Response of composite steel-concrete cellular beams of different concrete deck types under harmonic loads

Zahraa Hussien Dakhela; Shatha Dheyaa. Mohammed

doi:10.1515/jmbm-2022-0014

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Response of composite steel-concrete cellular beams of different concrete deck types under harmonic loads

Zahraa Hussien Dakhela and Shatha Dheyaa. Mohammed

Published/Copyright: May 18, 2022

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From the journal Journal of the Mechanical Behavior of Materials Volume 31 Issue 1

Abstract

This study aims to investigate the adequacy of composite cellular beams with lightweight reinforced concrete deck slab as a structural unit for harmonic loaded buildings. The experimental program involved three fixed-ends supported beams throughout 2140 mm. Three concrete types were included: Normal Weight Concrete (NWC), Lightweight Aggregate Concrete (LWAC), and Lightweight Fiber Reinforced Aggregate Concrete (LWACF). The considered frequencies were (5, 10, 15, 20, 25, and 30) Hz. It was indicated that the harmonic load caused a significant influence on LWAC response (64% greater than NWC) and lattice cracks were observed, especially at 30 Hz. As for LWACF slab, no cracks appeared, and the harmonic load had a minor effect on the vibration amplitude. Adding fiber to LWAC improved its behavior and made the amplitude no more than 11.11%, corresponding to NWC. So, the response variance for the LWACF was approximately negligible compared with NWC. It is worth mentioning that the study produced a lightweight structure that resists harmonic vibrations with a small strength reduction by using LWACF as a deck-slab for cellular specimens and provides a structural element with a smaller density of about 27%, which presents an advantage for the cellular beam that is adopted for low-loaded structures.

Keywords: Harmonic load application system; operation frequency; steel fiber; cellular beam; lightweight concrete; normal concrete; economic industrial buildings

1 Introduction

It is well known that the main problems in industrial buildings are the harmonic load and the heavyweight generated by the machine's motors, these can be considered as the most important loads the slab could be affected by, therefore, the critical challenge in industrial facilities subjected to harmonic loads (industrial motors) is how to obtain a lightweight structure that resists these vibrations with small strength reduction, i.e., long service life. Natural frequencies, mode shapes, and damping ratios are the most important parameters in the industrial structures that are subjected to vibration effects [1]. After excitation stopping (free vibration), the natural frequencies of a building or a structural component are those at which free oscillations continue. Large vibration amplitudes can occur when an excitation frequency coincides with or is close to the natural frequency [2]. This is known as resonance; it should be avoided in general. Most studies focused on dynamic loads caused by quakes and offshore waves. However, nothing was known about the effects of machine vibration on dynamic load structures. Modern industry has introduced massive machines that significantly affect the performance of structures, causing another type of vibration load. Machine vibration should be treated as an engineering problem, regardless of size or kind, and should be designed using sound engineering principles [3]. A dynamic load usually changes in magnitude, direction, and position throughout the time. Structures are often subjected to at least one type of dynamic load during their service life. When an applied load fluctuates as a sine or cosine function, this is called harmonic loading. The vibrations created by an unbalanced rotating machine, the vertical motion of a car on a sinusoidal road surface, and the oscillations of a tall chimney caused by vortex shedding in a steady wind are all examples of harmonic motion [4]. Structural engineers have long sought to develop innovative methods to enhance the design and construction of steel and composite structures. These methods were concerned with the overall costs and self-weight reduction, moreover increasing the structure's ultimate strength. Some of these ways used open web expanded steel beams that were characterized by web openings of the regular patterns each had different geometrical properties. These types of steel beams reduced story height, internal volume, outside surface area, and saved money on building construction. They’ve also been used for a long time to axes ductwork or other utility lines through the web holes [5]. Cellular beams are a modern version of the traditional castellated beams. The emergence of cellular beams was firstly for an architectural application, where exposed steelwork with circular web openings in the beam was considered aesthetically pleasing more than castellated beams. Moreover, 3500 projects used cellular steel beams all around the world [6] and lightweight concrete as a slab. The term “lightweight concrete” refers to concrete that has a low density of (1120–1920) kg/m³ and compressive strength of at least 17 MPa [7]. To gauge the adequacy of an existing building corresponding to its functionality or occupancy or to evaluate a complaint, the existing vibrations are measured and then compared to the appropriate criteria or acceptable limits (40–50 Hz) [8]. In this study, to enhance the vibration response and increase the structural ultimate strength under the effect of harmonic load, composite beams (cellular beams) of different concrete deck slabs (normal weight concrete (NWC), lightweight aggregate concrete (LWAC), and lightweight fiber-reinforced aggregate concrete (LWACF)) were implemented.

