Advanced Methods of Structural Analysis

444 12 Plastic Behavior of Structures

12.5.2 Sidesway Failure..............................................

This scheme of failure of the structure ischaracterized by the appearance of plastic
hinges at supportsAandBas well at jointsCandD; a failure of its horizontal el-
ement is absent (Fig.12.10c). In this case, the structure is ongoing the horizontal
displacement only. The inclination of the vertical membersACandBDare denoted
byˇ.
Equation of limit equilibrium using kinematical method is following:

Plimˇh4MyvertˇD0:

We can see that sidesway mechanism of the failure is realized only by loadP.Since
lD2h, then solution of this equation

PlimD

4Myvert

h

D

8Myvert

l

: (12.3)

12.5.3 Combined Failure.............................................

This scheme of failure of a structure is characterized by the appearance of plastic
hinges at supportsAandB, at jointDas well at pointK(Fig. 12.10a). In order to
the system becomes a mechanism the total number of plastic hinges must benC 1 ,
wherenis a degree of redundancy. In our case, the system becomes a mechanism
when the number of plastic hinges is 4 (Fig.12.10d). The inclination of the vertical
membersACandBDis denoted by. Since a jointCremains a rigid ones, then
inclination of the horizontal members is also.
As before, the equation of limit equilibrium using kinematical method is
following:

Qlim

l

2

CPlimh4Myvert2MyhorD0:

We can see that combined mechanism is realized by both loadsQandP.For
MyhorD2MyvertandlD2h; last equation may be rewritten as

Qliml

Myvert

C

Pliml

Myvert

D16: (12.4)

12.5.4 Limit Combination Diagram.................................

The result of the plastic analysis may be presented by diagram shown in Fig.12.10e.
The designations of the axis arePMlimvertl
y
andQMlimvertl
y
.