# Modelling Of High Strength Concrete Beams Biology Essay

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Concrete is a well-known, widely used construction material in todays society. The constituents of concrete consist of cement and water, aggregates such as sand and gravel, and additives, as either minerals or chemicals. Concrete is readily used in buildings and structures because of its strength and rigidity, and resistance to weathering. Concrete is long lasting, is easy to maintain, keeping costs down, and easily forms a variety of useful shapes, whilst also being corrosion resistant. While concrete is very strong under compressive loads, it is very weak in tension, creating limitations in its use areas where significant tensile stresses are developed, such as in beams, columns or slabs. However, carefully placed steel bars within the concrete allow it to carry loads in tension. This is known as reinforced concrete (Warner et al. 2007).

As time has gone by, the strength of concrete has increased, leading to the development of what is known as High Strength Concrete (HSC). AS 3600-2009 defines High Strength Concrete as concrete that has a compressive strength greater than 50MPa. High Strength Concrete can be reinforced with High Strength Steel (HSS), and has a wide variety of useful applications.

Base and Red (1965) showed that by helically confining HSC beams, the strength and ductility of the beam could be increased. Hatanka and Tanigawa (1992) showed that a confinement using a circular helix was more effective than the use of ties in the form of rectangles or squares.

With clear advantages coming from the use of helical confinement in the compression zone of concrete beams, further exploration into enhancing the confining effect is desirable.

Finite element modelling is used in this thesis to analyse the ductile and strength behaviours of high strength concrete beams provided with helical reinforcement in the compression zone. FEM provides engineers within the industry with a non-linear analysis of the behaviour of beam that reduces the need of experimental testing if the results can be calibrated to its real life counterpart.

Whitehead and Ibell (2005) analysed the shear behaviour of Fibre-reinforced polymers in the compression zone of concrete beams. Their analysis attempted to alleviate the poor design problems that nullify the advantages of FRP's. With FRP's being increasingly used as reinforcement and in structures under repair, this thesis undertakes the modelling of High Strength Concrete beams reinforced helically with Fibre-reinforced polymers using the Finite Element Modelling program, Strand7.

## 1.2 Aim and Objectives

The aim of this investigation is to develop a finite element model to analyse the strength and ductile behaviour of high strength concrete beams helically reinforced in the compression zone with Fibre-reinforced polymers. An analysis will be carried out to verify Cush's (2009) experimental results where polymer reinforced helices (PRH) were used with varying pitches and were compared with a steel helix.

The objectives of this thesis are;

Review literature of HSC reinforced with HSS and various polymers using helical confinement, and the use of FEM software and its application to reinforced HSC beams.

Develop a finite element model using Strand7 and calibrate the model to verify the experimental results of Cush (2009)

Analyse the strength and ductile behaviour of HSC beams reinforced helically with FRP's and make a comparison between the use of FRP's and HSS.

Conclude on the viability of the use of FRP's for helical reinforcement in HSC beams.

Provide direction for further research at the University of Wollongong.

## 1.3 Rationale

The undertaking of this thesis attempt to continue the analysis of the viability in using FRP's as an alternative reinforcement to HSS in HSC beams. The verification of the results of Cush (2009) and the further modelling of the strength and ductile behaviour of HSC beams reinforced helically with FRP's will provide analysis on the performance of FRP's and display its reinforcing capabilities in comparison to HSS.

## 1.4 Summary of Chapters

Chapter 2 reviews the literature in relation to HSC beams helically reinforced with HSS, and the effects of modifying various parameters in the reinforcement arrangement, including the pitch and diameter of the helix, the number of helixes used, the shape of the helix, the type of material providing the confinement, and the tensile reinforcement ratio.

Chapter 3 provides a brief introduction to the use of FEM and provides detail on their analysis of the behaviour of HSC beams reinforced with HSS, and the ability of FEM to replicate experimental results.

## CHAPTER 2

## HELICAL REINFORCEMENT IN HSC BEAMS

## 2.1 Introduction

Advancements in the production of concrete has lead to the availability of special purpose concretes, with strengths in excess of 100MPa. The combination of such high-strength concretes with reinforcing steel attempts to alleviate the problems with the tensile strength of concrete and take advantage of the high strengths of both materials.

