1 Introduction

Over the past few years, portal frame has been a steel structure building with extensive applications, which has been increasingly applied in the design of industrial plants. Some plants should be reconstructed and expanded due to the expansion of production and for other reasons, thus reducing plant stability and increasing deformation; as a result, these plants cannot meet the requirements of bearing capacity and the need for reinforcement [1].

Among numerous steel structure reinforcement methods [2], external prestressing reinforcement technology has been progressively applied to steel beam reinforcement. Based on the limited construction space and the unchanged reinforcement section, the application of prestressing makes the component generate the internal force opposite to the load effect to achieve reinforcement. For instance, Chen Y et al. [3] adopted external prestressing technology in the reinforcement of steel structure in a hospital hall, thus solving the problem economically and conveniently without having an effect on the function of the structure. Liao MJ et al. [4] also employed this technology to reinforce the grandstand of Wuhan Xinhua Road stadium. As a result, the problems of insufficient bearing capacity and excessive deflection of the original structure could be solved, future checking and maintenance were facilitated, and the later maintenance cost was reduced. Kambal et al. [5] measured the strength of two types of steel box beams (including prestressed beam and control beam). They also verified that prestressing technology can enhance the bending performance of steel beams. Furthermore, some scholars [6,7,8,9,10,11] investigated the portal frame technology strengthened using external prestressing technology. On that basis, the mid span deflection of steel beam has been improved, the bearing capacity of steel beam has increased, and the remarkable reinforcement effect has been achieved.

However, the difficulty in using the in external prestressing method to reinforce the steel beam lies in the loading of prestress on the steel strand. To solve this difficulty, a wide variety of ways to load prestress on the steel strand have been proposed by scholars. For instance, Shi XM et al. [12]. welded the loading strut on the lower flange of the steel beam (the corresponding position of the steel beam was processed with welded stiffening ribs); the steel strand was prestressed by turning the intermediate steel tube, and then the loading was achieved. Li XM et al. [13] set prestressing cable joints at the contact position of the steel strand and the steel beam and prestressed the steel strand by turning the intermediate sleeve. On that basis, the loading purpose was achieved.

In this study, a novel external prestressed strut loading device is designed. For this device, the principle of two-force rod is used to increase the strut by rotating the intermediate screw, and then the steel strais prestressed. The principle is found to be simple, easy to operate, without direct tension of steel strand, through which the purpose of loading could be achieved. Through a comparison of the internal force changes of steel beams before and after the reinforcement, the new loading device is verified to be safe and effective and could be applied to the actual reinforcement of cable-supported portal frame to achieve the prestressed loading.

The rest of this study is organized below. In Sect. 2, the external prestressing reinforcement technology is considered. In Sect. 3, the working principle of the novel loading strut is presented. In Sect. 4, the simulations of the external prestressing reinforcement of the portal frame using ANSYS are presented. In Sect. 5, the reinforcement effects are analyzed. In Sect. 6, the specific static tests of the in external prestressing reinforcement are introduced. In Sect. 7, a discussion is shown. In Sect. 8, the conclusions of this study are drawn.

2 Introduction of external prestressing reinforcement technology

External prestressing reinforcement technology forms a cable-supported portal frame with prestressing strands and beams [14], while reducing the moment and increasing the stiffness of the beam by prestressing the strands, which can increase its bearing capacity. The external prestressing reinforcement system of portal frames primarily comprise three parts, including an end anchorage, a strut and a steel strand, as presented in Fig. 1. This system is capable of achieving the purpose of reinforcement by prestressing the steel strand to generate the internal force opposite to the load effect under a limited construction space. The effective application of prestress on steel strands is considered the key of this technology. In this study, a novel type of loading strut was designed by combining the strut with the prestressing loading device. This novel type of strut could be elongated by turning the intermediate screw to apply the established prestressing force on the strand for loading.

