Moment Area Method

1. Moment-Area Theorems
dx
EI
M
d 






EI
M
dx
yd
2
2
EI
M
dx
dθ

dx
EI
MB
AAB 
AB/ 1st moment-area theorem
+
B
A

2. Moment-Area Theorems
• 2nd moment-area theorem
dx
EI
M
xdx
EI
M
xt
B
A
B
A
BA/  
dx
EI
M
xdxdt  
Horizontal dis btw A & centroid of M/EIA-B
M/EI area btw A & B
d
EI
M
dx
dθ


3. Moment-Area Theorems
dx
EI
M
xdx
EI
M
xt B
A
B
ABA/ 
dx
EI
M
xdx
EI
M
xt A
B
A
BAB '/ 
'x

4. Moment-Area Theorems
+
dx
EI
MB
A
AB/ 
1st moment-area theorem 2nd moment-area theorem
dx
EI
M
xt B
ABA/ 

5. Example 1
Determine the slope at points B & C of the beam. Take E = 200GPa, I = 360(106)mm4
ACCABB // ; 
rad
EI
kNm
m
EI
kNm
EI
kNm
m
EI
kNm
ABB
00521.0
375
)5(
50100
2
1
)5(
50
2
/















dx
EI
MB
A
AB/ 
radACC 00694.0/ 