chapter 5 5.pdf · title: microsoft word - chapter 5.doc author: owner created date: 8/11/2006...

137

Chapter 5

ANALYTICAL WORK

5.1 Introduction

This chapter presents the analytical component of this investigation. The finite element

analysis was used to investigate the performance of beam-column subassemblages. The

finite element modeling of the subassemblage was performed using Program ANSYS 8.0

(ANSYS, 2003). The test results were used to calibrate the initial finite element model.

Another finite element model was developed to test the performance of a similar

subassemblage with improved reinforcement detailing to overcome deficiencies identified

in the first test.

A time history analysis of prototype frame was performed using program RUAUMOKO

(Carr, 1998). Program RUAUMOKO is developed to carryout analysis of structures

subjected to earthquake and other dynamic excitations taking into account both material

and geometric non-linearity.

5.2 Finite element analysis

Program ANSYS is capable of handling dedicated numerical models for the non-linear

response of concrete under static and dynamic loading. Eight-node solid brick elements

(Solid 65) were used to model the concrete. These elements include a smeared crack

analogy for cracking in tension zones and a plasticity algorithm to account for the

possibility of concrete crushing in compression regions. Internal reinforcement was

Created with novaPDF Printer (www.novaPDF.com)

http://www.novapdf.com

138

modeled using 3-D spar elements (Link 8) and these elements allow the elastic-plastic

response of the reinforcing bars.

5.2.1 Element types

5.2.1.1 Reinforce concrete

The solid element (Solid 65) has eight nodes with three degrees of freedom at each node

and translations in the nodal x, y, and z directions. The element is capable of plastic

deformation, cracking in three orthogonal directions, and crushing. The geometry and

node locations for this element type are shown in Figure 5-1.

Figure 5-1: Solid65 – 3-D reinforced concrete solid (ANSYS 2003)

The geometry and node locations for Link 8 element used to model the steel reinforcement

are shown in Figure 5-2. Two nodes are required for this element. Each node has three

degrees of freedom, translations in the nodal x, y, and z directions. The element is also

capable of plastic deformation.



139

Figure 5-2: Link 8 – 3-D spar (ANSYS 2003)

5.2.2 Steel plates

An eight-node solid element, Solid45, was used for the steel plates at the top and bottom

end of column supports. The element is defined with eight nodes having three degrees of

freedom at each node and translations in the nodal x, y, and z directions. The geometry

and node locations for this element type are shown in Figure 5-3. A 50 mm thick steel

plate, modeled using Solid45 elements, was added at the support locations in order to

avoid stress concentration problems and to prevent localized crushing of concrete elements

near the supporting points and load application locations. This provided a more even stress

distribution over the support area.



140

Figure 5-3: Solid45 – 3-D solid (ANSYS 2003)

5.3 Material properties

5.3.1 Concrete

A nonlinear elasticity model was adopted for concrete. This nonlinear elasticity model is

based on the concept of variable moduli and matches well with several available test data.

For normal strength concrete, a stress-strain model as shown in Figure 5-4 is suggested by

Vecchio and Collins (1986). However, this ideal stress-strain curve was not used in the

finite element material model, as the negative slope portion will lead to convergence

problems. In this study, the negative slope was ignored and the stress-strain relation shown

in Figure 5-5 was used for the material model in ANSYS.



141

0

5

10

15

20

25

30

35

40

45

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Strain

Stre

ss (M

Pa)

Figure 5-4: Stress-strain curve for 40 MPa concrete (Vecchio and Collins, 1986)

0

5

10

15

20

25

30

35

40

45

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Strain

Stre

ss (M

Pa)

Figure 5-5: Simplified compressive stress-strain curve for concrete used in FE model



142

5.3.1.1 FEM Input Data

For concrete, ANSYS requires input data for material properties as follows:

Elastic modulus (Ec= 27,897 MPa used in this analysis)

Ultimate uniaxial compressive strength (f’c=40.6 MPa)

Ultimate uniaxial tensile strength (modulus of rupture, fr=2.55 MPa)

Poisson’s ratio (=0.2)

Shear transfer coefficient (t)

Compressive uniaxial stress-strain relationship for concrete.