Fig. 1
figure 1

Schematic diagram of external prestressing reinforcement

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3 Working principle of new loading strut

3.1 Strut structure

The strut, a prestressing loading device on steel strand, primarily comprised anchoring assembly, an upper round steel part, a loading screw, as well as a lower round steel part. To be specific, the anchoring component could be assembled with the lower flange of the steel beam, the upper and lower round steel parts are connected with the loading screw through screw threads, and the steel strand passed through the bottom reserved hole at the bottom of the lower round rod to achieve the articulated connection with the steel strand. Among them, the loading screw is a telescopic rotating component, which is rotated and extended by a spanner for loading and unloading. Figure 2 illustrates the strut in detail.

Fig. 2
figure 2

a Strut display: 1. Bolt, 2. Sleeve, 3. Pressing block, 4. Fixing components, 5. Upper round steel, 6. Retaining nut, 7. Loading block, 8. Loading screw, 9. Lower round steel, 10. Steel strand connection hole, 11. Steel beam; b 3D model of strut before loading; c 3D model of strut after loading

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3.2 Working principle

The fixing components Fig. 2 (4) are fixed to the lower flange of the steel beam (11) by pressing block (3) and sleeve (2) by bolt (1) to achieve the hinged connection between the steel beam and the upper round steel (5) of strut.

The steel strand is first fixed at the end anchorage joint at one end of the steel beam. Subsequently, it is fixed through the connection holes (10) at the bottom of each strut in turn. Next, it is fixed at the end anchorage joint at the other end of the steel beam.

Both the upper and lower round steel (5, 9) are equipped with internal sleeve wire, while the loading screw (8) was equipped with a reverse wire buckle at both ends. During the loading process, the length of the loading screw (8) could be regulated by rotating the loading block (7) in the middle to increase the length of the strut. As shown in Fig. 2 (b) and (c), the length of the loading screw (8) is L before loading and L1 after loading, the strut extends L1-L. The length of the strut is increased, so that the steel strand connected at the bottom of the strut is tensed, thus achieving the purpose of loading prestress on the strand.

When the prestress of the strand reached the established value, the retaining nuts (6) would be rotated at the upper and lower ends of the loading screw (8) for pretightening at the upper and lower round steel (5, 9) positions to prevent the loss of prestress due to the reverse rotation of the screw in use.

This method avoids the use of special cable prestressed loading device, and achieves the loading purpose by using the elongation of struts.

4 FEM simulation

4.1 Model parameter

The external prestressing reinforcement of a portal frame is simulated using ANSYS finite element analysis software. The portal frame selected in this study is a double-span single-slope structure with two 1.0 m-length braces at 1/3 and 2/3 of the span, respectively. The span of the portal frame is 28.4 m, and the heights of the side column and the middle column are 6 m and 7.4 m, respectively. The steel beam and the column are rigidly connected, as well as the column and the ground, and HN350 × 175 × 7 × 11 type I-beam is selected. The portal frame model is illustrated in Fig. 3.

Fig. 3
figure 3

Portal frame model: 1. End anchorage, 2. Loading strut

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4.1.1 Selection of end anchorage

The end anchorages in the external prestressing reinforcement are applied with 1-shaped anchoring joint [15], which is mainly composed of friction device, 1-shaped component and anchor fixed component. The joint is similar to “1”, so it is named “1-shaped” anchoring joint. The paper will use this anchoring device to connect steel strand and steel beam, which could evenly and effectively transfer the prestress on the steel strand to the upper and lower flange of the steel beam through friction and the pretightening process. Figure 4 illustrates the basic structure of anchoring joints, and Fig. 5 illustrates realistic picture of the anchoring joints. The upper and lower flange contact parts are sandblasted (shot) to increase the roughness of the contact surface.

Fig.4
figure 4

1-shaped anchoring joint: 1 upper triangle friction component, 2 lower triangle friction component, 3 1 type component; 4 anchoring component, 5 upper fixed rod, 6 lower fixed rod, 7, bolt rod, 8 adjusting rod, 9 steel beam

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Fig. 5
figure 5

Realistic picture of the1-shaped anchoring joint

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4.1.2 Strut structure

Impacted by the environment and force characteristics of the joint, Q345 steel is applied for the novel type of strut and end joint, and double-sided welding is used to weld all components. The bolts selected in the components are friction type high-strength bolts [16]. Figure 6 presents the dimensions of the new loading strut.

