# An experimental approach for strengthening of RC deep beams with web openings using GFRP fabrics and gas actuated fasteners

实验方法，使用 GFRP 织物和气体驱动的快速紧固件对具有网孔的 RC 深梁进行加固

工程技术TOPEI检索SCI升级版 工程技术2区SCI基础版 工程技术3区IF 6.7 IF (如果) 6.7## Keywords 请将以下文本翻译成中文。对于每一句，将其分割成更小、合理的部分，分别单独翻译每一部分，并将翻译后的部分放在原始部分之后（括号内）。最后，将每句话翻译后的部分连接成一个完整的句子。 关键词

钢筋混凝土深梁(Reinforced concrete deep beam) 玻璃纤维增强聚合物织物(Glass fibre reinforced polymer fabrics) 气动紧固件(Gas actuated fastener) 剪切加固(Shear strengthening) 网格开口(Web openings)

## 1. Introduction 1. 引言 (Introduction)

In the recent years, the use of reinforced concrete (RC) deep beams in tall structures for both residential and industrial purposes has increased rapidly because of their convenience and economical effectiveness. Beam having large depth in comparison to span is called as deep beam. Various codes define the deep beams in a different way. For example, as per IS 456 [1], a beam is to be said as a deep beam if the effective span is less than or equals to twice the depth of the beam. Similarly, ACI 318 [2] defines the deep beam as a beam in which the ratio of effective span to depth is less than or equal to four. These beams are mainly used where the columns are placed closer and the load on the beam is too high, i.e. in transfer girders, foundation pile caps, shear walls etc. [[3], [4], [5]]. It is a fact that the failure mode of RC deep beam is completely different from RC slender beam. In case of RC slender beams, the failure is either flexural or shear or both. However, in case of RC deep beams, more brittleness is associated as compared to the RC slender beam [[6], [7], [8]]. Deep beams transfer heavy shear loads through the strut and tie mechanism to their supports. So, the stress distribution in the deep beam is nonlinear due to its load transferring mechanism as well as the geometry, which leads to shear failure. This failure is likely to occur suddenly and brittle in nature, which is unsafe and critical in constrast to flexural failure [8,9].

在近年，由于其便利性和经济效率，对于住宅和工业用途，钢筋混凝土（RC）深梁在高层建筑中的使用迅速增加。具有与跨度相比深度较大的梁被称为深梁。不同的规范以不同的方式定义深梁。例如，根据 IS 456 [1]，如果有效跨度小于或等于梁深度的两倍，则将梁称为深梁。同样，ACI 318 [2] 将深梁定义为有效跨度与深度之比小于或等于四的梁。这些梁主要在柱子放置较近且梁上的载荷极高的情况下使用，例如在转换桁架、基础桩帽、剪力墙等中。[[3], [4], [5]]。一个事实是，钢筋混凝土深梁的失效模式与钢筋混凝土细长梁完全不同。对于钢筋混凝土细长梁，失效要么是弯曲的，要么是剪切的，要么两者都有。然而，在钢筋混凝土深梁的情况下，与钢筋混凝土细长梁相比，更多的脆性相关联[[6], [7], [8]]。深梁通过束和系机制将重大的剪切载荷传递到其支撑点。 因此，深梁内部的应力分布是非线性的，这不仅因为其负载传递机制，还因为其几何形状，这导致了剪切破坏。这种破坏可能突然且脆性地发生，与弯曲破坏相比，这是不安全和关键的 [8,9]。（So, the stress distribution in the deep beam is nonlinear due to its load transferring mechanism as well as the geometry, which leads to shear failure.（因此，深梁内部的应力分布是非线性的，这不仅因为其负载传递机制，还因为其几何形状，这导致了剪切破坏。） This failure is likely to occur suddenly and brittle in nature, which is unsafe and critical in constrast to flexural failure [8,9].（这种破坏可能突然且脆性地发生，与弯曲破坏相比，这是不安全和关键的 [8,9]。））

Inclusion of web openings in such RC deep beams is often required for the installation of the essential services like air-conditioning, electricity and computer network pipes, water supply pipes, heating ducts, etc. [10,11]. But, these beams with web openings undergo decrease in their shear capacity and stiffness due to disrupt in the stress flow at the natural load path [[12], [13], [14]]. Some notable researches [[15], [16], [17]] on deep beams with web openings reveal that creation of web opening in deep beams leads to development of premature inclined crack and thereby reduces the shear strength and stiffness. Enlargement of such openings in the deep beam as per the demand would cause drastic reduction in its shear capacity, thus results in severe safety hazard [18,19]. If such enlargement is become unavoidable, suitable measures need to be taken to recover/regain the required strength. In this context, external strengthening system is an effective way to enhance/regain the required shear strength and stiffness of deep beams [20,21].

