Transient response and performance of prestressed concrete deep T-beams with large web openings under impact loading

1 Introduction

In structural applications, reinforced concrete (RC) deep members are commonly constructed with a small span/depth ratio not exceeding four, in which case the loads are transferred to the supports through the strut-and-tie model in a direct direction and mainly fail due to shear rather than flexure. These beams usually distribute loads to other structural elements as in the case of pile caps, shear wall to counter act earthquake and wind loads, transfer girders in buildings, and foundation walls [1].

In RC members, openings act as a way to provide passage through members for utility pipes or ducts rather than extending these services below members, which create a blank space, increase the overall building height, and require additional aesthetic ceiling. Creating web openings in a beam for the passage of these services changes the behavior of these members to be more complex one and leads to the reduction in their strength. The presence of openings in deep beams leads to many problems in the behavior of the beams such as reduction in its strength and excessive cracking and deflection [2,3]. The first cracking load and failure mode are dependent on the presence and position of the openings [4]. The results for the mid span deflection of concrete beams indicated a minor effect for the web opening existence, but it substantially increased after the formation of the first shear crack [5]. The strength of a deep beam is considerably affected by the opening location, whereas the shape of the opening has a minimal effect, and the minimal effect on shear strength is for the opening near the upper corners of the beam [6]. However, openings located at the mid depth of the shear span remarkably affect the deflection and shear strength compared with openings located above or below the mid depth of the beam. The circular opening shape is preferable than the square opening shape, and an increase in opening size results in a decrease in beam load carrying capacities [7,8]. The test results for deep beams revealed that the ultimate shear stress is size dependent [9], while increasing the opening ratio for deep beams causes a decrease in the first crack and ultimate loads, and an increase in midspan deflection [10].

Evaluating the impact load transient response characteristics is still a continually forward developing research area to achieve remarkable results in this field. The impact loading effects can be classified as local and flexural. Local effects include penetration, scabbing, perforation, and cracks. Flexural effects include energy losses, deflection, reduction in moment capacity, and shear failure. Many researchers have investigated the behavior of unreinforced and RC beams under impact loading [11,12], and some of these studies attempted to propose an equation to predict beam deflection under impact loading [13]. Researchers have investigated the effect of low-velocity impact [14], whereas failure behaviors due to high-velocity impact were examined by others [15]. Weight-dropping tests on four different kinds of deep beam specimens were executed to obtain stress wave propagation characteristics [16]. Previous studies showed that the application of impact force can be accomplished by one of the following ways: impact due to a single mass drop to fracture specimens [17,18], specimens impacted continuously with the same impact force until failure [19,20], and repeatedly impacting the specimens with continuously increasing impact force intensity from elevated heights until failure [21,22].

Based on the review of previous studies concerning the behavior of deep beams, up to date, no analytical, numerical, or experimental studies or investigations are related to the transient response of prestressed concrete deep beams with large web openings due to impact loading. Most of the previous studies were related to deep beams made of ordinary RC without web opening or prestressing. This work aims to address this gap and to highlight the performance of these beams when impacted under the effect of dropped mass with increase in the impact velocity with emphases on the effects of opening size and prestressing location.

2 Methodology

To achieve the goals, an experimental testing program was planned, designed, and conducted to evaluate the structural transient behavior of post tensioned and ordinary RC deep beams constructed with variable prestressing strand locations and different sizes for web openings when impacted by falling mass. To accomplish this task, seven RC deep beams with T-shape cross-section were fabricated and tested using repeatedly dropped mass from different heights at the mid span of these beams. Each specimen was impacted first for five times with mass dropped from a moderate height and then impacted for five additional times with the same mass dropped from an elevated height to evaluate the accumulative transient damage due to the increasing impact force. The transient performance of these beams was evaluated by considering specimen deflection, concrete and reinforcing steel strain distribution, and concrete cracking pattern.

All specimens were cast with the same dimensions, concrete compressive strength, and main and shear reinforcement. The influential variables considered included impact force strength, size of the web openings, and the existence of prestressing force with different locations. Two sizes for the opening depth (D) were adopted for the fabricated openings in the beam’s web, namely, 0.48 and 0.6 D/H, where H is the beam section depth, whereas the opening width was kept constant with a value of 0.53 of the shear span. Two positions for the prestressing strands were adopted when investigating the prestress force effect on the dynamic response. The strands were assumed to be positioned at a distance of 0.07 of the beam depth H above the beam soffit for the first position and the same distance above the opening for the second strand location. Finally, for a complete understanding of the goals, solid ordinary RC deep beam with no prestressing or web openings was tested, and the transient response was evaluated in comparison with other beams.

