Experimental study of continuous T-beams with negative bending moment using UHPC instead of prestressed tendons under flexure

Abstract

In order to explore the flexural performance of the two-span simply supported to continuous T-beam using UHPC material instead of prestressed tendons in the negative bending moment zone and the effect of the UHPC material connection length on the bearing capacity of the test beam, the flexural tests of three beams with different UHPC connection lengths were carried out. The results show that by using UHPC material instead of prestressed tendons to make continuous beams in the negative bending moment region, the tensile properties and high elastic modulus characteristics of UHPC material can be better exerted. The three test beams were all resistant to bending failure, and the cracks were distributed in the two positive and negative bending moment sections. Increasing the connection length of the UHPC material will increase the distribution range of cracks and the number of cracks in the positive moment section and the cracking load in the negative moment section. The ductility was reduced. When the connection length was increased from 300 mm to 2200 mm and 2300 mm, respectively, the bearing capacity of the test beam was increased by 4% and 6%, respectively, and the mid-span ultimate displacement was reduced by 7% and 12%, respectively. The flexural performance of the test beam was improved.

Keywords

Continuous beam UHPC positive moment concrete experimental study

1. Introduction

Compared with simply supported beams, the internal force distribution of the continuous beam is more reasonable, the stiffness is greater, and the safety is higher. However, due to negative bending moments at the fulcrums of continuous beams, the upper edge of the concrete beams will crack prematurely, weakening the section stiffness of the continuous beam and increasing the probability of reinforcement corrosion. To solve the crack problem in negative moment region, many methods have been proposed and there are some related researches [1]. In addition, ultra high-performance concrete (UHPC) [2, 3, 4, 5], which is a kind of concrete with high elastic modulus, high tensile strength, and high compression resistance, can also be used to solve the problem.

Existing research shows that applying UHPC materials in bridge engineering can greatly improve the crack resistance of bridge structures, reduce self-weight, enhance durability, increase bending resistance, and be used in bridge reinforcement engineering [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19].

Based on the excellent properties of UHPC materials, this paper investigates a two-span simply supported to continuous T-beam structure that cancels the prestressing in the negative bending moment section and uses UHPC materials to connect. However, due to the absence of tensile stresses in the negative moment section of the T-beam flange concrete and the relatively high manufacturing cost of UHPC material, it is not necessary to use UHPC for all the flange plates of the test beam. A total of three connection lengths are proposed in this paper to investigate the effect of different UHPC connection lengths on the load-carrying capacity of the test beam, and a total of three 1:5 scaled-down model beams were carried out for the experimental study.

2. Experimental programs

2.1 Design of continuous T-beams

The size of the specimen was scaled by 1:5 according to the actual project. Three T-shaped test beams with different connection lengths were designed and manufactured, numbered L3, L22 and L23, respectively, with the UHPC length as the parameter. The dimensions of the test beams are shown in Fig. 1 and Table 1, where L1 and L2 are the UHPC connection length and the ordinary concrete section length, respectively.

Table 1
The value of L1 and L2

Number	L1 (mm)	L2 (mm)
L3	300	2730
L22	2200	1780
L23	2300	1730

Figure 1.

The dimensions of beam (All dimensions in mm).

The whole beam concrete was made of commercial concrete with a strength of C30, the steel bar was HRB400 steel bar, the left and right spans were arranged with $\varphi$ 12.7 prestressed steel strands, and the prestressed steel strands were provided with anchoring structures at both ends of the beam.

The test beam was first poured with ordinary concrete and cured. During the curing period, the tension of the prestressed reinforcement was completed. After the concrete strength reached the requirements, the two beams were connected by pouring ordinary concrete at the middle support reinforcement section. After 21 days of curing, UHPC was poured to complete the production of the continuous beam. UHPC was only used for flange plate in negative bending moment area.The material parameters of the test beams are shown in Table 2.

