4 defleksi.ppsx
TRANSCRIPT
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RA + RC
= PA B C
RA RC
L1 L
2
L
P
PRA
RC
RA =
RC =
ΔL1
ΔL2
A1 E1 A2 E2
A1 E1 L1
A2 E2 L2
L! = L +ΔL = LΔL1 + ΔL2 =ΔL = "
ΔL ="ΔL1 + ΔL2 = "
ΔL2 =−ΔL1
=P1 L1
A1 E1
P2 L2
A2 E2 =
RA L1
A1 E1
RC L2
A2 E2
=RC
A2 E2
L2
RA L1
A1
E1
=
A2 E2 L1
A1
E1
L2
RA
RA + RC
= P
RA =P
A2 E2 L1
A1 E1
L2
+
RA RA =P
A2 E2 L1
A1 E1
L2
1+
#
RA PA1 E1 L2
A1 E1 L2 + A2 E2 L1
=
RC PA2 E2 L1
A1 E1 L2 + A2 E2 L1
=
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A B C
RA RC
1""$% &"$%
L
'"()
'"2"
*"
A1 E1 A2 E2
RA PA1 E1 L2
A1
E1
L2
+ A2
E2 L1
=
A1 = A2 = 1 $%2E1 = E2 = 2"" ()/%%2
L2
L=
P = 2"
()
RC PA2 E2 L1
A1 E1 L2 + A2
E2 L1
=
L1
L=
P = *"()
P1 L1
A1 E1 ΔL1
=
RA L1
A1 E1 = = 1
%%
P2 L2
A2 E2 ΔL2
=
RC L2
A2 E2 = = −1
%%
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A B C
RA RC
1""$% &"$%
L
1'"()
1'"2
12,
A1 E1 A2 E2
RA PA
1
E1
L2
A1 E1 L2 + A2
E2 L1
=
A1 = 1 $%2 E1 = 2"" ()/%%2
= 2()
RC PA2 E2 L1
A1 E1 L2 + A2
E2 L1
=
= 12,()
P1 L1
A1 E1 ΔL1 =
RA L1
A1 E1 = = 1-'%%
P2 L2
A2 E2 ΔL2
=
RC L2
A2 E2 = = −1-'
%%
A2 = 2 $%2 E2 = 2"" ()/%%2
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A B D
RA RDA
1 E1 A EA2 E2
11"()
C
1""$% ,"$%
RA1 11
"
12"
22"
=
= '"()
A1 = A2 = A = 1 $%2E1 = E2 = E = 2"" ()/%
*"$%A B
C
RA RD
L
1'&()A1 E1 A EA2 E2
11"()
D
11"'"
&"
1'&'"1"&
A B C
RA RD
1'&()A1 E1 A EA2 E2
D
RD1 11
"
1""
22"
=
= &"()
RA2 1'
&
,"
22"
=
= '"()
RD2 1'
&
1*"
22"
=
= 1"&()
1'&11"
&&
RA = RA1 + RA
2 = '" −
'" = " ()RD = RD
1 + RD2 = &" −
1"& = && ()P1 L1
A1 E1
ΔL1
=
RA L1
A1 E1
= = "
%%
P2 L2
A2 E2
ΔL2
=
= 2-2
%%
RD L
A E
ΔL
=
= −2-2
%%
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1""$% ,"$%
A1 = 2 $%2
*"$%A B C
RA RD
L
1'&()A1 E1 A EA2 E2
11"()
DE1 = E2 = E = 2"" ()/%%2
A2 = 1 $%2 A = 1-& $%2
P1 A E L2 P2 + A2
E2 L
P
A2 E2 A E
=
P1 L1
A1 E1
P2 L2
A2 E2 =
P L
A E +
ΔL = ΔLAB + ΔLBC + ΔLCD = "
ΔLAB = ΔLBC + ΔLCD
A1 E1
L1
RA
1
A E L2 RD1 + A2 E2
L RD1A2 E2 A
E
=
A1 E1
L1
RA
1
A E L2 + A2
E LA2
E
A E
=
RD
1
A1 E
L1
A L2 +
A2 LA2
A
= RD
1
A1
L1
A
B C
RA RD
LA1 E1 A EA2 E2
11"()
D
RA1
RA1 + RD
1 = P
1&"*"" +1"",""
1""1&"
= RD1
2""
1"""= 1-,''' RD
1
11071,6
38,4
1-,''' RD1
+ RD1 = 11"
RD1
= ,-2"0 ()RA1
