Advanced Methods of Structural Analysis

10.2 Construction of Influence Lines by the Displacement Method 351

2.If a load is located in the right span, thenMk^0 andQ^0 kare zero. In the force
method it happens because the primary system presents twoseparatebeams;
therefore, the load from one beam cannotbe transmitted to another. In the dis-
placement method it happens because the introduced support in the primary
system does not allow transmitting of internal forces from the right span to the
left one.

Example 10.3.The two-span beam with equal spanslis subjected to forcePas

shown in Fig.10.14a. The beam is divided into ten equal portions; the number of

joints is presented in Fig.10.11e. Find the reaction at the middle supportB.Solve

this problem by three different ways (a) Use the influence lines forMkandQk;(b)

use the influence lines for primary unknown of the displacement method; (c) use the

influence lines for primary unknown of the force method.

P

k

6

8

1 3 11

0.096P

0.096P

0.0384 Pl

0.4l 0.6l l

R 0.4l

B

P

kB

8

AC

0.4l 0.6l l

0.4l

RA RB R

C

a

P

B 8

A C

l

ul=0.6l

l

RA

Z 1

ul=0.4l

RB R

C

b

P

B

8

1 11

l

0.6l

l

X 1 X 1

X 1 /l X 1 /l+0.6P

c

Fig. 10.14 (a) Design diagram of the beam and calculation of reaction at supportBusing the influ-

ence line for internal forces at section k. (b) Calculation of reaction at supportBusing the influence

lineZ 1 of the displacement method. (c) Calculation of reaction at supportBusing the influence

lineX 1 of the force method