Civil Engineering Reference
In-Depth Information
14
400
w/o joint shear model
w/ joint shear model
12
300
10
8
200
6
4
100
2
No1
No2
No3
No4
No5
0
0
0
0.002
0.004
0.006
0.008
0.01
0
50
100
150
200
Shear strain (rad)
Top Lateral Displacement (mm)
Figure 4.19
Beam - to - column joint modelling: trilinear shear strength - strain curves (
left
) and lateral global of the
frame with and without joint modelling (
right
)
Key
: No1 = knee joint; No2 = external joint without transverse beams; No3 = external joint with transverse beams;
No4 = internal joint without transverse beams; No5 = internal joint without transverse beams
to special applications, e.g. fracture mechanics or when complex local three- dimensional stress -
strain distributions need to be determined, e.g. in beam- to - column connection sub - assemblages
(e.g. El- Tawil
et al
., 2000, among others). They are, however, suitable for the derivation of
moment-rotation relationships, which are then implemented as mathematical models (type
i
above).
Phenomenological and physical models are widely used in structural analysis to account for connec-
tion behaviour. They are utilized in planar or space frame analysis to model pin joints, inclined supports,
elastic - plastic joint behaviour, soil -structure interaction and structural gaps through employing appro-
priate joint curves. Seven force-displacement curves are, for example, available for use with joint ele-
ments in the computer program Zeus- NL (Elnashai
et al
., 2003): elastic linear, trilinear symmetrical
and asymmetrical elastic-plastic curves, hysteretic shear model under constant axial load or with axial
force variation, hysteretic fl exure model under constant axial load or with axial force variation. Figure
4.19 shows trilinear symmetrical shear strength- strain relationships utilized to model beam - to - column
joints of the SPEAR frame. In the same fi gure, the lateral response of the frame (pushover) with and
without the joint modelling is provided, for the weak
x
-direction as per Figure 4.2. Shear joint relation-
ships in Figure 4.19 require the defi nition of stiffness (initial and post-cracking) and strength (shear
stress at cracking and at maximum capacity) parameters. The plot of the base shear- versus - lateral dis-
placement curves in Figure 4.19 demonstrates that modelling of beam-to-column joints may lead to
lower values of all global structural response characteristics discussed in Section 2.3, i.e. stiffness,
strength and ductility.
4.5.3.3 Diaphragms
Framed structures are analysed using spatial FE discretizations with the common assumption that deck
systems serve as rigid diaphragms between the vertical elements of the lateral load- resisting system.
In-plane stiffness of bridge decks and fl oor slabs in buildings with regular plan layout are indeed very
high compared to the lateral stiffness of the frame (Jain, 1983). However, the validity of this assump-
tion should sometimes be checked, because the fl exibility of diaphragms can signifi cantly affect the
three-dimensional dynamic behaviour of structural systems. This is especially the case when exception-
ally shallow slabs are used or where the slab has large openings.