3 Experimental work

The experimental program included testing seven RC T-section deep beam specimens. Six beams were constructed with two symmetrical web openings so that one opening was located at the center of each shear span relative to the application of the impact force. The openings were fabricated using two sizes, namely, 480 mm × 480 mm and 600 mm × 480 mm. These beams were classified into two groups. The first group consisted of three specimens where the prestressing strand was positioned above the soffit of the beam, whereas the three remaining specimens had strands above the openings. The seventh specimen was fabricated as an ordinary RC deep beam without web openings used as a reference beam. All specimens had the same dimension of 1,950 × 1,000 × 250 mm for the span length, depth, and web width, respectively, with 900 mm shear span, 750 mm flange width, and 125 mm flange thickness.

Details of the specimen’s designation, dimensions, openings, and material properties are compiled in Table 1. The opening dimensions are denoted with D × E for the depth and width of the openings, whereas d _b is the location of the strands relative to the top of the beam flange. Each prestressed specimen was provided with two (ϕ 12.7 mm) high-yield strands. A prestressing force (286 kN) equivalent to (0.62 f pu ) stress in the strands was applied throughout the tests. Typical details of the tested deep beams are shown in Figure 1. The details for the provided reinforcement shown in this figure for the casted beams were selected to satisfy the requirements of the strut-and-tie method recommended by the ACI 318-2019 for the design of deep members.

Figure 1

Cross-section, details, and reinforcement of tested deep beams.

3.1 Impact test setup

A dropped weight impact test rig was used and consisted of a falling mass of 65 kg (including the mass of cylindrical steel shaft and stainless steel impactor) that can be dropped from a maximum height of 2,000 mm. The dropping weight was suspended by a magnetic device with a maximum capacity of 200 kg. The impact process depended on the free release of the mass from the magnetic device to achieve complete free falling impact effect. To center the position of the falling mass, the beam was positioned into the impact frame, and the vertical and horizontal movements of the specimen were restricted using two steel yokes. The tested specimens were simply supported, and the bearing plates above the supports were used to improve stress distribution and to avoid any local crushing of concrete. Figure 2 shows the impact loading frame test setup.

Figure 2

Impact frame test setup.

For all the impact tests carried out in this study, PCB piezotronic^TM accelerometers were used to record the impact energy. These accelerometers were fixed to the specimens at selected points before conducting the experiments. Four locations at the corners of the beam’s flange were used to mount the accelerometers, and the induced vertical acceleration due to impact force was recorded using National Instruments^TM VI logger software. These accelerometers were verified to record the impact force–time history data correctly by making a calibration using 2.5 kg falling mass, as shown in Figure 3. The impact force–time history as the weight of 2.5 kg mass dropped from height of 1,000 mm was used as a sample for calibration. Then, to obtain the impact force–time history of the 65 kg falling mass, only the accelerometer data were used, and the data of the dropping weight of the 2.5 kg accelerometer were calibrated to determine the impact force–time history in the current tests.

Figure 3

The calibration sample of 2.5 kg weight.

4 Test results

Energy can be defined as the ability to do work. Hence, work is the transfer of energy from one form to another. Impact testing was performed in the current work to investigate the effect of the impact energy due to moving load when impacted by a concrete member. These effects include transient deformations, strains, and cracking. Generally, impact energy in structural engineering can be classified into kinetic and potential. Potential energy is the stored energy due to deformations in the material generally known as strain energy, whereas kinetic energy is due to the movement of an object. Considering that energy can be converted from one form to another, the law of conservation of energy, the following equation can be stated [23]:

where m = dropped mass (kg), h = drop height (m), g = acceleration of gravity 9.81 ( m / s 2 ) , and v = impact velocity, ( m / s ) . The impact velocity and the momentum are as follows:

In the current work, a mass of 65 kg was set to be dropped from two increasing heights (1,000 and 2,000 mm). The mass was dropped repeatedly five times from 1,000 mm height and five times from 2,000 mm height to achieve a minimum crack width of 0.3 mm (i.e., the service load crack width limit permitted by ACI 318M-19) [24]. The obtained impact characteristics for the two dropping heights, obtained from the equations, are presented in Table 2.

The stress wave propagation characteristics and the longitudinal stress wave velocity are given by the following equation [16,25]:

At the region of impact period, taken approximately from a knock sensor distance of 150–200 mm, the duration average of the impact was 46–61 µs, as shown in Table 3.

