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Lx = a = 5.100 mLy = b = 4.000 mBeban qo pada bagian diarsir (setempat)qo = 2008.0 kg/m2
tebal u = 1 a = 5.100 mv = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m
Peningkatan Beban (%p) = 100qo = 1004 kg/m2
Untuk x = 2.550 my = 2.000 mE = 2E+09 kg/m2h = 0.1 mν = 0.2D = 173611.1 kg.m2p = 3.1416 m
x ym n m n m n
m 1 1 3 3 5 5n 0 393.7255 4947.7
amn
m n7 7
TUGAS : PELAT & CANGKANGDiketahui :Struktur Pelat spt gbr
Gambar : Tumpuan sendi pada 4 sisiLx = a = 5.100 m
u Ly = b = 4.000 mBeban qo pada bagian diarsir (setempat)qo = 2008.0 kg/m2tebal u = 1 a = 5.100 m
v b b v = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m
Peningkatan Beban (%p) = 100qo = 1004 kg/m2
a
Untuk x = 2.550 my = 2.000 mE = 2E+09 kg/m2h = 0.1 mν = 0.2D = 173611.11 kg.m2p = 3.1416 m
Penyelesaian :
Perhitungan dengan cara Navier dengan beban setempat ( u x v ) :
Perhitungan jarak :ξ-u/2 = 0 mξ+u/2 = 5.1 mη-v/2 = 0 mη+v/2 = 4 m
Mencari amn dengan rumus :
ξ+u/2 η+v/2
amn = 4/(a*b) ò òξ-u/2 η-v/2
ξ+u/2 η+v/2
= 4/(a*b)*qo * ò òξ-u/2 η-v/2
4 ξ+u/2
= 4/(a*b)*qo * * ò0 ξ-u/2
n = 15.1
am1 = 393.73 * 1.2732 * 2.0000 * ò0
m = 15.1
a11 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a11 = 3255.247 aplikasikan -------->
m = 35.1
a31 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a31 = 1085.082 aplikasikan -------->
m = 55.1
a51 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a51 = 651.0494 aplikasikan -------->
m = 75.1
a71 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a71 = 465.0353 aplikasikan -------->
m = 95.1
a91 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a91 = 361.6941 aplikasikan -------->
m = 115.1
a111 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a111 = 295.9315 aplikasikan -------->
qo * sin (mpx/a)*sin (mpy/b) dx dy
sin (mpx/a)*sin (mpy/b) dx dy
(b/np) * [(-cos(npy/b)] sin (mpx/a) dx
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
m = 135.1
a131 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a131 = 250.4036 aplikasikan -------->
m = 155.1
a151 = 1002.61 * 0
= 1002.61 * 0.1082 * 2.0000
a151 = 217.0165 aplikasikan -------->
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
n = 35.1
am3 = 393.73 * 0.4244 * 2.0000 * ò0
m = 15.1
a13 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a13 = 3255.247 aplikasikan -------->
m = 35.1
a33 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a33 = 1085.082 aplikasikan -------->
m = 55.1
a53 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a53 = 651.0494 aplikasikan -------->
m = 75.1
a73 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a73 = 465.0353 aplikasikan -------->
m = 95.1
a93 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a93 = 361.6941 aplikasikan -------->
m = 115.1
a113 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a113 = 295.9315 aplikasikan -------->
m = 135.1
a133 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a133 = 250.4036 aplikasikan -------->