= 1-'201 ()
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1""$% ,"$%*"$%A B C
RA RD
L
1'&()A1 E1 A EA2 E2
11"()
D
A B C
RA RD
LA1 E1 A EA2 E2
11"()
D
RD1
= ,-2"0 ()RA1
= 1-'201 ()
A B C
RA RD
L
1'&()A1 E1 A EA2 E2
D
P A2 E2 L1 P1 + A1 E1 L2 P2A1 E1 A2
E2
=
P L
A E
P1 L1
A1 E1 =
P2 L2
A2 E2 +
RD
2
A2 E2 L1 RA2 + A1 E1
L2 RA2A1 E1 A2
E2
=
A E
L
A E
L
RD
2 =
A2 L1 +
A1 L2A1
A2
RA
2
A
L
A1 = 2 $%2
E1 = E2 = E = 2"" ()/%%2
A2 = 1 $%2 A = 1-& $%2
= 1-',& RA2
RA2 + RD
2 = P RA2 + 1-',& RA
2 = 1'&
RA2 = '1-0&& ()RD
2 = 1"-'"*'& ()
11071,6
38,4
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1""$% ,"$%*"$%A B C
RA RD
L
1'&()A1 E1 A EA2 E2
11"()
D
A B C
RA RD
LA1 E1 A EA2 E2
11"()
D
11071,6
38,4
RD1
= ,-2"0 ()RA1
= 1-'201 ()
A B C
RA RD
L
1'&()A1 E1 A EA2 E2
D
A1 = 2 $%2
E1 = E2 = E = 2"" ()/%%2
A2 = 1 $%2 A = 1-& $%2
RA2
= '1-0&& ()RD2
= 1"-'"*'& ()
16561,4
103,6
RA = 1"-22&' ()
RD = '&-22&' ()
11010,2
65,2
165P1 = PAB = 1"-2 ()
(tekan)P2 = PBC = 00-, () (tarik )
P = PCD = '&-2 () (tekan)
∆L1 =
"-2&'%% (−)∆L2 =
1-00'%% (+)
∆L =1-*"%% (−)
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IV.
DEFLECTI
N!
A
B
C
D
E
12 ()
LAB
LBC
LBD LDE
" ()
Baan AB3 LAB
= '" "mAAB
= 1&" mm2
Baan BC3 LBC = 0" "mABC = 1"" mm2
Baan BDE3 LBD = LDEABD = ADE
M4d5657 86a797 :a;an3 21" GPa
H95n <8<9nda;an 99( C >δC#- ?9(a3PERPI)DAHA)@I@IK
9(a P d9 C 8a< 12 ()- :8a<a P d9 E aa 99( C
8a< d9 8%<ana
9(a P d9 E 8a< " ()- :8a<a P d9 C aa 99( C 8a< d9 8%<ana
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IV.
DEFLECTI
N!
A
C
E
12 ()
LAB
LBC
LBD LDE
" ()
PERPI)DAHA)@I@IK
RD
RB
PB
∑MD = " RB LBD + " LDE = "
RB = " LDE / LDE = " ()
PB = RB = " ()
PBC = PC = 12 ()
PAB = PB PC = " 12 = 1, ()
a# P8<9nda;an 99( C3
PAB LAB
AAB EAB
PBC LBC
ABC EBC = +C = ∆LAB + ∆LBC
(desak )
(tarik )
(desak )
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IV.
DEFLECTI
N!
A
C
E
PC
LAB
LBC
LBD LDE
" ()
PERPI)DAHA)@I@IK
RD
PB
∑MD = " RB LBD + " LDE = "
RB = " LDE / LDE = " ()
PB = RB = " ()
PBC = PC
PAB = PB PC = " PC
:# 9(a P d9 E 8a< " ()- :8a<a P d9 C aa 99( C 8a< d9 8%<ana
PAB LAB
AAB EAB
PBC LBC
ABC EBC = +C = ∆LAB + ∆LBC
(desak )
= "
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IV.
