The mechanical performance of concrete shear key for prefabricated structures

Abstract

The mechanical performance of concrete connection plays an important role in the response of precast concrete structures. Unlike conventional small concrete shear key which is mainly to help with alignment at installation, large concrete shear keys have been often designed in recent engineering practice to improve joint shear resistance. However, the mechanical properties of large concrete shear keys have not been properly studied. This paper utilizes experimental and numerical methods to investigate both direct shear and flexural bending properties of shear keys. Four types of shear keys comprised of trapezoidal shape, semi-spherical shape, dome shape and wave shape are investigated, which are found to strongly influence the mechanical properties of the keyed joint. Laboratory shear test found unlike conventional shear key, with increased tenon size failure moves to concrete mortise. A detailed numerical model is built to help understand stress developed at the key joint. Flexural bending tests are carried out to evaluate the flexural bending properties of these key joints. Through comparing with theoretical derivation for plain flat joint, similar bending moment resistances from the keyed joints are measured with that of plain flat joint, but larger rotation angles are recorded probably because more damages at the key joint. Among the four different joint patterns, shear key with smoothed pattern could effectively relief concrete damages.

Keywords

concrete shear key direct shear flexural bending

Introduction

Precast segmented concrete structures have gained much popularity in construction industry. Many studies have been conducted on precast segmented concrete structures to widen its applications (Kim et al., 2010; Li et al., 2018; Ou et al., 2007; Zhang et al., 2016a,b; Zhang et al., 2018a). Concrete shear key is one of the most common connections for precast concrete structure. It has been used for segmented decks for decades, which is designed to mainly help alignment during erection, transfer shear force between segments, and improve durability by protecting the prestress tendon against corrosion. Since concrete shear keys do not normally transfer bending force, steel reinforcements and/or prestress tendon are usually added to help resist the flexural bending load.

Different types of concrete joints have been introduced to connect precast concrete elements, which can be categorized as wet and dry joint. For a wet joint, two precast segments are glued together with epoxy or through injecting grout in ducts, which has good mechanical performance, nevertheless requires extra installation procedure. Dry joint is commonly adopted because it costs relatively less and is more effective in erection. Despite AASHTO (1999) and most designers would not recommend dry joint due to durability concern, it is getting more and more popular in practice because of its simplicity.

The failure mechanism of conventional concrete shear key has been studied by different researchers. Kaneko and his co-workers (Kaneko et al., 1993a,b; Kaneko and Mihashi, 1999) utilized fracture mechanics theory to predict the shear strength. The damage and failure process is described by a two-phase cracking process. Tensile stresses resulting from shear stress concentrations at the upper corner of the key cause a S-crack which induces rotation of the key and leads to M-cracks along the base of the specimen. The M-crack continuously increases as shear force increases. At the point before failure, the shear key is held in place by compressive struts. Kaneko et al. (1993a) implemented a linear elastic fracture mechanics for S-crack, and a smeared cracking and truss model for M-crack. The peak shear strength can be predicted with a close-loop formula. Hoek and Bray (2014) employed rock mechanics approach that considers tangential and normal displacements, which defines the initial relationship between shear and normal stresses in terms of the friction angle and the inclination angle of the male joint. This approach shows good agreement in shear failure prediction for normal stresses up to about one-half of the compressive strength of concrete. Afterwards, it predicts much higher shear strength than the other approach. The fracture mechanics approach is considered to provide a more accurate shear failure because it is based on the geometry of a shear key, while the rock mechanics approach is based on the geometry of small asperities in rough, undulating surfaces.

Different experimental investigations have also been conducted, which predominately focused on trapezoidal shape (Buyukozturk et al., 1990; Koseki and Breen, 1983; Mattock and Hawkins, 1972). For instance, Kaneko et al. (1993b) and Zhou et al. (2005) performed shear tests to investigate the crack formation of prism-shape shear key, and extended the deformation-to-failure process from theory-based two-stage cracking into three stages: (1) formation of single curvilinear crack phase, that is, S-crack, which grows into the shear key; (2) crack at the bottom of the concrete shear key starts to grow due to the high concentration of tensile stress, and crack development into multiple cracks; and (3) the multiple diagonal cracks continue to grow forming multiple cracks (M-crack) underneath the shear key tenon. For the short interlocking joint, crushing failure is reported by Chatveera and Nimityongskul (1994). In their experiment, crack grew at the embossment corner of the shear key instead of the base of the shear key. When the compression dominants, the shear friction effect might cause the surface bearing cracks of a shear key.

The pre-compression force, roughness of concrete surface and concrete strength could all influence the performance of the key joint. Ibrahim et al. (2014) studied the shear strength of shear key under different pre-compression loads, which found increasing the pre-compression from 2% to 8% of concrete compressive strength, the shear strength of the key increased 300%. Moreover, increasing surface roughness significantly improves shear resistance at key joints (Tassios and Vintzēleou, 1987). Based on experimental data and empirical relationship, AASHTO (1999) provides a simplified analytical formula to predict the shear strength of concrete shear key, which considers both shear resistance from the concrete tenon and the concrete friction contribution. Through numerical simulation, Rombach and Specker (2004) provided similar analysis and design formula to determine the shear strength of shear key. The accuracy of these formulas in predicting the shear resistance of shear key made of different patterns and geometries other than trapezoidal prism is not examined.