2 Literature review

Concerning the castellated structures, there are many continuous studies to this day that study the affected of these structures by various types of static loads, Oukaili and Seezar [9] studied composite concrete-open web expanded steel beams under combined flexure and torsion. Experimentation required 18 composite specimens with 300 mm open web extended section depths made from IPE-200 standard rolled sections, separated into two groups by hole form.

Each set has nine composite specimens with hexagonal or circular openings. All beams span 2900 mm in basic support with two equal concentrated loads. The first strengthening technique enhanced the load capacity of specimens with castellated holes by 26.08% and circular openings by 21.88% under pure bending, 16.36% and 33.33% under combined flexure and torsion, and 5.6% and 4.44% under pure torsion. The second strengthening technique, on the other hand, increased the load capacity of castellated and circular hole specimens by 186.95 and 134.38%, respectively, for pure bending, 136.36 and 116.66% for combination flexure and torsion effect, and 6.58 and 4.88% for pure torsion. While the effect of the harmonic load on this type of structures consider a little poor, most studies focused on dynamic loads caused by quakes and offshore waves. However, nothing was known about the effects of machine vibration on structures. Modern industry has introduced massive machines that significantly affect the performance of structures, causing another type of vibration load. Machine vibration should be treated as an engineering problem, regardless of size or kind, and should be designed using sound engineering principles. Authors in [1] studied the structural behavior of Bubble Deck reinforced concrete slabs under the effect of harmonic loads experimentally and theoretically. The effect of harmonic load on a tow-way Bubble Deck slab with dimensions of (2500*2500*200) mm and uniformly distributed bubbles of (120) mm diameter and (160) mm spacing c/c was tested experimentally. Moreover, numerical analysis was included using the ABAQUS program. The results showed that the distribution of bubbles had a significant effect on the structural behavior in the dynamic analysis, and the numerical model used was in good agreement with the experimental data. The effect of a moving harmonic load on beams with different boundary conditions was studied analytically by authors in [2], several parameters were considered, including the kind of supports, excitation frequency, and harmonic load speed. All of the beams under study were homogenous, isotropic, and at rest at the start. Concentrated harmonic forces of constant amplitudes were applied to all of them. For the lightweight concrete, the authors in [10] examined three kinds of fibers which are carbon, steel, and polypropylene. The outcome (1%) was the number of fibers separately and with different combinations. It was recorded that reinforced LWAC with steel fiber presented the optimum for splitting strength by almost 24% while 16% enhanced for carbon fiber. Polypropylene fiber resulted in a slight decrease of around 2%. Nevertheless, hybrid fibers have been shown to have a substantially greater positive effect on the strength of compression and splitting. The best results are given by a combination of steel and carbon between all of the considered combinations. This combination improved tensile strength by upwards of 39%. It was recognized that it might be based on the assumption that a mixture of fibers of different cracking scales and various sizes controls and types. Many researchers work to indicate the behavior of the fiber-reinforced lightweight concrete structure and the results agree with outcomes of Chen and Liu [10] such as [11, 12, 13, 14, 15].

3 Experimental investigation

3.1 Test specimens

Throughout a span of 2140 mm, three composite cellular steel-concrete specimens were fabricated according to AISC-Design Guide 31 [16] and tested as fixed-ends supported beams. Since the adopted overall height after castellation is 400 mm, a hot rolled steel I-section (IPE 200) was employed, with a 100 mm concrete deck slab. A full bond between the two components of the composite system was adopted. Accordingly, shear connectors made of fabricated steel channel section 60 × 30 × 5 mm with a total length of 50 mm were distributed perpendicularly at 187 mm c/c a part on the top flange of the steel beam. Steel stiffeners 284 × 47.2 × 6 mm were distributed in the middle and the two ends of the web on both faces of the steel beam. The deck was reinforced in both directions by deformed steel bars of 10 mm diameter spaced at 125 mm c/c. Figure 1 and Plate 1 show the details of the adopted specimens.

