Advanced Methods of Structural Analysis

3.5 Special Types of Trusses 71

Ta b l e 3. 1

Computation of internal force in substitute bar

State

Design diagram

Free-body diagram

Equilibrium equations

P

-loading

Substituted system in

Fig.

3.25

b subjected to

given load

P.

#/

;inthis

case

R

A

D

0:5P.

"

/

RA

=0.5

P

1

K

1

N

1 P

A

L

30

°

N

1P

!

X

M

leftK

D

0



R

3dA

C

N

1P

cos

30

ı

2d

C

N

1P

sin

30

ı

d

D

0

N

1P

.2

cos

30

ı

C

sin

30

ı/

D

3R

A

N

1P

D

3P =2

p 2

3=2

C

1=2

D

0:672P

C

FP

N

1 P

N

2 P

30

°

P

X

D

0

!

N

1P

D

N

2P

D

N

P

Y

D

0

!

F

P

C

2N

sin

30

ı

D

0

F

P

D

2N

sin

30

ı

D

0:672P

X

-loadingC

Substituted system in

Fig.

3.25

b subjected to unit

force

X

C

D

1(

"/

;inthis

case

R

A

=0.5(

#/

RA

=0.5

1

K

1

N

1 X

A

L

30

°

N

1X

!

X

M

leftK

D

0

R

3dA

C

N

1X

cos

30

ı

2d

C

N

1X

sin

30

ı

d

D

0

N

1X

.2

cos

30

ı

C

sin

30

ı/

D

3R

A

N

1X

D

3



1=2

p 2

3

=

2

C

1=2

D

0:672

F

N

1X

N

2X

C X

=C

1

30

°

P

X

D

0

!

N

1X

D

N

2X

D

N

X

P

Y

D

0

!

F

C

2N

X

sin

30

ı

C

1

D

0

F

D

2N

X

sin

30

ı



1

D

0:328