Shear Strength of Concrete Wide Beams Shear Reinforced with GFRP Plates

Abstract

This paper discusses the experimental results on the shear behavior of concrete wide beams reinforced with glass fiber reinforced polymer (GFRP) plates as shear reinforcement. In order to examine the shear performance, a total of six concrete wide beams were manufactured and tested. All the specimens were designed to have the same number of legs of shear reinforcement. The transverse spacing of shear reinforcement was considered as a variable to investigate the influence of transverse spacing of concrete wide beams. From the test results, it is observed that the shear strength increased when transverse spacing of the shear reinforcement decreased. In addition, an equation is proposed to predict the shear strength of concrete wide beams in order to consider the influence of transverse spacing of the shear reinforcement. The equation is based on the test results and modified ACI 318–14. It is verified that the proposed equation is considered to be better than ACI 318–14.

1. Introduction

A beam is classified as a wide beam when the width of the beam is wider than the column width; or when the width of the beam is more than twice the beams’ height. The concrete wide beams, which are simple and economical systems, can provide shallower structural depth. Therefore, wide beams are utilized in warehouses, commercial buildings, parking areas in order to reduce floor height. According to ACI 318–14 code ¹ , shear strength of reinforced concrete beams is determined by the summation of concrete and longitudinal stirrups as expressed by Equation (1) to (3).

$$V_n=V_c+V_{sL}$$

(1)

$$V_c=V\frac{1}{6}({\sqrt{f^{\text{'}}}}_c{b}_{w}d)$$

(2)

$$V_{sL}=\frac{A_f{F}_{y}d}{S_L}$$

(3)

where V _n is nominal shear strength; V _c is the nominal shear strength provided by concrete; V _sL is the nominal shear strength provided by longitudinal stirrups; f' _c is the compressive strength of concrete; b _w is the width of the beams, d is the depth of beam; A _v is the shear reinforcement area; f _y is the yield strength of stirrups; and S _L is the longitudinal spacing of the stirrups.

In shear reinforcement of wide beams, the stirrups legs are normally placed around the outermost longitudinal reinforcement. The lack of shear reinforcement across the web of the beam could lead to a concentration of diagonal compressive stresses. Nevertheless, the influence of transverse shear reinforcement is not considered in ACI 318–14.

Some researchers had tested several beams with different stirrup configurations^2–4. They concluded that the use of a single leg could lead to a concentration of diagonal compressive stresses at the joint of the stirrup leg. Lubell et al. ⁴ performed a test on the concrete wide beams, in which the variables included were the transverse spacing of stirrups and shear reinforcement area. The test results showed that the shear capacities decreased as transverse spacing of stirrups increased. They recommended a maximum transverse spacing of stirrups. Shuarim ⁵ experimentally evaluated the influence of stirrup configurations in wide beams, and observed that by reducing the transverse spacing of stirrups, the shear capacities can be improved. In addition, he proposed an equivalent spacing design equation and a transverse spacing limit for stirrups.

The transverse stirrup spacing for concrete wide beams must be considered for an accurate prediction of shear strength. However, ACI 318–14 code does not provide a shear strength equation, which includes transverse spacing. The main objective of this paper is to propose a shear strength equation, which includes transverse spacing, and a modified shear design of the existing ACI 318–14 for concrete beams.

In this study, shear testes on six concrete wide beams shear reinforced with glass fiber reinforced polymer (GFRP) plates were performed in order to evaluate the shear capacity considering the transverse spacing of shear reinforcement. In addition, the shear strength equation for shear reinforcement is proposed by modifying the equation in the ACI 318–14.

2. Experimental Program

2.1 Materials

The design compressive strength of the concrete used for the fabrication of the specimens was 35 MPa. The average compressive strength measured at the end of 28 days was 35.2 MPa. The deformed steel bars with a diameter of 22 mm and 16 mm were used as longitudinal reinforcement. In addition, their tensile strength and modulus of elasticity were 400 MPa and 200 GPa, respectively. The GFRP plate with openings is used as shear reinforcement and was embedded in concrete. The tensile stress of the GFRP plate was 480 MPa. The GFRP plates were manufactured as shown Figure 1 ^6,7.

