Advanced Methods of Structural Analysis

Appendix 553

Tabulated data for standard uniform beams:

Ta b l eA.3andA.4contain the reactions at supports for uniform fixed–pinned
(rolled) and fixed–fixed beams subjected to different exposures. TableA.5andA.6
present the reactions at supports for beams with sliding and elastic supports, respec-
tively. These tables show the actual direction for reactive forces and moments. The
bending moment diagrams are traced on the side of the extended fibers. Parameter
iDEI=lis the bending stiffness per unit length. Parameteruis related to the fixed
support,hdenotes the depth of the cross section and ̨is the coefficient of thermal
expansion.
The tables for the reactions of single-span beams with stepped flexural stiffness
are presented TableA.7andA.8

Ta b l e A. 3 Reactions of fixed-pinned beams

l

EI, a

A B

h

No Loading conditions

Reactions and bending

moment diagrams

Expressions for bending

moments and reactions

1

jA=1

jA=1

RA RB

MA

MA

MAD

3 EI

l D3i; iD

EI

l

RADRBD^3 lEI 2 D3il

2

Δ=1 RA

RB

MA

MA

MAD^3 EI

l^2

D3i

l

RADRBD

3 EI

l^3

D3i

l^2

(^3) (u+u=1)
P
a=ul b=ul
C RA
RB
MA
MA
ul ul
C
MADPl 2 

1 ^2

MCDPl 2 u^2 . 3 u/
RADP 2

3 ^2

RBDPu
2
2

. 3 u/
uDD0:5
RAD^1116 PIRBD 165 P
MAD 163 PlIMCD 325 Pl

(continued)