m = 155.1
a153 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 2.0000
a153 = 217.0165
n = 55.1
am5 = 393.73 * 0.2546 * 2.0000 * ò0
m = 15.1
a15 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a15 = 3255.247 aplikasikan -------->
m = 35.1
a35 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a35 = 1085.082 aplikasikan -------->
m = 55.1
a55 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a55 = 651.0494 aplikasikan -------->
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
Mencari w dengan rumus :
∞ ∞
w = ∑ ∑m=1,3… n=1,3…
1/(p4*D) amn /((m^2/a^2+n^2/b^2)^2) * (sin (mpx/a)*sin (mpy/b))
Jumlahkan Jawaban! !! !V V
w11 = 0.0188896 m 0.0189 m 18.88958 mm
w31 = -0.0003845 m 0.0185 18.50511 mm
w51 = 0.0000367 m 0.0185 18.54185 mm
w71 = -0.0000073 m 0.0185 18.53459 mm
w91 = 0.0000021 m 0.0185 18.53671 mm
w111 = -0.0000008 m 0.0185 18.53592 mm
w131 = 0.0000003 m 0.0185 18.53627 mm
w151 = -0.0000002 m 0.0185 18.5361 mm
w13 = -0.0005330 m 0.0180 18.00309 mm
w33 = 0.0000777 m 0.0181 18.08082 mm
w53 = -0.0000166 m 0.0181 18.06424 mm
w73 = 0.0000046 m 0.0181 18.06884 mm
w93 = -0.0000016 m 0.0181 18.06725 mm
w113 = 0.0000006 m 0.0181 18.0679 mm
w133 = -0.0000003 m 0.0181 18.0676 mm
w153 = 0.0000002 m 0.0181 18.06775 mm
w15 = 0.0000751 m 0.0181 18.14285 mm
w35 = -0.0000176 m 0.0181 18.12524 mm
w55 = 0.0000060 m 0.0181 18.13128 mm Sampai disiniSudah cukup teliti
TUGAS : PELAT & CANGKANGDiketahui :Struktur Pelat spt gbr
Gambar : Tumpuan sendi pada 4 sisiLx = a = 5.100 m
u Ly = b = 4.000 mBeban qo pada bagian diarsir (setempat)qo = 2008.0 kg/m2tebal u = 1 a = 5.100 m
v b b v = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m
Peningkatan Beban (%p) = 100qo = 1004 kg/m2
a
Untuk x = 2.550 my = 2.000 mE = 2E+09 kg/m2h = 0.1 mν = 0.2D = 173611 kg.m2p = 3.1416 m
Penyelesaian :
Perhitungan dengan cara Navier dengan beban setempat ( u x v ) :
Perhitungan jarak :ξ-u/2 = 0 mξ+u/2 = 5.1 mη-v/2 = 0 mη+v/2 = 4 m
Mencari amn dengan rumus :
ξ+u/2 η+v/2
amn = 4/(a*b) ò òξ-u/2 η-v/2
ξ+u/2 η+v/2
= 4/(a*b)*qo * ò òξ-u/2 η-v/2
4 ξ+u/2
= 4/(a*b)*qo * * ò0 ξ-u/2
qo * sin (mpx/a)*sin (mpy/b) dx dy
sin (mpx/a)*sin (mpy/b) dx dy
(b/np) * [(-cos(npy/b)] sin (mpx/a) dx
n = 15.1
am1 = 393.73 * 1.2732 * 2.0000 * ò0
m = 15.1
a11 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a11 = 3255.247 aplikasikan -------->
m = 35.1
a31 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a31 = 1085.082 aplikasikan -------->
m = 55.1
a51 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a51 = 651.0494 aplikasikan -------->
m = 75.1
a71 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a71 = 465.0353 aplikasikan -------->
m = 95.1
a91 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a91 = 361.6941 aplikasikan -------->
m = 115.1
a111 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a111 = 295.9315 aplikasikan -------->
m = 135.1
a131 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a131 = 250.4036 aplikasikan -------->
