COMPOSITE GIRDER PARTIALLY REINFORCED WITH CARBON FIBER REINFORCED POLYMER

Abstract

The composite girder partially reinforced with carbon fiber reinforced polymer is a composite steel-concrete beam partially reinforced with a sheet of carbon fiber reinforced polymer bonded to a concrete slab secured to a flange of the steel beam by shear studs, the sheet of CFRP extending across the length and width of the negative moment region of the beam. The negative moment region may be centered about a point of interior support of the composite steel-concrete beam. The carbon fiber reinforced polymer may have a thickness of about 0.25 mm.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to construction elements and supports, and particularly to a composite girder partially reinforced with carbon fiber reinforced polymer that provides a composite steel-concrete beam or girder that is reinforced with a layer of carbon fiber reinforced polymer over a negative moment region of the composite steel-concrete girder.

2. Description of the Related Art

As shown in FIG. 2A, conventional steel beams B are typically used to carry a concrete slab CS supported by a metal deck D. FIG. 2A illustrates typical non-composite construction, in which the beam B does not interact structurally with the concrete slab CS; i.e., the concrete slab is essentially dead weight on the metal deck D disposed between the slab CS and the steel beam B. This is because the slab CS is not adequately bonded to the beam B. In contrast, as shown in FIG. 2B, in composite construction, the concrete slab CS is adequately bonded to the steel beam B by headed shear studs S welded through the deck D to the top flange of the steel beam B, resulting in a composite beam. The concrete, in the composite case, acts like a large flange in compression, while a much greater portion of the steel beam acts in tension. The result is a very efficient beam that is as much as 40% to 60% lighter in steel (in terms of weight) than an equivalent non-composite beam.

Both composite and non-composite beams undergo bending, and thus have bending moments. A bending moment exists in a structural element when a moment is applied to the element so that the element bends. Tensile and compressive stresses increase proportionally with bending moment, but are also dependent on the second moment of area of the cross-section of the structural element. Failure in bending will occur when the bending moment is sufficient to induce tensile stresses greater than the yield stress of the material throughout the entire cross-section.

The bending moment at a section through a structural element may be defined as the sum of the moments about that section of all external forces acting to one side of that section. The forces and moments on either side of the section must be equal in order to counteract each other and maintain a state of equilibrium so that the same bending moment will result from summing the moments, regardless of which side of the section is selected. Moments are calculated by multiplying the external vector forces (loads or reactions) by the vector distance at which they are applied.

If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause “sagging”, and a positive moment will cause “hogging”. Thus, a point of zero bending moment within a beam is a point of contraflexure; i.e., the point of transition from hogging to sagging or vice versa. It is, however, more common to use the convention that a clockwise bending moment to the left of the point under consideration is taken as positive. This then corresponds to the second derivative of a function that, when positive, indicates a curvature that is lower at the center; i.e., sagging. When defining moments and curvatures in this way, calculus can be more readily used to find slopes and deflections.

Thus, for the conventional composite beam shown in FIG. 3, shown here with a pair of end steel stiffeners SS, as is common, the negative moment region (NMR) is positioned about a cross beam CB, which acts as a fulcrum for bending of the beam. It would be desirable to be able to provide the efficiency of a composite beam structure with economical and lightweight reinforcement for the negative moment region.

Carbon fiber reinforced polymer (also known as carbon fiber reinforced plastic or carbon fiber reinforced thermoplastic) is an extremely strong and light fiber-reinforced polymer that is formed by a polymer that contains carbon fibers. Carbon fiber reinforced polymers (CFRPs) are composite materials. In this case, the composite consists of two parts: a matrix and a reinforcement. In CFRP, the reinforcement is carbon fiber, which provides the strength. The matrix is usually a polymer resin, such as epoxy or a plastic material, to bind the reinforcements together.

Thus, a composite girder partially reinforced with carbon fiber reinforced polymer solving the aforementioned problems is desired.