DEFLECTI
N!
A
C
E
12 ()
LAB
LBC
LBD LDE
PE
PERPI)DAHA)@I@IK
RD
PB
∑MD = " RB LBD + PE LDE = "
RB = PE LDE / LDE = PE
PB = RB = PE
PBC = PC = 12 ()
PAB = PB PC = PE 12
$# 9(a P d9 C 8a< 12 ()- :8a<a P d9 E aa 99( C 8a< d9 8%<ana
PAB LAB
AAB EAB
PBC LBC
ABC EBC = +C = ∆LAB + ∆LBC = "
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1()
"
1()
"
1 / 7 9 n
" F
1/an"
IV.
DEFLECTI
N!
A =
0 " " %
% 2
A =2'""%%2
L =2-*%
A
BC
H95n <8<9nda;an 99( Baa; 89(a6 >B# dan ;494na6>B;#.
P A B = +
2 ' - " "
" ( )
PBC
=
22-&1''()ΔLAB
=
PAB LAB
AAB EAB
E ="G<a
=1-1**%%
ΔLBC
=
PBC LBC
ABC EBC ="-20%%
B
PERPI)DAHA)@I@IK
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1()
"
IV.
DEFLECTI
N!
A =
0 " " %
% 2
A =2'""%%2
L =2-*%
A
BC
P A B = +
2 ' - " "
" ( )
PBC
=
22-&1''()
E ="G<a
ΔLAB =
1-1**%%
ΔLBC =
"-20%%
"
A
BC
CB
BB
A
BB
C
B!
B;
B
#B$ = − 0,2%7 &' 301,144 + 0,2%7 *" 30
* 30= 2,803mm (ke bawah)
#B- = 0,2%7mm (ke kanan)
PERPI)DAHA)@I@IK
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2()
"
IV.
DEFLECTI
N!
A =0"%%2
A
B
C
*&
L =
+ " " $ %
L = 1 , " $ %
H95n <8<9nda;an 99( Baa; 89(a6 >B# dan ;494na6>B;#.
E =
21"GPa
2()
"
*&
B
PBC $47 " =
P B
C
P B
A
PBA $47 *&
PBC $47 "
P B A 7
9 n
* & F P B C
7 9 n
+ " F
PBC =PBA $47 *&
$47 "
PBA 79n *&+ PBC 79n "= 2PBA 79n *& +PBA $47 *&
$47 "79n " = 2
PBA = 2*-01& () >tarik #PBC = 2"-* () >tekan#
PERPI)DAHA)@I@IK
IV
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2()
"
IV.
DEFLECTI
N!
A =0"%%2
A
B
C
*&
L =
+ " " $ %
L = 1 , " $ %
E =
21"GPa
P B A =
2 * - 0 1
& ( )
P B C = 2 " - + * + ( )
ΔLBA =
PBA LBA
ABA EBA ="-01%%
ΔLBC
=
PBC LBC
ABC EBC ="-**%%
"
A
B
C
*&
ΔLBA
=
"-01%% ΔLBC = − "-**%%
PERPI)DAHA)@I@IK
IV
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"
IV.
DEFLECTI
N! A
B
C
*&
ΔLBA
=
"-01%% ΔLBC = − "-**%%
B!
B
C
APERPI)DAHA)@I@IK
IV
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IV.
DEFLECTI
N!ΔLBA
=
"-01%% ΔLBC = − "-**%%
*& "1"&
&
"
A
B
C
*&
B
B!
PERPI)DAHA)@I@IK
IV
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IV.
DEFLECTI
N!ΔLBA
=
"-01%% ΔLBC = − "-**%%
1"&
&
B
B!