HSC beams with HSS reinforcement arrangements have many benefits to the engineering industry such as reducing the size of columns in tall city buildings, reducing slab thicknesses, and hence reducing the weight and saving money in construction.

While High Strength Concrete reinforced with High Strength Steel has large compressive strength, it has very low ductility. The low ductility of both materials leads to sudden failure without warning. This is known as brittle failure. Nawy (2001) identifies an increase in the brittleness of concrete as its strength increases . Brittle failure is unsafe and undesirable, therefore limiting the use of HSC reinforced with HSS in the industry despite is advantageous strength properties (Warner et al. 2007).

The helical confinement of concrete has been shown to increase the strength and ductility characteristics of HSC beams reinforced with either HSS or FRP's. Despite the brittle nature of FRP's, they still have a positive effect on the ductility characteristics of HSC beams. They also provide many advantages when being considered over the use of HSS. FRP's are extremely light, strong, are non-magnetic, and are no susceptible to corrosion.

Further research into the viability of FRP's as an alternative reinforcement to HSS could take advantage of their increased strength and lightness characteristics so that they can be fully utilised in the engineering industry.

## 2.2 Effect of Helical Reinforcement in Concrete Beams

Typically, helical reinforcement in concrete beams uses a high strength steel in the shape of a helix. This is placed in the compression region of concrete beams, and is considered to increase the strength and ductility of High Strength Concrete Beams.

Hadi and Schmidt (2003 and 2005) confined high strength concrete beams in the compression zone through the use of one or two helixes. It was predicted that there would be an improvement in the strength, and hence, load carrying capacity of the concrete. This was supplemented by the prediction that there would be an increase in the ductility of the high strength concrete beams as the use of high strength materials is normally to the detriment of a beams ductility characteristics.

Hadi and Schmidt (2003) found that use of the helical reinforcement in the compression zone had the effect of dramatically increasing the ductility of the HSC beam. Poisson's effect is defined as the ratio between the change in length of an object due to either its elongation or compression in the transverse direction, against the length change in the axial direction. The confinement of the concrete in the compressive region using helical reinforcement provides a lateral compressive force on the confined concrete core, which prevents the concrete from expanding in the axial direction. This allows the multi-axial compression of the concrete core (Hadi and Schmidt, 2005). Figure 1 (Hadi and Schmidt, 2003) below shows the effect of helical reinforcement on ductility, by making a direct comparison between the reference beam UR-PL and the helically reinforced beam OR-SH-P1.

## Figure 2.1: Load-central deflection curves (Hadi and Schmidt, 2003)

Hadi and Schmidt (2005) found that use of the helical reinforcement in the compression zone had the effect of also noticeably increasing the strength and load carrying capacity of the HSC beam. Beam 1 was the reference beam containing no helical reinforcement whilst beam 2 contained an N12 helix of pitch 50mm.

## Figure 2.2: Cross-sections of Beam 1 and Beam 2 (Hadi and Schmidt, 2005)

Comparing the beams 1 and 2, the reference and helically confined beams respectively, it was seen that there was a 24% increase in the load carrying capacity from beam 1 to beam 2, with beam 2 carrying a total load of 245.91KN compared to 198.5KN for beam 1.

Further studies into the helical confinement of HSC beams in the compression zone has found that effectiveness of the helical confinement is influenced by a number of factors including the pitch and diameter of the helix, the number of helixes used, the shape of the helix, the type of material providing the confinement, and the tensile reinforcement ratio.

## 2.2.1 Effect of Helical Pitch

The pitch of a helix is defined as the distance in which one full turn of the helix is achieved. The helical pitch of reinforcement in compression region of HSC beams has a critical impact on the strength and ductility properties of the beam.

Hadi and Elbasha (2007) tested 5 beams confined helically with varying pitches. The beams had a cross section of 200mm x 300mm and were a length of 4m. The diameter of the helixes was kept at a constant 160mm while the pitches varied from 24, 50, 75, 100 and 160mm. A number of conclusions were drawn from the investigation in regards to the effect of helical pitch on the performance of HSC beams.