Figure 1

Schematic view of a wide beam reinforced with GFRP plates

2.2 Specimen Details

A total of six concrete wide beams embedded with GFRP plates with opening were tested. The transverse spacing of shear reinforcement is selected as a variable in the shear performance test of concrete wide beams. Each beam had the same number of legs of transverse shear reinforcement. Also, all specimens were designed to have the same longitudinal shear reinforcement area and spacing. The specimen details are shown in Table 1 . The width, height, and effective depth of the specimen were 800 mm, 300 mm, and 225.6 mm respectively. The total span length and clear span length were 3100 mm and 2700 mm, respectively. The arrangement of shear reinforcement in the specimen is shown in Figure 1 and Figure 2 . All the specimens were designed to ensure shear failure before flexural failure.

Figure 2

Cross-section of specimens

Table 1

Details of specimens

	Width of vertical strip (w f ) (mm)	Thickness of plate (t f ) (mm)	Transverse spacing (s w ) (mm)	Effective depth (d) (mm)	Spacing of longitudinal shear reinforcement (s L ) (mm)	Amount of shear reinforcement (A v × f t ) (kN)
WF-151	22	2.5	151	225.5	120	52.8
WF-199			199
WF-262			262
WF-321			321
WF-373			373
WF-500			500

2.3 Test Setup

Load was applied to each specimen using a hydraulic jack with maximum capacity of 5000 kN as shown in Figure 3 . The force generated by the hydraulic jack was transmitted to the center of a steel spreader beam, which was installed to apply a two-point loading to the specimen. All specimens were loaded until failure to observe the ultimate load-carrying capacity. A linear variable displacement transducer (LVDT's) was installed at the bottom of the specimen to measure the vertical displacement. A data logger was used to collect load, displacement, and strain data.

Figure 3

Test setup

3. Test Results and Discussion

The crack distributions of specimens are shown Figure 4 and Figure 5 . All of the specimens experienced shear-compression failure. Similar behavior and crack development were observed in all specimens. It was observed that initially flexural cracks appeared in the middle of the beam, subsequently, flexural shear cracks occurred at an effective depth far from the point of support. As the flexural shear cracks propagated toward the loading point, crushing of concrete occurred. The diagonal crack and concrete crushing occurred at the loading point. The specimens with the closest and the widest spacing (WF-151 and WF-500 specimens) had more cracks than the other specimens.

Figure 4

Shear failure

Figure 5

Crack patterns of the specimens

Figure 6 and Figure 7 show the comparisons of the load-displacement relations and maximum shear strength by transverse spacing of shear reinforcement. The test results are given in Table 2 . WF-500 with the widest transverse spacing indicated load reduction at the earliest loading level. The maximum shear strength of WF-500 specimen was approximately 252 kN, while the maximum shear strength of WF-262 specimen was approximately 293 kN. For WF-262 specimen, the maximum shear strength was increased by 16% than the WF-500 specimen. However, the maximum shear strength of WF-151 specimen, which the transverse spacing was set as the narrowest, was measured to be lower than those of WF-262 specimen. As transverse spacing of shear reinforcement decreased, the maximum load was observed to increase to a certain point. However, when transverse spacing decreases further, the maximum shear strength begins to decrease. It could be confirmed that the limit transverse spacing of GFRP shear reinforcement, at which the shear strength begins to decrease, is approximately 1.16 times the effective depth of wide beams.

Figure 6

Effect of transverse spacing on shear strength

Figure 7

Load-displacement curves

Table 2

Test results

	V exp (kN)	Failure mode
WF-151	269.58	Shear
WF-199	277.13	Shear
WF-262	292.65	Shear
WF-321	274.61	Shear
WF-373	267.67	Shear
WF-500	251.63	Shear

4. Proposed Shear Strength Equaiton

According to the ACI 318–14, V _sL can be calculated using equation (3). In this paper, equation (4) and equation (5) were derived by replacing the sectional areas of steel stirrups with those of vertical components of the GFRP shear reinforcement. The amount of shear reinforcement was the product of the number of vertical components in the critical shear span, width of the vertical components and thickness of vertical components. In Figure 8 , the GFRP width of component and spacing are defined. The accuracy of equation (4) was verified by earlier researchers^6,7.

$$V_{sL}=\frac{A_f{F}_{fu}d}{S_L}$$

(4)

$$A_f=2t_f{W}_f$$

(5)

where, V _sL is the nominal shear strength provided by longitudinal shear reinforcement, A _f is sectional area of a vertical component of GFRP shear reinforcement, f _fu is tensile strength of GFRP shear reinforcement, t _f is thickness of GFRP shear reinforcement, w _f is width of shear reinforcement, and s is center-to-center spacing of longitudinal shear reinforcement.