The elastic modulus of concrete was calculated by using the slope of the tangent to the

stress-strain curve through the zero stress and strain point. The ultimate uniaxial

compressive strength of concrete was taken from the mean value of cylinder test results.

The tensile strength of concrete was assumed to be equal to the value given in the

Australian concrete structures code (AS-3600, 2001). This formula is given in Equation

5-1.

cr ff '4.0 Equation 5-1

The shear transfer coefficient for open cracks, t, represents the conditions at the crack

face. The value of t ranges from 0.0 to 1.0, with 0.0 representing a smooth crack

(complete loss of shear transfer) and 1.0 representing a rough crack (no loss of shear

transfer) (ANSYS, 2003). The value of t used in many finite element studies of

reinforced concrete structures, however, varied between 0.05 and 0.25 (Bangash, 1989;

Hemmaty, 1998; Huyse, Hemmaty and L.Vandewalle, 1994). A number of comparative

analytical studies have been attempted by Kachlakev et al (2001) to evaluate the influence

of shear transfer coefficient. They used finite element models of reinforced concrete

beams and bridge decks with t values within the range 0.05-0.25 and encountered



143

convergence problems at low loads with t values less than 0.2. Therefore, a shear transfer

coefficient of 0.2 has been used. However, in a recent study, Stehle (2002) recommended

to use shear transfer coefficient of 0.125. Therefore, for this study, both shear transfer

coefficient of 0.125 and 0.2 were used to derive the theoretical load-displacement

relationship for comparison with experimental results.

For closed cracks, the shear transfer coefficient assumed by both researchers (Kachlakev,

T. Miller, Yim and Chansawat, 2001; Stehle, 2002) found to be equal to 1.0. This

represents the shear stiffness reduction in the model is set to zero. In the analysis crack

closure was not expected, since the specimen was loaded from crack free initial state to

ultimate load monotonously.

5.3.1.2 Reinforcement

Steel reinforcement stress-strain curve for the finite element model was based on the

actual stress-stain curve obtained from tensile tests. The actual stress-strain curve for the

reinforcement is shown in Figure 5-6. However, this stress-strain curve was modified to

improve the convergence of finite element model by removing the negative slope portion

of the curve. Also the zero slope portion after yielding was slightly modified to a mild

positive slope. Figure 5-7 shows the stress-strain relationship used in this study.

Material properties for the steel reinforcement model is as follows:

Elastic modulus- Es = 200,000 MPa, Yield stress- fy = 450 MPa, Poisson’s ratio- =0.3.



144

0

100

200

300

400

500

600

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

Strain

Stre

ss (M

Pa)

Figure 5-6: Stress-strain curve for steel (obtained from testing reinforcement)

0

100

200

300

400

500

600

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

Strain

Stre

ss (M

Pa)

Figure 5-7: Modified stress-strain curve for steel (adopted in ANSYS model)

5.3.1.3 Geometry and finite mesh

The test subassemblage was modeled in ANSYS taking the advantage of symmetry across

the width of the flange beam and column. This plane of symmetry was represented using



145

relevant constrains in the finite element node points. This approach reduced computational

time and computer disk space requirements significantly.

The beam and column mesh was selected such that the node points of the solid elements

will coincide with the actual reinforcement locations. An additional node points were

provided by sub dividing the mesh, so that a reasonable mesh density was obtained in the

joint regions with recommended aspect ratio of elements.

In the finite element model, solid elements, Solid45, were used to model the steel plates.

Nodes of the solid elements (solid 45) were connected to those of adjacent concrete solid

elements (solid 65) in order to satisfy the perfect bond assumption. Link 8 elements were

employed to represent the steel reinforcement, referred to here as link elements. Ideally,

the bond strength between the concrete and steel reinforcement should be considered.

However, in this study, perfect bond between materials was assumed due to the limitations

in ANSYS. To provide a perfect bond, the link element for the steel reinforcing was

connected between nodes of each adjacent concrete solid elements, so the two materials

shared the same nodes. Figure 5-8 illustrates the element connectivity.

