Hybrid flexural components: Testing pre-stressed steel and GFRP bars together as reinforcement for flexural members

Abstract

Concrete members historically have used either pre-stressed steel or steel bars. In recent years there has been an increased interest in the use of fiber reinforced polymer (FRP) materials. However, the flexure behavior of a hybrid system reinforced by the combination of pre-stressed steel and glass fiber reinforced (GFRP) is still relatively unknown. The purpose of this work is to study this. Two slabs of 100 and 150-millimeter thickness, with a span of 2.1 m reinforced with both pre-stressing steel and GFRP were constructed and tested to failure using ACI 318-11 and ACI 440.1R-15. The concrete had strength of 31 MPa and the slabs were respectively reinforced with 5#4 bars and 3#5 bars. Each slab had 37.41 mm² prestressing wire with a failure stress of 1722.5 MPa. The experimental flexural strength and deflection of slabs were compared with their respective sizes theoretical slabs. The theoretical slabs were either reinforced with pre-stressed steel or GFRP rebars, or a hybrid system. It was found that the hybrid system produces better results.

Keywords

Partial pre-stressing / composite structures / GFRP bars

Introduction

Reinforced concrete members fulfill their composite profile with either pre-stressed steel and/or steel bars. In other instances, we also have a member reinforced with fiber reinforced polymer (FRP) bars. However, this study involves a combination of pre-stressed steel and glass fiber reinforced bars. This is because, there has not been any advancement in the study or practice of the flexural capacity of hybrid members. This hybrid approach, a reinforced member with minimal pre-stressed steel and primarily glass reinforced polymer bars (GFRP), exceeds the flexural capacity of a typical steel reinforced concrete member and supports an extended life of the member for aggressive environments of which fiber reinforced polymer bars are mostly in use for [¹].

The use of glass FRP rebar have increased in popularity in the past 2 decades. Some unique projects utilizing FRP are provided below:

(1) Structures that host equipment sensitive to electromagnetic fields [¹]. For example, MRI rooms.

(2) Temporary structures which may require demolition, thus GFRP facilitating the deconstruction process. For example, “soft eyes” for tunnel excavation [¹].

(3) Extended Service life due to aggressive environments.

GFRP bars exhibit high tensile strength, but have no yielding phase within a stress and strain curve [²]. The lack of a yielding phase, for a member with GFRP bars as reinforcement, provides an invitation for innovation to take place and use other reinforcement to add this characteristic to the system. The use of pre-stressing wire, of small diameter, serves as the facilitator for the needed yielding stage the GFRP member lacks. Very importantly, the level of pre-stress to the added wire is what really helps this hybrid component. The small diameter wire being used for the hybrid members will not experience full pre-stress as a typical pre-stress member would. In this case, partial pre-stressing of the small diameter steel wire was taken. It is an approach where some cracking is acceptable at service loads, camber is not an absolute priority, and better performance than typical mild reinforcement can be obtained at a reasonable cost [³]. A hybrid, pre-stressed wire and GFRP bars, system proves to exceed typical steel reinforced components and promises more service life, compared to fully pre-stressed members and mildly reinforced members, when exposed to aggressive environments.

Design approach for pre-stress, GFRP alone and hybrid systems

Deflection

Full pre-stressed, GFRP bar alone, and hybrid member’s deflections were calculated with the elastic beam deflection formula [⁴].

(1){{\displaystyle \delta }}_{\max }={\displaystyle \frac{{pl}^{\mathrm{3}}}{\mathrm{48}EI}}.

A factor of 1 was used for the simply supported aspect of the members. For members which included pre-stress steel wire the value for camber has been considered and is reflected in table results. The following equation was used for camber deflection of constant eccentricity [³].

(2)\Lambda ={\displaystyle \frac{{FeL}^{\mathrm{2}}}{\mathrm{8}EI}}.

All values reflect immediate deflection and long term deflection is not considered in this study.

Nominal moment capacity and deflection of pre-stressed alone concrete members

The service loads for the theoretical calculations are as follows.

The self-weight of concrete was 24722 N/m³. So, for a 150 mm member the load is:

(3)\mathrm{24722}\hspace{0.17em}\mathrm{N}/{\mathrm{m}}^{\mathrm{3}}\times {\displaystyle \frac{\mathrm{600}\hspace{0.17em}\mathrm{m}\mathrm{m}\times \mathrm{150}\hspace{0.17em}\mathrm{m}\mathrm{m}}{{{\mathrm{10}}^{\mathrm{6}}\hspace{0.17em}\mathrm{m}\mathrm{m}}^{\mathrm{2}}}}=\mathrm{2225}\hspace{0.17em}\mathrm{N}/\mathrm{m}.

