Advanced Methods of Structural Analysis

10.3 Comparison of the Force and Displacements Methods 355

PD 1 in the right span

IL.Z 1 /D

1

10i

u.1u/^2 lD

u

10

.1u/^2

l^2

EI

:

Left and right spans are divided for five equal portions. Calculation of ordi-

nates of influence line of primary unknown at specified points 1–10 is presented

in Table10.6.

Table 10.6 Ordinates of influence line of primary unknown (factorl^2 =EI)

LoadPD 1 in left span LoadPD 1 in right span

Points u IL.Z 1 /D

u

20

.1u^2 /

l^2

EI

Points u IL.Z 1 /D

u

10

.1u/^2

l^2

EI

0 0.0 0.0 5 0.0 0.0

1 0.2 0:0096 6 0.2 0.0128

2 0.4 0:0168 7 0.4 0.0144

3 0.6 0:0192 8 0.6 0.0096

4 0.8 0:0144 9 0.8 0.0032

5 1.0 0.0 10 1.0 0.0

Factor l^2 =EI l^2 =EI

The final influence line for primary unknownZ 1 is presented in Fig.10.15e.

Once constructed influence line for primary unknown presents the fundamental

data, because it carries comprehensive andimportant information about structure.

This key influence line can be used for analysis of structure subjected toarbitrary

load placed along the loaded counter.

10.3 Comparison of the Force and Displacements Methods

For summarizing, let us compare two fundamental analytical methods of structural

analysis for construction of influence lines; some results are presented in Table10.7.

As in the case of the dead loads, construction of influence lines for any statically

indeterminate structures starts from determining of number and types of unknown

and presentation of corresponding primary system of the force and displacement

methods.

Notes:

1.In case of continuous beams with pinned end supports both methods lead to the
approximately same time consuming.
2.In case of continuous beams with one or two fixed end supports the displacement
method is more preferable.
3.In case of frames the preferable method depends on the number of the primary
unknowns. For frames similar to those in Sect.10.2.2, the displacement method is