Structural Analysis Methods II: Structural Systems - Mechanics of Structures: Variational and Computational Methods - page 245

TABLE 5.1
Transfer Matrices for Bar with Extension and Bending (Sign Convention 1)
Transfer Matrix

u
w
N
V
M

1 / EA u

w
N
V
M

3 2

− − / − /

1 6 EI 2 EI

2

1 / 2 EI / EI

=

1

1

1

b a

U i z b = z a

Point Matrix for Joint

+ −

cos α sin α

u
w
N
V
M

u
w
N
V
M

− sin α cos α

1

=

− cos α − sin α

sin α − cos α

− 1

k k

z k z k = U k

Point Matrix for Spring Supports

+ −

1

u
w
N
V
M

u
w
N
V
M

1

1

=

k u 1

k w 1

k θ 1

k k

z k z k

= U k

Point Matrix Extended for Applied Concentrated Forces

+ −

u
w
N
V
M
1

1 u

w
N
V
M
1

1

1

1 − N

=

1 − P

1 − M

1

k k

z k z k = U k