Figure 5-9 shows the finite element model used to simulate the first test. It should be noted

that main reinforcement and shear ligatures in rib beam and column were precisely located

as per the actual first test subassembly. Steel reinforcement for the half beam model was

entered into the model as half the actual area. The finite element model had exactly 7067

total numbers of elements. Consist 5480 solid 65 elements, 1542 link 8 elements and 35

solid 45 elements.



146

Concrete solid element (Solid 65)

Link element (Link 8) Solid element (Solid 45)

(a) (b)

Figure 5-8: Element connectivity: (a) concrete solid and link elements; (b) concrete solid and steel solid element

Mesh R/FBar # 01, 02, 03

Main Top R/F

Main bottom R/F(Link 8)

Column R/F (Link 8)

Column & Rib beam shear links (link 8)

Steel plate (Solid 45)

Concrete (Solid 65)

Figure 5-9: Finite element mesh used (selected concrete elements removed to illustrate internal reinforcement)



147

5.3.1.4 Boundary conditions and loading

The boundary conditions were exactly simulated as in the test set up shown in Figure 3-20.

Horizontal and vertical restraints, representing a pin connection were applied at the top of

the column. At the end of rib beams, only vertical restrains were provided to simulate the

roller support conditions used in the test. Figures 5-10 and 5-11 show the restraints used in

the finite element model at beam-ends and column top end respectively. Figure 5-10 also

shows an additional reinforcement mesh provided at the end of beam face. This was

provided to prevent any localized crushing of concrete elements near the supporting

points.

Restraints at beam end

Restraints to maintain plane of symmetry

R/F mesh provided at beam support face

Figure 5-10: Rib beam end restraints used in FE model



148

Restraints at column top end

Restraints to maintain plane of symmetry

Figure 5-11: Column top end restraints used in FE model

A constant axial load of 200 kN (half of total column load due to symmetry) was applied

to bottom end of the column. The application of gravity loading (1.2G+0.4Q) to the finite

element model was slightly modified to reduce the number of loading steps, thus reducing

the number of analysis stages. The self-weight of the beam was not applied to the beam as

a uniformly distributed load, instead it was applied as a prescribed vertical downward

displacement (1.7 mm) at each the beam support. This will create similar negative bending

moments as shown in Figure 3-23. The program RESPONSE-2000 (Bentz and Collins,

2000) was used to calculate the amount of displacement required to create the adopted

bending moment in the test. More details are given in Appendix D.

The horizontal displacement at the column bottom end was applied in a slowly increasing

monotonic manner, with results recorded every one-millimeter lateral displacement. The

loading was applied in one-millimeter increments up to 75 mm. It was found that after



149

several unsuccessful solution runs, the application of lateral load in very small steps is

very important to obtain the full load-deformation curve without convergence problems.

5.3.2 Non-linear solution

In nonlinear analysis, the total load applied to a finite element model is divided into a

series of load increments called load steps. At the completion of each incremental solution,

the stiffness matrix of the model is adjusted to reflect nonlinear changes in structural

stiffness before proceeding to the next load increment. The ANSYS program (ANSYS

2003) uses Newton-Raphson equilibrium iterations for updating the model stiffness.

Newton-Raphson equilibrium iterations provide convergence at the end of each load

increment within tolerance limits. In this study, for the reinforced concrete solid elements,

convergence criteria were based on force and displacement, and the convergence tolerance

limits were initially selected by the ANSYS program. It was found that convergence of

solutions for the models was difficult to achieve due to the nonlinear behavior of

reinforced concrete. Therefore, the convergence tolerance limits were increased to a

maximum of 5 times the default tolerance limits (0.5% for force checking and 5% for

displacement checking) in order to obtain convergence of the solutions.

5.3.2.1 Calibration

As mentioned earlier in chapter 5.3.1.1, the finite element model required calibration with

respect to the shear transfer factor across open cracks. For the calibration process, two

values (0.125 and 0.2) were used for the shear transfer coefficients. The results of the

finite element pushover analysis are compared to the back-born curve of the hysteresis of

the tested subassemblage, in Figure 5-12. A shear transfer coefficient of 0.2 appears to be

best fit.



