CIVIL ENGINEERING FORMULAS

BEAM FORMULAS 47

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
4.8MP/Llaterally and 7.2MP/Lvertically at midspan.
Maximum moment occurs in the interior spans ABandCDwhen

x (2.5)

L

2



M

wL

A

B

MB

kMP kMP

kMP kMP

wL^2

8

MP

MC

C

D

w

L

x x

L

(a)

(b)

(c)

Moment diagram

for redundants

Moment diagram

for determinate beam

L

2 w

w

wL^2

4

wL^2

8

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.