WO2007137365A1

WO2007137365A1 - Reinforced structural concrete members and methods concerning same

Info

Publication number: WO2007137365A1
Application number: PCT/AU2007/000766
Authority: WO
Inventors: Muhammad Najib Sadraddin Hadi; Nuri Elbasha
Original assignee: The University Of Wollongong
Priority date: 2006-05-31
Filing date: 2007-05-31
Publication date: 2007-12-06

Abstract

A method for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μd), the method including determining the helical pitch (S) using the relationship wherein the displacement ductility (μd) of the reinforced concrete beam is inversely proportional to the helical pitch (S) of the reinforcement member.

Description

REINFORCED STRUCTURAL CONCRETE MEMBERS AND METHODS

CONCERNING SAME

This invention relates to reinforced structural concrete beams and methods for determining the parameters of the structural concrete beams in order to obtain certain desired physical properties.

Ductility is an important physical property of concrete structural members. A concrete structural member having high ductility ensures that a large deflection will occur during overload conditions prior to the failure of the structure. As such, concrete structural members exhibiting high ductility are particularly useful for buildings or structures that are erected in zones subject to earthquakes or similar destructive forces.

One method whereby the ductility of a concrete structural member is increased is by using helically shaped reinforcement members. In this regard, the present invention seeks to provide a way of determining the parameters of a concrete structural member including helical reinforcement members that would provide a sufficient level of ductility required for a specific application.

Summary of the Invention

According to one aspect the present invention provides a method for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μ,d), the method including determining the helical pitch (S) using the relationship wherein the displacement ductility (μ._d) of the reinforced concrete beam is inversely proportional to the helical pitch (S) of the reinforcement member.

According to a preferred form the method includes determining the helical pitch (S) using the relationship wherein the displacement ductility (μ^) of the reinforced concrete beam is proportional to the total volumetric ratio of the helices of the reinforcement member (p\_Λ)

wherein the total volumetric ratio of helices (Pi₁) ⁼ — — , '

wherein: d_h is the diameter of the helical reinforcement member (mm) S is the helical pitch of the helical reinforcement member

(mm); and,

D is the diameter of the confined concrete within the helical reinforcement member (mm).

According to a further preferred form the method includes determining the helical pitch (S) using the relationship wherein:

the displacement ductility (μa) °c ( 0.7 )

wherein: S is the helical pitch of the helical reinforcement member

(mm); and, D is the diameter of the confined concrete within the helical reinforcement member (mm).

According to a further preferred form the method includes determining the helical pitch (S) using the formula (i)

wherein,

Ph is the total volumetric ratio of helices = — — ;

d_h is the diameter of the helical reinforcement member (mm) fc is the concrete compressive strength (MPa); fyh is the yield stress of helical reinforcement (MPa); P_rnax is the maximum allowable tensile reinforcement;

p is the longitudinal reinforcement ratio = — ^ ; bd

A_s is the total area reinforcement in the tension side of the beam (mm ); b is the width of the beam (mm); d is the effective depth of the beam (mm);

D is the diameter of the confined concrete within the helical reinforcement member (mm);

S is the helical pitch of the helical reinforcement member (mm); a has a value between 35 and 49; β has a value between -0.1 and 0.1; γ has a value between 0.005 and 0.25; and ψ has a value between 2.5 and 3.5.

Preferably a has a value between 39 and 44, β has a value between -0.05 and 0.05, γhas a value between 0.01 and 0.18 and φ has a value between 3.0 and 3.18.