150

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80

Displacement (mm)

Loa

d (k

N)

Test-1 results0.125 Shear0.2 Shear

Figure 5-12: Load versus displacement-1st test specimen test results and FE results

A plot showing extent of cracking is shown in Figure 5-13. This is at a displacement of 65

mm (3.42 % drift). As described below, the cracking patterns observed in testing and finite

element analysis matched reasonably well.

Plane of Symmetry

Half column width

Location of main cracks

Main top reinforcement curtailed at 1000 mm from column center

(a)

(b)

Figure 5-13: Smeared cracks formed parallel to vertical dashed lines at 65 mm displacement (3.42 % drift)- (a) Top view of full beam, (b) Enlarged part



151

As mentioned in chapter 2.5.3, in ANSYS a cracking sign represented by a circle appears

when a principal tensile stress exceeds the ultimate tensile strength of concrete. The

cracking sign appears perpendicular to the direction of the principal stress. The red circles

at each element centroid in the figure have their plane aligned with the plane of cracking.

Hence, what appears to be a dashed line is in fact row of circles with a plane (i.e. plane of

cracking) perpendicular to the plane of beam top surface, indicating flexural cracking.

The yellow dashed line shown in Figure 5-13 is the location of main cracks appeared in

the first test (see Figures 4-2 and 4-3). It should be noted that these main cracks could be

identified among other smeared cracks, by having well defined straight red dashed lines.

For a concrete structure subjected to uniaxial compression, cracks propagate primarily

parallel to the direction of the applied compressive load, since the cracks result from

tensile strains develop due to Poisson’s effect. The red circles on right hand side of the

column (Figure 5-13) appeared perpendicular to the principal tensile strains in the upward

direction at integration points in the concrete elements near the right hand side of column,

where high concentration of compressive stresses occur. These will be referred to as

compressive cracks. These types of cracks were not seen during the test, as these cracks

are formed parallel to the concrete surface. These cracks lead to crushing of concrete at

very high compressive stress. Figure 5-14 shows the compressive stress vector flow

within the whole subassembly and the red arrows show the direction of compressive stress

flow in the rib beam and the flange slab. Figure 5-15 shows the compressive stress

concentration near the column.



152

Figure 5-14: Compressive stress vectors flow at 65 mm displacement

Column

Figure 5-15: Compressive stresses direction in the flange slab at 65 mm displacement

Figure 5-16 shows the deformation pattern of first subassembly model at 65 mm lateral

displacement. It is very clear from the deformation pattern that the negative hinging of

beam has shifted away from column face and coincides with the beam top main



153

reinforcement curtailment point. This behaviour was observed during the testing as well.

Figures 5-17 and 5-18 show the stress and strain distribution respectively. These

distributions help to identify the hinging locations.

Hinging near R/F curtailment location

Hinging near column face

Figure 5-16: Deformation of subassembly at 65 mm displacement- 1st specimen

Hinge Location at top bar curtailment point

High compressive stress locations

Figure 5-17: Longitudinal stress distribution of subassembly at 65 mm displacement-1st FE model



154

High strain point

Figure 5-18: 3rd principal strain distribution of subassembly at 65 mm displacement

Finite element analysis results were used to obtain detail information on concrete and

reinforcement stress variation in different areas of the subassembly. Figure 5-19 illustrates

horizontal and vertical deformation of the rib beam obtained from the finite element

model. During the first test, this type of continuous deformation was not monitored due to

the complexity of instrumentation and the cost involvement. However FEM can be used to

predict such detail information without considerable effort. Horizontal deformation

exhibits sudden change in deformation. This type of deformation cannot happen without

severe cracking. The location and the crack width obtained from the finite element model

are quite similar to the main crack observed during the test. As illustrated in Figure 5-13,

the smeared crack prediction is consistent with discrete flexural cracking predicted by

horizontal deformation graph. The vertical deformation graph (Figure 5-19) shows the

possible plastic hinge location. This matches very well with the experimental observations.



155

-10

0

10

20

30

40

50

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

Deformation (mm)

Distance from column center (mm)

Vertical

Horizontal

Crack = 6.8 mm

Crack = 1.9 mm

Top R/F cut off point

Figure 5-19: Deformation along the beam at 65 mm displacement-1st FEM results

The reinforcement stress variation along the beam is plotted in Figure 5-20. The finite

element model predicts a peak stress of 639 MPa in one of the mesh reinforcement bars.

