Kuliah materi MEKANIKA MATERIAL BAHAN

MEKANIKA MATERIAL (BAHAN)
1.Jenis pembebanan pada material
2.Jenis tegangan (stress)
3.Perhitungan kekuatan material untuk
menentukan dimensi dan pemilihan bahan
berdasarkan jenis pembebanan yang terjadi

Terminology for Mechanical Properties


Stress - Force or load per unit area of cross-section over
which the force or load is acting.

 Strain - Elongation change in dimension per unit length.
 Young’s modulus - The slope of the linear part of the
stress-strain curve in the elastic region, same as modulus of
elasticity.
 Shear modulus (G) - The slope of the linear part of the
shear stress-shear strain curve.

Engineering Stress

Tegangan Normal (): intensitas gaya yang bekerja tegak
lurus bidang irisan
Ft
contoh: Tensile stress, ()
F
 t
Area, A

Ao

original area
before loading

Ft

Tegangan geser (): intensitas gaya yang bekerja sejajar bidang irisan
Contoh : Shear stress, ():
Ft
F
Fs

Area, A

Fs
F

Ft

Fs

Ao

Stress has units: N/m2 (or lb/in2
)

Modes of loading and states of stress

Modes of loading and states of
stress

Modes of loading and states of
stress

PEMBEBANAN PADA BEJANA TEKAN

PEMBEBANAN PADA BEJANA TEKAN

Tegangan Hoop pada bejana tekan

Gaya Hoop pada bejana tekan

Berdasarkan gambar d akan diuraikan gaya-gaya yg berlaku

F

y

0


 tl c  tl c  dPsin 0
0



2tl c dPsin
0


D
2tl c  dlpsin
2
0

D
2tl c  lp sin d
2 0
D

2tl c  lp  cos  0

2
D
Dp
2tl c  lp[2]  c 
2
2t

F

x

0

D
d
d
d  lp  tl  c sin
 tl  c sin
0
2

2
2
d
D
d
d
2 tl  c sin
 d  lp  sin

2
2
2
2
d
D
2 tl  c
 d  lp
2
2
D

d  lp
c  2
d
2 tl
2
Dp
c 
2t

F

z

0

 2
  L  ( D  t ) t  p D 0
4
D2
L

p   D  t  D
4  D  t t
D
L p
4t

F

x

0

D
d
d
d  lp  tl  c sin
 tl  c sin

2
2

2
d
D
d
d
2 tl  c sin
 d  lp  sin

2
2
2
2
d
D
2 tl  c
 d  lp
2
2
D
d  lp

2
c 
d
2 tl
2
Dp
c 
2t

F

z

0

  L ( D  t )t  p

 2
D 0
4

D2
L
p   D  t  D


4 D t t
D
L p
4t

Pure Tension
stress  e 
strain

Pure Compression

Fnormal

e 

Ao
l  lo
lo

Elastic
 E
response e

stress  e 

Fshear

Pure Shear

Ao

strain  tan 
Elastic
response

 e G
Pure Torsional Shear
26

MEKANIKA BAHAN
KONSEP STRESS

P

P
 
A

P
P

A

Gage length

P

P



Stress, 
Ultimate stress,  u
Yield stress,  y

1

2

3

4

5

Strain, 
1.
2.
3.
4.

Linear elastic: region of proportional elastic loading
Nonlinear elastic: up to yield
Perfect plasticity: plastic flow at constant load
Strain hardening: plastic flow with the increase of stress



Linear
Elastic

Nonlinear
Elastic



Extension Contraction
 



Hooke’s law for extension:

Shearing



Loading
Unloading

σ=E


Hooke’s law for shear:

=G


p



A

1 Pa = 145.04×10−6 psi



1 N
1 Pa 
1 m2

10 6 Pa 1 MPa

1 lb
1 Psi 
1 in 2

10 3 Psi 1 Ksi

V

V

A

 

E
G
2(1   )

Hooke’s law for extension:



σ=E

Hooke’s law for shear:



=G

F
F

d
F

t
t

F
F

F

t
 
a

p
Cylindrical bolt or rivet
F
t
t

F

F
b 
td

u

h


1


u
  tan( ) 
h

 




u

h
for   1

 y or  u
 allow 
n
 y or  u
 allow 
n

Common States of Stress
• Simple tension: cable

F

F

Ao = cross sectional
Area (when unloaded)

F


Ao



• Simple shear: drive shaft

M

Ac
M

2R

Fs

Ao

Ski lift

Fs
 
Ao

(photo courtesy P.M. Anderson)



Note:  = M/AcR here.
34

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Figure. A unidirectional force is applied to a specimen in the tensile
test by means of the moveable crosshead. The cross-head movement
can be performed using screws or a hydraulic mechanism

gauge
length

Properties Obtained from the Tensile
Test
 Elastic limit
 Tensile strength, Necking
 Hooke’s law
 Poisson’s ratio
 Modulus of resilience (Er)
 Tensile toughness
 Ductility

Test Specimen Standard

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc.
Thomson Learning™ is a trademark used herein under license.

Figure. The stress-strain curve for an aluminum alloy

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Figure. (a) Determining the 0.2% offset yield strength
in gray cast ion, and (b) upper and lower yield point
behavior in a low-carbon steel

cup-and-cone fracture
in Al
Figure. Localized
deformation of a ductile
material during a tensile
test produces a necked
region

brittle fracture in mild
steel

40

(Ultimate) Tensile Strength, σTS
• Maximum possible engineering stress in tension.

engineering
stress

TS
F = fracture
or
ultimate
strength

y

Typical response of a metal

strain
engineering strain

Neck – acts
as stress
concentrator

•
Metals: occurs when necking starts.
• Ceramics: occurs when crack propagation
starts.
• Polymers: occurs when polymer backbones
are

41

Deformation
Process During Test

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson
Learning™ is a trademark used herein under license.

cup-and-cone fracture
in Al
Figure. Localized
deformation of a ductile
material during a tensile
test produces a necked
region

brittle fracture in mild
steel

46

EULER CRITERIA

Modes of loading and states of
stress

PROBLEM

PROBLE
M

PROBLE
M

Rod AB

Rod BC

PROBLE
M

PROBLE
M