m = 155.1
a151 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 2.0000
a151 = 217.0165 aplikasikan -------->
n = 35.1
am3 = 393.73 * 0.4244 * 2.0000 * ò0
m = 15.1
a13 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a13 = 3255.247 aplikasikan -------->
m = 35.1
a33 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a33 = 1085.082 aplikasikan -------->
m = 55.1
a53 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a53 = 651.0494 aplikasikan -------->
m = 75.1
a73 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a73 = 465.0353 aplikasikan -------->
m = 95.1
a93 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a93 = 361.6941 aplikasikan -------->
m = 115.1
a113 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a113 = 295.9315 aplikasikan -------->
m = 135.1
a133 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a133 = 250.4036 aplikasikan -------->
m = 155.1
a153 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 2.0000
a153 = 217.0165
n = 55.1
am5 = 393.73 * 0.2546 * 2.0000 * ò0
m = 15.1
a15 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a15 = 3255.247 aplikasikan -------->
m = 35.1
a35 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a35 = 1085.082 aplikasikan -------->
m = 55.1
a55 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a55 = 651.0494 aplikasikan -------->
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
Mencari w dengan rumus :
∞ ∞
w = ∑ ∑m=1,3… n=1,3…
1/(p4*D) amn /((m^2/a^2+n^2/b^2)^2) * (sin (mpx/a)*sin (mpy/b))
Jumlahkan Jawaban! !! !V V
w11 = 0.0188896 m 0.0189 m 18.88958 mm
w31 = -0.0003845 m 0.0185 18.50511 mm
w51 = 0.0000367 m 0.0185 18.54185 mm
w71 = -0.0000073 m 0.0185 18.53459 mm
w91 = 0.0000021 m 0.0185 18.53671 mm
w111 = -0.0000008 m 0.0185 18.53592 mm
w131 = 0.0000003 m 0.0185 18.53627 mm
w151 = -0.0000002 m 0.0185 18.5361 mm
w13 = -0.0005330 m 0.0180 18.00309 mm
w33 = 0.0000777 m 0.0181 18.08082 mm
w53 = -0.0000166 m 0.0181 18.06424 mm
w73 = 0.0000046 m 0.0181 18.06884 mm
w93 = -0.0000016 m 0.0181 18.06725 mm
w113 = 0.0000006 m 0.0181 18.0679 mm
w133 = -0.0000003 m 0.0181 18.0676 mm
w153 = 0.0000002 m 0.0181 18.06775 mm
w15 = 0.0000751 m 0.0181 18.14285 mm
w35 = -0.0000176 m 0.0181 18.12524 mm
w55 = 0.0000060 m 0.0181 18.13128 mm Sampai disiniSudah cukup teliti
TUGAS : PELAT & CANGKANGDiketahui :Struktur Pelat spt gbr
Gambar : Tumpuan sendi pada 4 sisiLx = a = 5.100 m
u Ly = b = 4.000 mBeban qo pada bagian diarsir (setempat)qo = 2008.0 kg/m2tebal u = 1 a = 5.100 m
v b b v = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m
Peningkatan Beban (%p) = 100qo = 1004 kg/m2
a
Untuk x = 2.550 my = 2.000 mE = 2E+09 kg/m2h = 0.1 mν = 0.2D = 173611 kg.m2p = 3.1416 m
Penyelesaian :
Perhitungan dengan cara Navier dengan beban setempat ( u x v ) :
Perhitungan jarak :ξ-u/2 = 0 mξ+u/2 = 5.1 mη-v/2 = 0 mη+v/2 = 4 m
Mencari amn dengan rumus :
ξ+u/2 η+v/2
amn = 4/(a*b) ò òξ-u/2 η-v/2
ξ+u/2 η+v/2
= 4/(a*b)*qo * ò òξ-u/2 η-v/2
4 ξ+u/2
= 4/(a*b)*qo * * ò0 ξ-u/2