A commonly used live load in construction is 4940 N/m². So,

(4)\mathrm{4940}\hspace{0.17em}\mathrm{N}/{\mathrm{m}}^{\mathrm{2}}\times \mathrm{0.60}\hspace{0.17em}\mathrm{m}=\mathrm{2964}\hspace{0.17em}\mathrm{N}/\mathrm{m}.

Therefore, a total distributive load of 5180 N/m were used over the members. For the 100 mm member, the self-weight of the member lowers to 1480 N/m for a total distributive load of 4444 N/m. Moment capacities were calculated using a resultant force to the distributive load mentioned above. Fig. 1 shows this.

Following the approach for designing pre-stressed members with added mild steel reinforcement for flexural purposes ACI 318-11 introduces the following equation:

(5){{\displaystyle M}}_{\mathrm{n}}={{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{p}\mathrm{s}}\left({{\displaystyle d}}_{\mathrm{p}}-{\displaystyle \frac{a}{\mathrm{2}}}\right)+{{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{y}}\left(d-{\displaystyle \frac{a}{\mathrm{2}}}\right),

where

(6)a={\displaystyle \frac{({{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{p}\mathrm{s}}+{{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{y}})}{\mathrm{0.85}{{\displaystyle f}}_{\mathrm{c}}^{\text{'}}b}},

and

(7){{\displaystyle f}}_{\mathrm{p}\mathrm{s}}={{\displaystyle f}}_{\mathrm{p}\mathrm{u}}\left(\mathrm{1}-{\displaystyle \frac{{{\displaystyle \gamma }}_{\mathrm{p}}}{{{\displaystyle \beta }}_{\mathrm{1}}}}\left[{\displaystyle \frac{{{\displaystyle \rho }}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{p}\mathrm{u}}}{{{\displaystyle f^{\text{'}}}}_{\mathrm{c}}}}+{\displaystyle \frac{d}{{{\displaystyle d}}_{\mathrm{p}}}}(\omega -{\omega }^{\text{'}})\right]\right),

where

(8)\omega ={\displaystyle \frac{{{\displaystyle \rho f}}_{\mathrm{y}}}{{{\displaystyle f^{\text{'}}}}_{\mathrm{c}}}},\hspace{0.17em}\mathrm{and}\hspace{0.17em}{\omega }^{\text{'}}={\displaystyle \frac{{\rho }^{\text{'}}{{\displaystyle f}}_{\mathrm{y}}}{{{\displaystyle f^{\text{'}}}}_{\mathrm{c}}}}.

Based on ACI 318-11, section 18.7.2 states the above calculation for f_ps is permitted, provided f_pe is not less than 0.5f_pu. Strain compatibility is used to obtain f_ps. The summation of ,{{\displaystyle \epsilon }}_{\mathrm{1}}={\displaystyle \frac{{{\displaystyle f}}_{\mathrm{pe}}}{{{\displaystyle E}}_{\mathrm{p}}}},{{\displaystyle \epsilon }}_{\mathrm{2}}={\displaystyle \frac{{{\displaystyle P}}_e}{{{\displaystyle A}}_{\mathrm{c}}*{{\displaystyle E}}_{\mathrm{c}}}}*\left(\mathrm{1}+{\displaystyle \frac{e^{\mathrm{2}}}{r^{\mathrm{2}}}}\right), and {{\displaystyle \epsilon }}_{\mathrm{3}}={{\displaystyle \epsilon }}_{\mathrm{cu}}*\left({\displaystyle \frac{{{\displaystyle d}}_p-c}{c}}\right) is equal to {{\displaystyle \in }}_{\mathrm{ps}} . This is compared to the strain in the stress and strain curves for the respective wire being stressed. Based on the above equations. A value of f_ps of 1446.9 MPa is assumed. Furthermore, {\omega }^{\text{'}} is omitted from the equation since there is no compression reinforcement added to the member.

Calculations with a pre-stressed force of twice the force applied in the hybrid members are performed. This is because the moment capacity calculated in the table below does not reflect any non-pre-stressed reinforcement. We calculate the theoretical moment capacity using the same geometric and material properties for both members. Area of the pre-stress used was 37.41 mm². The width of both members was approximately 609.6 mm. The heights of the members were 150 and 100 mm. A value of d_p = 125.4 mm and eccentricity of 47.6 mm for the 150 mm member and for the 100 mm member d_p = 74.6 mm and an eccentricity of 22.5 mm were used. Figure 2 shows approximate schematic of the members.

