CONTOH SOAL ANALISA PORTAL 2 TINGKAT
1T
1t/m’ 1,5EI 4m
1t/m’
2EI
2EI 2t/m’
2T
2T 2EI 2t/m 2,5EI
2,5EI 4m
3M
3M
HITUNG DAN GAMBAR BIDANG M, D, N DENGAN METODE SLOPE DEFLECTION PORTAL PORTAL MENGALAMI MENG ALAMI PERGOYANGAN FORMULA MOMEN AKHIR
MAB MFAB ! 2EI/L"#2 2EI/L"#2 $ % & ! 3R$' MBA MFBA ! 2EI/L"#2 2EI/L"#2 & % $! 3R&'
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A( MOMEN AKHIR MEF
1 TED MEC
MFE 1t/m’ FDA 1,5EI MFD 4m
2EI MCE
MCD 2T
2t 2t/m’
2EI MDF
MDC
DA
CA
2EI
MCA
MDB 2,5EI
2,5EI
)
4m MBD
MAC
A
BA 3M
3M
B( MOMEN PRIMER MFEF
1 T ED
MFFE 1t/m’ FDA 1,5EI
MFEC
MFFD 4m 1t/m
2EI
MFCE
MFCD 2T
CA
MFCA
2t 2t/m’
MFDE
2EI MFDF DA
2EI MFDB
2,5EI
2,5EI
2t/m 4m MFAC A
MFBD BA
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MOMEN PRIMER/MOMEN *EPIT U*UNG MFAC !1/12(+$(L$2 ! 1/12(2(42 !2,--. tm MFCA # 2,--. tm MFBD "t0$ $$ &&$' MFDB "t0$ $$ &&$' MFCE !1/12(+(L2 ! 1/12(1(42 !1,333 tm MFEC #1,333 tm MFFD "t0$ $$ &&$' MFDF "t0$ $$ &&$' MFCD !1/(P(L ! "11/162'(+(L2 ! 1/(2(- ! "11/162'(2(-2 !5,-25 tm MFDC #1/(P(L # "5/162'(+(L2 # 1/(2(- # " 5/162'(2(-2 !3,3.5 tm MFFE # "1/12'(+(L2 # 1/12(1(-2 # 3, tm MFEF !3, tm C( DEFORMASI STRUKTUR 1( PUTARAN SUDUT PADA *OINT " SEMUA SEMUA PUTARAN PUTARAN SUDUT SUDUT DIASUMSIK DIASUMSIKAN AN SEARAH SEARAH JARUM JAM JAM ' 7 ED
FDA
e
1,5EI 4m
2EI
2EI CA
DA
2EI
2,5EI
2,5EI
A
BA 3M
3M
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2( TRANSLASI/DEFLEKSI HORISONTAL PADA TIAP TINGKAT " ASUMSI ASUMSI BERGESER BERGESER KE ARAH ARAH KANAN KANAN '
E D A
F D A
1,5EI
4m 2EI
2EI
R
C A R$ 2,5EI
R$
R7
D A
2EI
2,5EI
4m
R&
A
B A 3M
3M
PUTARAN SUDUT AKIBAT AKIBAT PERGOYANGAN PERGOYANGAN R$R$ 1/4 8 R& R& 1/4 RR 2/4 8 R&7 R7& 2/4 a = 0 (PERLETAKAN JEPIT) ; b = 0 (PERLET ( PERLETAKAN AKAN JEPIT) ; MOMEN AKHIR DALAM FUNGSI DEFORMASI STRUKTUR MAC ! 2,--. ! 2,5/4"#2 2,5/4"#2a - c + 3.Rac) = ! 2,--. ! 2,5/4 (- c + 3.1/4 1) = +2,667 0,62! c + 0,46" 1
#$% = ! 2,5/4"#2 2,5/4"#2b - & + 3. Rb&) = ! 2,5/4 (-& + 3.1/4 1) = 0,62!& + 0,46" 1 #'A = #2,--. ! 2,5/4"#2 2,5/4"#2c - a + 3. Rca) = # 2,--. ! 2,5/4 (-2c + 3.1/4 1) = -2,667 1,2! c + 0,46" 1 #'% = +!,62! + 2/6 (- 2c - &) = +!,62! 0,667 c 0,333 &
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= -1,2!& + 0,46" 1 #%' = -3,37! + 2/6 (-2& - c) = -3,37! 0,667 & 0,333 c #% =0 + 2/4(- 2& - + 3.R&) = 0 - & + 2/4.3/4 2 = -& + 0,37! 2 #E' =-1,333 + 2/4(- 2e - c + 3.Rec) = -1,333 - e 0,! c + 2/4. 3.1/4 2 = -1,333 - e -0,!c + 0,37! 2 #E = +3 + 1,!/6(1,!/6(- 2e - ) = +3 0,! e 0,2! #E =-3 + 1,!/6(- 2 - e) = -3 0,! - 0,2! e #% =0 + 2/4(- 2 - & + 3.R&) = - - 0,! & + 2/4.3.1/4 2 = - - 0,! & + 0,37!2 Ut9 mt9$ :;9<9= m>m $=0< =$<9: 0t$=90 ? ? c, &, e, &a* 1 &a* 2 "HARUS DISIAPKAN DISIAPKAN/DISU /DISUSUN SUN 6 PERSAMAAN, PERSAMAAN, DENGAN DENGAN MENGGUNAKA MENGGUNAKAN N SYARA SYARAT T BATAS YAITU : 1) SETIAP SETIA P JOINT JUMLAH MOMEN MOME N =0 KECUALI KECU ALI PERLETAKAN PERL ETAKAN JEPIT, JEPIT, 2) JUMLAH GAYA HORISONTAL TIAP TINGKAT = 0 ' A. SYARAT BATAS JUMLAH MOMEN SETIAP JOIN = 0
