Mekanika Rekayasa 2 - Materi 4.docx

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TEGANGAN LENTUR P

a

b SB X/ GRS NETRAL

c

d

M

M

a

бl = M Y / I = M / W

b

W=I/Y M = MOMEN LENTUR Y = JARAK SISI ATAU

c

d

ELEMEN DITINJAU TERHADAP GRS NETRAL I = MOMEN INERSIA

SUATU BALOK DIBEBANI BEBAN P, SEHINGGA BALOK TERSEBUT AKAN MELENDUT. DAPAT DILIHAT PADA TITIK a b DAN TITIK c d , DIMANA SERAT ATAS a b MEMENDEK ( TERTEKAN ), SEDANG SERAT BAWAHc d MEMANJANG ( TERTARIK ), MOMEN DIATAS ADALAHMOMEN POSITIF. DIAGRAM TEGANGAN LENTUR бla = M Ya / I X

elemen 1 Y1

Ya

Yb

бl 1 = M Y 1 / I x

бlb = M Yb / I X

GAMBAR DIAGRAM TEGANGAN LENTUR

-

-

+

-

-

-

+

+

+

+ +

+

+

+

-

-

-

+

-

+

-

CONTOH SOAL

1 t/m

5T

4T

α A

3T

B

C

5m

5m

tg α = 3/4

D 3m

DIKETAHUI SUATU KONSTRUKSI DENGAN BEBAN SEPERTI TERGAMBAR DIATAS HITUNG DAN GAMBAR DIAGRAM TEGANGAN NORMAL DAN LENTUR UNTUK : 1 . POTONGAN SEDIKIT SEBELAH KIRI B 2 . POTONGAN TENGAH BC 3 . POTONGAN SEDIKIT SEBELAH KANAN C ( HITUNG JUGA KOMBINASI TEGANGAN ) 15 cm 3 cm

YA

Garis netral

33 cm YB

5 cm MENCARI LETAK TITIK BERAT STATIS MOMEN TERHADAP SISI ATAS Y A ( 15. 3 + 5 . 30 ) = 15. 3 . 1,5 + 5 . 30 . 18 YA = 2767, 5 / 195 = 14, 19 CM

IX

3

2

Y B = 33 CM – 14, 19 CM = 18, 81 CM 3

2

= 1/12 . 15 . 3 + ( 14, 19 – 1,5 ) . 15 . 3 + 1/12 .5 30 + ( 18, 81 – 15 ) .30 .3 = 33, 75 + 7246, 62 + 11250 + 1306, 45 = 19836, 82 CM

1 . POTONGAN SEDIKIT SEBELAH KIRI B

4

∑H

=0

+ HA – 4 + 3 = 0

HA = 1 T

∑ MC

= O VA . 10 – 5. 7,5 – 3 . 5 + 4 . 3 = 0

VA = 4, 05 T

∑ MA

=0

VC = 7, 95 T

- VC . 10 + 4. 13 + 3. 5 + 5 . 2,5 = 0 3T 1 t /m

LIHAT KIRI POTONGAN

HA = 1T

4T A

N=+1T

B

M = = 4, 05 . 5 – 5 . 2,5 = 8 TM

4, 05 T 5m

бn =

1 . 10

3

2 = 5, 13 KG/ CM ( TARIK )

( 15 . 3 + 5 . 30 ) Ingat momen positif, serat bawah tertarik, serat atas tertekan . 3

бl a = =

= 572, 27 KG / CM

2

( TEKAN )

= 758, 59 KG / CM

2

( TARIK )

19836, 82

3

бl b = =

2

8. 10 . 10 . 14, 19

2

8. 10 . 10 . 18, 81 19836, 82

5, 13 -

572, 27 -

+ + 5, 13 DIAGRAM TEG. NORMAL

+ 758, 59 DIAGRAM TEG. LENTUR

17

2 . POTONGAN TENGAH BC LIHAT KANAN POTONGAN 4T C

N=+3T D

3T

M = - 4 , 5. 5 + 7, 95 . 2, 5 = = - 2, 65 TM

7, 95 T 2, 5 m

3m

3 . 10 3

бn =

=

2

15, 38 KG / CM ( TARIK )

( 15. 3 + 5 . 30 ) Ingat momen negatif,serat atas tertarik, serat bawah tertekan.

бl a = =

3

2

2, 65 . 10 . 10 . 14, 19 19836, 82 3

бl b = =

= 189, 56 KG / CM 2 ( TARIK )

2

2, 65 . 10 . 10 . 18, 81

= 251, 28 KG / CM 2 ( TEKAN )

19836, 82

DIAGRAM TEGANGAN

189, 56

15, 38

+

+ -+ 15, 38 TEG. NORMAL

251, 28 TEG. LENTUR

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