Table 2

Material parameters value

Material	Mechanical properties/MPa	Reference value
C30	$f_{c}$	32.8
	$f_{t}$	2.1
	$E_{c}$	30000
UHPC	$f_{c}$	142
	$f_{t}$	8.1
	$E_{c}$	46000
HRB400	$f_{yk}$	400
	$E_{s}$	200000
Prestressed steel strand	$f_{ptk}$	1860
	$E_{s}$	195000

2.2 Instrumentation and loading

Strain gauges were placed in the left span of the test beam at mid-span and at the quarter section and displacement meters were set up at the support of the test beam and at 1/4 span, 1/2 span and 3/4 span of each span to measure displacement deformation. Through the jack and with the distribution beam, the concentrated load was applied step by step in the middle position of the two spans of the continuous beam. During the loading process, the pressure sensor was used to measure the magnitude of the applied load. The loading system and layout of measuring points of the test beam are shown in Fig. 2.

Figure 2.

Loading system and layout of measuring points of beam (All dimensions in mm).

3. Analysis of test results

3.1 Distribution and development of test beam cracks

During the test, the distribution and development of cracks with the increase of load were measured and described on the test beam. The crack distribution is shown in Fig. 3.

Figure 3.

The crack distribution of beam: a) L3 beam; b) L22 beam; c) L23 beam.

The crack distribution and development of the three test beams were basically similar. Cracks occurred in two positive moment sections and negative moment sections of the three test beams. When the loads reached 110 kN, 100 kN and 120 kN, respectively, the first crack (No. 1 crack) appeared in the L3, L22 and L23 test beams, which were distributed at the bottom of the mid-span of the test beams. With the increase of the load, the first crack gradually developed upward, and the remaining cracks took the mid-span section as the symmetry axis and gradually developed upward from the bottom. When the loads reached 210 kN, 220 kN and 290 kN, respectively, cracks appeared in the negative moment section of the three test beams and gradually developed to the top of the test beams, forming longitudinal cracks. When the L3, L22 and L23 test beams were damaged, the No. 1 crack developed into the largest crack, and the crack width increased from 0.04 mm, 0.02 mm and 0.02 mm at the initial cracking to 1 mm, 0.5 mm and 0.4 mm. It can be concluded that with the increase of the UHPC connection length, the distribution range of crack becomes larger, the width of the No. 1 crack decreases, the number of cracks increases significantly, and the cracking load in the negative bending moment section is increased.

3.2 Load-displacement curve

The deflection of the beam under various loads can effectively reflect the stress stage of the beam. The load-displacement curves of the three test beams at the mid-span are shown in Fig. 4.

Figure 4.

The load-displacement curves of the beams at the mid-span.

The test beam experienced three stages from the beginning of loading to the final failure:

(1)

Elasticity stage (PA part). Before the load reached 110 kN, 100 kN and 120 kN, all materials of the test beam were in the elastic state, the concrete members had no cracks, the curve changed linearly, and the first inflection point (point A) appeared. It can be seen from the figure that the load-displacement curve of the L23 test beam in the elastic stage has a large difference from the curves of the other two beams. Under the same load, the displacement of the L23 test beam is smaller, while the curves of L3 and L22 test beams in the elastic stage basically coincide, indicating that when the UHPC connection length increases from 300 mm to 2200 mm, the bearing capacity of the test beam in the elastic stage is not significantly enhanced; when it increases from 2200 mm to 2300 mm, the bearing capacity of the test beam in the elastic stage is greatly improved.

Figure 5.

The comparison of load.

(2)

Plastic stage (AB part). This stage could be further divided into the elastic-plastic and crack development stages. Because after the concrete reached the cracking load, the concrete cracked and withdrew from the work, the reinforcement would carry the load. However, the reinforcement was still in an elastic state, and the stiffness of the test beam didn’t change significantly. There were many cracks in the concrete, but the width was small. As the load increased to 340 kN, 380 kN and 400 kN, respectively, the reinforcement yielded, the second inflection point (point B) would appear in the curve. Although the existence of a prestressed steel tendon still gave the test beam a certain bearing capacity, the stiffness of the test beam has been greatly reduced. The cracks developed rapidly at this time, and the width gradually widened.

At this stage, the bearing capacity of the test beam is L23 beam $>$ L22 beam $>$ L3 beam, the curve changes nonlinearly and the slope decreases.