Material testing shows that mesh steel used in the subassembly has an ultimate strength of

684MPa. As reported in chapter 4.2.1.3, during the last cycle (75 mm displacement) of the

test, a snapping sound came as a result of breaking internal mesh reinforcement. This

shows that the mesh steel has reached its ultimate strength. FEM analysis could not

achieve a converged solution beyond the 65 mm displacement. It could be expected that if

the FEM analysis was able to run up to 75 mm displacement, similar stress levels would

be obtained.



156

-100

0

100

200

300

400

500

600

700

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500


R/F

stre

ss (M

Pa) Main Top R/F

Mesh R/F # 01

Mesh R/F # 02

Mesh R/F # 03

Peak stress= 639 MPa

Figure 5-20: Variation of reinforcement stresses along the beam at 65 mm displacement

- 1st FEM results

Figures 5-21 and 5-22 show the stress distribution of top and bottom main reinforcement

along the beam length at lateral displacements of 19, 38, 57 mm and 65 mm, which

correspond to drift ratios of 1%, 2%, 3% and 3.42 %. It can be seen from the plots that the

bottom bar reached the yield stress at 1% drift level, whereas the top bar started yielding

only at 3 % drift.

Figure 5-23 shows the stress variation of longitudinal mesh reinforcement at 19 mm

displacement. It can be seen from the plot that the mesh bars has started yielding just after

the main reinforcement curtailment location. Referring to the Figure 5-21, the main top

reinforcement has reached only about 250 MPa stress level at 19 mm displacement. This is

a clear indication of inadequacy of main top reinforcement length (i.e. curtailment of bars

too close to the joint) provided in the first test subassemblage.



157

-500

50100150200250300350400450500

-1500 -1000 -500 0 500 1000 1500


R/F

stre

ss (M

Pa)

65 mm displacement

57 mm displacement

38 mm displacement

19 mm displacement


Figure 5-21: Variation of top main reinforcement stresses along the beam at different displacements

- 1st FEM results

-300

-200

-100

0

100

200

300

400

500

600

-3000 -2000 -1000 0 1000 2000 3000


R/F

stre

ss (M

Pa)

65 mm displacement

57 mm displacement

38 mm displacement

19 mm displacement


Figure 5-22: Variation of bottom main reinforcement stresses along the beam at different

displacements-1st FEM results

-100

0

100

200

300

400

500

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500


Mes

h R

/F st

ress

(MPa

)

Mesh R/F # 01

Mesh R/F # 02

Mesh R/F # 03


Figure 5-23: Variation of mesh reinforcement stresses along the beam at 19 mm displacement

-1st FEM results



158

5.4 The second finite element model

By modifying the first finite element model the second FE model was created. The only

modification made was extending the length of main top reinforcement bar to 1600 mm

from 1000 mm. This modification was based on the observations made during the test

program. It was very clear from the first test that the inadequate length of main top bar

was the reason for the main cracking and subsequent failure. In the second test with the

retrofitted specimen, the extension of CFRP layer on the top flange beyond the curtailment

point of the top bar, led to a significant improvement in the performance.

Further to the above, the Australian code(AS-3600, 2001) recommendation for beams was

considered. According to the clause 8.1.8.6 of AS 3600 (i.e. Deemed to comply

arrangement of flexural reinforcement) the reinforcement curtailment length was

calculated. For this calculation the span length of 9600 mm was considered, as this was the

greater span of the first interior support of the prototype structure. The length of bar

required from the column centre was 3130 mm and the half of this length was rounded to

1600 mm considering the scale factor for test specimen.

The second FE model analysis was performed using the same shear transfer factor (i.e.

0.2), which gave the best match with the test results. The boundary conditions and the load

steps were same as in the first FE model. Figure 5-24 shows the results of the second finite

element pushover analysis. The results are compared to the back-born curve of the

hysteresis of the first test and the results of the first FE model. It should be noted that the

results of the second FE model cannot be directly compared with the results of the

retrofitted specimen.