## Table 2.1: Summary of beam results (Hadi and Elbasha, 2007)

The spalling off load refers to the load that causes the concrete cover to separate from the core of the concrete that is confined by the helical reinforcement. As the pitch of the helix increased, it was found that the spalling of load increased proportionally. However, the failure load of the beams decreased as the pitch of the helix increased.

The ductility of the beams was found to also decrease as the pitch of the helix increased. In this case, the yield deflection and ultimate deflection converged to a point where at a helical pitch of 160mm they were equal. The remaining beams experience ductile failure where by the displacement ductility index âË†â€ u/âË†â€ y was greater than one. It was also concluded that when the pitch of the helix was equal to its diameter, the effect of the helical confinement was considered minor.

## 2.2.2 Effect of rectangular and circular helices

The shape of the confinement region in the compression zone of HSC beams has an important effect on the strength and ductility characteristics of the beam. The compression zone of the beam can be confined using helical reinforcement or through the us of rectangular or square ties.

As described earlier, the main advantage of helical reinforcement is that it provides a lateral compressive force on the confined concrete core, which prevents the concrete from expanding in the axial direction. This allows the multi-axial compression of the concrete core (Hadi and Schmidt 2005). A rectangular or square tie applies only around 30-50% of the lateral force of a circular helix (Hatanaka and Tanigawa, 1992). The resulting reduction in the compressive force means that the multi axial compression of the core is restricted to the area best confined by the rectangular or square tie, which occurs in the corners of the tie.

## Figure 2.3: Confinement Areas of Helix and tie reinforcement (Hadi and Schmidt, 2007)

## 2.2.3 Effect of the number of helices

The confining of HSC in the compression region can be achieved through the use single or dual helices. Dual helices are placed directly next to one another in the compression zone of HSC beams.

Hadi and Schmidt (2003) conducted research into the use of a single helix in comparison to that of a dual helix arrangement. A beam containing a single helix had a diameter of 50mm, while the arrangement containing two helices had diameters of 25mm each. Therefore the total area confined in both beams was the same. The pitch of all helices was kept constant.

Comparisons between single and dual helices found little difference in the ductility and strength characteristics of each beam, as the experiments for both beam produced very similar results. Hadi and Schmidt, however, did make the point that less steel was used in the reinforcement arrangement using a single helix, and that therefore, in industry the more economical solution would be to use a single helix over dual helices.

## 2.2.4 Fibre-Reinforced polymers used for Helical Confinement in the compression zone of HSC beams

The use of fibre-reinforced polymers as opposed to the use of high strength steel has been considered for helically reinforcing HSC beams in the compression zone. However, there are some drawbacks to the use of FRP's including cost, and brittle failure mechanism of the material (Whitehead and Ibell, 2005)

Whitehead and Ibell (2005) analysed the shear behaviour of FRP's in concrete beams in an attempt to alleviate the poor design problems that nullify the advantages of FRP's. The various arrangements looked to improve the reinforcement arrangements of FRP's as Ibell and Burgoyne (1999) found that bonding and geometry of the FRP was a large contributory factor in the influence of FPR's used for shear reinforcement.

The arrangements of the FRP reinforcement considered bonded and unbonded helices, as well as helices that were entirely in the compression zone of the beam or draped into shear zones following the line of principal compression.

## Figure 2.4: Helical Reinforcement shapes (Whitehead and Ibell, 2005)

Whitehead and Ibell found that when comparing unbonded helixes to those who were intermittently or fully bonded, the pitch of the helix was required to be closer to achieve similar increases in failure capacity. Unbonded helixes were 50% less effective than fully or intermittently bonded helixes when it came to shear resistance. They also found that prestressing within the FRP had a much greater effect on the shear capacity, especially when in comparison the HSS reinforced confinement. The most effective arrangement determined was found the incorporated a fully bonded circular or rectangular helix place in the constant moment area. This was combined with an intermittently bonded rectangular helix placed within shear zones.

