Patent Application
20150013252
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
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
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.
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.
Similar reference characters denote corresponding features consistently throughout the attached drawings.
The composite girder partially reinforced with carbon fiber reinforced polymer (CFRP) 10, as shown in
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
As shown in
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
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.
The ultimate capacity of girders with differing thickness of CFRP and ratio of tensile stress to ultimate stress of CFRP are shown in
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.
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.
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
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.
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.