Recent studies on precast segmental column found that the introduction of concrete shear key could also effectively improve the segment shear resistance. However, more severe concrete damage is resulted when the joint is subjected to combined flexural bending and shear forces where large trapezoidal prism-shape shear key was used due to stress concentration (Zhang et al., 2016a,b). By introducing smoothed dome shape shear key, stress concentration induced concrete damage could be reduced, but the shear resistance properties are not known (Hao et al., 2017; Zhang et al., 2018b). Therefore, a comprehensive study on the mechanical properties of concrete shear key is needed. In this study, direct shear tests are conducted on four different types of concrete shear keys to evaluate their performance. Flexural bending tests are also conducted to examine their bending resistance. The failure modes of these shear keys are examined, and the shear strengths are compared with available prediction models and formulas.

Shear key design and sample preparation

Four types of shear keys, that is, trapezoidal, semi-spherical, dome and wave, are assessed. Figure 1 shows the dimensions and the render of the concrete blocks. The trapezoidal-shape shear key inherits conventional design but with enlarged tenon size. To reduce local stress concentration, it is smoothed into a semi-spherical shape. The effective projection area for shear key is kept to similar scale. To relieve concrete damage during flexural bending, a dome shape shear key with entire section smoothed is introduced with dome radius 175 mm. A wave shape shear key with continuous smooth key profile is introduced to optimize the shear resistance and reduce bending induced damage. The amplitude of the wave is 20 mm which is the same as the tenon height of the trapezoidal and semi-spherical shear keys.

Figure 1.

Design of shear keys.

To reduce mold imperfection induced local damage, 3D printing technique is utilized for mold preparation. Keyed concrete segments are then cast and cured for 28 days. Averaged compressive stregnth after curing is 18.4 MPa and Young’s modulus is 20.7 GPa.

Shear performance

Test setup

Figure 2(a) illustrates the test setup. Three concrete segments are clamped together with four M24 threaded rods and two end plates. A pre-compression force of 20kN is applied. The two side segments are simply supported and the center segment is slowly pushed downwards. Each specimen comprises of two keyed joints. Instron 1196 system is utilized to apply the vertical shear force. The setup refers to British Standards EN1052-3 (2002), which differs from previous studies where only include single small shear key clamped together by two big chucks of blocks (Kaneko et al., 1993b). This is because relatively large concrete shear key is investigated in this study, where concrete mortise failure could be formed before the shear-off failure of concrete tenon.

Figure 2.

Illustration of test setups: (a) Shear test and (b) Flexural bending test.

Test results

Trapezoid shear key

Figure 3(a) shows the shear force versus relative displacement curves. It can be observed that the initial stiffness of the joint is relatively low because of the micro-gaps between the segments due to mold imperfection. As the vertical displacement increases, the shear force quickly rises to an initial peak of 30kN at 2.2 mm displacement. The load then drops slightly followed by gradual increase to a second peak at around 6 mm displacement. The shear resistance of the keyed segments then drops to zero as the concrete fails. The double-peak in the shear force-displacement curve differs from previous studies on trapezoidal shear key where only single peak is observed when the shear key is sheared off (Kaneko et al., 1993b). This difference is investigated and explained in Section 3.3.

Figure 3.

Shear force versus relative displacement: (a) trapezoidal, (b) semi-spherical, (c) dome, and (d) wave.

The tenon of the key suffers minor damages from bearing force in contact with the mortise (Figure 4(a)). Major concrete damage occurs on the mortise which fails under diagonal cracks that lead to the ultimate failure of the shear key. This failure mode differs substantially from conventional shear keys with small tenon, where the failure of shear key is primarily due to the shear-off of the concrete tenon. This implies that available design formula for small concrete shear key may not necessarily give accurate prediction of shear strength when employed for large concrete shear key because it fails in totally different failure mode. Moreover, an optimized design of tenon and mortise would be necessary when a relatively large shear key is to be used.

Figure 4.

Damage of shear keys. (a) trapezoidal shear key, (b) semi-spherical shear key, (c) dome shear key, and (d) wave-shape shear key.

Semi-spherical shear key

Being different from the trapezoidal shear key, the curves of semi-spherical key joints only have a single peak. As the relative displacement increases, the shear force increases gradually. An insignficant kink on the curves can be observed around 3kN for all three specimens tested when local damage occurs around the shear key. As the displacement further increases, the load continues to increase until a peak shear force of about 30kN is reached, after which it quickly drops, indicating the total failure of the joint.

As shown in Figure 4(b), a large portion of the semi-circle concrete tenon is damaged by the shear force. Similar to the trapezoidal shear key, the concrete mortise experiences severe damage. A larger area of surrounding concrete in the mortise is damaged than that of the trapezoidal shape shear key. This is because the depth of the semi-spherical tenon (30 mm) is higher than that of the trapezoidal tenon (20 mm). The influential area in the mortise is therefore larger, which leads to a larger portition of concrete mortise being damaged.