Another study was conducted by Leung and Burgoyne (2001), who analysed the effect of overlapping helixes of Aramid in the compression region of HSC beams. The overlapping portions of the concrete within the compression zone created regions of doubly reinforced concrete. Results found that both the load carrying capacity and ductility increased as a result of the double confinement. The failure of the beams in the experiment was due to the gradual crushing of the flange of the T-beam, as opposed to the sudden failure caused when there were no helices contained in the compression region (Burgoyne and Guimararaes, 1992).

## 2.2.5 Effect of Tensile Reinforcement Ratio

The ratio of tensile reinforcement to the effective cross section of the beam is known as the tensile reinforcement ratio. The maximum allowable tensile reinforcement ratio is defined in AS3600 by the following formula:

where;

É£ = ratio under design bending or combined bending and compression of the depth of assumed rectangular compressive stress block to kud;

f'c = characteristic concrete compressive strength at 28 days, MPa;

fsy = yield strength of reinforcing steel, MPa;

ku = ratio of depth to neutral axis to the effective depth

d = effective depth

Hadi and Schmidt (2002) analysed the effect of increasing the tensile reinforcement ratio by creating 7 beams, including one reference beam, with the remaining six beams testing helices in the compression region with design reinforcement ratios of pmax, 1.5pmax, and 2pmax. This was achieved through increasing the number and size of the reinforcement bars in the tensile region, as well as decreasing the effective depth of the beams.

## Table 2.2: Beam characteristics (Hadi and Schmidt, 2002)

Hadi and Schmidt concluded that the pmax set of beams had the greatest ductility, followed by 1.5pmax and finally 2pmax. The load carrying capacity also increased as the tensile reinforcement ratio increased, particularly in beams 6 and 7 where the helixes benefited form the increased stability given by the reinforcement provided.

## 2.3 Review of past thesis at the University of Wollongong

## 2.3.1 Review of Cush (2009)

Cush conducted an experiment into the use of Polymer rope helices (PRH), instead of the high strength steel typically used for helical reinforcement. Constructing beams of 1200mm x 150mm x 100mm, Cush used a variety of reinforcement arrangements. The reinforcement arrangements provided a comparison between the use of a HSS helix and a PRH. He also verified the work of previous studies by looking at the effect of varying the pitch and diameter of the helix in PRH.

## Table 2.3: Beam Reinforcement arrangements (Cush, 2009)

Beam

No.

Dimension

(L x D x B, mm)

Confinement Reinforcement

Tensile Reinforcement

Type

Pitch

(mm)

Diameter

(mm)

Type

1

1200 x 150 x 100

None

## -

## -

2N12

2

1200 x 150 x 100

Steel Helix

25

57

2N16

3

1200 x 150 x 100

Rope Helix

25

75

2N16

4

1200 x 150 x 100

Rope Helix

50

75

2N16

5

1200 x 150 x 100

Rope Helix

25

96

2N16

## Figure 2.5: Beam Cross-sections (Cush, 2009)

The four point load test was used to undertake testing, however the test was compromised due to the fact that the beams were not able to be loaded until failure, and therefore results for the maximum mid-span deflection were taken at the maximum load produced by the apparatus. This was due to the fact that the apparatus was not designed for the testing of HSC beams.

The reduced beam sizes compared to previous years lead to similar values for the yield and ultimate loads for each beam. This meant that there was little solid evidence in the results from which conclusions could be drawn, particularly as there were no values available for loadings after the beams had failed.

For the PRH, the ultimate mid-span deflection decreased as the pitch increased, however the ultimate load increased. The introduction of a larger diameter to the PRH and hence an increased area of confined concrete caused a greater ultimate mid-span deflection. Given that steel rope helix was not of the same diameter as the polymer rope helix, it is difficult to draw direct comparisons between steel helices and PRH.

However, Cush was satisfied that the PRH were effective in replicating the advantages of helices in the compression zone of HSC beams as both the strength and ductility of the beams increased. The lightweight nature of the PRH and the cost of the polymer used provides an interesting path for further research as finding the optimum arrangement for such a material would reap both cost and weight benefits to the industry.

## 2.4 Summary

The confinement of the concrete in the compressive region using helical reinforcement provides a lateral compressive force on the confined concrete core, which prevents the concrete from expanding in the axial direction. This allows the multi-axial compression of the concrete core (Hadi and Schmidt, 2005).