(3)

Yield stage (BC part). At this stage, both the concrete and the steel bars were in a plastic state, a small load increment would cause a large deformation of the beam, the slope of the load-displacement curve was further reduced, and the third inflection point (point C) would appear in the curve.At this time, the test beams have been completely destroyed and are no longer able to bear the load The failure mode of the left span of each test beam is shown in Fig. 5.

The test results of the cracking load, yield load and ultimate load of each test beam, as well as the corresponding deformation and displacement values, are shown in Table 3.

Table 3

Test results of the test beam

Number	Cracking		Yield		Ultimate
	Load value (kN)	Displacement value (mm)	Load value (kN)	Displacement value (mm)	Load value (kN)	Displacement value (mm)
L3	110	2.01	460	12.54	545	27.26
L22	100	1.99	463	14.56	565	25.37
L23	120	1.46	547	18.26	575	24.07

Figure 6.

The failure mode of the left span of beam: a) L3 beam; b) L22 beam; c) L23 beam.

Compared with the L3 test beam, after reaching the cracking load, the mid-span displacement of L22 beam and L23 beam decreased by 1% and 27%, respectively, and when the ultimate load was reached, the mid-span displacement were minimized by 7% and 12%, respectively. It shows that at this stage, increasing the connection length of the UHPC material leads to an increase in the structural stiffness of the test beam, thereby reducing the mid-span displacement.

Compared to the L3 beam, there is a load diagram at the yield and limit state (Fig. 6).

It can be seen from the above figure that based on the excellent mechanical properties of UHPC material, with the increase of its connection length, the stiffness of the test beam is increased and the bearing capacity of the test beam is improved.

3.3 Ductility analysis

Ductility refers to the plastic deformation ability of structures, components and materials under load or other actions when the bearing capacity is not reduced or not significantly reduced before failure. Among them, the structure’s ductility depends on its inelastic deformation or energy dissipation capacity, the ductility of the structure is characterized by introducing a displacement ductility factor $\mu$ , defined as the ratio of the total displacement when the structure reaches its ultimate state to the yield displacement [20], as shown in Eq. (1):

$\displaystyle\mu=f_{u}/f_{y}$ (1)

where $f_{u}$ is the mid-span vertical displacement under the ultimate load;

$f_{y}$ is the mid-span vertical displacement under the yield load.

The calculation results of the ductility coefficient of the three test beams are shown in Table 4.

Table 4

The calculation result of the displacement ductility coefficient

Number	$f_{y}$ (mm)	$f_{u}$ (mm)	$\mu$
L3	12.54	27.26	2.17
L22	14.56	25.37	1.74
L23	18.26	24.07	1.32

Compared to the L3 beam, the displacement ductility coefficients of the L22 beam and L23 beam were reduced by 19.84% and 39.36%, respectively. It can be seen that increasing the length of the UHPC will cause a reduction in the ductility of the test beam. This is because the UHPC has higher stiffness and the increase in its length will lead to a consequent increase in the stiffness of the test beam, reducing its displacement in the ultimate state and resulting in poor ductility. A structure with poor ductility is prone to brittle damage after reaching the ultimate limit state, which is not conducive to normal use. Therefore, to ensure the ductility of the structure, the UHPC length should not be too long.

3.4 Strain analysis of test beam concrete

3.4.1 Strain analysis of top and bottom of mid-span section

Under the load, the strain of the top and bottom of the mid-span section is shown in Fig. 7.

Figure 7.

Strain at the top and bottom of the beam.

Figure 8.

The strain-load distribution of the mid-span section of the beam along the beam height: a) L3 beam; b) L22 beam; c) L23 beam.

The strain of the L3 test beam’s top shows a different trend from the strain of the L22 and L23 beam’s top. Under the same load, the top strain of the L3 beam is greater than the bottom strain, while the L22 beam and the L23 beam show that the top strain is smaller than the bottom strain. This is because as the length of UHPC increases, its length gradually enters the positive bending moment section, while the higher elastic modulus of UHPC increases the stiffness of the test beam, and under the same stress, the resulting strain becomes smaller.

Figure 9.

The strain at the top of the flange plate at the mid-span section of the test beam along the transverse direction: a) L3 beam; b) L22 beam; c) L23 beam.