qo * sin (mpx/a)*sin (mpy/b) dx dy
sin (mpx/a)*sin (mpy/b) dx dy
(b/np) * [(-cos(npy/b)] sin (mpx/a) dx
n = 15.1
am1 = 393.73 * 1.2732 * 2.0000 * ò0
m = 15.1
a11 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a11 = 3255.247 aplikasikan -------->
m = 35.1
a31 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a31 = 1085.082 aplikasikan -------->
m = 55.1
a51 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a51 = 651.0494 aplikasikan -------->
m = 75.1
a71 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a71 = 465.0353 aplikasikan -------->
m = 95.1
a91 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a91 = 361.6941 aplikasikan -------->
m = 115.1
a111 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a111 = 295.9315 aplikasikan -------->
m = 135.1
a131 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a131 = 250.4036 aplikasikan -------->
m = 155.1
a151 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 2.0000
a151 = 217.0165 aplikasikan -------->
n = 35.1
am3 = 393.73 * 0.4244 * 2.0000 * ò0
m = 15.1
a13 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a13 = 3255.247 aplikasikan -------->
m = 35.1
a33 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a33 = 1085.082 aplikasikan -------->
m = 55.1
a53 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a53 = 651.0494 aplikasikan -------->
m = 75.1
a73 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a73 = 465.0353 aplikasikan -------->
m = 95.1
a93 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a93 = 361.6941 aplikasikan -------->
m = 115.1
a113 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a113 = 295.9315 aplikasikan -------->
m = 135.1
a133 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a133 = 250.4036 aplikasikan -------->
m = 155.1
a153 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 2.0000
a153 = 217.0165
n = 55.1
am5 = 393.73 * 0.2546 * 2.0000 * ò0
m = 15.1
a15 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a15 = 3255.247 aplikasikan -------->
m = 35.1
a35 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a35 = 1085.082 aplikasikan -------->
m = 55.1
a55 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a55 = 651.0494 aplikasikan -------->
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
Mencari w dengan rumus :
∞ ∞
w = ∑ ∑m=1,3… n=1,3…
1/(p4*D) amn /((m^2/a^2+n^2/b^2)^2) * (sin (mpx/a)*sin (mpy/b))
Jumlahkan Jawaban! !! !V V
w11 = 0.0188896 m 0.0189 m 18.88958 mm
w31 = -0.0003845 m 0.0185 18.50511 mm
w51 = 0.0000367 m 0.0185 18.54185 mm
w71 = -0.0000073 m 0.0185 18.53459 mm
w91 = 0.0000021 m 0.0185 18.53671 mm
w111 = -0.0000008 m 0.0185 18.53592 mm
w131 = 0.0000003 m 0.0185 18.53627 mm
w151 = -0.0000002 m 0.0185 18.5361 mm
w13 = -0.0005330 m 0.0180 18.00309 mm
w33 = 0.0000777 m 0.0181 18.08082 mm
w53 = -0.0000166 m 0.0181 18.06424 mm
w73 = 0.0000046 m 0.0181 18.06884 mm
w93 = -0.0000016 m 0.0181 18.06725 mm
w113 = 0.0000006 m 0.0181 18.0679 mm
w133 = -0.0000003 m 0.0181 18.0676 mm
