Conjugate Beam Method for Determinate Beams

1. Conjugate-Beam Method
• Mathematical analogy
-slope-deflection Load-shear-moment
EI
M
EI
M
dx
dθ

θ
dx
dy

EI
M
dx
yd
2
2
w
dx
dV

V
dx
dM

w
dx
Md
2
2

2. Conjugate-Beam Method
• Mathematical equivalence
-slope-deflection Load-shear-moment
EI
M
EI
M
θ
y
w
V
M
Actual beam Conjugate beam

3. Conjugate-Beam Method
P
EI
M
EI
PL
Actual beam Conjugate beam
0
0


y
θ
0
0


y
θ
0
0


M
V
0
0


M
V
EI
PL
w
V







L
x
EI
PL
1









L
x
x
EI
PL
2
2









L
xx
EI
PL
62
32
P
My
θ
?

4.  or
Conjugate-Beam Method

5. Conjugate-Beam Method
Conjugate beams are mathematical/imaginative beams
No need to worry about their stability
Just use EQ concept to obtain V and M from w