Figure 1

Cellular beam details

Plate 1

Fabricated and cast of the composite cellular beam

There were two concrete mixes, the first was normal weight concrete that's prepared using ordinary Portland cement type (CEM I 32.5 R) according to Iraqi specification No. 5/2019 [17], crushed stone of 10 mm maximum size and fine aggregate that's classified as zone (2) conferring to Iraqi specification No. 45/1993 [18]. The aggregate: sand: cement designed proportions by weight were (1.6:1.33:1) with water-cement ratio equal to (0.29) according to ACI 211.1 [19]. The second one was a lightweight concrete, Table 1 shows the lightweight concrete mix proportions, the ratios of all the constituent materials were compatible with the standard of the Regular Practice for Structural Lightweight Concrete Collection Proportion according to ACI 211.2 [20]. Light Expanded Clay Aggregate (LECA) as shown in Plate 2 was adopted to cast the lightweight concrete as a coarse aggregate ASTM C330 [21]. The coarse aggregate's grain size is 10 mm [22]. One type of fiber was adopted in this work with a volume fraction of 1.5%: hooked steel fiber of 30 mm length, the steel fiber properties are illustrated in Table 2. The concrete compressive strength was determined by testing three standard 150 × 300 mm concrete cylinders for each specimen according to ASTM C39 [23], where the target value was 40 MPa.

Plate 2

Light Expanded Clay Aggregate (LECA)

Table 1

The adopted lightweight concrete mix

Material	Proportion
Cement	677 (kg/m³⁾
Water	237 (kg/m³)
Coarse Agg. (LECA)	210 (kg/m³)
Fine Agg	884 (kg/m³)
Silica Fume	170 (kg/m³)
Superplasticizer	7 (litter/m³)

Table 2

Steel fiber characteristics

Fiber type	Diameters (mm)	Length (mm)	Aspect ratio	Tensile strength (MPa)	Modulus of elasticity (GPa)	Density (kg/m³)
Hooked	0.5	30	60	1700	200	7800

3.2 Testing procedure

An advanced digital data logger was connected to a computer device provided by a specific program to record and save data as an excel sheet, making it suitable for long-term measurements. As shown in Plate 3, this instrument includes 24 channels divided into four groups that can record strain values, vibration amplitude, and the instantaneous applied load at a rate of 1000 records per second. Calibrated Piezo (vibration type) was considered to measure the vibration wave in the middle of specimens and the harmonic applied force, Plate 4. The application system of the harmonic load consists of a vibration motor of (3 HP) capacity combined with a steel mass of 278 kg weight. The specimen was set to the test frame so that it behave as a fixed-ends supported beam. The fixed system comprised two steel plates 600 × 100 × 40 mm connected by a steel thread rod 25 mm diameter so that they prevent the specimen from any movement, Plate 4. The application system of the harmonic load and the piezo sensors were set in their right position as shown in Figure 2. The time duration of the applied harmonic load, for each frequency, was 120 sec. Table 3 shows the details of the tested specimens.

Plate 3

Test instruments

Plate 4

Specimens set up

Figure 2

The application system of the harmonic load

Table 3

Details of the tested specimens

Specimen's designation	Deck slab type	fc′ (MPa)	f_t^* (MPa)	E_c (MPa)	Frequencies (Hz)
HS-CL0	LWC	38	3.2	20407	5, 10, 15, 20, 25, and 30
HS-CN0	NWC	40	3.54	28333
HS-CL1.5	LWCF	40	3.7	23584

*
According to ASTM C496/C496M-17 [24].

4 Results and discussions

Harmonic load of different frequencies (5–30) Hz was applied to the tested specimens. Data were recorded from the piezo sensors to measure the vertical vibration amplitude and vibration sine wave for the applied harmonic loads of different frequencies. Build up computer program has been developed to modify the recorded date from piezo records (remove the noise) as shown in Figure 3.

Figure 3

Noise removing, (a) before noise removing (b) after noise removing

4.1 Load time history

The harmonic load was the considered dynamic load in this study. In general, there are two parts to the mathematical formula for this load. The first characterizes the amplitude of the harmonic load ( 2mew02 ) while the second represents the sine wave term (sin(wt)), Eq. (1) [25].

(1) Pd=2mew02sin(w0t)

Where: P_d: harmonic load (N). m: eccentric rotating mass (kg) e: eccentric distance (m), and w₀: operating frequency of the machine (rad/sec).

A wide range of frequencies (5–30) Hz were considered to realize better consideration for this parameter's effect on the response of cellular composite beam. The recorded load time histories for the adopted load frequencies are shown in Figure 4 and Table 4.

Figure 4

The recorded load time histories for the adopted load frequencies

Table 4

The amplitude of the harmonic load ( 2mew02 )

Frequency cycle/sec	Frequency rad/sec	Amplitude force N
5	31.42	473.9
10	62.831	1895
15	94.25	4263.87
20	125.67	7573
25	157.1	11846.6
30	188.5	17055

Note: The magnitude of (m and e) were measured experimentally in the lab to be (m = 3 kg and e = 0.08 m).

4.2 Vibration-time history

In this object, vibration characteristics for all the adopted frequencies were illustrated in Table 5. The recorded amplitude differed from one specimen to another. Especially between the specimen with LWAC deck slab and the NWC deck slab. The natural frequency was theoretically measured.