w153 = 0.0000002 m 0.0181 18.06775 mm
w15 = 0.0000751 m 0.0181 18.14285 mm
w35 = -0.0000176 m 0.0181 18.12524 mm
w55 = 0.0000060 m 0.0181 18.13128 mm Sampai disiniSudah cukup teliti
TUGAS : PELAT & CANGKANGDiketahui :Struktur Pelat spt gbr
Gambar : Tumpuan sendi pada 4 sisiLx = a = 5.100 m
u Ly = b = 4.000 mBeban qo pada bagian diarsir (setempat)qo = 2008.0 kg/m2tebal u = 1 a = 5.100 m
v b b v = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m
Peningkatan Beban (%p) = 100qo = 1004 kg/m2
a
Untuk x = 2.550 my = 2.000 mE = 2E+09 kg/m2h = 0.1 mν = 0.2D = 173611 kg.m2p = 3.1416 m
Penyelesaian :
Perhitungan dengan cara Navier dengan beban setempat ( u x v ) :
Perhitungan jarak :ξ-u/2 = 0 mξ+u/2 = 5.1 mη-v/2 = 0 mη+v/2 = 4 m
Mencari amn dengan rumus :
ξ+u/2 η+v/2
amn = 4/(a*b) ò òξ-u/2 η-v/2
ξ+u/2 η+v/2
= 4/(a*b)*qo * ò òξ-u/2 η-v/2
4 ξ+u/2
= 4/(a*b)*qo * * ò0 ξ-u/2
qo * sin (mpx/a)*sin (mpy/b) dx dy
sin (mpx/a)*sin (mpy/b) dx dy
(b/np) * [(-cos(npy/b)] sin (mpx/a) dx
n = 15.1
am1 = 393.73 * 1.2732 * 2.0000 * ò0
m = 15.1
a11 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a11 = 3255.247 aplikasikan -------->
m = 35.1
a31 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a31 = 1085.082 aplikasikan -------->
m = 55.1
a51 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a51 = 651.0494 aplikasikan -------->
m = 75.1
a71 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a71 = 465.0353 aplikasikan -------->
m = 95.1
a91 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a91 = 361.6941 aplikasikan -------->
m = 115.1
a111 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a111 = 295.9315 aplikasikan -------->
m = 135.1
a131 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a131 = 250.4036 aplikasikan -------->
m = 155.1
a151 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 2.0000
a151 = 217.0165 aplikasikan -------->
n = 35.1
am3 = 393.73 * 0.4244 * 2.0000 * ò0
m = 15.1
a13 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a13 = 3255.247 aplikasikan -------->
m = 35.1
a33 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a33 = 1085.082 aplikasikan -------->
m = 55.1
a53 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a53 = 651.0494 aplikasikan -------->
m = 75.1
a73 = 1002.61 * 0
= 1002.61 * 0.2319 * 2.0000
a73 = 465.0353 aplikasikan -------->
m = 95.1
a93 = 1002.61 * 0
= 1002.61 * 0.1804 * 2.0000
a93 = 361.6941 aplikasikan -------->
m = 115.1
a113 = 1002.61 * 0
= 1002.61 * 0.1476 * 2.0000
a113 = 295.9315 aplikasikan -------->
m = 135.1
a133 = 1002.61 * 0
= 1002.61 * 0.1249 * 2.0000
a133 = 250.4036 aplikasikan -------->
m = 155.1
a153 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 2.0000
a153 = 217.0165
n = 55.1
am5 = 393.73 * 0.2546 * 2.0000 * ò0
m = 15.1
a15 = 1002.61 * 0
= 1002.61 * 1.6234 * 2.0000
a15 = 3255.247 aplikasikan -------->
m = 35.1
a35 = 1002.61 * 0
= 1002.61 * 0.5411 * 2.0000
a35 = 1085.082 aplikasikan -------->
m = 55.1
a55 = 1002.61 * 0