1"&−
0 ,4 4 7
0 , % 1 3
BB! =
ΔLBA
$47
ΔLBC
$47 >1"&−#=
ΔLBA
ΔLBC
$47
$47 >1"&−#= = 2-"*
$47
$47 >$47 1"& + 79n 1"& an #= 2-"*
1
$47 1"&+
79n 1"& an = 2-"*
1
"-2&0 + "-0'' an = 2-"*
an = "-& = -'
BB! =ΔLBA
$47
"-01ΔLBA
$47 $47 -'= 1-1&&%%
*&
D B G
B = 1-1&& $47 >*&#= 1-1*'%%
B;
B; = 1-1&& 79n >*&#= "-1*&%%
PERPI)DAHA)@I@IK
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1""$% ,"$%*"$%A B C
RA RD
L
1'&()A1 E1 A EA2 E2
11"()
D
A B C
RA RDLA1 E1 A EA2 E2
11"()
D
11071,6
38,4
RD1
= ,-2"0 ()RA1
= 1-'201 ()
A B C
RA RD
L
1'&()A1 E1 A EA2 E2
D
A1 = 2 $%2
E1 = E2 = E = 2"" ()/%%2
A2 = 1 $%2 A = 1-& $%2
RA2
= '1-0&& ()RD2
= 1"-'"*'& ()
1'&'1-*1"-'
RA = 1"-22&' ()
RD = '&-22&' ()
11010,2
65,2
165 P1 = PAB = 1"-2 ()
(tekan)P2 = PBC = 00-, () (tarik )
P = PCD = '&-2 () (tekan)
P1 L1
A1 E1
P2 L2
A2 E2 =
P L
A E +
∆L1 =
"-2&&%% (−)∆L2 =
1-00'%% (+)∆L =
−
IV
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"
IV.
DEFLECTI
N! A
B
C
P8<9nda;an@99(.
*&
ΔLBA
=
"-01%% ΔLBC = − "-**%%
" - 0 1 + %
%
" - * * / % % 1"&
&
1"&−
" - 0 1 + %
%
"-01%%
= 2-"* >"-2&0 + "-0'' an #
= 1-0* >"-2', + an #
an = "-& = -'
BB! =ΔLBA
$47
ΔLBC
$47 >1"&−#=
BB! = 1-1&&B = 1-1&& $47 >*&# = 1-1*'
B; = 1-1&& 79n >*&# = "-1*&%%
B = 1-1&& $47 >1"&'"# = 1-1*'
B;
IV
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"
IV.
DEFLECTI
N! A
B
C
P8<9nda;an@99(.
*&
ΔLBA
=
"-01%% ΔLBC = − "-**%%
" - 0 1 + %
%
" - * * / % %
*& "
1"&
&
IV
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IV.
DEFLECTI
N!P8<9nda;an@99(.
ΔLBA
=
"-01%% ΔLBC = − "-**%%
"
A
B
C
*&
IV
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IV.
DEFLECTI
N!P8<9nda;an@99(.
ΔLBA
=
"-01%% ΔLBC = − "-**%%
0 ,4 4 7 1"&
&
1"&− 0
, % 1 3
BB! =
ΔLBA
$47
ΔLBC
$47 >1"&−#=
ΔLBA
ΔLBC
$47
$47 >1"&−#= = 2-"*
B!
$47
$47 >$47 1"& + 79n 1"& an #= 2-"*
1
$47 1"&+
79n 1"& an = 2-"*
1
"-2&0 + "-0'' an = 2-"*
an = "-& = -'
IV
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"
IV.
DEFLECTI
N! A
B
C
P8<9nda;an@99(.
*&
ΔLBA
=
"-01%% ΔLBC = − "-**%%
" - 0 1 + %
%
" - * * / % % 1"&
&
1"&−
" - 0 1 + %
%
"-01%%
$47
$47 >1"&−#= 2-"*
$47
$47 1"& $47 + 79n 1"& 79n
$47
$47 >$47 1"& + 79n 1"& an #
1
$47 1"& + 79n 1"& an
1
"-2&0 + "-0'' an
1 = 2-"* >"-2&0 + "-0'' an #
1 = 1-0* >"-2', + an #
an = "-& = -'
IV
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IV.
DEFLECTI
N!P8<9nda;an@99(.
ΔLBA
=
"-01%% ΔLBC = − "-**%%
1"&
&
B
B!