159

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80

Displacement (mm)

Loa

d (k

N)

Test1 results

Main top bar L=1000 mmMain top bar L=1600 mm

Figure 5-24: Load versus displacement-1st test specimen test results and FE model 1 &2 results

Figure 5-25 shows the deformation pattern obtained from the second FE model at 65 mm

lateral displacement. The second FE model solution converged up to a lateral displacement

of 70 mm. However the results are compared at the maximum displacement obtained in

the first FE model (i.e. 65 mm displacement). The hinging location could not be clearly

identified by the deformation. The vertical deformation of the beam shown in Figure 5-26

was used to identify the hinge location.



Figure 5-25: Deformation of subassembly at 65 mm displacement- 2nd FE model



160

-10

0

10

20

30

40

50

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

Deformation (mm)


Vertical

Horizontal

Crack = 1.1 mm

Crack = 4.1 mm Top R/F cut off point

Figure 5-26: Deformation along the beam at 65 mm displacement- 2nd FE model

It can be seen from the axial deformation plot shown in Figure 5-26 that the prediction of

cracking at beam top reinforcement curtailment point has reduced significantly. The

cracking near the column face has increased as expected due to the formation of hinge

close to the joint. The vertical and horizontal deformations from photogrammetry

measurements were also consistent with the FE predictions. However, as mentioned

previously these results cannot be compared directly.

Figures 5-27 and 5-28 show the longitudinal stress and strain distributions of the second

subassemblage at 65 mm lateral displacement. It should be noted that the strain contour

range in Figure 5-28 was set equal to that in Figure 5-18. Thus it is possible to compare

the locations of high strain regions in the FE models. The high stress and strain

concentrations were observed only at the column face. High stress region was not seen

near the reinforcement curtailment point, as observed in the first FE model.



161

Hinge Location at column face

High compressive stress locations

Figure 5-27: Longitudinal stress distribution of subassembly at 65 mm displacement-2nd FE model

Figure 5-28: 3rd principal strain distribution of subassembly at 65 mm displacement-2nd FE model



162

The stress variation along the beam of main top and mesh reinforcement is plotted in

Figure 5-29. The finite element model predicts a peak stress of 511 MPa in one of the

mesh reinforcement bars. This is a stress reduction of 20 % compared to the reinforcement

stresses predicted by the first FE model. However, this highest stress recorded location

was not tallying with the first FE model location. The stress increase in mesh

reinforcement near the main top bar curtailment point was around 450 MPa, which is

acceptable at a very large lateral displacement of 65 mm (3.4 % lateral displacement

level). Therefore, the provided length of top bar in second FE model is considered to be

adequate.

Distance from column centre (mm)-100

0

100

200

300

400

500

600

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

R/F

stre

ss (M

Pa) Main top R/F

Mesh R/F # 01Mesh R/F # 02Mesh R/F # 03



0

100

200

300

400

500

600

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

R/F

stre

ss (M

Pa) Main top R/F



Figure 5-29: Variation of reinforcement stresses along the beam at 65 mm displacement

- 2nd FEM results

Figures 5-30 and 5-31 show the stress distribution of top and bottom main reinforcement

along the beam length at lateral displacements of 19, 38, 57 and 65 mm respectively. It can

be seen that the bottom bar had reached a higher stress level compared to the stress in the

first FE model. This indicates that main top bar length provided is adequate to resist the

bending moments at each displacement level. The bottom bar stress development with the

lateral displacement level has not changed significantly compared to the first FE model.

However, a slight reduction of maximum stress (from 521 to 509 MPa) was noted. This



163

reduction in stress must be due to the higher beam stiffness compared to the column in

second FE model due to lesser cracking, resulting in a reduction of beam rotation and

lower reinforcement stresses and strains.


