Page 92 - Civil Engineering Formulas

BEAM FORMULAS 47

2w
w w

A D
B C

L L L
(a)

Moment diagram
for redundants

M B
M C
wL 2 wL 2
8 8
wL 2
4
Moment diagram
for determinate beam
(b)

x kM P kM P x

kM P kM P
M P

(c)
FIGURE 2.10 Continuous beam shown in (a) carries twice as much uniform
load in the center span as in the side span. In (b) are shown the moment diagrams
for this loading condition with redundants removed and for the redundants. The
two moment diagrams are combined in (c), producing peaks at which plastic hinges
are assumed to form.

The mechanism method can be used to analyze rigid frames of constant sec-
tion with fixed bases, as in Fig. 2.11. Using this method with the vertical load at
midspan equal to 1.5 times the lateral load, the ultimate load for the frame is
4.8M P /L laterally and 7.2M P /L vertically at midspan.
Maximum moment occurs in the interior spans AB and CD when
L M
x (2.5)
2 wL