Advanced Methods of Structural Analysis

562 Appendix

Unit reactions of nonuniform standard members:

Ta b l eA.7andA.8present the reactive moments for fixed–pinned and fixed–fixed
elements with stepped bending stiffness. For both cases D.EI 1 =EI 2 /1; aD
1 C"; bD 1 C"^2 ; cD 1 C"^3 ; fD 1 C"^4

Ta b l e A. 7 Fixed–pinned beam with stepped bending stiffness

el

RB

A

B

l

EI 1 EI 2

RB

AB

q

RB = ql

8 c

3 f R

B

A B

D=1

l^3 c

RB =

3 EI 1

Ta b l e A. 8 Fixed–fixed beam with stepped bending stiffness

q

el MB

RB

A

B

l

EI 1 EI 2

MB =^9 bf −^8 c ql^2

2

12 ( 4 ac − 3 b^2 )

RB =^2 bc −^3 af ql

2 ( 4 ac − 3 b^2 )

RB

A B

D=1

MB

EI 1

l^2

MB = −^6 b

4 ac − 3 b^2

EI 1

l^3

RB =^12 a

4 ac − 3 b^2

MB

RB

A B

j =1

EI 1

l

MB =^4 c

4 ac − 3 b^2

EI 1

l^2

MB = −^6 b

4 ac − 3 b^2