Dome shear key

To reduce stress concentration around shear key, a total smoothed dome shape shear key is designed. Figure 3© presents the load-displacement curves for the dome shape shear key. For Specimen 1 the shear force increases almost linearly with the applied relative displacement until about 18kN, then the slope of the curve becomes smaller due to local cracks in the mortise. The shear force continues to increase till about 27kN at a relative displacement of 9.5 mm when the mortise completely fails. Premature cracks occur earlier on Specimen 2 and 3 at about 5kN and 3kN. Nevertheless, the shear force continues to increase until a complete failure of the mortises at about 29kN and 21kN, respectively. Because of the larger variation, a fourth specimen is also tested. Similar to Specimen 1, the shear force increases nearly linearly till 25kN when crack initiates in the mortise. The curves between the four tested specimens vary more significantly than the two previous shear keys because the mortise to confine the large dome key comprises of pointy corners which could break prematurely. Nevertheless, because friction between the male and female segments would contribute to the shear resistance and the relatively large tenon, the peak shear forces of the four specimens all reach above 20kN.

From Figure 4(c) it can be found cracking occurs on the covering concrete of the mortise segment which leads to the shear failure of the joint. The large dome shear tenon is totally intact without any noticable damage. This failure mode differs from the trapezoidal and semi-spherical shear key because the large dome with gradual curvature over the contact surface elimiates stress concentration on the tenon. The shear component from the bearing force acting on the dome tenon is also relatively small due to the small inclination angle along the surface of the tenon.

Wave-shape shear key

Figure 3(d) shows the load-displacement curves of the wave shape shear key. The initial stiffness of the four specimens are very close until about 5kN that premature crack occurs on Specimen 4. As the applied vertical displacement further increases, concrete on mortise segments start to crack on Specimen 1 and 3 at about 10kN, which leads to the slight degradation of shear stiffness. But the shear forces continue to increase until the total failure of the concrete mortise. An average peak force of 36kN is found with an average relative shear displacement of 4.8 mm.

Because of the wave profile at the joint, the male segment comprises a large central tenon as well as four protruded corners, while the female segment has a large central mortise and four tipps along edges. When subjected to shear force, the central tenon and protruded corners in the male segment as well as the tipping edges in the female segment would provide shear resistance. As shown in Figure 4(d), the two bottom corners in the male segment are sheared off at early stage. As shear force increases, cracks are formed in the mortise of the female segment, which grow more significantly and eventually lead to the ultimate failure of the concrete mortise. Similar to the dome shape shear key, the large central tenon in the wave shear key does not suffer any shear damage.

Numerical simulation

To better understand the failure mechanism, numerical simulation is carried out to model the direct shear of the four types of shear keys.

Model set-up

Detailed three-dimensional numerical models are created to simulate the direct shear tests of the trapezoidal and wave shear key. Finite element (FE) analyses are performed using the commercial FE package Abaqus (2009). As shown in Figure 5, only a half of the experimental set-up is modeled considering the symmetry of the problem. The segments are discretized using 4-node linear tetrahedron elements, while the plates and roller supports are discretized using 8-node hexahedral elements. Fine mesh is defined for the shear key and the contact surfaces between the segments with a element size of 4 mm. A frictional contact is considered for the plate-roller support, plate-segment and segment-segment interactions based on the Coulomb friction model with the coefficient of friction equals to 0.5 (Farny et al., 2008; Precast/Prestressed Concrete Institute (PCI), 2017). The analysis consists of two steps: (1) applying horizontal pre-compression of 2000 kPa (maintained for the entire analysis); (2) applying vertical prescribed displacement. Accordingly, the right end is restrained in all directions except for the horizontal degree of freedom. For the direct shearing, restrains are induced in all directions for the roller support. Meanwhile, a vertical displacement is applied to the loading plate at the top edge that sits on the plane of symmetry, simulating the process of direct shearing.

Figure 5.

Numerical model and mesh discretization constitutive modeling.

The behaviors of concrete segments are modeled by the concrete damaged plasticity model. The uniaxial compressive and tensile stress-strain relationships for concrete are shown in Figure 6(a). Compression damage and tension damage are both considered, with the damage parameters varying with the inelastic strain and cracking strain (Figure 6(b)). A detailed description of the constitutive model can be found in (Genikomsou and Polak, 2015), who adopted the same constitutive model for the analysis of punching shear of concrete slabs. The steel plates and rollers are modeled as an elastic material. For concrete material, the average compressive strength of 18.3 MPa and Young’s modulus of 20.7 GPa from the tests are adopted, while the tensile strength is taken as $f_{t}^{'} = 0.33 \sqrt{f_{c}^{'}}$ . For steel, Young’s modulus equals to 200 GPa and Poisson’s ratio equals to 0.25.

Figure 6.

(a) Uniaxial stress-strain relationship for concrete; (b) Damage-strain relationship for concrete.