0

100

200

300

400

500

600

-2000 -1500 -1000 -500 0 500 1000 1500 2000

R/F

stre

ss (M

Pa) 19 mm displacement

38 mm displacement57 mm displacement65 mm displacement



0

100

200

300

400

500

600

-2000 -1500 -1000 -500 0 500 1000 1500 2000

R/F

stre

ss (M

Pa) 19 mm displacement

38 mm displacement57 mm displacement65 mm displacement


Figure 5-30: Variation of top main reinforcement stresses along the beam at 65 mm displacement

- 2nd FEM results


-300

-200

-100

0

100

200

300

400

500

600

-3000 -2000 -1000 0 1000 2000 3000R/F

stre

ss (M

Pa)

19 mm displacement38 mm displacement57 mm displacement65 mm displacement



-300

-200

-100

0

100

200

300

400

500

600

-3000 -2000 -1000 0 1000 2000 3000R/F

stre

ss (M

Pa)

19 mm displacement38 mm displacement57 mm displacement65 mm displacement


Figure 5-31: Variation of bottom main reinforcement stresses along the beam at different

displacements- 2nd FEM results

Figures 5-32 and 5-33 illustrate the stress variation of longitudinal mesh reinforcement at

19 mm and 38 mm lateral displacement level respectively. It can be seen from the plot that

the mesh bars have high stress peaks along the beam length in negative bending moment



164

area. However, these high stress peaks seen at low drift levels gradually reduced as the

drift level increased. This indicates that at higher drift levels flange slab reinforcement

contributes more for resisting lateral loading.


0

100

200

300

400

500

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

R/F

stre

ss (M

Pa) Main top R/F

Mesh R/F # 01

Mesh R/F # 02

Mesh R/F # 03



0

100

200

300

400

500

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

R/F

stre

ss (M

Pa) Main top R/F

Mesh R/F # 01

Mesh R/F # 02

Mesh R/F # 03



-2nd FEM results


0

100

200

300

400

500

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

R/F

stre

ss (M

Pa) Main top-R/F




0

100

200

300

400

500

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

R/F

stre

ss (M

Pa) Main top-R/F




-2nd FEM results

5.5 Time history analysis

A time history analysis of model frame was performed using the program RUAUMOKO

(Carr, 1998), which was designed to carryout the analysis of structures subjected to



165

earthquake and other dynamic excitations taking into account both material and geometric

non linearity (P-Delta effects). The models used in this study were non-degrading beam-

column yield interaction surface for columns and modified TAKEDA(Takeda, Sozen and

Nielsen, 1970) hysteresis for the beams. These models are shown in Figures 5-34 and

5-35. Elastic damping is modeled using Rayleigh initial stiffness damping of 5% in mode

1 & 4.

Figure 5-34: Modified Takeda Degrading Stiffness Hysteresis Rule [After (Carr, 1998)]

Figure 5-35: Concrete Beam-Column Yield Interaction Surface [After (Carr, 1998)]

Moment curvature and column interaction diagrams were developed using RESPONSE

2000 (Bentz and Collins, 2000) reinforced concrete sectional analysis program and more



166

details are given in Appendix-D. As described in chapter 2.2.2.1, cracked stiffness of the

frame elements were estimated using the method specified by Priestley (1998b).

It is very important to evaluate member properties for the dynamic analysis. The New

Zealand building code (SANZ, 1995) recommends a value for beam stiffness of Ie=0.4Ig

for rectangular sections, and Ie=0.35Ig for T-beam sections. As highlighted by Priestley,

the beam stiffness depends strongly on reinforcement content; therefore use of above

recommendation may lead to significant error in calculating building period and drift

level.

For the analysis, the prototype frame beam members were modeled by using four-hinge

beam members, which can allow for two plastic hinges within the span of the member in

addition to the two hinges at its ends. This beam element was recommended to use to

model gravity dominated beams where under seismic loading in one direction yielding

occurs at one end hinge and at the interior hinge near the other end of the beam while

under reversed loading yielding occurs at the other two hinges.

The prototype frame beam members were modeled by using inelastic beam-column

elements, which take into account the interaction of axial load and bending moment on

strength. The calculation of relevant parameters for time history analysis is presented in

Appendix D.

The time-history analyses were conducted with an ensemble of earthquake records. These

records were obtained from COSMOS Virtual Data Center and European Strong Motion

data Base (COSMOS, 2004). The records were selected on the criteria that they had been

corrected, were on rock or soft soil and were within the range of Richter magnitude-

epicentral distances combinations used by Stehle (2002). An arbitrary classification is



167

applied to the groups, with categories of low (1) to extreme (6) seismicity as shown in

Table 5-1.