Fig. 6
figure 6

Detail of strut 1 and strut 2

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4.2 Selection of load conditions

Load conditions: 1.2D (dead load) + 1.4L (live load).

Standard value of dead load: 0.20kN/m2; Standard value of live load: 0.30kN/m2; Prestress value in steel strand: 40kN; The ground roughness is class B.

4.3 Finite element modeling of the portal frame and end joints

In FEM model, all steels were Q345, and bolts were 10.9 friction high-strength bolts. See Table 1 for specific material properties.

Table 1 The material properties
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To simulate the real situation more truly and effectively, the solid model is established during the calculation. Moreover, to reduce the amount of calculation, a half of the model is built based on the symmetry relationship. The contact between the anchor joint and the inclined I-beam is the standard contact type, with a friction coefficient of 0.3 [17]. Figure 7 presents the three-dimensional (3D) finite element model.

Fig. 7
figure 7

Finite element model

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4.4 Finite element modeling of strut

A section of the rigid frame inclined I-beam is employed to build a 3D model. Subsequently, the novel strut structure is modeled and then meshed to build a finite element model as presented in Fig. 8, and the mesh size in the joint positions of the strut is reduced.

Fig. 8
figure 8

Strut model

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4.5 Finite element simulation instructions

Due to the calculation amount and to ensure the calculation accuracy, the symmetrical part of the model is taken for calculation and analysis in this simulation. The corresponding parts are put in a PART; the vertical I-beam and the inclined I-beam are bound to each other; the joints of the connection between the strut and the I-beam are bound to each other, thus allowing them to be completely against the I-beam; the connection between the end of the prestressing cable and the solid is in the form of General in Joint.

Solid high-order element SOLID186 / 187 are applied in the simulation. The key point of simulation would lie in the connection between models, which is impacted by the considerable number of model parts and complex mechanism. Figure 9 illustrates the connection between strut and steel beam.

Fig. 9
figure 9

Contact connection

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4.6 Simulation results and analysis of strut

Figure 10, 11, 12 present the simulation results with the calculation of the strut tilt of 2° as an example.

Fig. 10
figure 10

Displacement nephogram

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Fig. 11
figure 11

Equivalent stress nephogram of strut joint corresponding to bottom flange of I-beam

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Fig. 12
figure 12

Equivalent stress nephogram of each part of strut joint

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The analysis from Fig. 10, 11, 12 is presented below:

  • (1) According to Fig. 10, the lower end of the strut has the most significant displacement, followed by the upper end of the strut, and the steel beam has the smallest displacement, consistent with the mechanical calculation law.

  • (2) Fig. 11 shows that the stress is primarily concentrated at the contact position between the strut and the lower flange of the steel beam. At this position, the lower flange of the steel beam tended to concave upward, thus verifying the effectiveness of simulation constraints and contact simplification. In the strut joint area, the stress on the left is significantly higher than that on the right due to the steel beam tilting from left to right, consistent with the reality.

  • (3) In Fig. 12, the bolt of part 2 has the largest equivalent stress, largely because it played a limiting role through shearing, so the use of a high-strength bolt would be recommended. The strut is mainly bent, and the maximum stress is 145.14 MPa, which is within a reasonable range.

5 Analysis of reinforcement effect

In Sect. 4, the simulation of the connection joint between the strut and the steel beam and the strut during the reinforcement of the portal frame has been analyzed.

Next, the five positions of the end column top, the left 1-shaped anchor joint on the steel beam, the middle span, the right 1-shaped anchor joint on the steel beam and the middle column top of the portal frame (Fig. 7) are mainly selected. And they are named as “A joint, B joint, C joint, D joint and E joint” respectively. Then the bending moment, shear force and axial force and deflection values before and after reinforcement are simulated to reflect the overall effect of reinforcement. (Before the reinforcement, the portal frame not installed with novel struts and steel strands and other components.)