Table 1 shows the effective pre-stress, nominal moment capacity values and deflection results for pre-stress concrete members only.

GFRP-reinforcement alone approach for nominal flexural strength and deflection

Due to the lack of plastic deformation phase in FRP rebar the approach on the design of an FRP concrete member is for it to “possess a higher reserve of strength [²] ”. However, a FRP reinforced concrete member would show extensive cracking as failure of the member nears due to its elastic phase [²]. For nominal flexural strength of GFRP reinforced concrete members the ACI 440.1R-15 [²] states the following equation:

(9){{\displaystyle M}}_{\mathrm{n}}={{\displaystyle \rho }}_{\mathrm{f}}{{\displaystyle f}}_{\mathrm{f}}\left(\mathrm{1}-\mathrm{0.59}{\displaystyle \frac{{{\displaystyle \rho }}_{\mathrm{f}}{{\displaystyle f}}_{\mathrm{f}}}{{{\displaystyle f}}_{\mathrm{c}}^{\text{'}}}}\right){bd}^{\mathrm{2}},

where,

(10){{\displaystyle f}}_{\mathrm{f}}=\sqrt{{\displaystyle \frac{{{{\displaystyle E}}_f{{\displaystyle \epsilon }}_{\mathrm{cu}}}^{\mathrm{2}}}{\mathrm{4}}}+{\displaystyle \frac{\mathrm{0.85}{{\displaystyle \beta }}_{\mathrm{1}}{f}^{\text{'}}}{{{\displaystyle \rho }}_f}}{{\displaystyle E}}_f{{\displaystyle \epsilon }}_{\mathrm{cu}}}-\mathrm{0.5}{{\displaystyle E}}_f{{\displaystyle \epsilon }}_{\mathrm{cu}}\le {{\displaystyle f}}_{\mathrm{fu}},

and for the stress block,

(11)a={\displaystyle \frac{({{\displaystyle A}}_{\mathrm{f}}{{\displaystyle f}}_{\mathrm{f}})}{\mathrm{0.85}{{\displaystyle f}}_{\mathrm{c}}^{\text{'}}b}}.

Following the geometric and material properties of both the 150 mm and 100 mm members we calculate the nominal moment capacity for the concrete with GFRP reinforcement alone. Figure 3 shows the schematic of GFRP reinforced member. Table 2 below shows the relevant results.

Hybrid approach for nominal flexural strength

The design approach for the hybrid concrete members was performed by using ACI 318-11 [⁵] and ACI 440.1R-15 [²]. Steps to a promising design for a hybrid member must take into account both ACI codes mentioned above. In this approach a 100% GFRP rebar design and 20% pre-stressed design of steel wire was considered. This provided no sacrifice in flexural strength design for GFRP bar design, but an aid in flexural capacity by the partially pre-stressed steel wire.

In the hybrid profile, we altered the nominal moment equation by replacing the mild steel calculations with the glass fiber reinforced polymer (GFRP) bar calculations. This is to satisfy the full flexural capacity needed for the concrete member. The design equations are shown below:

(12){{\displaystyle M}}_{\mathrm{n}}={{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{p}\mathrm{s}}\left({{\displaystyle d}}_{\mathrm{p}}-{\displaystyle \frac{a}{\mathrm{2}}}\right)+{{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{y}}\left(d-{\displaystyle \frac{a}{\mathrm{2}}}\right).

It then becomes,

(13){{\displaystyle M}}_{\mathrm{n}}={{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{p}\mathrm{s}}\left({{\displaystyle d}}_{\mathrm{p}}-{\displaystyle \frac{a}{\mathrm{2}}}\right)+{{\displaystyle \rho }}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{f}}\left(\mathrm{1}-\mathrm{0.59}{\displaystyle \frac{{{\displaystyle \rho }}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{f}}}{{{\displaystyle f}}_{\mathrm{c}}^{\text{'}}}}\right){bd}^{\mathrm{2}},

where,

(14){{\displaystyle f}}_{\mathrm{f}}=\sqrt{{\displaystyle \frac{{{{\displaystyle E}}_f{{\displaystyle \epsilon }}_{\mathrm{cu}}}^{\mathrm{2}}}{\mathrm{4}}}+{\displaystyle \frac{\mathrm{0.85}{{\displaystyle \beta }}_{\mathrm{1}}{{\displaystyle f^{\text{'}}}}_c}{{{\displaystyle \rho }}_f}}\times {{\displaystyle Ef}}_f{{\displaystyle \epsilon }}_{\mathrm{cu}}}-\mathrm{0.5}{{\displaystyle E}}_f{{\displaystyle \epsilon }}_{\mathrm{cu}}\le {{\displaystyle f}}_{\mathrm{fu}}.