= 1002.61 * 0.3247 * 2.0000
a55 = 651.0494 aplikasikan -------->
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
Mencari w dengan rumus :
∞ ∞
w = ∑ ∑m=1,3… n=1,3…
1/(p4*D) amn /((m^2/a^2+n^2/b^2)^2) * (sin (mpx/a)*sin (mpy/b))
Jumlahkan Jawaban! !! !V V
w11 = 0.0188896 m 0.0189 m 18.88958 mm
w31 = -0.0003845 m 0.0185 18.50511 mm
w51 = 0.0000367 m 0.0185 18.54185 mm
w71 = -0.0000073 m 0.0185 18.53459 mm
w91 = 0.0000021 m 0.0185 18.53671 mm
w111 = -0.0000008 m 0.0185 18.53592 mm
w131 = 0.0000003 m 0.0185 18.53627 mm
w151 = -0.0000002 m 0.0185 18.5361 mm
w13 = -0.0005330 m 0.0180 18.00309 mm
w33 = 0.0000777 m 0.0181 18.08082 mm
w53 = -0.0000166 m 0.0181 18.06424 mm
w73 = 0.0000046 m 0.0181 18.06884 mm
w93 = -0.0000016 m 0.0181 18.06725 mm
w113 = 0.0000006 m 0.0181 18.0679 mm
w133 = -0.0000003 m 0.0181 18.0676 mm
w153 = 0.0000002 m 0.0181 18.06775 mm
w15 = 0.0000751 m 0.0181 18.14285 mm
w35 = -0.0000176 m 0.0181 18.12524 mm
w55 = 0.0000060 m 0.0181 18.13128 mm Sampai disiniSudah cukup teliti
TUGAS : PELAT & CANGKANGDiketahui :Struktur Pelat spt gbr
Gambar : Tumpuan sendi pada 4 sisiLx = a = 5.100 m
u Ly = b = 4.000 mBeban qo pada bagian diarsir (setempat)qo = 2008.0 kg/m2
vtebal u = 1 a = 5.100 m
b v = 0.5 b = 2.000 mξ = 0.5 a = 2.550 mη = 0.25 b = 1.000 m
Peningkatan Beban (%p) = 100 %qo = 1004 kg/m2
a
Untuk x = 2.550 my = 2.000 mE = 2E+09 kg/m2h = 0.1 mν = 0.2D = 173611 kg.m2p = 3.1416 m
Penyelesaian :
Perhitungan dengan cara Navier dengan beban setempat ( u x v ) :
Perhitungan jarak :ξ-u/2 = 0 mξ+u/2 = 5.1 mη-v/2 = 0 mη+v/2 = 2 m
Mencari amn dengan rumus :
ξ+u/2 η+v/2
amn = 4/(a*b) ò òξ-u/2 η-v/2
ξ+u/2 η+v/2
= 4/(a*b)*qo * ò òξ-u/2 η-v/2
2 ξ+u/2
= 4/(a*b)*qo * * ò0 ξ-u/2
qo * sin (mpx/a)*sin (mpy/b) dx dy
sin (mpx/a)*sin (mpy/b) dx dy
(b/np) * [(-cos(npy/b)] sin (mpx/a) dx
n = 15.1
am1 = 393.73 * 1.2732 * 1.0000 * ò0
m = 15.1
a11 = 501.31 * 0
= 501.31 * 1.6234 * 2.0000
a11 = 1627.62 aplikasikan -------->
m = 35.1
a31 = 501.31 * 0
= 501.31 * 0.5411 * 2.0000
a31 = 542.541 aplikasikan -------->
m = 55.1
a51 = 501.31 * 0
= 501.31 * 0.3247 * 2.0000
a51 = 325.525 aplikasikan -------->
m = 75.1
a71 = 501.31 * 0
= 501.31 * 0.2319 * 2.0000
a71 = 232.518 aplikasikan -------->
m = 95.1
a91 = 501.31 * 0
= 501.31 * 0.1804 * 2.0000
a91 = 180.847 aplikasikan -------->
m = 115.1
a111 = 501.31 * 0
= 501.31 * 0.1476 * 2.0000
a111 = 147.966 aplikasikan -------->
m = 135.1
a131 = 501.31 * 0
= 501.31 * 0.1249 * 2.0000
a131 = 125.202 aplikasikan -------->
m = 155.1
a151 = 501.31 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 501.31 * 0.1082 * 2.0000
a151 = 108.508 aplikasikan -------->
n = 35.1
am3 = 393.73 * 0.4244 * 1.0000 * ò0
m = 15.1
a13 = 501.31 * 0
= 501.31 * 1.6234 * 2.0000
a13 = 1627.62 aplikasikan -------->
m = 35.1
a33 = 501.31 * 0
= 501.31 * 0.5411 * 2.0000
a33 = 542.541 aplikasikan -------->
m = 55.1
a53 = 501.31 * 0
= 501.31 * 0.3247 * 2.0000
a53 = 325.525 aplikasikan -------->
m = 75.1
a73 = 501.31 * 0
= 501.31 * 0.2319 * 2.0000
