Slide CIV 209 AnalisisStruktur CIV 209 P4

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Mata Kuliah
Kode
SKS

: Analisis Struktur
: CIV – 209
: 4 SKS

Deformasi Elastis
Struktur Balok dan Portal
(Moment Area Method)
Pertemuan - 4

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• Kemampuan Akhir yang Diharapkan
• Mahasiswa dapat menganalisis deformasi struktur balok dengan
metode Luas Momen

• Sub Pokok Bahasan :
• Metode Luas Momen

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Moment Area Theorem
• Metode ini dikenal juga dengan metode
Mohr dan cukup unggul penggunaanya
untuk mengetahui putaran sudut dan
perpindahan vertikal pada titik tertentu
suatu struktur akibat rangkaian
pembebanan.
• Perhatikan struktur balok seperti
terlihat pada gambar 4.1.
Akibat
pembebanan yang terjadi, maka akan
terbentuk kurva diagram momen

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Teori I :

The change in slope between any two points on the

elastic curve equals the area of the M/EI diagram
between these two points.
B/ A 

 EI dx
B

A

M

B/A dalam radian

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Teori II : The vertical deviation of the tangent at a point (A)
on the elastic curve with respect to the tangent extended
from another point (B) e uals the o e t of the a ea
under the M/EI diagram between the two points (A and B).
This moment is computed about point A (the point on the
elastic curve), where the deviation is to be determined.

t A/ B  x

 EI dx
B

A

M

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• Note that in general tA/B is not equal to tB/A
• The moment of area under the M/EI diagram
between A and B is computed about point A
to determine tA/B, and it is computed about
point B to determine tB/A

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SHAPE

AREA

CENTROID

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Example 1
• Determine the slope at points B and C
• Take E = 200 GPa, I = 250(106) mm4.

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4,5 m

4,5 m

- 45/EI

- 90/EI

 45

303,75
 1  45

 4 ,5    
 4 ,5   
kN.m 2
EI
 EI
 2  EI


B  B/ A  

1  90 
405
kN.m 2
 9  
2  EI

EI


C  C / A   

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Example 2
• Determine the deflection at points B and C
• Take E = 200 GPa

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By inspection, the moment diagram for the beam is a rectangle.
Here we will construct the M/EI diagram relative to IBC, realizing that IAB
= 2IBC

 250

2000
B  tB / A  

 4 2  
N.m 3
EI BC
 EI BC


 250

 500

7250
N.m 3
 C  tC / A  
 4 5  
 3 1,5 
EI BC
 EI BC

 EI BC


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Example 3
Determine the slope at C. Take E = 200 GPa, I = 6(106)
mm4.

135
 30  1  60 30  135

kN .m 2 
 0,112 rad
  3

EI
2
EI
EI
EI
200


6
 



 C   D / C  3

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Example 4
• Determine the deflection at point C
• Take E = 200 GPa, I = 250(106) mm4.

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 C  t C / A  2t B / A

t C / A   8  8 
  
   8  8  8 

  2  EI 
 4   3  EI   3

1

3

 192   1

2.048
 1   1  192 
t B / A   8  8 
  
EI
 3   2  EI 
C  

11.264
EI

 1

 192 

11.264
EI

7.168
7.168
 2048 

 0 ,143 m
 2 

200

250
EI
EI



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Soal Latihan (Chapter VIII)

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8.10
8.11
8.12
8.13
8.14
8.15

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8.16
8.17
8.18
8.19
8.20
8.21

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8.22
8.23
8.24
8.25