Numerical results

Figure 7 compares the numerical and experimental results in terms of the equivalent shear stress versus shear strains. The equivalent shear stress is calculated by using the applied shear force divided by nominal cross-section area of the segment (100 mm by 100 mm). The shear strain is calculated by using the vertical displacement over the initial horizontal distance from shear plane to the roller support. Because of the micro-gaps between the two concrete segments in the lab test, and also the imperfect boundary condition such as deformation of lateral pre-compression frame which cannot be modeled in the numerical simulation, relatively large initial displacement is always measured in the experiments. A correction factor of two is applied to scale the measured platen displacement before being used to derive the shear strain. Since in engineering practice, it is difficult to achieve perfectly closed matching shear keys in precast concrete construction, a gap between the concrete tenon and mortise almost always results from molding. The shear displacement/strain is therefore not a practical parameter to consider in design but the shear strength is more crucial in design practice. In this study, shear strain is mainly for validation of numerical model.

Figure 7.

Equivalent shear stress vs. strain curves: (a) trapezoidal shear key, (b) Semi-spherical, (c) dome shape, and (d) wave shape shear key.

Trapezoidal shear key

As shown in Figure 7(a), the computed shear stress versus strain curve could closely match that measured from laboratory test. Both the first and second peaks are predicted in the numerical model. Figure 8(a) shows the principal stress and strain contours of the trapezoidal shear key. As can be seen, stress concentration is developped at the bottom tip of the concrete tenon, which leads to the damage of the tenon forming the initial peak in loading time history. Stress also concentrates on the concrete mortise leading to a digonal crack initated and extended throughout the section which results in the ultimate failure of the covering mortise and the eventual failure of the shear key.

Figure 8.

Stress and strain contour at failure for shear key on side view of the middle depth: (a) trapezoidal, (b) wave, (c) semi-spherical, and (d) dome

Semi-spherical shear key

Figure 7(b) compares the shear stress-strain curves for the semi-spherical shear key. Close match can be found from the numerical simulation and the lab testing results. As discussed above, because of the inperfection in the lab specimen, the initial shear stiffness of the numerical model is slightly higher than that from the lab test. But micro-gap between two concrete segment closes under gradually increased shear force, the shear stiffness become very similar for the test and the numerical simulation. Simialr peak shear strength is estimated by the numerical model as well. Figure 8(b) illustrates the damages of the shear key. Diagonal stress is developed in the mortise and plastic strain is also developed from the base of the concrete tendon reflecting concrete damages intiated.

Dome-shape shear key

Figure 7(c) compares the stress-strain curves for the dome-shape shear key. The peak shear strengths from the numerical model and the laboratory test are very close. Again, the initial shear stiffness in the numerical model appears to be larger than that in the laboratory test. This is because of the closure of mico-gaps between the concrete segment in the lab test. Figure 8(c) shows the plastic strain contour of the dome-shape shear key. Concrete damage is primarily on the mortise which confines the tenon. But comparing with the trapezoidal and semi-shperical shear key, the stress influential zone in the mortise is relatively smaller.

Wave-shape shear key

Figure 7(d) shows the shear stress-strain cuvre for the wave-shape shear key. The numerical model could approximately predict the shear behavior of the wave shear key. Smaller peak shear strength of 1.7 MPa is predicted in the numerical model as compared to 1.9 MPa in the lab testing. Figure 8(d) shows the plastic strain contour of the wave shear key at the ultimate failure state. Because of the 3D shear key pattern, the contours at the both sides and the middle plane of the specimen are plotted. As can be obseved, the upper corner in the male key segment is subjected to large plastic strain indicating its shear resistance effect. As shown the primary shear resistance is provided by the mortise in the female key segment, which fails under the shear load. It is worth noticing that because of the wave curvature the effective confinement region in the female shear key is relatively small compared to that in the trapezoidal shear key.

Analysis and discussion

Influence of shear key shape and pattern

Table 1 summaries the shear properties of the shear keys in different shapes. For reference, a flat joint comprised of two plain segments whose shear force is purely resisted by friction is introduced. A friction coefficient of 0.5 and 20kN pre-compression is assumed which leads to 10kN friction by the reference flat joint. It is worth pointing out that the design handbook by Martin and Perry (PCI, 2017) and Concrete Masonry Handbook by Portland Cement Association (Farny et al., 2008) suggest concrete-to-concrete friction coefficient between 0.4 and 0.8. Without under- or over-estimating friction, a conservative coefficient of 0.5 is therefore used in this study. All the four types of shear key provide higher shear reistance as compared to the flat joint, of which at least 28% increment is provided by dome shear key. The conventional trapezoidal shear key provides 79% more shear resistance than flat joint with the inclined shear tenon. By smoothing the tenon into semi-spherical shape, the shear resistance reduces from 17.9kN to 14.6kN (–18%). This is because relatively less tenon projection area is resisting the shear force. By converting the entire cross-section into wave shape, a highest shear resistance capacity (18.2kN) is achieved among the four tested shear key patterns. Despite the clear profile height of the wave shear key is the same as the trapezoidal tenon, much larger projection area on the shear plane is resulted. Morever, the entire curved surface in contact will contribute to the friction resistance. The corresponding relative displacements at maximum shear forces are also summarized in Table 1. It is clear that for the trapezoial (for the 1^st peak) and semi-spherical shape shear keys, relatively small displacements are resulted at the peak shear strengths indicating high shear stiffnesses. About 6.9 mm relative displacement is required for the dome shape shear key when the maximum shear resistance is achieved. This is because the male segment is relatively easy to move along the curved surface of the female segment, which reflects the flexibility of the dome shape shear key.