The maximum inter-storey drift ratios of the time-history analyses using earthquake

ensemble are plotted in Figure 5-36, grouped according to the seismic classification of low

to extreme seismicity. Of most interest is the maximum inter-storey drift ratio as this best

assesses damage. The prototype structure was designed for low seismicity (earthquake

category 1), less than 0.5 interstorey drift level expected. For this level of drift, there will

be no damage as observed in test results. The high level seismicity (category between 4

and 5), less than 4 % interstorey drift is encountered. Hence the structure should be able to

withstand without significant structural damage as observed from the second FE modeling

results with modified reinforcement detail.



168

Table 5-1:Definition of earthquake categories

Note: Only EQ’s chosen which have: -vertical and horizontal record -corrected record

Epicentral distance (km) Soil Type: Rock 10-30 30-70 70-120 120-500

Richter Magnitude 4.5-5.5 1 - - - 5.5-6.5 2 1 - - 6.5-7.5 3 2 1 - 7.5-8.5 4 3 2 1

Epicentral distance (km) Soil Type: Soft soil

10-30 30-70 70-120 120-500 Richter Magnitude 4.5-5.5 2 - - - 5.5-6.5 4 2 - - 6.5-7.5 6 4 2 - 7.5-8.5 - 6 4 2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6

Earthquake Category

Dri

ft R

atio

(%)

Time-history resultsAverage plus 2 standard deviations

Figure 5-36: Peak interstorey drift ratio versus earthquake category

Earthquake Category Seismicity 1 Low 2 Moderate 3 High 4 Very High 6 Extreme



169

1. ANSYS (2003). ANSYS v 8.0, Swanson Analysis System, U.S. 2. AS-3600 (2001). Concrete Structures, Standard Association of Australia, Sydney, Australia. 3. Bangash, M. Y. H. (1989). "Concrete and Concrete Structures: Numerical Modeling and Applications." Elsevier Science Publishers Ltd., London, England. 4. Bentz, E. C. and M. P. Collins (2000). RESPONSE-2000 Reinforced Concrete Sectional Analysis Program Manual. 5. Carr, A. J. (1998). RUAUMOKO User Manual, University of Canterbury. 6. COSMOS (2004). Virtual Data Center and European Strong Motion data Base, http://db.cosmos-eq.org/scripts/default.plx, http://www.isesd.cv.ic.ac.uk/. 7. Hemmaty, Y. (1998). Modelling of the Shear Force Transferred Between Cracks in Reinforced and Fibre Reinforced Concrete Structures,. Proceedings of the ANSYS Conference ,Vol. 1, Pittsburgh, Pennsylvania. 8. Huyse, L., Y. Hemmaty and L.Vandewalle (1994). Finite Element Modeling of Fiber Reinforced Concrete Beams. Proceedings of the ANSYS Conference, Vol. 2,, Pittsburgh, Pennsylvania. 9. Kachlakev, D., T. Miller, S. Yim and K. Chansawat (2001). Finite Element Modeling of Reinforced Concrete Structures Strengthened with FRP Laminates, Civil and Environmental Engineering, DepartmentCalifornia Polytechnic State University, San Luis Obispo. 10. SANZ (1995). NZS3101: 1995- Concrete Structures Standard, Standards New Zealand, Wellington [2 Vols: Code & commentry]. 11. Stehle, J. S. (2002). The Seismic Performance of Reinforced Concrete Wide Band Beam Frames: Interior Connections, The University of Melbourne, Australia. 12. Takeda, T., M. A. Sozen and N. N. Nielsen (1970). "Reinforced concrete response to simulated earthquakes." Journal of Structural Division, A.S.C.E 96(ST12) : 2557-2573. 13. Vecchio, F. J. and M. P. Collins (1986). "The Modified Compression Theory for Reinforced Concrete Elements Subjected to Shear." ACI Structural Journal, Proceedings V. 83, No. 2, March-April 1986, pp. 219-231. 14.


http://db.cosmos-eq.org/scripts/default.plx,

http://www.isesd.cv.ic.ac.uk/.


chapter 5 5.pdf · title: microsoft word - chapter 5.doc author: owner created date: 8/11/2006...

Documents