a73 = 232.518 aplikasikan -------->
m = 95.1
a93 = 501.31 * 0
= 501.31 * 0.1804 * 2.0000
a93 = 180.847 aplikasikan -------->
m = 115.1
a113 = 501.31 * 0
= 501.31 * 0.1476 * 2.0000
a113 = 147.966 aplikasikan -------->
m = 135.1
a133 = 501.31 * 0
= 501.31 * 0.1249 * 2.0000
a133 = 125.202 aplikasikan -------->
m = 155.1
a153 = 501.31 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 501.31 * 0.1082 * 2.0000
a153 = 108.508
n = 55.1
am5 = 393.73 * 0.2546 * 1.0000 * ò0
m = 15.1
a15 = 501.31 * 0
= 501.31 * 1.6234 * 2.0000
a15 = 1627.62 aplikasikan -------->
m = 35.1
a35 = 501.31 * 0
= 501.31 * 0.5411 * 2.0000
a35 = 542.541 aplikasikan -------->
m = 55.1
a55 = 501.31 * 0
= 501.31 * 0.3247 * 2.0000
a55 = 325.525 aplikasikan -------->
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
Mencari w dengan rumus :
∞ ∞
w = ∑ ∑m=1,3… n=1,3…
1/(p4*D) amn /((m^2/a^2+n^2/b^2)^2) * (sin (mpx/a)*sin (mpy/b))
Jumlahkan Jawaban! !! !V V
w11 = 0.0094448 m 0.0094 m 9.444789 mm
w31 = -0.0001922 m 0.0093 9.252556 mm
w51 = 0.0000184 m 0.0093 9.270925 mm
w71 = -0.0000036 m 0.0093 9.267296 mm
w91 = 0.0000011 m 0.0093 9.268356 mm
w111 = -0.0000004 m 0.0093 9.267962 mm
w131 = 0.0000002 m 0.0093 9.268134 mm
w151 = -0.0000001 m 0.0093 9.268049 mm
w13 = -0.0002665 m 0.0090 9.001545 mm
w33 = 0.0000389 m 0.0090 9.040412 mm
w53 = -0.0000083 m 0.0090 9.032121 mm
w73 = 0.0000023 m 0.0090 9.034418 mm
w93 = -0.0000008 m 0.0090 9.033627 mm
w113 = 0.0000003 m 0.0090 9.033949 mm
w133 = -0.0000001 m 0.0090 9.0338 mm
w153 = 0.0000001 m 0.0090 9.033876 mm
w15 = 0.0000376 m 0.0091 9.071427 mm
w35 = -0.0000088 m 0.0091 9.062619 mm
w55 = 0.0000030 m 0.0091 9.065642 mm Sampai disiniSudah cukup teliti
TUGAS : PELAT & CANGKANGDiketahui :Struktur Pelat spt gbr
Gambar : Tumpuan sendi pada 4 sisiLx = a = 5.100 m
a Ly = b = 4.000 mBeban qo pada bagian diarsir (setempat)qo = 2008 kg/m2tebal u = 0.5 a = 2.550 mv = 1 b = 4.000 m
b v ξ = 0.25 a = 1.275 mη = 0.5 b = 2.000 m
Peningkatan Beban (%p) = 100 %qo = 1004 kg/m2
u
x = 2.550 my = 2.000 mE = 2E+09 kg/m2h = 0.1 mν = 0.2D = 173611 kg.m2p = 3.1416 m
Penyelesaian :
Perhitungan dengan cara Navier dengan beban setempat ( u x v ) :
Perhitungan jarak :ξ-u/2 = 0 mξ+u/2 = 2.55 mη-v/2 = 0 mη+v/2 = 4 m
Mencari amn dengan rumus :
ξ+u/2 η+v/2
amn = 4/(a*b) ò òξ-u/2 η-v/2
ξ+u/2 η+v/2
= 4/(a*b)*qo * ò òξ-u/2 η-v/2
4 ξ+u/2
= 4/(a*b)*qo * * ò0 ξ-u/2
qo * sin (mpx/a)*sin (mpy/b) dx dy
sin (mpx/a)*sin (mpy/b) dx dy
(b/np) * [(-cos(npy/b)] sin (mpx/a) dx
n = 12.55
am1 = 393.73 * 1.2732 * 2.0000 * ò0
m = 12.55
a11 = 1002.61 * 0
= 1002.61 * 1.6234 * 1.0000
a11 = 1627.62 aplikasikan -------->
m = 32.55
a31 = 1002.61 * 0
= 1002.61 * 0.5411 * 1.0000
a31 = 542.541 aplikasikan -------->
m = 52.55
a51 = 1002.61 * 0
= 1002.61 * 0.3247 * 1.0000
a51 = 325.525 aplikasikan -------->
m = 72.55
a71 = 1002.61 * 0
= 1002.61 * 0.2319 * 1.0000
a71 = 232.518 aplikasikan -------->
m = 92.55
a91 = 1002.61 * 0
= 1002.61 * 0.1804 * 1.0000