Material strain data were recorded at different locations on the concrete surface and steel rebars, as shown in Figure 4. Hence, s2 and s3 were used to collect the strain readings for the steel rebars, whereas s6 and s12 were used for the strain readings for the concrete surfaces. During each test for the specimens, the resulting transient response data were reported in the following.

Figure 4

Locations of strain gauges on steel rebars and concrete surface.

4.1 Impact force–time history

All the tested beam specimens were knocked by the same mass of 65 kg and from the same heights of 1,000 and 2,000 mm. The resulting force–time histories were identical for all tested specimens. The strain energy achieved due to impact force is equal to the impact force multiplied by the developed penetration [23].

Energy E = kg . m 2 s 2 = Impact force N = kg . m s 2 × Penetration ( m )

(4) E net = 1 / 2 m v final 2 − 1 / 2 m v initial 2 ,

(5) I . F = E / Penetration .

Table 4 shows the physical properties for the impact force and the resulting penetration. The impact force–time history for 65 kg drop mass with falling height of 1,000 mm, calibrated from the data of the dropping weight of 2.5 kg accelerometer as presented in Section 3.3, is shown in Figure 5. At the end of the testing, the penetration reached about 20 mm after the 10 blows.

Table 4

Physical properties of each impact load

Drop height (mm)	Dropping mass (kg)	Impact velocity (m/s)	Kinetic energy (J)	Impact force I.F. (kN)	Penetration (mm)
1,000	65	4.43	637.8	255	2.5
2,000	65	6.26	1273.6	364	3.5

Figure 5

Impact force–time history for 65 kg drop mass with 1,000 mm falling height.

4.2 Deflection–time history

The results for the transient deflection–time histories for the tested beams are shown in Figure 6. For a drop height of 2 m, response oscillations at longer time periods or duration were higher than that of 1 m falling mass impact. Generally, responses shown in this figure indicate that as the opening depth increased, the transient deflection increased. Moreover, the mass of the beam decreased, resulting in an increase in the beam’s natural frequency. Comparison of the deflection–time history for the beam models with web openings and the response of a solid deep T-beam with the same properties and dimensions can be assessed from this figure. The solid deep beam exhibited small deflection and response oscillations, and the solid beam transient response quickly damped out compared with the response of the same beam when large openings were introduced in the web. This result indicated that the existence of web opening greatly enhances the ductile behavior of such beams. The solid deep T-beam transient deflection increased by about 200% when large openings were introduced in the beam’s web.

Figure 6

Transient deflection–time histories for tested specimens.

The pulse duration and response amplitudes for prestressed specimens were less than those for ordinary reinforced deep beams with the same properties. The pre-stressed force at the tendons worked as a damping to the impact force. It decreased the deflection and the pulse–time duration. Prestressing location above the openings was more effective in reducing the pulse duration and response amplitudes than prestressing location above the soffit. The response amplitude for the solid deep beam was 25% less than the response amplitude for prestressed deep beam above the openings.

4.3 Strain–time history

4.3.1 Reinforcement strain–time history

The results of the reinforcement strains due to the applied impact forces are presented in Figure 7. Generally, the strains at gauge s3 were larger than those at gauge s2. The steel strains in the tie reinforcement at the soffit of the beam were maximum at mid span where the s3 gauge location showed that the tie reinforcement was affected by the flexural stresses in addition to the tensile stresses of the strut-and-tie model. Moreover, a time lag for the maximum strain response at the same strain gauge location was noticed when comparing responses for different impact forces. However, for the solid beam, no time lag was noticed for the maximum strain response, showing that the existence of the openings in the web interferes in impact wave propagation and alters the time for maximum steel strain. Accordingly, the difference in the time for maximum response is attributed to the presence of the web openings, prestressing, and the drop height of the impact load.

Figure 7

Reinforcement steel strain–time history at different drop heights.

The results in Figure 8 show that as the opening depth increases, the transient strain in the reinforcement increases with higher amplitude for the response oscillations, revealing a higher damping for the strains in the reinforcement as the opening size decreases. An increase in the reinforcement strains of about 33% was observed when opening depth was increased from 0.48 to 0.60 D/H. The results for the solid deep beam showed slight reinforcement strain values and response oscillations. The transient reinforcement strains for the solid deep increased by about 400 and 166% when large openings, 600 mm × 480 mm, were introduced in the ordinary reinforced beam and for the partially prestressed above the soffit of the deep beam, respectively.

Figure 8

Concrete surface strain–time history at s6 location at different drop heights.

