4 - UTM

bulgefetaUrban and Civil

Nov 29, 2013 (3 years and 6 months ago)

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CHAPTER IV





RESULTS AND DICUSSION





4.1

Parameter
o
f Concrete Strain
a
t Zero Tensile Stress



The parameter of concrete strain at zero tensile stress which is affected by
tension stiffening effect was searched using trial and converged method ranging f
rom
0.00001 to 0.0001 at increment of 0.00001, from 0.0001 to 0.001 at increment of
0.0001 and from 0.001 to 0.01 at increment of 0.001. NLFEA were tried more detail
in the range at 0.00013 to 0.00015 with increment of 0.000001. The value 0.000138,
which h
ad given the highest step of solutions (33 steps), is adopted
.



The value 0.000138 is adopted in the analysis as it reached the highest step of
the solutions, in which it is predicted the solutions are closed to the convergence.
Besides that, the behaviou
r of the beam
-
to
-
column connection from the analysis is
also within the predicted behaviour.








43

4.2

Behaviour of the Connection



The behaviour of the connection is mainly observed through the result
s

from
the maximum principal stress
,

P1 and minimum princi
pal stress
,
P3, which indicate

the tension
and compression
stress
es

in model respectively. Whereas, the stress
concentration pattern of the connection can be seen through the contour plot of either
P1 or P3.
There are two types of failure that had been obs
erved from the NLFEA’s
results. The connection is said to be failed in concrete cracking (tensile splitting)
when the tensile strength of concrete reached
0.1f
cu

and failed in concrete
compression crushing when the

ultimate compressive strength reached 0.8
f
cu
.




Assumptions that are
used in
analysis to determine the f
ailure of
c
oncrete and
s
teel

are listed as following:


1.

Concrete cracking or tensile splitting is assumed to be occurred in concrete
elements when the maximum principal stress, P
1
, of concrete

exceeded 0.1
f
cu

i.e. 2.5 N/mm
2
. 0.1
f
cu

is the limit of concrete to withstand stress

in tension.


2.

The concrete elements are assumed to be failed in crushing in the
compression state

if

the minimum principal stress, P
3
, of concrete is greater
than 0.8
f
cu

i.
e. 20 N/mm
2
.


3.

T
he steel

elements, which include steel connector, steel plate connected to
beam and column element, and “bean shape” steel reinforcement

are assumed
to

start
yield
ing
at 87% of the
tensile
stress, i.e. 356.7 N/mm
2
. The steel is
assumed to yi
eld in tension if the maximum principal stress, P
1
, of steel
reached
356.7 N/mm
2

and
buckle

in compression if the minimum principal
stress, P
3
, of steel is exceeded
-
356.7 N/mm
2
.






44

4.2.1

Concrete Cracking



At the initial stage of
the
applied load, there are n
o signs of distress or visible
cracking occurred at the connection.

As the NLFEA proceed
s

to load parameter
1.8527 (about 374

k
N of total load) at arc step 8, the concrete at the edge of the
lower column beneath the longer beam (element 1151, node
1170 and

1571
; element
1149, node 1575 and 1169
) start to crack. The value of stress is P1 = 2.53 N/mm
2
,
which exceeded the allowable tension stress, 0.1
f
cu

= 2.5 N/mm
2

(refer to Figure
4.1
).



















Figure 4.1

Contour plot of maximum principal stress,
P
1

and location of the
concrete cracking area

at arc step 8






Cracking Area
(Node 1571,
1170, 1169,
1575)


Element 1149

Element 1151


45

4.2.2

Concrete Crushing



The concrete crushing is occurred at arc step 16 at same location in the lower
column but the node adjacent to the beam, which
is

at both node 2009 and 2010 in
element 115
0
. The element 1150 is located in between element 1149 and 1151,
which shares the same node at the adjacent face.

The minimum principal stress, P3
had reached 21.33 N/mm
2
, which is exceed
ed

the allowable compression stress,
0.8
f
cu

= 20 N/mm
2

when the load
parameter reached 4.1437 (about 837

kN of total
load)
.

The location of the concrete crushing area is shown in
Figure
4.2
.


















Figure 4.
2

Contour plot of
minimum

principal stress, P
3
and location of the
concrete cr
ush
ing area

at arc step
16






Crushing area
(Element 1150,
N
ode 2009 and
2010)



46

4.2.3

Stress Concentration at Steel Connector



As c
oncrete crushing occurred at arc step 16,
the tension stress concentrated
mostly at top edge of the steel connector and some part of the bottom edge, while the
compression stress occurred beneath the steel c
onnector. T
he P1 of the steel
connect
or
is about 48.72 N/mm
2

at node 97 (element 25, 28) and node 103 (element
27, 30), which are located at bottom
edge
of the
steel
connecto
r

closed to steel plate
connected to
the longer beam. Meanwhile, P3 is about 127.1
8 N/mm
2

at node 82
(element 20, 22, 23) and at node 85 (element 21, 22, 24), which are located at bottom
the
steel
connecto
r

close
d

to the steel plate
connected to
column.

The location of the
maximum tension and compression stress at the steel connector at

arc step 16 can be
seen in
Figure 4.3 and 4.4
r
espectively.
















Figure 4.
3

Contour plot of
maximum
principal stress, P
1 at steel connector
and steel plate connected to beam and column





Maximum
tension stress


47














Figure 4.
4

Contour plot of
minimum princi
pal

stress, P
3 at steel connector
and steel plate connected to beam and column




4.3

Discussion


Load-Deflection Curve
0.0
1.0
2.0
3.0
4.0
5.0
0.0
0.2
0.4
0.6
Deflection (mm)
Load Parameter

Figure 4.5

Load
-
deflection curve

Maximum
compression stress

Concrete crushing

(21.33N/mm
2
)

Concrete cracking

(2.53N/mm
2
)


48

The load
-
deflection curve shown in Figure
4
.
5

indicated the location of
concrete cracking and crushing at
the
associated lo
ad parameter.

When the concrete
failed by crushing at arc step 16, the steel connection is still not reached the yield
condition denoting that there is still some reserved strength in the connections. Both
of
the tension and compression stress
of the steel

connector
are far less
than

the
allowable stresses, which is 0.87
f
y

= 356.7 N/mm
2
. Earlier cracking and crushing of
the concrete compared to yielding of steel is probably because of no co
ncrete in the
connection panel.