momen pelat dan lendutan pelat

1. Nama : SHALEH AFIF HASIBUAN
NIM :16-009

2. JAWAB
Diketahui
Lx = 5 m ; Ly = 4m ; h = 10 cm
LL = 400 kg/m2
f’c = 30 mpa
E = 4700√30 = 25742.96 𝑚𝑝𝑎
𝐼 =
1
12
𝑏ℎ =
1
12
𝑥1000𝑥100
𝛾 = 2.5 𝑡/𝑚
Dead load
Berat sendiri (DL) = 2.5𝑥10 𝑥0.1 = 250 𝑘𝑔 𝑚⁄
P = 1.2 (250) + 1.6 (400) = 940 𝑘𝑔 𝑚⁄
a) Jepit – jepit
𝜀 =
5
4
= 1.25
𝑘 = 1 +
1
1.25
= 0.709
𝑎𝑟𝑎ℎ 𝑥
𝑃 = (1 − 𝑘)𝑝 = (1 − 0.709)𝑥940 = 273.54 𝑘𝑔 𝑚⁄
𝑀𝑗𝑒𝑝𝑖𝑡 =
1
12
𝑝 𝐿 =
1
12
𝑥273.54𝑥5 = 569,875 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 =
1
24
𝑃 𝐿 =
1
24
𝑥273.54𝑥5 = 284,9375 𝑘𝑔𝑚
𝑎𝑟𝑎ℎ 𝑦
𝑃 = 𝑘𝑥𝑝 = 0.709𝑥940 = 666.46 𝑘𝑔 𝑚⁄

3. 𝑀𝑗𝑒𝑝𝑖𝑡 =
1
12
𝑝 𝐿 =
1
12
𝑥666.46𝑥4 = 888,613 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 =
1
24
𝑃 𝐿 =
1
24
𝑥273.54𝑥4 = 444,306 𝑘𝑔𝑚
Momen arah xMomen arah x

4. Lendutan
Arah x
𝑤 = 𝑃 𝐿 =
, ,
,
= 0,002 𝑚𝑚
Arah y
𝑤 = 𝑃 𝐿 =
666.46 ,
,
= 0,002 𝑚𝑚
Momen arah y
Lendutan arah x

5. b) Sendi – sendi
𝜀 =
5
4
= 1.25
𝑘 = 1 +
1
1.25
= 0.709
𝑎𝑟𝑎ℎ 𝑥
𝑃 = (1 − 𝑘)𝑝 = (1 − 0.709)𝑥940 = 273.54 𝑘𝑔 𝑚⁄
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 =
1
8
𝑝 𝐿 =
1
8
𝑥273.54𝑥5 = 854,8125 𝑘𝑔𝑚
𝑎𝑟𝑎ℎ 𝑦
𝑃 = 𝑘𝑥𝑝 = 0.709𝑥940 = 666.46 𝑘𝑔 𝑚⁄
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 =
1
8
𝑝 𝐿 =
1
8
𝑥666.46𝑥4 = 1332,92 𝑘𝑔𝑚
Lendutan arah y

6. Lendutan
Arah x
𝑤 = 𝑃 𝐿 =
5𝑥273,54𝑥9,8𝑥5000
4
𝑥12
384𝑥25742,96𝑥106
𝑥1000𝑥1003 = 0,01 𝑚𝑚
Arah y
𝑤 = 𝑃 𝐿 =
. ,
,
= 0,01 𝑚𝑚
Momen arah x
Momen arah y

7. Lendutan arah x
Lendutan arah y

8. c) Jepit – sendi
𝜀 =
5
4
= 1.25
𝑘 = 1 +
1
1.25
= 0.709
𝑎𝑟𝑎ℎ 𝑥
𝑃 = (1 − 𝑘)𝑝 = (1 − 0.709)𝑥940 = 273.54 𝑘𝑔 𝑚⁄
𝑀𝑗𝑒𝑝𝑖𝑡 =
1
8
𝑝 𝐿 =
1
8
𝑥273.54𝑥5 = 854,8125 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 =
9
128
𝑝 𝐿 =
9
128
𝑥273.54𝑥5 = 480,83 𝑘𝑔𝑚
𝑎𝑟𝑎ℎ 𝑦
𝑃 = 𝑘𝑥𝑝 = 0.709𝑥940 = 666.46 𝑘𝑔 𝑚⁄
𝑀𝑗𝑒𝑝𝑖𝑡 =
1
8
𝑝 𝐿 =
1
8
𝑥666.46𝑥4 = 1332,92 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 =
9
128
𝑝 𝐿 =
9
128
𝑥666,46𝑥4 = 749,76 𝑘𝑔𝑚

9. Lendutan Arah x
𝑤 = =
, ,
,
= 0,004 𝑚𝑚
Lendutan Arah y
𝑤 = =
. ,
,
= 0,004 𝑚𝑚
Lendutan arah x

10. Lendutan arah y

11. KESIMPULAN
ARAH X (bentang terpanjang)
ARAH Y (bentang terpendek)
Perletakan Momen lendutan
Jepit - Jepit
𝑀𝑗𝑒𝑝𝑖𝑡 = 888,613 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 = 444,306 𝑘𝑔𝑚 𝑦 = 0,002 𝑚𝑚
Sendi - Sendi 𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 = 1332,92 𝑘𝑔𝑚 𝑦 = 0,01 𝑚𝑚
Jepit - Sendi
𝑀𝑗𝑒𝑝𝑖𝑡 = 1332,92 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 = 749,76 𝑘𝑔𝑚 𝑦 = 0,004 𝑚𝑚
Momen terbesar berada di bentang terpendek
Momen lapangan terbesar di arah y dengan perletakan sendi – sendi adalah 1332,92 kgm
Momen Perletakan terbesar di arah y dengan perletakan Jepit – sendi adalah 1332,92 kgm
Lendutan terbesar terjadi di perletakan sendi – sendi dengan 𝑦 = 𝑥 = 0,01 𝑚𝑚
Perletakan Momen lendutan
Jepit - Jepit
𝑀𝑗𝑒𝑝𝑖𝑡 = 569,875 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 = 284,9375 𝑘𝑔𝑚 𝑥 = 0,002 𝑚𝑚
Sendi - Sendi 𝑀𝑙𝑎𝑝𝑛𝑔𝑎𝑛 = 854,8125 𝑘𝑔𝑚 𝑥 = 0,01 𝑚𝑚
Jepit - Sendi
𝑀𝑗𝑒𝑝𝑖𝑡 = 854,8125 𝑘𝑔𝑚
𝑀𝑙𝑎𝑝𝑎𝑛𝑔𝑎𝑛 = 480,83 𝑘𝑔𝑚 𝑥 = 0,004 𝑚𝑚