It should be noted ACI 440.1R-15 states that if , then, conservatively,

(15){{\displaystyle M}}_{\mathrm{n}}={{\displaystyle A}}_{\mathrm{p}}{{\displaystyle f}}_{\mathrm{f}\mathrm{u}}\left(d-{\displaystyle \frac{{{\displaystyle \beta }}_{\mathrm{1}}{{\displaystyle c}}_{\mathrm{b}}}{\mathrm{2}}}\right),

where,

(16){{\displaystyle c}}_{\mathrm{b}}=\left({\displaystyle \frac{{{\displaystyle \epsilon }}_{\mathrm{cu}}}{{{\displaystyle \epsilon }}_{\mathrm{cu}}+{{\displaystyle \epsilon }}_{\mathrm{fu}}}}\right)d.

The nominal moment capacity for the hybrid concrete members are shown in Table 3.

Experimental details

Two reinforced concrete slab members were tested. The 28-days compressive strength of concrete was 31.005 MPa. Our slabs had cross-sectional areas of 100 mm ´ 600 mm and 150 mm ´ 600 mm with a span of 2.1 m. The members were reinforced with both pre-stressing steel and GFRP bars. Each slab had two 4.88 mm prestressing wires with a failure stress of 1722.5 MPa. The wires were loaded to a stress of 4.2 MPa. The 100 mm slab had 5 #4 rebar and the 150 mm slab had 3 #5 rebar. The GFRP rebar had an average tensile strength of 898.46 MPa. One #3 GFRP bar was transversely placed every 150 mm throughout each slab as temperature and shrinkage reinforcement. In order to ease the construction process, the #3 bars were wire tied to the prestressing wires. The idea of using chairs for the transverse bars was considered; however, after using chairs for the longitudinal rebar it was decided more chairs would amount to excessive obstructions in concrete. The prestressing wire data and tensile strength test data was provided by Bonarc Inc. and Hughes Brothers. They provided the testing material at an educational price. Figure 4 shows slab with three chairs supporting the GFRP rebar for proper cover. Each slab held at least nine chairs. Figure 5 shows the overall arrangement.

Three support columns to support the concrete members for loading were constructed. Each support had a cross-sectional area of 900 mm ´ 450 mm with a height of 600 mm. A steel angle of cross-sectional area of 15 mm ´ 150 mm ´ was embedded at the end of each of the support columns. The purpose of this angle was to provide the prestressing wire with an anchor and to help reach its stress potential. Support columns were designed with 30 #6 steel bars (413.4 MPa). Ten bars at each of the 900 mm column faces and five bars at each of the 450 mm faces. The column was carefully formed to receive the steel angle and its anchorage. Holes were drilled to the angle to receive ´diameter anchor bolts and an extrusion with reinforcement was also formed for added support to angle. The slabs were shored up and supported at each column. This is shown in Fig. 6. Figures. 7, 8, 9, and 10 respectively show the support forms (column), angle, poured concrete columns, and string line for displacement inspection.

Loading procedure

To load the hybrid concrete members a frame press was designed and constructed on site. A 150 mm ´ 250 mm ´ 12.5 mm rectangular HSS member was cut to serve as the top and base of the press frame. Two 37.5 mm galvanized steel bolts with a coarse six threads per 25 mm held washer and nuts in place without potential elongation of the members while they served as the vertical supports of the frame press. One 200 mm ´ 50 mm ´ 6.25 mm channel was bolted to each concrete column to serve as the anchorage for the crossing 100 mm ´ 50 mm ´ 12.5 mm rectangular HSS members that were being pressed upon by a 300 kN hydraulic cylinder operated by an electric hydraulic pump. Figure 11 shows the frame press used to break the hybrid members.

Every component of the frame press was confirmed to be leveled for accurate load transfer. The hydraulic electric pump operated the cylinder at 3.45 MPa at a time approximately. The area of the piston was 3069 mm², therefore the load applied by the cylinder jack to the member was 13.1 kN. Every load iteration applied allowed for checks on deflection, crack widths, location, and inspection of overall structural integrity of the hybrid members. Figures 12 and 13 show the hydraulic equipment used to load the frame press and the hybrid member loaded at first iteration.

