !"!!!( ! !"#'$* !"!!$& !"!!) !"#%(( !"!!$!( !"!()
$ !"%'# !"!!!*% ! !"%#() !"!!!)% !"!!'% !"%*!# !"!!'% !"!%%
(!"!#' !"!!!%* ! !"!#%' !"!!!*% !"!!*$# !"!*& !"!!! !"!!('
)*+
!"
# #$%& #$&
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
42
g
!" x!" #!" !" x!" #!" !" x!" #!"
! ! ! ! ! ! ! ! !
!" !"!!#& !"!&%%) !"!*# !"!!!&' !"!$)(!* !"!!%'* #"#+,!# !"!% !"!!!'
!#$ !"!&(# !"&'# !"!#()' !"!!%()$ !"!(&'$* !"!##) !"!!!($ !"!#$( !"!!'*
!%$ !"!*$)' !"%$*)# !"!%% !"!!)$*( !"(*$# !"!%('% !"!!%% !"!'&( !"!%'
!$ !"!())' !"%#'%( !"*!*$ !"!('* !"#!(' !"!#*% !"!!#&) !"!&$)% !"!%$%$
!&$ !"#'$) !"%*!& !"(% !"!*'()& !"))%* !"!(($ !"!)( !"%%!$ !"!**&*" !"%!*($ !"%!*($ !"&!&& !"!)&*(( !")(%)* !"#%# !"!$$$$ !"$') !"!''
"!#$ !"%$*$) !"'))) !"(*&& !"!&'& !"'##(& !"$!*$ !"!#&* !"$&! !"!($$)
"!$ !"%#!!# !"$#*' !")(& !"$*$$ !"*)%&* !"$' !"!)!#& !"$*%# !"!*&
"!&$ !"%#'%) !"!(&* !"#'%' !"#%))* !"%)&%) !"$#%( !"!()' !"%#!& !"!%'(
# !"%#'%( !"!())' !"*!*$ !"'##(& !"!&'& !"$!*$ !"!%% !"$(( !"!#)(
% !"%%&(& !"!$&$ !"!(&$* !")&))& !"!#)')$ !"!&('% !"$*%# !"!)!#& !"!*&
' !"&'# !"!&(# !"!#()' !"')&&$ !"!$''* !"!)!'& !"$()) !"!*%*& !"!)#$#
$ !"')'* !"!# !"!*!)# !"#!(' !"!('* !"!#*% !"$%!) !"!%'*% !"!#)&(
( !"*# !"!!'( !"!%&'* !"$**(& !"!)!' !"!$(*( !"%%!$ !"!)( !"!**&*
)*+
!"
' '$& %
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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2
43BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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2
44
Th dH
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
45/94
45
Solution
2
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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46/94
46
=
2sin
2
1
B
xqz
2.3.4 *ng su't do tLi trJng tam gic
+=
2sin
2
1ln
2
2
2
1
R
R
B
z
B
xqx
+=
B
zqzx 22cos1
2
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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47BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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48
2.3.5 *ng su't )$ngdo tLi trJng n2n )%Dng
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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49
2Iqoz=
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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50
Th dH
Figure 9.12
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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51
Solution
,A1
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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52
,A2
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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53
2.3.6 *ng su't )$ngdo tLi trJng parabolic v nn
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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54BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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55
2.3.7 *ng su't do tLi trJng )2u kh?p (mRt chi2u)
BM,.a C1N2n MngTS Nguy6n Minh Tm
x
z = q
z
q
2 *ng su't
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56
2.3.8 *ng su't do tLi trJng )2u phn btrn di5n tch chSnhPt
,Gc
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
57/94
57BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
58/94
58BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
59/94
59BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
60/94
60BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
61/94
61
,Tm
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
62/94
62BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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63
=
3
2
13
1tan2 RR
LBz
zR
LBqx
=
3
2
23
1tan2 RR
LBz
zR
LBqy
= 32
1
2
22 RR
Bz
R
Bqzx
22
1 zLR +=22
2 zBR +=222
3 zBLR ++=
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
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64
Ph%1ng php g8n )ng xc ).nh $ng su't th;ng )$ng
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
2 3 9 * 't d tLi t )2 h b t di5 t h h h t
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65
2.3.9 *ng su't do tLi trJng )2u phn btrn di5n tch hnh trn
Bn d%Ei tm cNa tLi trJng tc dHng
( )( )[ ] ( )[ ]
++
+
++=
2/322/12/1
1
/1
)1(221
2 zRzR
qr
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
T )i>m b't kV
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66
T)i>m b't kV
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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67BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
68/94
68BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
69/94
69BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
70/94
70BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
71/94
71BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
72/94
72BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
73/94
73BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
74/94
74BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
75/94
75BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
76/94
76BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
77/94
77BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
78/94
78BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
79/94
79BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
80/94
80BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
Th dH
7/25/2019 2011 06 Files Ung Suat Chap 2
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81BM,.a C1N2n MngTS Nguy6n Minh Tm
Solution
2 *ng su't
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82BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
Ph%1ng php bi>u )XNewmark
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83
Nz IqN =
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
2.3.10 *ng su't do l=c tPp trung ngang
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84BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
2.3.11 *ng su't do tLi trJng )%Dng th;ng nYm ngang
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85BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
86/94
86BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
2.3.12 *ng su't do tLi trJng )%Dng th;ng nYm
ngang bn trong khi )'t
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87
ngang bn trong khi )'t
BM,.a C1N2n MngTS Nguy6n Minh Tm
*ng su't2
2.3.13 *ng su't do tLi trJng phn b)Zu hnh bYng nYm ngang
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88/94
88BM,.a C1N2n MngTS Nguy6n Minh Tm
*ng su't2
7/25/2019 2011 06 Files Ung Suat Chap 2
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89BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
2.3.14 QuLB8u,Xng*ng su't
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90BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
7/25/2019 2011 06 Files Ung Suat Chap 2
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91BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
2.4*ng su't trong n2n khng )Xng nh't
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92
S/thay #1i 4ng su6t bn d09i mng trn (H = R)
BM,.a C1N2n MngTS Nguy6n Minh Tm
2 *ng su't
2.5 *ng su't d%Ei )y mng
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93/94
93BM,.a C1N2n MngTS Nguy6n Minh Tm
:6t st
2 *ng su't
:6t ct
7/25/2019 2011 06 Files Ung Suat Chap 2
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94BM,.a C1N2n MngTS Nguy6n Minh Tm