After the L3 test beam enters the elastic-plastic stage, the tensile strain under the same load is significantly smaller than that of the other two beams. With the increase of the length of the UHPC material, the contact area between the UHPC and the web concrete will increase, and the bonding effect with concrete will also increase. The fact is that when external forces deform the test beam, the UHPC material, which has a higher resistance to deformation, will limit the deformation of the ordinary concreteï¼Œleaving the side of the concrete at the bottom of the mid-span of the test beam under tension. As a result, local stress is generated where the crack develops, and the stress is released after the crack of the concrete floor appears, resulting in a large tensile strain at the position of the floor.

The compressive strain at the top of the mid-span section of the test beam decreases with the increase of UHPC connection length, due to the increased stiffness of the test beam caused by the presence of UHPC, the longer the UHPC material, the greater the stiffness. Under the action of the load, the test beam produces less strain.

3.4.2 Strain analysis of the mid-span section along with the beam height

The strain-load distribution of the mid-span section of the test beam along the beam height is shown in Fig. 8. It can be seen that the strain is basically linearly distributed. With the load increase, except for some deviation of individual measuring points, the overall distribution is still linear, which is in line with the assumption of plane section.

In the elastic stage, the stress state at 250 mm from the L3 beam bottom, 275 mm from the L22 beam bottom, and 325 mm from the L23 beam bottom is basically 0, which is the position of the neutral axis. When the test beam is loaded into the yielding state, the concrete is pulled to pieces and exits the work as the tensile stress at the bottom of the beam exceeds the ultimate tensile stress and the assumption of a flat section is no longer met.

Analysis of the position of the neutral axis in the elastic stage shows that with the increase of the length of the UHPC, the part of the neutral axis gradually moves closer to the flange plate. The reason for this phenomenon is that the elastic modulus of the UHPC material is relatively large. As the length increases and enters the positive bending moment section, the overall stiffness of the flange plate of the test beam will be greatly improved, resulting in the rise of the position of the neutral axis of the test beam.

3.4.3 Lateral strain analysis of flange plate mid-span section

s The distribution of strain along the transverse direction at the top of the flange of the mid-span section of the beam under each level of loading is shown in Fig. 9.

It can be seen from the above figure that before the load reaches the cracking load, the top strain of the flange plate is uniformly distributed in the lateral direction. After exceeding the cracking load, the top compressive strain gradually produces shear lag along the transverse direction, and there is a difference in the strains on both sides of the flange plate. The maximum difference of compressive strain between the two sides of the flange plate before the failure of the test beam is 153 $\mu\varepsilon$ . The above shows that when the test beam is in the elastic stage, the shear lag effect at the top of the flange plate is not obvious, and there is obvious shear lag effect near the failure stage.

4. Conclusion

After analyzing the test results, the conclusions are as follows:

(1)

By using UHPC material instead of prestressing to make continuous beams in the negative moment region, the tensile properties and high elastic modulus of UHPC materials can be better utilized.

(2)

Cracks occurred in the two positive moment sections and the negative moment area, and the beams exhibited flexural damage. With the increase of UHPC connection length, the distribution range of cracks in the positive moment section became larger, the width of the widest crack decreased, the number of cracks increased obviously, and the cracking load in the negative moment section increased.

(3)

When the connection length was extended from 300 mm to 2200 mm and 2300 mm, the bearing capacity of the test beam increased by 4% and 6%, the ultimate mid-span displacement reduced by 7% and 12%, and the ductility decreased by 19.84% and 39.36% respectively.

(4)

With the increase of the UHPC connection length, the strain at the top of the flange plate of the mid-span section of the test beam will decrease, and the strain at the bottom of the web plate will increase. The flexural performance of the test beam will be improved.

Footnotes

Funding

This work was supported by the Ningbo Transportation Science and Technology Project (Grant NO.202115).

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Experimental study of continuous T-beams with negative bending moment using UHPC instead of prestressed tendons under flexure

Abstract

Keywords

1. Introduction

2. Experimental programs

2.1 Design of continuous T-beams

Table 1 The value of L1 and L2

3.1 Distribution and development of test beam cracks

3.4.1 Strain analysis of top and bottom of mid-span section

3.4.3 Lateral strain analysis of flange plate mid-span section

4. Conclusion

Footnotes

Funding

References

Table 1
The value of L1 and L2