Independently, the effectiveness of the helical confinement is by the pitch and diameter of the helix, the number of helixes used, the shape of the helix, the type of material providing the confinement, and the tensile reinforcement ratio.

The introduction of Helical reinforcement improves the strength and ductility characteristics of HSC (Hadi and Schmidt, 2003 and 2005) beams and supports the viability of the use of HSC beams reinforced with either HSS or FRP's (Whitehead and Ibell, 2005) .

## CHAPTER 3

## FINITE ELEMENT MODELLING IN REIFORCED CONCRETE

## 3.1 Introduction

Finite Element Analysis is a technique involving the use of a mathematical model that is used to provide solutions to engineering problems. The use of Finite Element Analysis (FEA) software predicts the behaviour of concrete structures allowing the experimentation and verification of various designs and reinforcing arrangement within the structure.

Cook (1995) alludes to the division of elements into several smaller elements that are linked through nodes within the program. The combination of nodes and elements forms the creation of what is known as a mesh. The mesh is calibrated through the input of various material and structural properties, and models the influence of these properties on the behaviour of the mesh under the load provided.

Reinforcing steel can be accurately represented using three different models; smeared, embedded, or discrete.

The smeared model is applied for models that are larger and hence the effect of the reinforcement is less than it would otherwise be in a smaller structure (Srinivasan and Sathiya, 2010). Reinforcement is assumed to be constant through concrete element sections within a mesh, as shown below.

## Figure 3.1: Smeared Model (Wolanski, 2004)

the discrete model shares nodes between reinforcement and concrete elements. This provides the disadvantage of not being able to distinguish the reinforcement volume from the concrete volume, as well as the restriction of the concrete mesh position due to the reinforcement (Taravez, 2001)

## Figure 3.2: Discrete model (Wolanski, 2004)

the embedded model evaluates the stiffness of the reinforcing bars separately from the concrete mesh by providing compatible displacements between the concrete and reinforcement nodes respectively. This however, does increase the complexity of the model.

## Figure 3.3: Embedded Model (Wolanski, 2004)

## 3.2 Review of Past FEM of reinforced concrete

## 3.2.1 Fanning (2001)

Fanning (2001) modelled a simply reinforced concrete beam, of dimensions 3000mm x 240 mm x 155mm. The reinforcement consisting of two bars in the compression zone and three bars in tension zone, is detail below.

## Figure 3.4: Cross section details for beam (Fanning, 2001)

The bonding between the reinforcement and the concrete was assumed to be perfect in the FEM and that the reinforcement and the concrete displace uniformly together.

The FEM calculated the ultimate load of the beam to be 66.1KN whilst adequately resisting non-linear deflection up until failure. This compared favourably with the experimental value of 66.18KN, providing very good collaboration between the FEM and the experimental data. The first crack occurred in the FEM at a load of 17KN, which coincided with the first crack occurrence in the experimental model too. The FEM however, differed from the experimental values when comparing the ultimate deflection, with the FEM model aching a deflection of 27mm during its analysis while the experimental model showed a deflection of 45mm.

The smeared crack model used in the study for the cracking of the concrete, while a discrete model was used to analyse the reinforcement. Fanning (2001) concluded that the use of these models for their respective analysis was justified as the accurate results showed the appropriateness of each model.

## 3.2.2 Wolanski (2004)

Wolanski's analysis using a FEM consisted of verifying the results of the Buckhouse (1997), who constructed beams that were 4725mm x 254mm x 457mm. Wolanski (2001) wanted to develop an accurate FEM inputting all element and material properties so to ensure that the data from the FEM correlated as closely as possible with the experimental results of Buckhouse (1997).

One quarter of the beam was modelled due to the symmetrical nature of Buckhouse's beam. The model is shown in the figure below.

## Figure 3.5: Concrete, steel plate and support element (Wolanski, 2004)

The mesh for the reinforcement was created through the use of nodes already within the concrete volume mesh. Wolanski (2004) merged the items in ANSYS that had a common node to obtain an accurate model. The boundary conditions provided in the experiment by Buckhouse (1997) were recreated through assigning UX = UZ = 0 and with the support constraint conditions being UY = UZ = 0 to represent the presence of a roller.