5.1 Comparison of the bending moment

Figure 13 shows the comparison of bending moment values of portal frame before and after reinforcement.

Fig. 13
figure 13

The comparison of bending moment

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By comparing the bending moment values of portal frame sections before and after reinforcement, through calculation, the absolute values of bending moment at the five joints of A-E are reduced by 37.29, 38.64, 46.79, 24.86 and 25.36% respectively. It shows that after prestressed reinforcement, the bending moment of each key section of steel beam and column of portal frame is significantly reduced compared with the structure before reinforcement.

5.2 Comparison of the shear force

Figure 14 shows the comparison of shear force values of portal frame before and after reinforcement.

Fig. 14
figure 14

The comparison of shear force

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It can be seen from Fig. 14 that the shear force on the portal frame is reduced after reinforcement. Among them, the shear force at the end column top (A joint) decreases because the prestress reduces the bending moment at the end column top, and the prestress offsets the horizontal shear force of some steel beams to the end column.

5.3 Comparison of the axial force

The comparison of axial force values before and after portal frame reinforcement is shown in Fig. 15.

Fig. 15
figure 15

The comparison of axial force

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According to Fig. 15, the axial force at the end column top (A joint and E joint) changes little after reinforcement, the absolute value of the axial force at the anchor joint (B joint and D joint) of the steel beam decreases, and the absolute value of the axial force at the middle span (C joint) increases. Mainly because the steel strand, strut and steel beam form a chord supported portal frame, the axial force of part of the middle beam section is transmitted to the steel strand through the anchor joint, which reduces the axial force of the beam section outside the anchor joint. At the same time, the prestress of the steel strand mainly acts on the middle beam section and increases the axial force of the middle beam section.

5.4 Comparison of the deflection

The comparison of deflection values before and after portal frame reinforcement is shown in Fig. 16.

Fig. 16
figure 16

The comparison of deflection

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By comparing the deflection of portal frame before and after reinforcement, it is found that the middle span (C joint) deflection of the structure before reinforcement is −22.85 mm (downward direction), and the middle span deflection after reinforcement is −12.63 mm (downward direction), which is relatively reduced by 44.73%. The deflection of other parts of the rigid frame has also been reduced.

Through the above comparison of the internal force and deflection of before and after reinforcement of portal frame section, it can be seen that the internal force and deflection of each key section of the portal frame are significantly reduced by using this reinforcement method, so as to improve the bearing capacity of the portal frame.

6 Static test

6.1 Test design

6.1.1 Instrument selection

The set of the device comprised two end anchoring joints, two struts, a CZ-6A magnetic table seat, a dialgage, two stress anchors (Model: 2D001V; Range: 0-220kN), a steel strand (diameter 15.2 mm), as well as DHDAS(Dong-Hua Test Real Time Data Measurement and Analysis Software System).

6.1.2 Test equipment installation

In the external prestressing reinforcement test, double struts are used to reinforce steel beams. The 1-shaped end anchoring joint is installed at both ends of the steel beam, the struts were installed at 1/3 and 2/3 of the steel beam, the heavy hammer is installed at the mid span of the steel beam, and the dialgage and magnetic table seat steel plate are installed at the lower side in turn. Figure 17 presents the installation positions of components.

Fig. 17
figure 17

Installation diagram: 1. Side column, 2. Middle column, 3. Strut, 4. I-shaped end anchor joint, 5. Steel strand, 6. Heavy hammer, 7. Dialgage, 8. Magnetic table seat, 9. Steel beam

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6.1.3 Sticking of strain gauge

On the eight key positions of the single span of the portal frame, the strain is measured using the DHDAS (temperature compensation is set to reduce the error), as illustrated in Fig. 18.