SUMMARY OF THE INVENTION

The composite girder partially reinforced with carbon fiber reinforced polymer includes a steel beam having upper and lower flanges connected by a web, and a concrete slab having opposed upper and lower surfaces, such that the lower surface of the slab is secured to the upper flange of the steel beam (either an I-beam or an H-beam) to form a composite concrete-steel girder. A layer of carbon fiber reinforced polymer is secured to the upper surface of the concrete slab to extend across a negative moment region of the composite concrete-steel girder. The negative moment region may be centered about a point of interior support of the composite concrete-steel girder. The carbon fiber reinforced polymer may have a thickness of about 0.25 mm.

These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic side view of a composite girder partially reinforced with carbon fiber reinforced polymer according to the present invention.

FIG. 2A is a partial perspective view of a prior art non-composite steel beam, partially broken away and in section to show details thereof.

FIG. 2B is a partial perspective view of a prior art composite steel-concrete beam, partially broken away and in section to show details thereof.

FIG. 3 is a diagrammatic side view of a prior art composite steel-concrete beam.

FIG. 4 is a graph showing load deflection curves of a conventional composite steel-concrete girder compared against a composite girder partially reinforced with carbon fiber reinforced polymer according to the present invention.

FIG. 5 is a graph comparing load deflection curves of composite girders partially reinforced with carbon fiber reinforced polymer according to the present invention with beam samples having varying thicknesses of 0.15, 0.25, 0.5, 1.0 and 3 mm.

FIG. 6 is a chart comparing the ultimate capacities and the ratios of tensile stress to ultimate stress for the composite girder samples of FIG. 5.

FIG. 7 is a graph comparing load deflection curves of composite girders partially reinforced with carbon fiber reinforced polymer according to the present invention with varying lengths of a layer of the carbon fiber reinforced polymer.

Similar reference characters denote corresponding features consistently throughout the attached drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The composite girder partially reinforced with carbon fiber reinforced polymer (CFRP) 10, as shown in FIG. 1, is similar to the prior art steel-concrete composite beam shown in FIG. 3, but with a layer 12 of carbon fiber reinforced polymer mounted on the upper surface of concrete slab CS and extending across the negative moment region NMR. For a conventional composite construction girder having a length of 9.6 m, the NMR has a length of about 2.36 m; i.e., extending 1.18 m along either side of the fulcrum point of cross beam CB. The polymer is preferably epoxy, although polyester, vinyl ester, or nylon may be used. The sheet of CFRP is bonded to the concrete slab by an adhesive, which is preferably a 2-part epoxy impregnation resin, although any suitable concrete adhesive may be used.

In order to examine the effectiveness of the carbon fiber reinforced polymer layer 12 a finite element analysis was performed, comparing a conventional continuous composite steel-concrete (CSC) girder against the present composite girder partially reinforced with carbon fiber reinforced polymer 10. In FIG. 4, one sample of the composite girder 10 having a CFRP layer with a length of 2.36 m and a thickness of 0.25 mm, referred to as sample CSCC2, is shown, although analysis of other samples with varying parameters will be discussed below.

As shown in FIG. 4, the addition of the CFRP layer 12 over the negative moment region NMR increased the strength and stiffness of the girder significantly, in addition to improving ductility of the girder. The ultimate load carrying capacity of the CSC was increased by 39%. The CFRP layer 12 maintains the composite action at the negative moment region (NMR) because CFRP has high tensile strength, which prevents concrete cracking. The finite element results showed that adding CFRP over the negative moment region prevented concrete cracking at that region.

In order to find the most effective thickness of the CFRP layer 12, composite steel-concrete girders with different five different thicknesses of CFRP were investigated. These girders, referred to as CSCC1, CSCC2, CSCC3, CSCC4 and CSCC5, had respective CFRP thickness of 0.15, 0.25, 0.5, 1.0 and 3.0 mm. As shown in FIG. 5, the finite element results showed that increasing the thickness of CFRP increases the ultimate capacity of the girder and decreases the efficiency of using the tensile capacity of CFRP. However, it is clear that no change of the stiffness occurs with regard to varying CFRP thickness. As can be seen in FIG. 5, each girder sample exhibits the same behavior up to reaching capacity of the steel section over the interior support. The thickness of the CFRP layer, however, changes the maximum deflection before failure. As the thickness of the CFRP increases, the maximum deflection at failure increases.