According to another aspect the present invention provides a system for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μ^), the system including:

(1) an input device to receive one or more parameters of the concrete beam including: d_h - the diameter of the helical reinforcement member (mm), fc - the concrete compressive strength (MPa), fyi> - the yield stress of helical reinforcement (MPa),

Pmax - the maximum allowable tensile reinforcement, A_s - the total area reinforcement in the tension side of the beam (mm²), b - the width of the beam (mm), d - the effective depth of the beam (mm), D - the diameter of the confined concrete within the helical reinforcement member (mm), a - which has a value between 35 and 49, β — which has a value between —0.1 and 0.1, 7— which has a value between 0.005 and 0.25, and, φ - which has a value between 2.5 and 3.5;

(2) an output device to provide an indication of the helical pitch (S); and,

(3) a processor, the processor being adapted to determine a value for the helical pitch (S) of the concrete beam using the relationship wherein the displacement ductility (jU_d) of the reinforced concrete beam is inversely proportional to the helical pitch (S) of the reinforcement member.

In a preferred form the system includes a processor being adapted to determine a value for the helical pitch (S) of the concrete beam using the relationship wherein the displacement ductility (μ,j) of the reinforced concrete beam is proportional to the total volumetric ratio of the helices of the reinforcement member (β_h) wherein the total volumetric ratio of helices

(mm); and,

In a further preferred form the system includes a processor being adapted to determine a value for the helical pitch (S) of the concrete beam using the relationship wherein:

the displacement ductility (μ._d) ∞ ( 0.7 )

wherein: S is the helical pitch of the helical reinforcement member (mm); and, D is the diameter of the confined concrete within the helical reinforcement member (mm).

In a further preferred form the system includes a processor being adapted to determine a value for the helical pitch (S) of the concrete beam using formula (i):

wherein,

TECl Ph is the total volumetric ratio of helices = — *- ;

SD

A p is the longitudinal reinforcement ratio = — *- . bd

According to another aspect the present invention provides a computer program product for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μ_d), said computer program product comprising a procedure for determining the helical pitch (S) using any one of the aforementioned methods.

Brief Description of Figures

An example embodiment of the present invention should become apparent from the following description, which is given by way of example only, preferred but non-limiting embodiments, described in connection with the accompanying figures.

Fig. 1 illustrates an example functional block diagram of a processing system that can be utilised to embody or give effect to a particular embodiment of the present invention.

Detailed Description of the Invention Tlie insertion of a helical reinforcement member within the compression zone of over- reinforced high strength concrete (HSC) beams has been shown to improve the ductility of the concrete beam. Typically there is a limit to the ratio of longitudinal reinforcement that may be installed in a particular cross section of a concrete beam. More longitudinal reinforcement can be installed if the flexural strength required is more than the capacity of a particular cross section, where such a section becomes under- reinforced rather than over-reinforced section. However, such over-reinforced sections have been found to fail in a brittle mode. The installation of a helical reinforcement with a suitable pitch in the compression zone of the concrete beam will reduce this unwanted effect.

Ductility is an important property of structural members as it ensures that large deflections will occur during overload conditions prior to the failure of the structure. A large deflection warns of the nearness of failure. In this regard, ductility becomes a very important design requirement for structures built in earthquake prone areas.

Ductility may be estimated by the displacement ductility (/i_d), which is defined as the ratio of deflection at ultimate load to the deflection when the tensile steel yields.

It was found that the relationship between displacement ductility (μϊ) and the helical pitch (S) of the reinforcement member of the concrete beam could be expressed in the following ways:

β, * -_s ;

/a ^ocl O.7— 1, wherein: d_h is the diameter of the helical reinforcement member (mm)

S is the helical pitch of the helical reinforcement member (mm); and, D is the diameter of the confined concrete within the helical reinforcement member (mm).