MC 8 MCA ! MCD ! MCE (-2,667 1,2! c + 0,46" 1) + (+!,62! 0,667 c 0,333 &) + (+1,333 - c 0,! e + 0,37!2) = 0
(-2,667 + !,62! + 1,333) +( 1,2! c c - 0,667c) + ( 0,333 &) +( 0,! e) +(+ 0,46" 1+ 0,37!2 = 0 +4,2"1 2,"17 c 0,333 & 0,! e + 0,46" 1+ 0,37!2 = 0 -2,"17c 0,333 & 0,! e + 0,46" 1+ 0,37!2 = - 4,2"1 +2,"17c + 0,333 & + 0,! e - 0,46"1 - 0,37!2 = + 4,2"1 ....................... ................................. .......... (1) MD 8 MDB ! MDC ! MDF "-1,2!& + 0,46" 1)+( -3,37! 0,667 & 0,333 c)+( -& + 0,37! 2) = 0 (-3,37!) +( 0,333c) + (-1,2!& 0,667&-&) + (0,46"1)+ (0,37!2) = 0 c 2,"17 & + 0,46" 1+ 0,37!2 = 0 c 2,"17 & + 0,46" 1+ 0,37!2 = +3,37! ...................... ................................... ......................... ....................(2) ........(2) ME 8 MEC ! MEF "-1,333 - e -0,!c + 0,37! 2)+( +3 0,! e 0,2! ) = 0 "#1,333!3' !"# !"#e 0,! e)+( -0,!c) +( 0,2! ) + (0,37! 2) = 0 !1,--. #1,5 #1,5e 0,! c 0,2! + 0,37! 2 = 0
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MF 8 MFE ! MFD "-3 0,! - 0,2! e)+( - - 0,! & + 0,37!2) = 0 0,! )+ (- 0,! &)+(- 0,2!e) +(0,37!2) = 0 0,! & 0,2! e + 0,37! 2 = 0 0,! & 0,2! e + 0,37! 2 = + 3 + 0,! & + 0,2! e - 0,37! 2 = - 3 ...................... ................................... ......................... ........................(4) ............(4) SYARAT BATAS JUMLAH GAYA HORISONTAL TIAP TINGKAT = 0
H2 8 "MEC ! MCE'/L MCE'/L ! "MFD ! MDF'/L7 % 1 % "-1,333 - e -0,!c + 0,37! 2)+( (+1,333 - c 0,! e + 0,37! 2))/4 + @"- - 0,! & + 0,37! 2)+( -& + 0,37! 2) -! = 0 "!1,333#1,333' !"-0,!c-c) + (- 0,! &-&) + ( 0,! e- e) +(- ) + (+ 0,37! 2+ 0,37!2 + 0,37!2+ 0,37!2)/4 - != 0
-! +(-1,!c 1,!& 1,! e - + 1,! 2)/4 = 0 (-1,!c 1,! & 1,! e - + 1,! 2 )/4= +! -1,!c 1,!& 1,! e - + 1,! 2 = +20 ....................... ................................... ........................ ..................(!) ......(!)
H1 8 "MAC ! MCA'/L$ MCA'/L$ ! "MBD "MBD ! MDB'/L& MDB'/L& % 1 # 2 % "MAC ! MCA'/L$ ! "MBD ! MDB'/L& % 15 "MAC ! MCA'/L$ ! "MBD ! MDB'/L& !15 (+2,667 0,62! c + 0,46" 1)+ (-2,667 1,3! c + 0,46" 1)/4 +( 0,62! & + 0,46" 1)+ (-1,2!& + 0,46" 1)/4 = +1!
(+2,667 0,62! c + 0,46" 1)+ (-2,667 1,3! c + 0,46" 1) +( 0,62! & + 0,46" 1)+ (-1,2!& + 0,46" 1) = +60 (2,667-2,667) + ( 0,62! c 1,2!c) +( 0,62! &-1,2!&)+( + 0,46" 1+ 0,46" 1+ 0,46" 1+ 0,46" 1) = + 60 1,7!c 1,7!&+ 1,6 1 = + 60 ....................... .................................... ......................... ............(6) (6) PERSAMAAN MATRIK
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