a91 = 180.847 aplikasikan -------->
m = 112.55
a111 = 1002.61 * 0
= 1002.61 * 0.1476 * 1.0000
a111 = 147.966 aplikasikan -------->
m = 132.55
a131 = 1002.61 * 0
= 1002.61 * 0.1249 * 1.0000
a131 = 125.202 aplikasikan -------->
m = 152.55
a151 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 1.0000
a151 = 108.508 aplikasikan -------->
n = 32.55
am3 = 393.73 * 0.4244 * 2.0000 * ò0
m = 12.55
a13 = 1002.61 * 0
= 1002.61 * 1.6234 * 1.0000
a13 = 1627.62 aplikasikan -------->
m = 32.55
a33 = 1002.61 * 0
= 1002.61 * 0.5411 * 1.0000
a33 = 542.541 aplikasikan -------->
m = 52.55
a53 = 1002.61 * 0
= 1002.61 * 0.3247 * 1.0000
a53 = 325.525 aplikasikan -------->
m = 72.55
a73 = 1002.61 * 0
= 1002.61 * 0.2319 * 1.0000
a73 = 232.518 aplikasikan -------->
m = 92.55
a93 = 1002.61 * 0
= 1002.61 * 0.1804 * 1.0000
a93 = 180.847 aplikasikan -------->
m = 112.55
a113 = 1002.61 * 0
= 1002.61 * 0.1476 * 1.0000
a113 = 147.966 aplikasikan -------->
m = 132.55
a133 = 1002.61 * 0
= 1002.61 * 0.1249 * 1.0000
a133 = 125.202 aplikasikan -------->
m = 152.55
a153 = 1002.61 * 0
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
= 1002.61 * 0.1082 * 1.0000
a153 = 108.508
n = 52.55
am5 = 393.73 * 0.2546 * 2.0000 * ò0
m = 12.55
a15 = 1002.61 * 0
= 1002.61 * 1.6234 * 1.0000
a15 = 1627.62 aplikasikan -------->
m = 32.55
a35 = 1002.61 * 0
= 1002.61 * 0.5411 * 1.0000
a35 = 542.541 aplikasikan -------->
m = 52.55
a55 = 1002.61 * 0
= 1002.61 * 0.3247 * 1.0000
a55 = 325.525 aplikasikan -------->
sin (mpx/a) dx
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
(a/mp) [(-cos(mpy/a)]
Mencari w dengan rumus :
∞ ∞
w = ∑ ∑m=1,3… n=1,3…
1/(p4*D) amn /((m^2/a^2+n^2/b^2)^2) * (sin (mpx/a)*sin (mpy/b))
Jumlahkan Jawaban! !! !V V
w11 = 0.0094448 m 0.0094 m 9.444789 mm
w31 = -0.0001922 m 0.0093 9.252556 mm
w51 = 0.0000184 m 0.0093 9.270925 mm
w71 = -0.0000036 m 0.0093 9.267296 mm
w91 = 0.0000011 m 0.0093 9.268356 mm
w111 = -0.0000004 m 0.0093 9.267962 mm
w131 = 0.0000002 m 0.0093 9.268134 mm
w151 = -0.0000001 m 0.0093 9.268049 mm
w13 = -0.0002665 m 0.0090 9.001545 mm
w33 = 0.0000389 m 0.0090 9.040412 mm
w53 = -0.0000083 m 0.0090 9.032121 mm
w73 = 0.0000023 m 0.0090 9.034418 mm
w93 = -0.0000008 m 0.0090 9.033627 mm
w113 = 0.0000003 m 0.0090 9.033949 mm
w133 = -0.0000001 m 0.0090 9.0338 mm
w153 = 0.0000001 m 0.0090 9.033876 mm
w15 = 0.0000376 m 0.0091 9.071427 mm
w35 = -0.0000088 m 0.0091 9.062619 mm
w55 = 0.0000030 m 0.0091 9.065642 mm Sampai disiniSudah cukup teliti
Kesimpulan dari peningkatan beban setiap 10% dari beban semula adalah
1.Lendutan semakin membesar setiap peninggkatan beban
2.semakin besar beban maka tebal plat dibutuh semakin besar pula agar tidak terjadi deformasi/lendutan yang besar
Terima kasih
Kesimpulan dari peningkatan beban setiap 10% dari beban semula adalah
1.Lendutan semakin membesar setiap peninggkatan beban
2.semakin besar beban maka tebal plat dibutuh semakin besar pula agar tidak terjadi deformasi/lendutan yang besar
Terima kasih