Table 1.

Shear properties of shear keys.

Shear keyshape	Specimen no.	Maximum shear force	Equivalent stress	Displacement atmax. shear force
Shear keyshape	Specimen no.	kN	MPa	Mm
Trapezoidal	Trap.-S1	17.41	1.74	(2.23)^* 7.26
	Trap.-S2	16.40	1.64	(2.39)^* 7.92
	Trap.-S3	19.90	1.99	(2.18)^* 6.07
	Average	17.90	1.79	(2.27)^* 7.08
Semi-spherical	Semi-S1	15.09	1.51	2.64
	Semi-S2	13.63	1.36	2.51
	Semi-S3	15.00	1.50	2.39
	Average	14.57	1.46	2.51
Dome	Dome-S1	13.40	1.34	9.45
	Dome-S2	10.74	1.07	6.91
	Dome-S3	14.36	1.44	6.65
	Dome-S4	12.63	1.26	4.41
	Average	12.78	1.28	6.85
Wave	Wave-S1	18.38	1.84	4.91
	Wave-S2	19.07	1.91	3.88
	Wave-S3	18.30	1.83	5.11
	Wave-S4	17.02	1.70	5.14
	Average	18.19	1.82	4.76

Displacement at 1st peak load.

Comparison with design code

The measured shear strengths of the joints are compared with AASHTO (1999) and design formula by Rombach and Specker (Rombach and Specker, 2004). Equation (1) gives the formula for estimating shear strength by AASHTO

V_{j} = A_{k} \sqrt{0.006792 \times f_{c}^{'}} (12 + 2.466 σ_{n}) + 0.6 A_{sm} σ_{n}

(1)

where A_k is the projection area of shear key on the shear plane; fc’ is the compressive strength of concrete; $σ_{n}$ is the normal compressive stress on concrete; and A_sm is the area of concrete in contact excluding shear key.

Equation (2) gives the estimated shear strength of shear key joint by Rombach and Specker

V_{j} = 0.14 f_{c}^{'} A_{k} + 0.65 (A_{k} + A_{sm}) σ_{n}

(2)

Table 2 compares the measured ultimate shear strength of joints with different shear keys and those estimated by AASHTO and Rombach and Specker’s predictions. It can be found that AASHTO code overestimates the shear capacity of the trapezoidal shear key by nearly 40%, and Rombach and Specker’s method also over-predicts the strength by 19%. For the semi-spherical shear key, even large errors are predicted (43% and 28% respectively). This is mainly because of the different failure mode of concrete joint comprising large and conventional small shear keys. As described above, with large shear tenon failure of the joint is dominated by the cracks and failure of the concrete mortise. In comparison, direct shear-off failure is always assumed for conventional small shear keys, which are the fundamentals of the AASHTO and Robach and Specker’s method. In addition, as shown in equations (1) and (2) the friction coefficient of 0.6 and 0.65 are used in these methods. The concrete specimens tested in the present study are made of low strength (fc’ = 18.4 MPa) concrete, and the shear keys are casted with 3D printed plastic mold leading to relatively good match and contact, which could therefore lead to lower friction coefficient. The dome and wave shape shear keys employ global curvature pattern across the entire cross-section of the joint. The entire cross-section contributes to surface friction and tenon-mortise shear resistance. AASHTO and Rombach and Specker’s method requires a clearly defined key shear projection area with tenon high/width ratio approximately 1:2. They are therefore not compared herein. Nevertheless, through the above comparison it can be found that the existing methods could not properly predict the shear resistance of precast concrete joint comprising large shear tenon. A revised method considering both tenon and mortise size and shape is needed for analysis and design purpose.

Table 2.

Comparison of shear strength from experiment, simulation and design code.

Shear key	Maximum shear force	AASHTO	error	Rombach and specker	error	Numerical simulation	error
Shear key	kN	kN	error	kN	error	kN	error
Trapezoidal	17.90	29.11	39%	22.17	19%	15.79	–13%
Semi-spherical	14.57	25.44	43%	20.20	28%	-	-
Dome	12.78	-	-	-	-	-	-
Wave	18.19	-	-	-	-	16.82	–8%

Flexural bending

Flexural bending performance of the joints with different shear keys are investigated in this section. Shear keys are not designed to improve joint flexural bending performance. But joints of segmented elements are evitable to experience both transverse shear load and flexural bending load. Also as mentioned in Section 1, because of geometry changes at the joint more severe concrete damage was reported due to stress concentration (Zhang et al., 2016a). It is therefore necessary to properly understand the flexural bending behavior of concrete joint comprising of shear keys. In this study, three-point bending tests are conducted to evaluate the flexural bending performance of the keyed joints. The flexural resistant of keyed joints are analyzed and compared with that of analytical derivation of flat joint.

