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ELEMEN MESIN (RI.1232) Dosen: Fahmi Mubarok, ST., MSc. Metallurgy Laboratory Mechanical Engineering ITS- Surabaya 2008 Tegangan Konsep Tegangan Tegangan Tarik dan Tekan Tegangan lentur Tegangan geser dan puntir LECTURE II LECTURE II http://www.its.ac.id/personal/material.php?id=fahmi

Tegangan Geser, Lengkung Dan Puntir

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Page 1: Tegangan Geser, Lengkung Dan Puntir

ELEMEN MESIN(RI.1232)

Dosen:

Fahmi Mubarok, ST., MSc.

Metallurgy Laboratory

Mechanical Engineering

ITS- Surabaya

2008

Tegangan� Konsep Tegangan

� Tegangan Tarik dan Tekan

� Tegangan lentur

� Tegangan geser dan puntir

LECTURE IILECTURE II

http://www.its.ac.id/personal/material.php?id=fahmi

Page 2: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 2Mech. Eng. Dept. ITS Surabaya

Definition

- Tegangan (stress)

intensitas gaya persatuan luas

- Regangan (strain)

deformasi (perubahan bentuk) akibat tegangan yang bekerja

oA

P=σ

ol

l∆=ε

Jenis-jenis tegangan

1. Tegangan tarik dan tekan (Tensile dan compression stress).

2. Tegangan Geser (Shears stress) disini termasuk tegangan puntir (Torsional Stress ).

3. Tegangan Bending / lengkung ( Bending stress ).

4. Tegangan kombinasi ( Combination stress ).

V

Start with internal system of forces as shown below to get proper signs for V, N and M.

Page 3: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 3Mech. Eng. Dept. ITS Surabaya

Various of Average Normal Stress

Page 4: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 4Mech. Eng. Dept. ITS Surabaya

Tegangan Tarik dan Tekan

Untuk membandingkan spesimen

dengan berbagai ukuran, maka

digunakan konsep tegangan

teknik

F = beban yang diberikan tegak

lurus terhadap penampang

spesimen

Ao = luas penampang awal

sebelum beban diberikan

∆l = perpanjanganlo = panjang awal sebelum beban

diberikan

Tegangan dan regangan akan memberikan

nilai positif pada kondisi tegangan tarik

sedang pada kondisi tegangan tekan akan

memberikan nilai negatif

Page 5: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 5Mech. Eng. Dept. ITS Surabaya

Normal Stress due to Bending Moment

Key Points:

1. Internal bending moment causes beam to deform.

2. For this case, top fibers in compression, bottom in tension.

Page 6: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 6Mech. Eng. Dept. ITS Surabaya

Normal Stress due to Bending Moment

I

My=σ

Bending stress, psi

Internal bending moment, lb-in

Distance from NA to

point of interest, in

Moment of inertia, in4

Page 7: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 7Mech. Eng. Dept. ITS Surabaya

Design of Beams

Page 8: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 8Mech. Eng. Dept. ITS Surabaya

Tegangan Geser dan Puntir

Page 9: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 9Mech. Eng. Dept. ITS Surabaya

Average Shear Stress

• Forces P and P’ are applied transversely to the

member AB.

A

P=aveτ

• The corresponding average shear stress is,

• The resultant of the internal shear force distribution is

defined as the shear of the section and is equal to the

load P.

• Corresponding internal forces act in the plane of

section C and are called shearing forces.

• Shear stress distribution varies from zero at the

member surfaces to maximum values that may be

much larger than the average value.

• The shear stress distribution cannot be assumed to be

uniform.

Page 10: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 10Mech. Eng. Dept. ITS Surabaya

Average Shear Stress

A

F

A

P==aveτ

Single Shear

A

F

A

P

2ave ==τ

Double Shear

Page 11: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 11Mech. Eng. Dept. ITS Surabaya

Torsion

Torque is a moment that tends to twist a

member about its longitudinal axis.

4

21 cJ π=

( )41422

1 ccJ −= π

Page 12: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 12Mech. Eng. Dept. ITS Surabaya

Shear and Bending Moment Diagrams

• Variation of shear and bending

moment along beam may be

plotted.

• Determine reactions at supports.

• Cut beam at C and consider

member AC,

22 PxMPV +=+=

• Cut beam at E and consider

member EB,

( ) 22 xLPMPV −+=−=

• For a beam subjected to

concentrated loads, shear is

constant between loading points

and moment varies linearly.

Page 13: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 13Mech. Eng. Dept. ITS Surabaya

Sample Problem Bending and Shear

For the timber beam and loading shown,

draw the shear and bend-moment

diagrams and determine the maximum

normal stress due to bending.

SOLUTION:

• Treating the entire beam as a rigid

body, determine the reaction forces

• Identify the maximum shear and

bending-moment from plots of their

distributions.

• Apply the elastic flexure formulas to

determine the corresponding maximum

normal stress.

• Section the beam at points near

supports and load application points.

Apply equilibrium analyses on resulting

free-bodies to determine internal shear

forces and bending couples

Page 14: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 14Mech. Eng. Dept. ITS Surabaya

Sample Problem 5.1

SOLUTION:

• Treating the entire beam as a rigid body, determine the

reaction forces

∑ ∑ ==== kN14kN46:0 from DBBy RRMF

• Section the beam and apply equilibrium analyses on

resulting free-bodies

( )( ) 00m0kN200

kN200kN200

111

11

==+∑ =

−==−−∑ =

MMM

VVFy

( )( ) mkN500m5.2kN200

kN200kN200

222

22

⋅−==+∑ =

−==−−∑ =

MMM

VVFy

0kN14

mkN28kN14

mkN28kN26

mkN50kN26

66

55

44

33

=−=

⋅+=−=

⋅+=+=

⋅−=+=

MV

MV

MV

MV

Page 15: Tegangan Geser, Lengkung Dan Puntir

Fahmi Mubarok

I ���� 15Mech. Eng. Dept. ITS Surabaya

Sample Problem 5.1

• Identify the maximum shear and bending-

moment from plots of their distributions.

mkN50kN26 ⋅=== Bmm MMV

• Apply the elastic flexure formulas to

determine the corresponding maximum

normal stress.

( )( )

36

3

36

2

612

61

m1033.833

mN1050

m1033.833

m250.0m080.0

×

⋅×==

×=

==

S

M

hbS

Bmσ

Pa100.60 6×=mσ

Page 16: Tegangan Geser, Lengkung Dan Puntir

ELEMEN MESIN(RI.1232)

Dosen:

Fahmi Mubarok, ST., MSc.

Metallurgy Laboratory

Mechanical Engineering

ITS- Surabaya

2008

LECTURE IIILECTURE III

Sambungan-Sambungan Keling

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