Furthermore, through trial and experimentation an analytical description for predicting the displacement ductility index (pt_d) was found. As a result, the relationship between the

displacement ductility and the non-dimensional ratios ( — ^l—r~ ), ( ) and (0.7 ) can f_c /W D be expressed as follows:

2 where p_k is the total volumetric ratio of helices and may be expressed as — — , wherein

d_h is the diameter of the helical reinforcement member (mm); f_c is the concrete compressive strength (MPa) and may be measure by conducting compressive strength tests on concrete cylinders (Tests can be conducted using the provisions of Australian Standards

AS 1012.9-1999); f_yh is the yield stress of helical reinforcement (MPa) (may be measured according to the provisions of AS/NZS 4671:2001); p_max is the maximum allowable tensile reinforcement (determined using the provisions of Australian Standard AS 3600:2001); p

is the longitudinal reinforcement ratio and may be expressed as — *- , wherein A_s is the total bd area of reinforcement in the tension side of the beam (mm²), b is the width of the beam (mm) and d is the effective depth of the beam (mm); D is the diameter of the confined concrete within the helix (mm) and S is the helical pitch (mm).

It was also found that the displacement ductility index increases as the helical reinforcement ratio increases and as the helical yield strength increases, but the displacement ductility index decreases as the concrete compressive strength increases. In

other words the displacement ductility index increases as the — '—p- increases.

is a factor in determining whether a beam is an under or over-reinforced section.

/Λnax

Also could be used to indicate the flexural ductility of a beam section. It is well

known that, for under-reinforced concrete beams the displacement ductility index

decreases as increases. Thus the non-dimensional parameter could be used for r τa&y. Amax predicting the displacement ductility.

The last parameter in the displacement ductility model is (0.7 ). The effect of the

helical pitch on the displacement ductility index is significant because it affects the distribution of confinement pressure. It was found that there is a significant effect caused by the helix pitch on the displacement ductility index for over-reinforced helically confined HSC beams. This parameter shows how decreasing the helical pitch increases the

effectiveness of helical confinement. Also (0.7 ) indicates that helical confinement is

negligible when the helical pitch is 70% of the confined concrete core diameter.

The relationship proposed above to predict the displacement ductility index of over- reinforced helically confined HSC beams can be modelled as follows:

where a,β,γ and φ are the unknown constants of confinement for the displacement ductility index. A regression analysis on experimental results may be performed to find the best combination of a,β ,γ and φ . After various trials and experimentation is was found that these constants had the following values: a has a value between 35 and 49; β has a value between -0.1 and 0.1 ; 5 7 has a value between 0.005 and 0.25; and φ has a value between 2.5 and 3.5.

An example of how these constants of confinement may be determined is provided below. In this example, Table 1 outlines various parameters of 14 beams that were the subject of 0 the experimental analysis, the results of which were used in a regression analysis to determine approximate values for a,β,γ and φ .

Table 1 Experimental data used for regression analysis

f_c is the concrete compressive strength, MPa f _h is the helical yield strength, MPa d is the helical diameter, mm

S is the helical pitch, mm p_h is the helical reinforcement ratio p is the actual reinforcement ratio

P_max is the maximum allowable tensile reinforcement as defined by AS 3600 (2001) μ_d is the displacement ductility index The relationship proposed above to predict the displacement ductility index of over- reinforced helically confined HSC beams can be modelled as follows:

where a,β,γ and φ are the unknown constants of confinement for the displacement ductility index. A regression analysis on the experimental results was performed to find the best combination of a,β,γ and φ . The test results of the displacement ductility index of the 14 beams were used to determine the best correlation between the predicted and the experimental values.

The regression analysis have been conducted using JMP software (Gary, 2002) where the first step was to transfer the equation into the form y = f(x_γ,x₂,x_n) by taking the logarithm for both sides of the equation as follows:

Ln(μ_d -ϊ)

Or simply: y =c + βx_λ + /x₂ + φx₃ Where

y = Ln(μ_d -l) c = Lna and then a =e^c

Applying the method of regression (Fit model) using the experimental results presented in Table 1. This result shows that only the factor x3 is significant where the P-value is 0.0013 which is less than 0.05. However the correlation factors for the model is 0.78

Then the unknown constants are determined as a = 96.139 /= - 0.976 β = 0.247 ^ = 2.914

Thus, the displacement ductility index as developed from the experimental data in this particular example are as follows: 2.914

It has to be noted that, when — is greater than or equal to 0.7, the second part of the

above equation has a negative or zero value. This indicates that the effect of the helical

confinement is negligible when the ratio — is greater than or equal to 0.7.