Test setup

Three-point bending test is setup with two concrete segments pre-compressed with a post-tensioning tendon in the center of the segments (Figure 3(b)). 20kN prestress is applied as pre-compression force using 9.3 mm diameter 7-wire prestress tendon. The segmented beam is then simply supported by two roller supports, and loaded at the center of the joint. The loading platen is displacement controlled. Each specimen is loaded with gradually increased displacement of about 1 mm to10 mm slowly at 0.1 mm/min loading rate. After the central displacement reaches the designated displacement, it is unloaded before applying the next increased load cycle. The loading/unloading method intends to examine the accumulative damage and residual displacement. Two specimens are tested for each type of shear keys. The applied load and central displacement are recorded. This setup is designed to introduce a controlled bending moment (through central displacement) at the shear key joint, which best replicates the practical loading condition for segmented elements jointed with shear key.

Test results

Trapezoid shear key

Figure 9(a) shows the load versus central displacement for the trapezoidal shear key. As the mid-span displacement gradually increases, the load at mid-span increases until it reaches a peak of about 25kN at 4.5 mm mid-span displacement. When the central deflection is small, the specimen behaves essentially elastic. Residual displacement begins to accumulate when the central displacement is 3 mm which indicates damage develops at the joint. Large residual displacement (3.5 mm) is measured after the peak strength is reached reflecting substantial damages in concrete at the key joint. The flexural strength reduces substantially from 25kN at mid-span to about 5.5kN. As the applied displacement further increases, the load-carrying capacity of the keyed joint further reduces to 1.8kN. Figure 10(a) depicts the damages of the blocks after the test. Concrete damage to the tenon and the compressive region of the male segment can be observed. Because the test extends to post-peak behavior, severe damage to the concrete mortise is observed.

Figure 9.

Central load versus mid-span displacement: (a) Trapezoidal, (b) Semi-spherical, (c) Dome, and (d) Wave.

Figure 10.

Damage of segments in flexural bending: (a) trapezoidal shear key, (b) semi-spherical shear key, (c) dome shear key, and (d) wave-shape shear key.

Semi-spherical shear key

Figure 9(b) shows the load versus central displacement curves for the semi-spherical keyed specimen. A residual deflection of 0.8 mm is measured when the central displacement reaches 3 mm. A slightly larger peak load of 26kN is measured on the segmented beam with semi-spherical shear key and the corresponding central displacement is also slightly larger (5.8 mm compared to 4.5 mm for the trapezoidal shear key). Minor damage to the concrete tenon can be observed, while almost half of the mortise segment is damaged (Figure 10(b)), which however is less severe than that for the segmented beam with trapezoidal shear key. As a result, higher residual resistance of the beam with the semi-spherical shear key is found than that with the trapezoidal shear key.

Dome shear key

Very different load-displacement curve can be found on the beam with the dome shape shear key (Figure 9(c)). A peak load of 28kN is achieved at 5.9 mm central displacement. Much smaller residual displacement is found for the beam with the dome shear key compared to those with the trapezoidal and semi-spherical shear keys. After the peak load, a residual displacement of about 1 mm is measured indicating much less damages at the key joint. This is because of the curved surface results in less stress concentration at the contact surface. Higher post-peak flexural resistance can also be observed. About 24.5kN applied load is measured at about 6.3 mm central deflection after the peak load (28kN), indicating over 86% residual strength. Figure 10(c) shows the damage of the dome shape segments. It is apparent that much less damages to the keyed segments especially on the curved mortise are induced compared to the other joints, and compressive failure occurs on the compressive side of the male segment.

Wave shear key

For the wave shape shear key, the load-displacement curve has similar feature as the dome shape shear key, that is, small residual displacement and high post-peak strength. A peak load of about 25.5kN is achieved with a mid-span displacement of 6.2 mm. And about 23kN is measured at 7 mm mid-span displacement which corresponds to about 90% of the peak strength, reflecting less severe damages at the keyed joint. About 1.1 mm residual displacement is measured after the specimen is loaded to its maximum flexural strength. As shown in Figure 10(d), the female segment suffers damages in the mortise and corners of the compressive side. The male segment also experiences compressive damage, and splits into halves under the combined effect of flexural bending and pre-compression from tendon.