Fig. 18
figure 18

Diagram of strain gauge sticking position: 1. 1 joint north (upper flange), 2. 1 joint south (lower flange), 3. Side column (south flange), 4. Middle span (lower flange), 5. 4 joint north (upper flange), 6. 4 joint south (lower flange), 7. Middle column (north flange), 8. Middle column (south flange)

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6.1.4 Selection of anchorage mode

The steel strand passed through the stress ring after passing through the anchor device and then through the anchor joint.

During the construction, the effective contact between the device and the flange of the steel beam should be strictly controlled to ensure the friction of the contact surface. The positioning of steel strand should be controlled since excessive deviation would easily lead to an excessive bending moment of the vertical strut, thus adversely affecting the lower flange of steel beam.

6.2 Installation of end anchorage joints

First, the upper fixing device is placed symmetrically on the lower side of the upper flange, and the lower fixing device is placed on the upper side of the lower flange of the I-beam, as presented in Fig. 19a. Second, the 1-shaped components and the steel strand anchorage devices are installed. Lastly, the steel strand passed through the anchor device, and it is fixed by the anchor joint. The installation effect is presented in Fig. 19.

Fig. 19
figure 19

Installation graph

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During the installation, the fixed components are first placed at 1/3 and 2/3 positions of the lower flange of the I-beam, and the pressing block is symmetrically placed on the upper side of the corresponding lower flange (both sides of the web) and then fixed by screw and pressing block. Subsequently, the upper round steel is installed, and the screw is installed on the upper round steel. Lastly, the lower round steel was installed on the screw (the connection hole is located on the lower round steel). After the strut is installed, the steel strand passed through the connection hole, as presented in Fig. 20.

Fig. 20
figure 20

Strut 1and 2 real graph

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During the loading process, the loading blocks of strut 1 and strut 2 are rotated, while the loading screw is extended for loading. Static loading was used as the test loading method.

6.3 Prestress loading

This test adopts the method of rotating telescopic device in the middle of strut to load. After the installation of the device, the stress ring reading was cleared, and the DHDAS was balanced and cleared. The loader rotated the middle loading strut at the same time, after the reading is stable, load it every 5 min with a loading step of 4kN and gradually load it to 40kN. Figure 21 shows the loading process.

Fig.21
figure 21

The loading process

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The stress ring is installed on the outside of the anchoring joint at both ends. The prestress of the steel strand is measured through the stress ring and the monitor, as shown in Fig. 22. After passing through the end anchoring joint, the steel strand first passes through the stress ring, and then is anchored through the anchor. Since the stress ring is instantaneous reading, as shown in Fig. 22b, the prestress value of steel strand is recorded every 4kN during loading.

Fig. 22
figure 22

Prestress measuring device

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6.4 Collection of test data

Strain measurement was performed on the 8 key positions in Fig. 18 respectively, and the measured positions were counted every 5 min. The micro-strain records of each position were shown in Table 2 below, and the simulated value of 40 kN of prestress was recorded.

Table 2 Comparison of strain results (με)
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It is found that the initial value is small. With the gradual increase of prestress, the strains of 1 joint north (upper flange), middle span (lower flange), 4 joint north (upper flange) and middle column (south flange) are all negative and gradually decreasing, indicating that the tensile stress at the position is gradually decreasing. With the gradual increase of prestress, the strains of 1 joint south (lower flange), side column (south flange), 4 joint south (lower flange) and middle column (north flange) are all positive and gradually increase, indicating that the compressive stress of the position is gradually decreasing (some position data are abnormal, so it is discarded).

Comparison was made between the test values and simulation values of 7 measuring positions with high strain of portal frame of 1 joint north (upper flange), 1 joint south (lower flange), side column (south flange), middle span (lower flange), 4 joint north (upper flange), 4 joint south (lower flange), and middle column (south flange). The comparison results are shown in Fig. 23 below. In addition, compared with the upper flange of the steel beam, the deformation of the lower flange is more obvious, because the force of the steel strand on the lower flange of the steel beam is larger. The comparison shows that the test value is close to the simulated value, which further indicates that the reinforcement effect is effective.