It has been noted that some beams have high error such as the beam R10P35-D85 has a maximum error of -52%, which could be due to low compaction of the concrete, but if these beams were not included in the regression analysis the correlated data can be improved. Thus by excluding these beams and applying the regression analysis again, the model will be as follows:

The above analytical model has application for estimating the various parameters for over- reinforced helically confined HSC beams such as for example the helical pitch (S) of the helical reinforcement member.

The present invention will become better understood from the following examples of preferred but non-limiting embodiments thereof.

Examples

The following examples illustrate how the present invention may be applied with respect to over-reinforced helically confined HSC beams. The first example deals with the analysis in which the displacement ductility index is predicted while the second example uses the proposed model to determine the helical pitch (S) of the helical reinforcement member of the over-reinforced confined HSC beams.

Example 1

Determine displacement ductility index, if the following information is given:

Beam concrete cross-section is 200 x 300 mm Concrete cover is 20 mm Longitudinal reinforcement is 4N32

Yield strength of longitudinal reinforcement is 500 MPa Concrete compressive strength is 80 MPa

Helical details: Helical diameter is 12 mm Yield strength of helical reinforcement is 250 MPa Helical pitch is 30 mm

Helical confinement concrete core diameter is 150 mm

Step 1 : Calculate

Where p_h =-^- = 0.10 ^Hh DS

Step 2, Calculate P

-^ — 1.93

/Λirax

O

Step 3, Calculate 0.7

0.7 -— = 0.5 D

Then the displacement ductility index for the above reinforced helically confined HSC beams could be predicted using the following equation:

/- _f S _s --00..000044 _/ /• \ N 00..0U9999 3.092

/ι_rf = 1+41.223 - -^- 0.7 -^- = 5 ..11 8 Example 2

The data used here is the same as that in the analysis problem (Example 1), but here the displacement ductility index is predetermined and the helical pitch of the reinforcement member (S) is required (unknown).

Firstly, substitute for the value of p_h and simplify

S is the only unknown in the above equation but by trial and error, the value of S is found to be 30 mm. Thus to gain a displacement ductility index of 5.18 with the concrete compressive strength, the longitudinal and helical reinforcement details given above, the helical pitch must be 30 mm.

In another embodiment of the present invention there is provided a system for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μi).

With respect to a networked information or data communications system, a user has access to one or more terminals that are capable of requesting and/or receiving information or data from local or remote information sources, hi such a communications system, a terminal may be a type of processing system, computer or computerised device, personal computer (PC), mobile, cellular or satellite telephone, mobile data terminal, portable computer, Personal Digital Assistant (PDA), pager, thin client, or any other similar type of digital electronic device. The capability of such a terminal to request and/or receive information or data can be provided by software, hardware and/or firmware. A terminal may include or be associated with other devices, for example a local data storage device such as a hard disk drive or solid state drive.

An information source can include a server, or any type of terminal, that may be associated with one or more storage devices that are able to store information or data, for example in one or more databases residing on a storage device. The exchange of information (ie. the request and/or receipt of information or data) between a terminal and an information source, or other terminal(s), is facilitated by a communication means. The communication means can be realised by physical cables, for example a metallic cable such as a telephone line, semi-conducting cables, electromagnetic signals, for example radio-frequency signals or infra-red signals, optical fibre cables, satellite links or any other such medium or combination thereof connected to a network infrastructure.

