navier

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


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)]






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 -------->



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









= 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




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




v b b v = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m


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 :




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 -------->

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









= 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









= 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





∞ ∞

w = ∑ ∑m=1,3… n=1,3…



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





v b b v = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m


a


Penyelesaian :




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 -------->

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









= 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









= 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





∞ ∞

w = ∑ ∑m=1,3… n=1,3…



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





v b b v = 1 b = 4.000 mξ = 0.5 a = 2.550 mη = 0.5 b = 2.000 m


a


Penyelesaian :




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 -------->

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









= 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









= 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





∞ ∞

w = ∑ ∑m=1,3… n=1,3…



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




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


Penyelesaian :




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




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









= 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









= 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





∞ ∞

w = ∑ ∑m=1,3… n=1,3…



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




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 :




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 = 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









= 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









= 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





∞ ∞

w = ∑ ∑m=1,3… n=1,3…



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


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

navier

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