Analysis and discussion

Influence of shear key shape and pattern

The peak load and corresponding central displacement are summarized and used to plot the backbone curves for beams with different shear keys. Figure 11 compares the backbone curves and Table 3 summarizes the maximum load achieved and the corresponding displacement. From Figure 11 it can be observed the initial relationships up to about 2 mm for all the specimens are similar because the responses at the keyed joints remain elastic without concrete damages. All the beams with different shear keys behave like a monolithic beam in this stage. Afterwards, damage in the segment joint starts to occur, which leads to the force-displacement curves of beams deviating from each other because different shear keys experience different levels and modes of damage. An average peak load of 24.7kN is found on the beam with trapezoidal shear key which is the lowest of the four-keyed joints. The corresponding mid-span displacement is about 4.7 mm which is also the lowest indicating the segmented beam with trapezoidal shear key has the lowest flexural strength and deformation capacity. It indicates that the conventional trapezoidal shear key would result in severe stress concentration and therefore leads to concrete damage at the key joint with low flexural resistance. The flexural performance is improved by smoothing the trapezoidal key into semi-spherical shape. The averaged peak load increases by 5.3% to 26kN and the corresponding mid-span displacement to 5.6 mm because less local damages occur with the round key tenon. An ultimate flexural resistance is achieved by introducing the dome shear key. An averaged load capacity of 28.5kN is resulted, and the corresponding displacement reaches 6.4 mm. It shows that the dome shear key could provide the highest flexural resistance with the largest deformation capability and smallest residual displacement indicating least damage among the four types of shear keys. When adjusting the key shape from dome to wave shape for better shear resistance, relatively more damages occur at the key joint of the wave shape tenon and mortise. As a result, a flexural resistance of 26.3kN is measured, however the corresponding central displacement is still relatively large (6.3 mm) reflecting its deformation capacity. Admittedly, the trapezoidal shape shear key is one of the most commonly-used patterns in practice because of easy manufacturing. Through the above comparisons, it can be found modification of the key shape could help to reduce stress concentration and improve flexural bending performance.

Figure 11.

Comparison of load-displacement curves for different shear keys in the flexural tests.

Table 3.

The bending property for different shear keys.

Shear key	Specimen no.	Max. load	Mid-span displacement^*	Max. moment	Joint rotation angle
Shear key	Specimen no.	kN	mm	kN mm	Joint rotation angle
Trapezoidal	Trap.-S1	24.9	4.5	1247	0.045
Trapezoidal	Trap.-S2	24.5	5.0	1225	0.050
Semi-spherical	Semi-S1	25.8	5.8	1290	0.058
Semi-spherical	Semi-S2	26.3	5.5	1314	0.054
Dome	Dome-S1	28.4	5.9	1418	0.059
Dome	Dome-S2	28.6	6.5	1430	0.065
Wave	Wave-S1	27.0	6.4	1349	0.064
Wave	Wave-S2	25.5	6.2	1276	0.062

corresponding to max. load.

Comparison with analytical derivation of flat joint

The flexural bending performance of the above tested beam with different keyed joints are compared with flat joint made of two plain segments. The moment-rotation relationship for the joint is derived and used in comparision. The resistance of the flat joint is calculated with analytical derviation. The bending moment (M) of the tested specimens is calculated based on the applied load (F) at mid-span and the span length (L), that is, $M = \frac{1}{4} FL$ . The joint rotation $θ_{c}$ is derived with the mid-span displacement (w) and span length of the tested beam specimen, that is, $θ_{c} = 2 ta n^{- 1} (\frac{w}{L / 2})$ . The analytical derivation for the flat joint employs plastic hinge theory as presented in (Bu and Ou, 2013; Hewes and Priestley, 2002). Detailed derivation is as follows:

The joint rotation angle $θ_{C}$ can be calculated by

θ_{C} = l_{p} φ_{p}

(3)

where $l_{p}$ is the plastic hinge length at joint. The plastic hinge length can be calculated as $l_{p}$ = 0.5 h (h is the sectional height and equals to 100 mm in this study) according to Priestley et al., 1996, and/or $l_{p} = 0.08 \frac{L}{2} + 0.022 d f_{y}$ (L is span length, d is the diameter of steel tendon and f_y is the steel yield stress) following Hewes and Priestley, 2002. $φ_{p}$ is the plastic curvature, which can be calculated with assumed total joint curvature $φ_{t}$ deducting elastic curvature $φ_{e} = \frac{2 ε_{c}}{h}$ , ( $ε_{c}$ is the initial concrete compressive strain due to pre-compression).

For a certain joint rotation, the elongation $Δ_{pt}$ and strain $ε_{pt}$ of prestress tendon laying in the center of the segment can be calculated by

Δ_{pt} = θ_{c} (\frac{h}{2} - c)

(4)

and

ε_{pt} = \frac{Δ_{pt}}{L_{pt}} + ε_{pi}

(5)

where c is the concrete compression depth, $L_{pt}$ is the length of the tendon and $ε_{pi}$ is the initial strain due to post-tensioning for segment precompression.

The force equilibrium in the joint cross-section can be checked by

C_{c} = T_{pt}

(6)

where $T_{pt}$ is the tensile force by prestress tendon, and $C_{c}$ is the concrete compressive force which can be calculated through integrition of stress on the segment cross-section $\int_{0}^{c} f_{c} (ε_{c}) bdy$ , in which b is the width of cross-section. The full concrete behavior including post-peak can therefore be considered with approporiate stress-strain curve.

The cross-sectional moment resistant capacity can be calculated by

M = M_{c} + M_{pt} = C_{c} \frac{c}{2} + T_{pt} \frac{h}{2}

(7)

Through iteration, the full moment-rotation curve can be derived with assumed joint rotation angle.