A particular embodiment of the present invention can be realised using a processing system, an example of which is shown in Fig. 1. hi particular, the processing system 100 generally includes at least one processor 102, or processing unit or plurality of processors, memory 104, at least one input device 106 and at least one output device 108, coupled together via a bus or group of buses 110. hi certain embodiments, input device 106 and output device 108 could be the same device. An interface 112 can also be provided for coupling the processing system 100 to one or more peripheral devices, for example interface 112 could be a PCI card or PC card. At least one storage device 114 which houses at least one database 116 can also be provided. The memory 104 can be any form of memory device, for example, volatile or non-volatile memory, solid state storage devices, magnetic devices, etc. The processor 102 could include more than one distinct processing device, for example to handle different functions within the processing system 100. Input device 106 receives input data 118 and can include, for example, a keyboard, a pointer device such as a pen-like device or a mouse, audio receiving device for voice controlled activation such as a microphone, data receiver or antenna such as a modem or wireless data adaptor, data acquisition card, etc. Input data 118 could come from different sources, for example keyboard instructions in conjunction with data received via a network. Output device 108 produces or generates output data 120 and can include, for example, a display device or monitor in which case output data 120 is visual, a printer in which case output data 120 is printed, a port for example a USB port, a peripheral component adaptor, a data transmitter or antenna such as a modem or wireless network adaptor, etc. Output data 120 could be distinct and derived from different output devices, for example a visual display on a monitor in conjunction with data transmitted to a network. A user could view data output, or an interpretation of the data output, on, for example, a monitor or using a printer. The storage device 114 can be any form of data or information storage means, for example, volatile or non-volatile memory, solid state storage devices, magnetic devices, etc.

In use, the processing system 100 is adapted to allow data or information to be stored in and/or retrieved from, via wired or wireless communication means, from the at least one database 116. The interface 112 may allow wired and/or wireless communication between the processing unit 102 and peripheral components that may serve a specialised purpose. The processor 102 receives instructions as input data 118 via input device 106 and can display processed results or other output to a user by utilising output device 108. More than one input device 106 and/or output device 108 can be provided. It should be appreciated that the processing system 100 may be any form of terminal, server, specialised hardware, or the like.

The processing system 100 may be a part of a networked communications system. Processing system 100 could connect to network, for example the Internet or a WAN. Input data 118 and output data 120 could be communicated to other devices via the network. The transfer of information and/or data over the network can be achieved using wired communications means or wireless communications means. A server can facilitate the transfer of data between the network and one or more databases. A server and one or more databases provide an example of an information source. In one particular form, the server may transfer, to the processing system 100, data indicative of a computer program which when executed in the processing system 100 performs the method described herein.

hi one embodiment, the above described method can be performed in the processing system 100 for determining the parameters of a concrete beam including a confined helical reinforcement member wherein the concrete beam has a predetermined displacement ductility (μa). The processing system can be configured to use the above-mentioned methods to determine the parameters of the concrete beam. The user may be able to selectively adjust at least one of the above-mentioned values in order to obtain a particular desired parameter. Additionally or alternatively, the user can select a range of values to be used in the above-mentioned formula such as to obtain a range of parameters.

In another embodiment of the present invention there is provided a computer program product for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (/X_d), said computer program product comprising a procedure for determining the helical pitch (S) using any one of the aforementioned methods. The computer program in accordance with this embodiment of the present invention may be written using any suitable computer programming language such as for example Ada, assembly language, APL, BASIC, C, C++, C#2, Clipper, D, FORTRAN, HASKELL, lo, Java, JavaScript, Lisp, ML, Objective-C, Pascal, Perl 1-5, Perl 6, PHP, Pike, Python, Ruby, Scheme, Smalltalk, Visual Basic and or xHarbour.

Although several preferred embodiments has been described in detail, it should be understood that various changes, substitutions, and alterations can be made by one of ordinary skill in the art without departing from the scope of the present invention.

Claims

The Claims:

1. A method for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μ^), the method including determining the helical pitch (S) using the relationship wherein the displacement ductility (μ^) of the reinforced concrete beam is inversely proportional to the helical pitch (S) of the reinforcement member.