Table 5

Maximum amplitude for the specimens under harmonic load

Specimens	HS-CN0	HS-CL0	Variation% (HS−CN0)	HS-CL1.5	Variation% (HS−CN0)
Natural frequency Hz	125.92	128.64	2.2	123.77	−1.7
Frequencies Hz	Amplitude (mm)	Amplitude (mm)	Variation% (HS-CN0)	Amplitude (mm)	Variation% (HS-CN0)
5	0.00899	0.010	11.234	0.0088	−2.113
10	0.0310	0.0399	28.7	0.0299	−3.55
15	0.0939	0.1199	27.7	0.0955	1.70
20	0.12299	0.1499	21.9	0.13	5.69
25	0.1899	0.27899	46.9	0.1999	5.27
30	0.27	0.445	64.8	0.3	11.11

4.3 Effect of a concrete type

In this article, the significance of the adopted concrete types was investigated. Regarding the specimen HS-CL0, Figures 5 to 10 and Table 5 showed that there was a variation in the amplitude for all the considered frequencies. A clear difference between the plain LWAC and the NWC specimen was detected for all considered frequencies 5–30 Hz to be 11.234–64.8%. Cracks began to appear during the test duration for LWAC deck slabs specimen at 20 Hz frequency and increased at 30 Hz, but they were slightly generated in the NWC at 30 Hz in the position of the load acting at the surface of the deck slab.

Figure 5

Vibration-time history under harmonic load with 5Hz frequency

Figure 6

Vibration-time history under harmonic load with 10Hz frequency

Figure 7

Vibration-time history under harmonic load with 15Hz frequency

Figure 8

Vibration-time history under harmonic load with 20Hz frequency

Figure 9

Vibration-time history under harmonic load with 25Hz frequency

Figure 10

Vibration-time history under harmonic load with 30Hz grequency

Adding fiber to lightweight concrete (LWAC) improved its structural behavior and decreased its variation amplitude compared to the normal weight concrete by no more 11.11%. It can be seen that under the influence of frequencies 5 and 10 Hz, LWACF amplitude variations were −2.11 and −3.55%, respectively, but for frequencies 15, 20, and 25 Hz there is a significant difference in the amplitude for both types of concrete (NWC and LWACF). At 30 Hz frequency the value of the LWACF amplitude was slightly higher than the normal weight concrete with a difference 11.11%, but no crack appeared during the operation time for the specimens with LWACF deck slab for all operating frequencies. The fiber-reinforced lightweight concrete behaves slightly similar to NWC under harmonic load. This behavior may be attributed to the presence of fibers, which enhanced the mechanical properties of lightweight concrete, as shown in Table 3, and enabled it to be used as an alternative to normal weight concrete in this study.

Figures 5 to 10 showed that the amplitude values of the vibration wave were mostly determined by the percentage of compatibility between the natural frequency of the specimen and the operating frequency of the vibrating motor. These figures indicated that the value of vibration amplitude was constant for all the operation frequencies during the operation time because the natural frequency of the specimen was so far from the motor operator frequency and the short operation time [26].

5 Conclusion

Depending on the outcomes of the harmonic load test for the three specimens, it can be detected that;

The concrete deck slab type has a significant effect on the response and structural behavior of the cellular composite beam under the effect of harmonic load.
For all the considered concrete types, the vibration amplitude was constant for each operating frequency throughout the testing time. This can be interrupted by the short operation duration and considered operation frequencies that are significantly different from the specimen's natural frequency.
Fiber-reinforced lightweight concrete showed approximately identical responses to those of the NWC specimen, no more than 11.11% variation was achieved, while the lightweight concrete specimen with no fiber showed a high diverge response from the NWC reached (64.8%) at the operation frequency (30 Hz). This means that fiber-reinforced lightweight concrete can be adopted as a significant choice for cellular composite beams under the effect of the harmonic load.
This choice provides a structural element of 27% less density compared to NWC, which presents an advantage for the cellular beam that is adopted for low-loaded structures.

Acknowledgement

This research was performed while the author was a PhD student in the Department of Civil Engineering. The author is grateful to both the Department and the College of Engineering and Hamorabi Contracting Co ./ Department of precast Bridges and Culvert Production for the opportunity to finishing this work.

Funding information: The authors state no funding involved.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.

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Received: 2022-02-19

Accepted: 2022-03-28

Published Online: 2022-05-18

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/jmbm-2022-0014

Keywords for this article

Harmonic load application system; operation frequency; steel fiber; cellular beam; lightweight concrete; normal concrete; economic industrial buildings

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