Figure 12(a) compares the moment-rotation curves for the tested beams with different shear keys and that predicted for plain joint with the above analytical derivation. A peak moment of 1390kN mm is predicted with the analytical solution for flat segmental joint. Very close peak moment is measured in the test on the dome shape shear key (1424kN mm). This is because the maximum moment resistant capacity is dominated by concrete crushing failure in the compression region because more severe damages occur in concrete joints with other types of shear keys, the peak moment resistant capacities are lower. This result is consistent with previous studies on segmental columns made of plain segments and trapezoidal shear keyed segments that more severe damage is found on column with trapezoidal shear key and therefore lower column flexural stiffness due to joint damage (Zhang et al., 2016a). It is also apparent that the rotation angles predicted using differnet plastic hinge lengths are very different. When the influence of reinforcement is not considered in calculating the plastic hinge length that is, $l_{p}$ = 0.5 h (Priestley et al., 1996), the predicted rotation angle is much smaller than those tested in the experiment. The joint rotation angle at maximum moment in the analytical solution is about 0.01, while those for the keyed joints in the experiment are between 0.04 and 0.065 which are 3-6 times larger than the prediction of simplified analytical model. When using hybrid method to calculate the plastic hinge length $l_{p} = 0.08 \frac{L}{2} + 0.022 d f_{y}$ (Hewes and Priestley, 2002), the predicted rotation angle is much closer to those from the laboratory testing results, despite the analytical solution still overpredict the flexural stiffness of the joint. To further evaluate the accuracy of the simplified analytical method, a moment-rotation curve for plain concrete segments is derived from a recent cyclic test on segmental column comprising of five plain segments (Zhang et al., 2016b). Figure 12(b) compares the moment-rotation curves from the cyclic test and that using the analytical models. It can be found that compared to the test, similar maximum moment and rotation angle are predicted by the analytical model with Hewes and Priestley hybrid plastic hinge length method, while much smaller rotation angle is esitamted with Priestley et al.’s conventional method. However, large flexural stiffnesses are also predicted by the anlytical derivation as compared to the laboratory test results. Similar observation was also reported by Bu and Ou (2013) when they modeled the cyclic responses of segemntal column using the simplified analytical method and fiber model. Higher initial flexural stiffness was found using the analytical method and fiber model as compared to the laboratory tested segmental column. It can be concluded that the simplified analytical model with hybrid plastic hinge length method could still reasonably predict the moment and joint rotation relationship for the plain segmental joint. But the flexural behavior of joint is strongly influence by shear key. As a result, the simplified analytical model under-predict joint rotation angle. In addtion, the large difference can also be attributed to the following possible reasons: firstly, the concrete molding method when casting the joints could not ensure perfect joint matching, which always introduces up to a few mm gaps between segments at joint. It combines with the testing error from the loading frame and the test setup, leading to large errors between analytical predictions and expeirmental observations. As can be observed from the moment-rotation curves in Figure 12a, the initial slope of the curves are always small indicating the gap closure. This is different from the assumption of perfect contact between two segments in the derivation. Secondly, the progressive damage of the concrete especially post-cracking behavior could not be fully considered in the analytical solution. Despite post-peak behavior of concrete material is employed in the analytical solution when deriving the sectional force equilibrium, the assumption of “plain remains plain” would introduce large error to the prediction.

Figure 12.

Comparison of moment vs rotation curves: (a) analytical versus keyed joints and (b) analytical versus plain segment (Zhang et al., 2016b).

Conclusions

This paper presents experimental and numerical studies to investigate the shear and flexural performance of concrete joint with different shear keys. The following findings are concluded:

With large shear tenon, the failure of joint under shear load differs from conventional small shear keyed joint. Joint failure is governed by the failure of concrete mortise rather than the shear-off of the tenon. Therefore, available design code and empirical formulas for prediction of shear resistance of concrete shear key is not appropriate.

Optimizing the trapezoidal shape key into smoothed semi-spherical shape tenon could relief local damages and therefore lead to higher shear resistance. Using a globally curved dome shape shear key, the shear resistance capacity would be sacrificed. But optimizing the dome into a global wave pattern could largely improve its shear performance because of larger projecting shear key area and global cross-sectional friction.

The keyed joints of different shear keys show very different flexural bending performance. The trapezoidal shape shear key gives the lowest flexural bending resistance among the four key geometries considered in this study because of excessive concrete damage due to local stress concentration, which can be improved by semi-spherical shear key. The dome shape shear key shows the good flexural bending performance with large bending moment capacity and good deformation capacity, which nevertheless has low shear resistance. The shear key with wave shape shows outstanding deformation capacity but has low bending resistance.

Through comparing with testing result, it is found that analytical derivation of moment-rotation angle relation gives reasonable prediction of keyed joint flexural bending strength, but would much under-estimate joint rotation angle. As a result, the analytical method over-estimate keyed joint flexural stiffness.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The first and second authors would like to acknowledge the financial support from Australian Research Council for financial support of this study.

ORCID iDs

Xihong Zhang

Francisco Hernandez

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