4.3.2 Concrete strain–time history

The results for the concrete strains due to the applied impact forces are presented in Figures 8 and 9. Generally, as the drop-height increased, larger concrete strain values were observed. A time-lag delay existed as dropping height increased this behavior as the result of the effects of the web opening’s location at the shear span that intersected the stress path. The transient concrete strains at gauge locations s12 and s6 were reduced substantially when prestressing strands were introduced, and prestressing location above the web openings was more effective.

Figure 9

Concrete surface strain–time history at s12 location at different drop heights.

Responses for the prestressed specimens due to 2,000 mm drop height were around 55 and 2.5 microstrain for prestress strands on top of the beam soffit or openings, respectively, and the impact pulse time was too small, around 1.5 ms. For the same specimen but without prestress, the response was about 125 microstrain, and the time duration reached 10 ms. For prestressing location above the openings, insignificant strain reading at s12 for drop height of 1,000 mm was recorded, indicating that the prestressing force due to tendons damped out the effect of the falling load efficiently, and for drop height of 2,000 mm, the response of about 6 microstrain at impulse time duration around 0.5 ms was recorded. Finally, the time lag for the maximum strain response was not consistent for each gauge location as for the reinforcement response. This behavior might be the result for the effect of opening depth variation, strain gauge location, and impact wave propagation.

5 Discussion of results

5.1 Deflection–time history

The results in Figure 6 represent the beam’s deflection due to the impact force as the result of the beam’s oscillation. The maximum midspan deflection of the specimens increased by increasing the opening depth by about 30% for specimens with prestress location above the openings, 6–10% for specimens with prestress strand location above the soffit, and around 8% for ordinary reinforced specimens. For deep beam without openings, the mid span deflection increased by about 200% when symmetrical openings were constructed in the web and about 25% as web opening and prestress strand located above the opening was introduced. Increasing dropping heights from 1,000 to 2,000 mm increased the maximum mid span deflection by around 50–70%. The comparison of the effect of the web opening size on the transient beam deflection due to the impact force is summarized in Figure 10.

Figure 10

Summary of maximum mid span deflections due to impact load.

5.2 Strain time–history

The presence of web opening can increase the steel and the concrete strains compared with the solid specimens, and steel and concrete strains increased as the drop height increased. As the opening depth increased from 0.48 D/H to 0.60 D/H, an increase in the steel strain of about 15–25% was observed in case of prestressed above the soffit and ordinary reinforced specimens, respectively. Introducing prestress above the soffit can reduce the steel strain of about 60%. Substantial reduction in concrete surface strains were observed when prestressing above the openings was introduced. The web opening size effects on the strain on steel and concrete due to the impact force for drop height of 2,000 mm are summarized in Figure 11. Generally, the results for the strain–time histories showed that strain in the steel bars and concrete increased when increasing the opening depth accompanied by higher amplitudes for response oscillations, revealing higher damping for the strains as the opening size decreased.

Figure 11

Summary of maximum concrete and steel strains for dropping height of 2,000 mm.

5.3 Cracking pattern

The tested specimens were subjected to five blows of 1,000 mm height and five more blows of 2,000 mm height. The first cracks propagated at the opening corners diagonally toward the point of the applied load and the support regions for all specimens due to the second blow. Flexural cracks appeared by the eighth blow only for specimens with prestressing above the openings, whereas at the openings upper corner junction cracks appeared around the seventh blow for the same specimens, as shown in Figure 12. For specimens with prestressing strands above the soffit, no flexural or opening junction cracks appeared. Finally, cracks in the flange appeared around the eighth blow for dropping height of 2,000 mm.

Figure 12

Cracks pattern around openings due to impact load.

6 Conclusion

The following conclusions are drawn:

• The maximum mid span deflection of the tested specimens increases by an average value of about 50% when doubling the dropped mass height. The greater the impact force is, the more strain energy and additional cracks propagate, and hence, the deflection is larger.

• The transient deflection of the solid deep beam increases by around 200% when a large opening is made in the web, whereas this increase due to the opening is reduced to 25% when introducing prestress above the openings.

• Increasing opening depth has a minimal effect on increasing deflection, and deflection increases by about 30% only in the case of prestressing above the openings.

• Introducing prestressing strands above the soffit has a remarkable effect on reducing main reinforcement steel strain by about 60%, whereas substantial reduction in concrete surface strains is observed as prestressing strands are introduced above the openings.

• For solid deep beam, small strain values are recorded for concrete and steel reinforcement, and the absence of the web openings results in higher damping for the transient response with minor cracks.

• Prestressing strand’s location above the openings has a greater effect on the strength and performance of deep beams than prestressing location above the soffit.

• The existence of web openings greatly affects the stress wave propagation and consequently, the transient response time for different dropping heights.