Table 1 below summarizes the ultimate capacity of girders with differing CFRP thickness, in addition to the increase in the ultimate capacity with respect to CSCC1. Table 1 also includes the ratio of tensile stress in CFRP to the ultimate stress. As shown below in Table 1, girder CSCC2 gives the best increase in capacity. The results show that increasing the capacity of the steel section, either by increasing ultimate stress or by increasing dimensions of the section, increases the tensile stress in the CFRP.

TABLE 1
Comparison Between Girders Having Different CFRP Thickness
					CFRP Tensile
	CFRP			Difference	Stress
	Thickness		Capacity	in	(% of Ultimate
Girder	(mm)	Capacity	Increase	Capacity	Stress)
CSCC1	0.15	698	—	—	11.3%
CSCC2	0.25	790	13.2%	13.2%	10.8%
CSCC3	0.5	820	17.5%	3.5%	7.9%
CSCC4	1.0	902	29.2%	11.7%	6.7%
CSCC5	3.0	971	39.1%	9.9%	5.7%

The ultimate capacity of girders with differing thickness of CFRP and ratio of tensile stress to ultimate stress of CFRP are shown in FIG. 6. All girders with different thickness of CFRP showed the same failure mechanism. However, different loads reached at each stage depended on the capacity of the girder. Table 2, below, summarizes failure mechanism stages of girders with different thickness of CFRP and the corresponding load at each stage.

TABLE 2
Loads Corresponding to Failure Mechanism Stages of Girders
with Different CFRP Thickness
	Girder
Failure Mechanism	CSCC1	CSCC2	CSCC3	CSCC4	CSCC5
Stage	(KN)	(KN)	(KN)	(KN)	(KN)
Yielding of steel	407	432	448	496	515
reinforcement in the
negative moment region
Yielding of bottom steel	454	462	468	472	482
flange (support)
Yielding of bottom steel	659	659	659	660	661
flange (mid-span)
Ultimate capacity of	523	601	643	723	821
section over interior
support
Failure	698	790	820	902	971

For girders CSCC4 and CSCC5, the yielding of the bottom flange at mid-span started before reaching the ultimate capacity of the section over the interior support. On the other hand, for samples CSCC1, CSCC2 and CSCC3, the yielding of the bottom steel flange at the mid-span started before reaching capacity of section at the negative moment (over the interior support). This is mainly due to the capacity of section at the positive moment region being approximately constant, whereas the capacity of section at the negative moment increases by increasing thickness of the CFRP.

The steel reinforcement at the negative moment region started yielding at the same stage of loading; i.e., at about 55% of the ultimate load, for all girders regardless of the thickness of the CFRP, as shown below in Table 3. Steel reinforcement at the positive moment region reached higher compression stress at ultimate load as the CFRP thickness increased, as shown in Table 4.

TABLE 3
Yielding of Steel Reinforcement Over Interior Support
	Stage of Loading
		Load at		Ratio of Yielding
	Girder	Yielding	Ultimate Load	to Ultimate Load
	CSCC1	407	698	0.583
	CSCC2	432	790	0.546
	CSCC3	448	820	0.546
	CSCC4	496	902	0.549
	CSCC5	535	971	0.55

TABLE 4
Compression Stress of Steel Reinforcement at Positive
Moment Region at Ultimate Load
Girder	Compression Steel Stress	% of Yielding
CSCC1	226	65%
CSCC2	248	71%
CSCC3	255	73%
CSCC4	280	80%
CSCC5	326	93%

Changing the thicknesses of the CFRP layer does not change the loads corresponding to yielding of the bottom steel flange over the interior support or at mid-span for girders significantly, as shown below in Table 5. Small variations observed in this load are due to small changes of the neutral axis location.