1"&−
0 ,4 4 7
0 , % 1 3
BB! =
ΔLBA
$47
ΔLBC
$47 >1"&−#=
ΔLBA
ΔLBC
$47
$47 >1"&−#= = 2-"*
$47
$47 >$47 1"& + 79n 1"& an #= 2-"*
1
$47 1"&+
79n 1"& an = 2-"*
1
"-2&0 + "-0'' an = 2-"*
an = "-& = -'
BB! =ΔLBA
$47
"-01ΔLBA
$47 $47 -'= 1-1&&%% B = 1-1&& $47 >*&#= 1-1*'%%
D B
G
IV
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1()
"
IV.
DEFLECTI
N!
A =
0 " " % %
2
A =2'""%%2
A =2-*%
A
BC
P A B = +
2 ' - " "
" ( )
PBC =
22-&1''()
E ="G<a
P8<9nda;an@99(.
ΔLAB =
1-1**%%
ΔLBC =
"-20%%
IV
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"
IV.
DEFLECTI
N!A
BC
P8<9nda;an@99(.
ΔLAB =
1-1**%%
ΔLBC =
"-20%%
CB
BB
A
BB
C
B!
B;
B
#B$ = − 0,2%7 &' 301,144 + 0,2%7 "*" 30
* 30= 2,803mm (ke bawah)
#B- = 0,2%7mm (ke kanan)
IV.
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∆L
IV.
DEFLECTI
N!
/B. DEFA!I A!IAL ' AA E =σξ
P/AΔL/L
=P L
ΔL A= ΔL =
LE A
P
A1 E1 L1 A2 E2 L2
L
P PΔL =
∑
LE A
P
Ø =100 mm1000 kN
Ø =65 mmA B C
L = 1,0 m L = 0,8 m
ΔL = ΔLAB
+ ΔLBC
=L1 P1
E1 A1
+L2 P2
E2 A2
= 0,606 + 1,148 = 1,754 mm
Ø =100 mm500 kN
Ø =65 mmA B C
L = 1,0 m L = 0,8 m
ΔL = ΔLAB + ΔLBC
= 0,606 + 0,574 = 1,180 mm
500 kN
Ø =100 mm1500 kN
Ø =65 mmA B C
L = 1,0 m L = 0,8 m
ΔL = ΔLAB + ΔLBC
= 0,606 + 0,574 = 1,180 mm
500 kN
IV.
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IV.
DEFLECTI
N!
/B. DEFA!I A!IAL ' AA E =σξ
P/AΔL/L
=P L
ΔL A= ΔL =
LE A
P
A1 E1 L1 A2 E2 L2
IV.
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IV.
DEFLECTI
N!
/B. DEFA!I A!IAL ' AA E =σξ
P/AΔL/L
=P L
ΔL A= ΔL =
LE A
P
A1 E1 L1 A2 E2 L2 ΔL =L
E AP
IV.
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DEFLECTI
N!
/B. DEFA!I A!IAL ' AA E =σξ
P/AΔL/L
=P L
ΔL A= ΔL =
LE A
P
A1 E1 L1 A2 E2 L2 ΔL =L
E AP
P l a n e T r u s
8/18/2019 4 Defleksi.ppsx
http://slidepdf.com/reader/full/4-defleksippsx 35/37
=
0
0
0
0
0
0
AE
L
AE L
−
0
0
AE
L
−
AE L
0
0
0
0
P l a n e T r u s
s
kl
e AE
L=
0
0
1
-1
0
0
0
0
0
0
-1
1
0
0
0
0
P l a n e T r u s
8/18/2019 4 Defleksi.ppsx
http://slidepdf.com/reader/full/4-defleksippsx 36/37
=
0
0
0
0
0
0
AE
L
AE L
−
0
0
AE
L
−
AE L
0
0
0
0
P l a n e T r u s
s
kl
e AE
L=
0
0
1
-1
0
0
0
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0
0
-1
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0
0
0
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IV.
8/18/2019 4 Defleksi.ppsx
http://slidepdf.com/reader/full/4-defleksippsx 37/37
"
DEFLECTI
N!A
BC
P8<9nda;an@99(.
ΔLAB =
1-1**%%
ΔLBC =
"-20%%
CB
BB
A
BB
C
B
B;
B