INTRODUCTION AND LITERATURE REVIEW
1.2 LITERATURE REVIEW
1.2.3 Size effect of concrete structural element
result as “log
NU
σ versus log D”. However, he did not try to describe this plot mathematically or generalize it. Walsh’s classical test was of limited range and included only one type of fracture specimen, which were not conclusive.
A stronger experimental verification was reported by Bažant and Pfeiffer [1986, 1987], which covers a broader size range and four different types of specimens. This research included test on mortar and test on concrete specimens. The results were plotted and found to satisfy the size effect law proposed by Bažant.
The result of the test performed by Jeng and Shah [1985] also support the size effect law proposed by Bažant, although a good fitting of the test data was not possible as the size range was very limited compared to the scatter obtained.
Sener et al. [1999] tested two groups of RC beams with splices located either in the mid span region with a uniform bending moment, or in one of the end regions with a uniform shear force. Beams of three different depths were considered, which were geometrically similar in all the three dimensions. The reinforcing bar diameters and cover thicknesses were also scaled in the same proportion. The results revealed the existence of a significant size effect, which was approximately described by the size effect law proposed by Bažant.
Sener et al. [2002] tested notched beams with and without steel fibres. Three different depths of beam were chosen and four point bending test were conducted. Failure bending stresses in all the cases were plotted in a bi-logarithmic plot and the results of failure of beams clearly confirm the existence of a significant size effect on the nominal strength with steel fibers, accompanied by an increase in failure brittleness followed Bažant’s size effect law.
Krauthammer et al. [2003] investigated numerically and experimentally the size effect phenomenon of high strength concrete (HSC) in the form of cylindrical specimens
subjected to axial impact load. Results from their tests and simulations showed the existence of size effect in HSC cylinders under impact loading.
Sener et al. [2004] tested a large number of geometrically similar columns with three different slenderness ratios. The failure strength was calculated from the failure load P found experimentally. Linear regression analysis was carried out to find characteristic depth D0 and dimensionless parameter B. Finally, bi-logarithmic plotting of log(D D0) versus log( t/)
NU Bf
σ was done and was found in agreement with Bažant’s size effect law. Further, the size effects become stronger as the slenderness ratio increases.
Elfahal et al. [2005] investigated numerically and experimentally the size effect phenomenon of normal strength concrete (NSC) for a cylindrical specimens that subject to axial load impact. Results from their tests and simulations showed the existence of a size effect in NSC cylinders under impact loading.
Bindiganavile and Banthia [2006] studied size effect of plain concrete beam under impact loading. Plain concrete of three different sizes were tested under three point impact load.
The result of the impact test from their study as well as those from some of the previous studies was fitted to Bažant’s size effect law. Similarly, same data were plotted according to Multifractal scaling law. The plot of compressive strength followed both Bažant’s size effect law and Multifractal scaling law.
Leung et al. [2007] conducted test on CFRP retrofitted beam (strengthened in shear) of three different sizes. A number of specimens with different retrofitting strategies were tested. It was observed that the retrofitted specimens with complete FRP wrapping did not show any size effect, whereas FRP-U stripped retrofitted specimen showed size effect in term of gain in strength. The result showed that the failure in the strengthened specimen
case it was due to rupture of strips. The authors concluded that for the debonding failure, the bond capacity was directly proportional to the square root of the thickness and hence, with increase in thickness of FRP strips, the shear capacity was at a slower rate. In the second case of failure by debonding, the failure strength was directly proportional to thickness and hence with increase in size, there was increase in strength in same proportion leading to no size effect.
Belgin and Sener [2008] reported the failure of full-scale singly over reinforced concrete beam under four-point loading. The specimens were made of concrete with a maximum aggregate size of 10 mm. The beams were geometrically similar in all the dimensions.
The bar diameter and cover thicknesses were similarly scaled in proportion. The results of a bi-logarithmic plot (log(D D0) versus log( t/)
NU Bf
σ ) revealed the existence of a significant size effect, which can approximately be described by the size effect law previously proposed by Bažant. Finally, they concluded that the size effect is stronger in two-dimensional similarities than for one and three-dimensional similarities.
Koc and Sener [2009] tested geometrically similar columns of different sizes with different types of notches for both normal and high strength concrete to study the size effect. Three different slenderness ratios were covered in their study. Some specimens were having very shallow wide notch, some with deep and some with narrow notches.
Axial loads were applied to the specimens till failure. Maximum ultimate stress was calculated and bi-logarithmic plot was drawn. The bi-logarithmic plots in all the cases followed Bažant’s size effect law. It was observed that, with increasing strength, the size effect becomes more pronounced as the brittleness is increased. The authors concluded that out of all three different types of notches, the specimens made with surface-notch showed more pronounced size effect than all other types of notches. Also, they observed
that, with increasing strength, the size effect becomes more pronounced as the brittleness is increased.
Choudhury [2010] tested eighteen specimens with nine control and nine retrofitted specimens of three different sizes (full, two third and one third) for exploring the existence of size effect. All the three dimensions of the specimens and the amplitude of the displacement histories were scaled down from the full scaled specimen for two third and one third size specimens. Diameter of the reinforcing bars, development length, length of special confinement zone, cover of reinforcing bars etc. were also scaled down appropriately. Three different typical deficient beam-column connections (beam weak in flexure, beam weak in shear and column weak in shear) were considered. The deficient connections were retrofitted using Carbon Fiber Reinforced Polymer (CFRP) and Glass Fiber Reinforced Polymer (GFRP) wrapping. All the specimens were tested under cyclic loading until failure. Correlation on various parameters like gain in ultimate strength, ductility, energy dissipation of specimens per unit volume of joint, cumulative energy dissipation and variation of stresses with respect to relative deflection for all specimens due to retrofitting indicated the existence of size effect. Moreover, maximum ultimate stresses were calculated and bi-logarithmic plots were drawn. The investigator observed that the bi-logarithmic plots for both control as well as retrofitted specimens followed closely the size effect law proposed by Bažant. However, the size effect became more pronounced with the increase in brittleness of specimens.
Literature survey showed experimental studies on size effect were mainly done for RC beams and column with limited studies on beam-column connections related to size effects were reported. Further, size effect study on beam and beam-column connections
literature could not however present any findings on size effect of rehabilitated beam- column connections.