TABLE 5
Yielding of Steel Section
	Load at Yielding of	Load at Yielding of	Ultimate
	Bottom Steel Flange	Bottom Steel Flange	Load
Girder	(Support) (KN)	(Mid-Span) (KN)	(KN)
CSCC1	454	659	698
CSCC2	462	659	790
CSCC3	468	659	820
CSCC4	472	660	902
CSCC5	482	661	971

In addition to thickness, variations in length of the CFRP layer 12 were also examined. Four different samples having different CFRP lengths (CSCC2, CSCC2L1, CSCC2L2 and CSCC2L3) were used. CFRP covered the negative moment region for all samples, except CSCC2L3. As shown in FIG. 7, extension of the CFRP layer beyond the negative moment region does not affect the ultimate capacity of the girder.

The ultimate load carrying capacity for girders in which the CFRP covers the negative moment region, or extended beyond the inflection point, is about 790 KN. Reduction of CFRP length within the negative moment region reduced the ultimate capacity of the girder to 678 KN. The stiffness of these girders remains the same, whereas maximum deflection before failure reduced greatly if the CFRP layer was cut short of the inflection point.

The shear and tensile stresses of the bonding material at the ends of the CFRP plate were less than the maximum values at the ultimate capacity for all girders, except for sample CSCC2L3. When the length of the CFRP plate was cut short of the inflection point, such stresses exceeded the maximum shear and tensile stresses of the bonding material. The failure mechanism of girders CSCC2L1 and CSCC2L2 followed similar failure mechanisms as that of girder CSCC2, as shown below in Table 6. No effect was seen when the CFRP extended beyond the inflection point. For girder CSCC2L3, the failure mechanism followed a similar pattern to that of the other girders up to reaching the ultimate capacity over the interior support. Beyond this loading, the bonding material reached the maximum shear and tensile stresses of bonding material at 620 KN. This was followed by yielding of the bottom flange at mid-span. Finally, the girder failed by crushing of concrete at the mid-span.

TABLE 6
Loads Corresponding to Failure Mechanism Stages of Girders
with Different CFRP Length
	CSCC2L1	CSCC2L2	CSCC2L3
Failure Mechanism Stage	(KN)	(KN)	(KN)
Yielding of steel reinforcement in the	436	437	430
negative moment region
Yielding of bottom steel flange	461	460	451
(support)
Yielding of bottom steel flange (mid-	667	667	635
span)
Ultimate capacity of section over	603	601	594
interior support
Failure	800	798	673

The bonding material of girder CSCC2L3 reached maximum tensile and shear stresses after reaching ultimate capacity over the interior support. Failure of the bonding material caused exceeding capacity of the section and premature failure at the mid-span. It should be noted that CSCC2L3 did not reach full plastic capacity because of its premature failure.

It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.

Claims

1. A composite girder partially reinforced with carbon fiber reinforced polymer, comprising:

a steel beam having elongated upper and lower flanges and a web connecting the flanges;

a concrete slab having opposed upper and lower surfaces, the lower surface thereof being secured to the upper end of the steel beam by shear studs to form a composite steel-concrete (CSC) beam, the CSC beam having a negative moment region; and

a sheet of carbon fiber reinforced polymer (CFRP) bonded to the upper surface of the concrete slab, the CFRP sheet extending across the entire negative moment region of the composite steel-concrete beam to cover an inflection point thereof.

2. The composite girder as recited in claim 1, wherein the negative moment region is centered about a point of interior support of the composite concrete-steel beam.

3. The composite girder as recited in claim 1, wherein the sheet of carbon fiber reinforced polymer has a thickness of about 0.25 mm.

4. The composite girder according to claim 1, wherein the polymer comprises epoxy.

5. The composite girder according to claim 1, wherein the CFRP sheet is bonded to the concrete slab by a 2-part epoxy impregnation resin,

6. The composite girder as recited in claim 3, wherein said composite steel-concrete beam has a length of approximately 9.6 m and said sheet of carbon fiber reinforced polymer has a length of approximately 2.36 m, such that the sheet of carbon fiber reinforced polymer extends approximately 1.18 m along either side of a fulcrum point of a cross-beam.