Advanced Methods of Structural Analysis

Appendix 555

Ta b l e A. 4

Reactions of fixed–fixed beams

l

A

B

EI,

a

h

No

Loading conditions

Reactions and bending momentdiagrams

Expressions for bendingmoments and reactions

1

jA

=1

jA

=1

RA

RB

M

A

M

A

M

B

M

B

M

A

D

4 EIl

;M

B

D

2 EIl

R

A

D

RB

D

6 EIl

2

2

Δ=1

RA

RB

M

A

M

A

M

B

M

B

M

A

D

M

B

D

6 EIl

2

R

A

D

RB

D

12

EI^3 l

3

P C

(u

+

u

=1)

ul

ul

RA

RB

M

A

M

A

ul

ul

C

M

B

M

C

M

B

M

A

D

u

2 Pl;

M

B

D

(^2) u
P l
M
C
D
2 u
2 
2 Pl
R
A
D
(^2) 

.^1

C

2 u

/P

R

B

D

(^2) u

.^1

C

2

/P

u

D



D

0:5

RA

D

R

B

D

P^2

M

A

D

M

B

D

Pl^8

;M



l 2

D

Pl^8