Figure 8

Components of GFRP shear reinforcement

The proposed shear strength equation has modified the ACI 318–14 code. It is intended to reflect the effect of transverse spacing of shear reinforcement. It is indicated that the transverse spacing of the shear reinforcement affected shear strength of wide beams. A shear strength equation incorporating the transverse spacing of shear reinforcement as a variable was proposed through the modification of ACI 318–14. ACI 318 code only used a spacing of longitudinal shear reinforcement whereas in proposed equation, the equivalent spacing S is used, which incorporates the spacing of transverse shear reinforcement. A concept of equivalent spacing proposed by Shuarim ⁵ was adopted. The equivalent spacing is used instead of spacing of longitudinal shear reinforcement in computing the shear reinforcement contribution to consider the influence of transverse reinforcement. It is expressed by equation (7) is a function of both longitudinal spacing s _L and transverse spacing s _T . In terms of equivalent spacing S, it was proposed as two equations based on the transverse spacing to effective of depth ratio. The proposed shear strength of GFRP shear reinforcement was expressed by equation (8).

$$\begin{array}{l}\frac{S_T}{d}>1.16,S=\frac{\sqrt{S_L{S}_T}}{28},\hfill \\ \frac{S_T}{d}>1.16,S=\frac{S_L}{\sqrt{{0.55}_{S_T}}}S\hfill \end{array}$$

(7)

$$V_s=\frac{A_f{f}_{fu}d}{S}$$

(8)

where, S is the equivalent spacing of shear reinforcement.

In Table 3 , the observed shear strength of specimens are compared with their corresponding predicted values according to the ACI 318–14 and proposed equation. The proposed equation indicated an average of 1.03 with standard deviation of 0.015. ACI 318–14 shows a mean shear strength ratio of 0.98 with standard deviation of 0.043. It was confirmed that the proposed equation showed good agreement with experimental data than ACI 318–14. Figure 10 shows the comparison of the ACI 318–14 tends to relatively overestimate the shear strength. The difference between the experimental results and calculated results is attributed to spacing of transverse shear reinforcement.

Table 3

Experimental versus predicted shear strength

		ACI-318		Proposed equation
	V exp (kN)	Vn, ACI (kN)	V exp /V n, ACI	V n,pro. (kN)	V exp /V n, pro.
WF-151	269.58	277.10	0.97	260.42	1.04
WF-199	277.13	277.10	1.00	272.63	1.02
WF-262	292.65	277.10	1.02	286.60	1.02
WF-321	274.61	277.10	0.99	272.68	1.01
WF-373	267.67	277.10	0.97	259.47	1.03
WF-500	251.63	277.10	0.91	238.74	1.05
Average		–	0.98	–	1.03
Standard deviation		–	0.043	–	0.015

Figure 9

Ratios of the test results to the ACI and proposed equation predictions on shear strength

5. Conclusions

In this paper, the behavior of concrete wide beams shear reinforced GFRP plates have been investigated experimentally. Shear tests on six wide concrete specimens were performed to examine the effect of the spacing of transverse shear reinforcement. The cracking pattern and maximum shear strength were analyzed. Also, shear strength equation was proposed based on test results. Test results were compared with the estimation calculated by ACI and proposed equation. The following conclusions were drawn from this study:

1. 1.

   In the wide beam shear reinforced with GFRP plates, it could be noted that the shear performance increases as the spacing of the traverse shear reinforcement decreases until the spacing of 1.16 times effective depth, and once the spacing decreases to below the value, the shear performance starts to decrease again. It is determined that the increase of spacing on the wide beam results in the occurrence of compression stress concentration while at a decrease below 1.16 d, it forms a spacing too narrow for its beam member, resulting in the decreases of shear performance.

2. 2.

   In case of shear strength calculation for a wide beam shear reinforced with GFRP plates based ACI 318–14, an accurate estimation of shear strength based on the transverse spacing variations could not be predicted as the influence of the transverse spacing was not considered. ACI 318–14 tends to relatively overestimate the shear strength. It is important to consider transverse spacing of shear reinforcement in the design of concrete wide beams.

3. 3.

   The proposed equation of shear strength that clearly showed a great improvement in predicting the shear reinforcement contribution. It is concluded that the spacing limit and its influence should be taken into consideration in shear strength calculations for accurate estimations in wide beams.