Results of hybrid breaks

Tables 4 and 5 below show data collected during the breaking process. Plots of crack width versus load for the 150 mm and the 100 mm hybrid members are respectively shown in Figs. 14 and 15. In sequence, Figs. 16-18 show sample pictures of the increase in crack width for the 150 mm hybrid member.

Figs. 19 and 20 show the four-inch hybrid system for cracks.

Comparison of results

Table 6 shows a comparison of deflections for the full prestressed, GFRP only, and the hybrid theoretical and experimental members under service loads.

We calculate two deflection limits used in building constructions under service loads, namely: L/360 and L/240.

(17){\displaystyle \frac{L}{\mathrm{360}}}={\displaystyle \frac{\mathrm{2.1}\mathrm{\times }\mathrm{1000}}{\mathrm{360}}}=\mathrm{5.83}\mathrm{mm,}

(18){\displaystyle \frac{L}{\mathrm{240}}}={\displaystyle \frac{\mathrm{2.1}\mathrm{\times }\mathrm{1000}}{\mathrm{240}}}=\mathrm{8.75}\mathrm{mm}.

Comparing deflections under service loads and the allowable limits, it can be seen that all are acceptable. However, hybrid experimental members prove to have better results. Both members failed at 50 mm deflection.

Next we compare the moment capacities of the theoretical full pre, GFRP only, hybrid member along with the hybrid experimental. Table 7 shows the comparison of 150 and 100 millimeter members.

Hybrid experimental and hybrid theoretical moment capacities differ by+15.9% and ‒25.7% respectively for 150 and 100 mm slabs. The difference can be attributed to testing procedures when applying load by the presser from the hydraulic jack. The load is applied in incremental bursts and not consistently as in a perfect laboratory setting. Improving tolerances in spacing between the slab and presser supporting beam can also facilitate better load transfer to the hybrid experimental members, thus collecting more accurate data in the yielding stage of the steel and GFRP.

Further, the 150 mm experimental slab has a moment capacity that is higher by 43% than the experimental 100 mm slab. This implies that a 50 mm increase in thickness produces a significant improvement in the flexural capacity of hybrid flexural members.

Overall, it can be seen from Table 7 that the hybrid moment capacities are higher than both the fully prestressed and the GFRP systems alone.

Conclusions

An approach to the design of hybrid reinforced concrete members has been presented. The theoretical design for full pre-stressed and GFRP bars and hybrid concrete members were introduced. The hybrid system was designed using both the ACI 318-11 and ACI 440.1R-15 codes. Actual data from loading and breaking of the hybrid concrete members was recorded. This data included moment capacity, crack widths and their location, along with deflection. The deflections and ultimate moment capacities of experimental members were compared with the theoretical members. It was found that the hybrid system produces better results in terms of structural integrity.

Future studies

Samples and support type

For upcoming studies, crack isolation and crack width need to be evaluated within a sample of members. Samples should be grouped according to support type. For example, a sample of members can be integrated at column supports or simply bearing without anchorage. This kind of criteria can influence crack location and correlates to crack width versus load plots.

Amount of partial pre-stress

The minimal pre-stressed steel added to the concrete members should be studied further with the intention of further minimizing the stress without sacrificing moment capacity and member failure results. Hybrid members prove to have a gradual total failure upon maximum loading which is the complete opposite to known failure results of fully pre-stressed members and members having only GFRP bars. Partial pre-stress may be performed and practiced more within the boundaries of the smallest steel wire possible.

References

[1] Nanni A, De Luca A, Zadeh J H. Introduction. In: Reinforced Concrete with FRP Bars. Florida: CRC Press-Taylor & Francis Group, 2014

[2] Guide for the Design and Construction of Structural Concrete Reinforced with Fiber-Reinforced Polymer (FRP) Bars. ACI 440.1R-15, 2015

[3] Nilson H A. Design of Prestressed Concrete. 2nd ed. Canada: John Wiley & Sons, Inc, 1987, 103

[4] Singh B S. Design of RC Structures Reinforced with FRP Bars. In: Analysis and Design of FRP Reinforced Concrete Structures. New Delhi: McGraw-Hill, 2015, 67–78

[5] Building Code Requirements for Structural Concrete. ACI 318-11, 2011

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