This chapter (a part of my doctoral thesis) reviews some studies that are relevant to the objectives of this research. A brief overview of research in the recent decades on the shear strength of the concrete structure without shear reinforcements is introduced firstly. Secondly, the beam shear-carrying action and arching action as two mechanisms that govern the shear resistance in structures are explained in detail with the factors that can influence it. The time-dependent effects on concrete under axial, flexure, and shear stresses are presented at the end of this chapter.
Shear resistance of RC beam without web reinforcements
Shear failures of reinforced concrete (RC) structures become a crucial issue because of its brittle nature. The shear failures are usually avoided by improving the shear strength exceeding the flexural capacity to induce the flexural failures that more ductile. However, for some particular structures which are dominated by shear behaviours (such as a transfer slab in building structures, a footing foundation, and a thick roof slab of a subway tunnel), the changing of failure mode is challenging to reach. The intensive researches on the shear strength have been triggered by the reports of shear failures of the concrete structures in many countries including the failure of deep beams of Air Force warehouses in USA. Fenwick and Paulay [1] pointed out that shear failure of RC structures depended on the relative contribution of beam shear-carrying action (moment can change by changing of tension in the reinforcement) and arching action (the inner lever arm of moment varying along the length of structure). Beam action would carry most of the shear until this mechanism failed. After redistribution of internal stresses, the arch action could then carry even higher shears if the distance between the loading point and the supports of structures was adequately short. Later, Taylor [2] and other researches indicated that the shear stresses in concrete structures was transmitted by aggregate interlocking (between cement matrix and aggregate) on the inclined flexural cracks of structures, dowel action by tension reinforcement, residual stresses of concrete after the peak strength and uncracked concrete in compression flexural zone. Vecchio and Collins [3] proposed the modified compression field theory (MCFT) to predict the shear response of cracked reinforced concrete elements based on their test on concrete structural components subjected to pure shear. The theory predicts that failure will occur when the shear stress on the crack faces required for equilibrium reaches the maximum shear stress that can be transmitted by aggregate interlock. The predicted failure shear stress decreases as the predicted width of the inclined crack increases. Furthermore, Kani [4,5] and other researchers emphasized that the shear strength of RC beams strongly depends on the ratio of shear span to the effective depth. It would also decrease with increasing member depth. Research on the shear strength of concrete structures continues up to now, and the present study attempts to fill the lack of investigations on the shear performance of concrete structures under sustained loading.
A. Shear Transfer Mechanisms
The shear resistance of reinforced concrete beams without shear reinforcements is carried out by beam shear-carrying action (consisted of uncracked concrete in the compression zone, aggregate interlocking, dowel action, the residual tensile strength of concrete) and arching action. The exact proportions of each mechanism vary in each case depending on the inclination and roughness of the cracks, the bond strength between tension reinforcement and the surrounding concrete, the depth of the compression zone, and material properties.
a. Uncracked concrete in the compression zone
The shear force carried by the uncracked flexural compression zone is limited by the depth of the compression zone. The compressive strength of concrete and the longitudinal reinforcement ratio greatly affect this mechanism because the concrete strength in the biaxial state and elastic modulus of concrete are the function of the compressive strength of concrete [6]. The increase of longitudinal reinforcement ratio causes the increased depth of the uncracked compression zone [7]. Moreover, the depth of the compression zone is also influenced by creep and shrinkage [8].
b. Aggregate interlocking
On the inclined crack plane of RC beam, the contact between aggregate and cement matrix provide resistance against slip that can transmit shear stress. Walraven [9] comprehensively investigated this mechanism and indicated that aggregate interlocking decreases as crack width increases and as aggregate size decreases. In the case of concrete with low strength aggregate, the contribution of the aggregate interlocking to the total shear strength will drop due to a flat crack plane.