The non-linear Newton-Raphson method was used in the FEM to produce data on the cracking of the beam, steel reinforcement and its yielding, and the strength limit state of the constructed beam. The experimental result of a deflection of 92.7mm was compared to the ANSYS calculation of 91.14mm, signifying the accuracy of the model produced by Wolanski (2004) when comparing the FEM analysis and the experimental analysis.

The FEM effectively displayed the steel reinforcement yielding at a force of 59606 N, and the subsequent deflection increase and formation of flexural and diagonal tension cracks. The beam was found to have failed at a load of 59526 N.

## 3.3 Review of past FEM thesis at the University of Wollongong

## 3.3.1 Review of Brahim (2006)

Brahim (2006) sought to further investigate the application of helical reinforcement in high strength concrete through the use of finite element programs. Brahim used to Finite element software programs, ANSYS and Strand7.

Brahim modelled the HSC beams that were constructed by Elbasha and Hadi (2005). Elbasha and Hadi (2005) were studying the effects of varying the size of the pitch of the helical reinforcement on the characteristics of strength and ductility in HSC beams. Constructing beams of 4000mm x 300mm x 200mm, Elbasha and Hadi varied the pitches of the helices from 25, 50, 75, 100 and 150mm. Brahim (2006) made a direct comparison between the results produced by finite element software and the experimental results found by Elbasha and Hadi (2005).

In Brahim's Strand7 model, reinforcement elements were modelled as trusses, while the concrete beam and steel plate were modelled as a brick elements. Brahim created an initial model in the 2D plane using constant strain triangle elements (TRI3) elements and linear quadrilateral elements (QUAD4 elements). Extruding the 2D plane model, the 3D concrete block was formed, with reinforcement being modelled by connecting each node within the concrete block. The concrete block and reinforcement share nodes as shown in figure 7 below.

## Figure 3.6: Node sharing in Strand7 model (Brahim, 2006)

Brahim assumed that the bonding between the concrete and the reinforcement was seamless. The steel plate elements were modelled using 8-node brick elements, while the load applied to the steel plate was done so through the centre line of the steel plate formed by the brick elements. This replicated the locations of the loadings in the experiment conducted by Elbasha and Hadi (2005).

## Figure 3.7: Steel plate loading along centreline (Brahim, 2006)

The support providing the boundary conditions was modelled as steel and given dimensions 100mm x 80mm x 30mm, and provided constraint in the z and x direction, (UX = UZ = 0).

Strand7 differed from ANSYS in convention used in the input of compressive and tensile strength values whereby compression values were negative while tensile values were positive. All other data input for Strand& including material properties, was similar to ANSYS.

Strand7 used the Newton-Raphson method for solving the non-linear problems in Finite Element Models. In this non-linear analysis, stress-strain relationships are input into the system along with the application of incremental loads, to more accurately model the behaviour of the concrete beam. However, this increases the simulation run time.

In his summary of results, Brahim (2006) states that there were obvious differences in the load versus deflection curves produced by Strand7 and ANSYS in comparison to the experimental data obtained by Elbasha and Hadi (2005). The major differences in the curves is visible after the spalling off of the concrete cover. An explanation may be given by the compromises made in the modelling of the helix in both Strand7 and ANSYS. Brahim was forced to simplify the helical model, substituting in a circular reinforcement model. The assumption was made that the performance of the circular reinforcement model was the same as the helical reinforcement model and that the compressive effects that create multi-axial compression would be the same in both methods of reinforcement.

## 3.4 Summary

FEA software provides a viable alternative to experimental testing that can save both time and money for engineers if the FEM is calibrated correctly.

Fanning's (2001) model provided to within 2% the data achieved during the experiment undertaken by Buckhouse (1997) showing the viability of FEA.

Both Strand7 and ANSYS provide engineers with useful tools to evaluate the behaviour of HSC beams helically reinforced with HSS. To accurately model this though, the compromises made by Brahim (2006) need to be eliminated to appropriately analyse the results of Cush (2009)