Fig. 23
figure 23

Micro strain comparison

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According to Table 3, as the intermediate strut is rotated, the loss of prestress and the length of the strut tended to increase, which revealed that the prestress could be used to load the steel strand. After 3 min of stable loading, there is a certain loss of prestress on the strand, and the average loss is nearly 4.4%.

Table 3 Prestress loss comparison
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The strains in the south of the side column, the north of the middle column and the south of the middle column (add negative sign, only see at the absolute value) tended to increase with the increase in the steel strand stress, as presented in Fig. 24. The above results revealed that the compressive stress on the south of the top of the side column and the north of the top of the middle column tended to decrease after the use of external prestressing reinforced steel beam; the tensile stress on the south of the top of the middle column tended to decrease, and the reinforcement is found with the intended effect.

Fig. 24
figure 24

Micro strain comparison

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With the increase in the steel strand stress, the compressive stress of 4 joint south (lower) and the tensile stress of 4 joint north (upper) (add negative sign, only see at the absolute value) tended to decrease, as presented in Fig. 25. The micro strain in 4 joint south (lower) is slightly larger than that in 4 joint north (upper), probably because the end anchorage joint wis located at the lower flange of the steel beam and the steel strand stress acted on the steel beam through it.

Fig. 25
figure 25

Micro strain comparison

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A comparison of the strain of the lower flange on 1 joint north and 4 joint south is drawn, as illustrated in Fig. 26. With the increase in the stress of the steel strand, the micro strain tended to increase, and their trends are the same. It is therefore revealed that the compressive stress of the two positions tended to decrease, and the external prestressing reinforcement is found to have a corresponding effect.

Fig. 26
figure 26

Micro strain comparison

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7 Discussion

In practical engineering, there have been two main methods of applying prestress, which are applying prestress by directly tensioning the steel strand and applying prestress by rotating the strut to make it elongate, so the steel strand can be tensioned. For instance, Li XM et al. [13] set prestressing cable joints on the steel strand and prestressed the steel strand by rotating the intermediate sleeve on the cable joints. However, the arrangement of prestressing steel cables is more complicated. The cables directly tensioned to apply prestress will bring inconvenience to the construction, and the overhead operation is difficult to avoid. Accordingly, the method of applying prestress by changing the length of the strut has been employed in increasing projects. When the strut is elongated, the steel strand will be tightened to apply prestress to the structure; when the strut is shortened, the steel strand will be relaxed to unload the prestress to the structure. For instance, Shi XM et al. [12] welded loading strut on the lower flange of a steel beam; by turning the middle steel tube, the strut prestressed the steel strands, and then achieved the loading purpose. In this study, a novel type of in prestressing strut loading device is designed to avoid welding the strut with the steel beam and to connect it with the steel beam using the fixing device. Furthermore, the device followed the principle of two-force rod to make the strut grow by turning the intermediate screw, and then prestressed the steel strand. This novel type of strut is confirmed as an easy to install and simple to operate prestressing loading device.

8 Conclusions

In this study, a novel type of strut device is proposed in the structural system of cable-supported portal rigid frame, and the feasibility of this novel type of strut was verified through the analysis of simulation and test results. In the practical engineering, the new loading strut could effectively serve as a prestress loading device for cable-supported portal frame by regulating the length of the strut for prestress loading, thus avoiding the inconvenience caused by direct tensioning of steel strands. Moreover, the end of the strut is connected with the steel beam primarily through mutual contact and frictional extrusion, and the strut is assumed to play a role of loading the prestress on the steel strand. The end of the loading strut is connected with the steel beam through the pressure block for assembly, thus avoiding the damage to the original structure. The loading strut is applied to the external prestressing reinforcement of portal frame, thus increasing the stiffness of the steel beam and reducing the deflection in the span, which led to a significant reinforcement effect.

In this study, the design, simulation and experimental research of a novel type of strut based on external prestressing steel beam strengthening technology were conducted. However, due to the limitations of technology and time, only static tests are performed in this study, and seismic tests should be further improved.