c. Dowel Action
When transverse stresses are working on the longitudinal reinforcement, the reinforcement bar can transmit the shear stresses through bending action and shear action. This mechanism is called dowel action. The ratio and diameter of longitudinal reinforcement, the compressive strength of concrete, and the concrete cover have significant and the most dominating interaction effect on dowel force [6,7]. However, the dowel action seems to be efficient for beams that cannot develop spalling cracks (for example short-span beams and beams with shear reinforcement). For relatively slender beams, the contribution of dowel action is insignificant and considered to be neglected by many researchers [10].
d. Residual tensile strength of concrete
Concrete can resist tensile stress even after the occurrence of cracks. The residual stresses are present at the fracture process zone at the crack and soften with increasing the crack width [10-12]. Fracture energy of concrete and tension softening parameter govern this mechanism.
e. Arching action
This mechanism becomes dominant in beams with shorter shear span where a single inclined strut (joining the applied load and the supports) carries concrete contribution, and the longitudinal reinforcement takes the tensile stresses. Full plastic strength is possible to reach in this type of beam [10].
B. Factors Affecting Shear Strength
a. Residual tensile strength of concrete
Failure modes of RC beam strongly depend on the ratio of shear span a to the effective depth d. One of the brief explanations regarding this parameter is presented by MacGregor and Wight [13]. For very short beams (with a/d from 0 to 1), the arch action will dominate the behaviour of the beam and the inclined cracks will directly join the applied load and the support points. In this case, the compressive strut of concrete will be developed, and the tension reinforcement will function as a tie which has a uniform tensile force. After developing inclined cracks, short beams (with a/d from 1 to 2.5) will redistribute internal stresses and still able to carry an additional load (in part by arch action). The final failure will be either shear-tension failure or shear compression failure. In case of slender beams (with a/d from 2.5 to 6.0), the beam will fail shortly after the occurrence of inclined cracks. Very slender beams (with a/d greater than 6.0) will fail in flexure before the formation of inclined cracks. Figure 2.1 shows several types of failure modes. Figure 2.1 shows the relationship between shear strength and the ratio of shear span to the effective depth of the beams. The shaded area indicates the reduction in strength due to shear.
b. Concrete strength
As the RC beams can fail either in shear-tension failure or shear compression failure, both compressive strength and tensile strength of concrete will affect the shear capacity of the beam depending on the failure mode. Fracture energy associated with the residual strength of concrete after cracking can also contribute to the shear strength. Compressive strength, tensile strength and fracture energy increase with time as a result of hydration process of cement paste. Conversely, they may decrease due to shrinkage, creep, and other external factors.
c. Longitudinal reinforcement ratio
Longitudinal reinforcement plays an essential role in controlling flexural cracks. If the reinforcement ratio decreases, tensile strain in the reinforcement increases, the width of flexural cracks becomes wider and furthermore the cracks can penetrate higher into the compression flexural zone of the beam. It will eventually reduce the contribution of aggregate interlocking, uncracked concrete in the compression zone, and dowel action to the total shear resistance. Some researchers designate this phenomenon as strain effect of longitudinal reinforcement.
d. Axial forces
The presence of axial compression forces will reduce the longitudinal strain of structures. The flexural cracks become narrower, the cracks difficult to extend higher into the beam, and finally it will increase the shear strength. Conversely, the axial tensile forces will reduce the shear capacity.
e. Size of beam
The spacing of flexural cracks and the cracks width tend to increase with the increase of the depth of the beam. This phenomenon is commonly known as size effect which results in lower shear strength. However, there is no significant change in shear strength when the width of structures is increased.
f. Coarse aggregate
The size and strength of aggregate are strongly related to the aggregate interlocking mechanism. The increase in aggregate size tends to increase the roughness of the crack surface and higher shear stresses that can be transferred. If the aggregate strength is much lower than that of the cement matrix, the aggregate interlocking will be diminished because the crack will tend to penetrate through the aggregate rather than going around them. It happens in the case of high-strength concrete and concrete with low aggregate strength (such as limestone aggregate) [14-16].