2. A method according to claim 1 wherein determining the helical pitch (S) further includes using the relationship wherein the displacement ductility (μa) of the reinforced concrete beam is proportional to the total volumetric ratio of the helices of the reinforcement member (ph) wherein the total volumetric ratio of helices (p_h)

SD '

wherein: dh is the diameter of the helical reinforcement member (mm)

<S is the helical pitch of the helical reinforcement member

(mm); and,

3. A method according to claim 1 or claim 2 wherein determining the helical pitch (S) further includes using the relationship wherein:

the displacement ductility (μ_&) ∞ (0.1 )

wherein: S is the helical pitch of the helical reinforcement member

(mm); and,

4. A method for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μ^), the method including determining the helical pitch (S) using formula (i)

wherein, πd,

Ph is the total volumetric ratio of helices =

SD ' dh is the diameter of the helical reinforcement member (mm) fc is the concrete compressive strength (MPa); fyh is the yield stress of helical reinforcement (MPa); P_max is the maximum allowable tensile reinforcement;

p is the longitudinal reinforcement ratio = — - ;

D is the diameter of the confined concrete within the helical reinforcement member (mm); S is the helical pitch of the helical reinforcement member (mm); a has a value between 35 and 49; β has a value between -0.1 and 0.1;

7 has a value between 0.005 and 0.25; and φ has a value between 2.5 and 3.5.

5. A method according to claim 4 wherein αhas a value between 39 and 44.

6. A method according to claim 4 or claim 5 wherein β has a value between —0.05 and 0.05.

7. A method according to any one of claims 4 to 6 wherein y has a value between 0.01 and 0.18.

8. A method according to any one of claims 4 to 7 wherein φ has a value between 3.0 and 3.18.

9. A system for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μa), the system including:

(1) an input device to receive one or more parameters of the concrete beam including: d_h - the diameter of the helical reinforcement member (mm), fc - the concrete compressive strength (MPa), fyh - the yield stress of helical reinforcement (MPa),

P_max - the maximum allowable tensile reinforcement,

A_s - the total area reinforcement in the tension side of the beam (mm²), b - the width of the beam (mm), d - the effective depth of the beam (mm),

D - the diameter of the confined concrete within the helical reinforcement member (mm), a— which has a value between 35 and 49, β - which has a value between -0.1 and 0.1, 7- which has a value between 0.005 and 0.25, and, φ - which has a value between 2.5 and 3.5;

(2) an output device to provide an indication of the helical pitch (S); and,

(3) a processor, the processor being adapted to determine a value for the helical pitch (S) of the concrete beam using the relationship wherein the displacement ductility (μ_<j) of the reinforced concrete beam is inversely proportional to the helical pitch (S) of the reinforcement member.

10. A system according to claim 9 wherein the processor is adapted to determine a value for the helical pitch (S) of the concrete beam using the relationship wherein the displacement ductility (/i_<j) of the reinforced concrete beam is proportional to the total volumetric ratio of the helices of the reinforcement πd_h member (p_h) wherein the total volumetric ratio of helices (pi,) ⁼

SD

wherein: d_h is the diameter of the helical reinforcement member

(mm) S is the helical pitch of the helical reinforcement member (mm); and,

11. A system according to claim 9 or claim 10 wherein the processor is adapted to determine a value for the helical pitch (S) of the concrete beam using the relationship wherein:

the displacement ductility (μ_<j) ∞ ( 0.7 )

wherein: S is the helical pitch of the helical reinforcement member (mm); and,

12. A system according to any one of claims 9 to 11 wherein the processor is adapted to determine a value for the helical pitch (S) of the concrete beam using formula (i):

wherein,

_/O_h is the total volumetric ratio of helices = — — ;

p is the longitudinal reinforcement ratio = -^- . bd

13. A computer program product for determining the helical pitch (S) of a helical reinforcement member required to provide a helically reinforced concrete beam with a predetermined displacement ductility (μ_<ϊ), said computer program product comprising a procedure for determining the helical pitch (S) using a method according to any one of claims 1 to 8.