在这样的 RC 深梁中包含网络入口通常是为了安装诸如空调、电力和计算机网络管道、供水管道、供暖风道等必要的服务[10,11]。但是，带有网络入口的这些梁由于自然载荷路径中的应力流动被打断，其剪切能力和刚度会有所下降[[12], [13], [14]]。关于带有网络入口的深梁的一些著名研究[[15], [16], [17]]揭示，深梁中创建网络入口会导致过早形成倾斜裂缝，从而降低剪切强度和刚度。根据需求扩大这样的开口会导致深梁的剪切能力急剧下降，从而引发严重的安全风险[18,19]。如果这样的扩大成为不可避免的情况，需要采取适当的措施来恢复/恢复所需的强度。在此背景下，外部加固系统是提高/恢复深梁所需剪切强度和刚度的有效方法[20,21]。

Moreover, several researchers have investigated the behaviour of RC deep beams strengthened using externally bonded (EB) fibre reinforced polymer (FRP) composites due to their unique properties, such as high specific strength, resistance to fatigue and corrosion, and easy and rapid application on the concrete surface. Lee et al. [22], Jayed et al. [23] and Hussain [24] have reported various studies on the shear strengthening of RC deep beams using EB carbon fibre reinforced polymer (CFRP) composites. Similarly, Kumari et al. [25] and Kumari and Nayak [26] have studied the behaviour of RC deep beams strengthened with EB glass fibre reinforced polymer (GFRP) composites. The test results demonstrate that the external strengthening using FRP sheets/laminates is an excellent solution for RC deep beams to delay and/or control the crack propagation and to improve the shear strength, stiffness and ductility.

此外，几位研究人员已经研究了使用外部粘贴（EB）纤维增强聚合物（FRP）复合材料加固的 RC 深梁的行为，由于其独特的性质，如高比强度、抗疲劳和抗腐蚀性，以及在混凝土表面易于快速应用。Lee 等人[22]、Jayed 等人[23]和 Hussain[24]报告了使用 EB 碳纤维增强聚合物（CFRP）复合材料加固 RC 深梁的剪切增强的各种研究。同样，Kumari 等人[25]和 Kumari 和 Nayak[26]研究了使用 EB 玻璃纤维增强聚合物（GFRP）复合材料加固的 RC 深梁的行为。测试结果表明，使用 FRP 片材/层压板的外部加固是 RC 深梁延迟和/或控制裂缝传播以及提高剪切强度、刚度和延性的优秀解决方案。

In contrast, very limited works are available in the literature on the shear strengthening of RC deep beams with web openings using EB-FRP composites. EI-Maaddawy and Sherif [27] have investigated the effectiveness of EB-CFRP sheets on RC deep beams with web openings. The test results reveal that the gain in strength due to EB-CFRP sheets on deep beams having web openings is up to 73%. Kumar [28] has investigated the influence of EB-GFRP sheets on strengthening of RC deep beams without shear reinforcements having web openings. It is found that EB-GFRP has significant effect on improving the shear capacity. Hussain and Pimanmas [29] have reported that the use of sprayed glass fibre reinforced polymer (SGFRP) composites in RC deep beams with web openings increases the shear strength significantly.

相比之下，关于使用 EB-FRP 复合材料加固 RC 深梁中设有翼缘开口的剪切增强，文献中可获取的资料非常有限。EI-Maaddawy 和 Sherif [27] 研究了 EB-CFRP 薄片对设有翼缘开口的 RC 深梁的增强效果。实验结果表明，EB-CFRP 薄片对设有翼缘开口的深梁的强度提升可达 73%。Kumar [28] 研究了 EB-GFRP 薄片对无剪切增强且设有翼缘开口的 RC 深梁加固效果的影响。研究发现，EB-GFRP 对提高剪切能力有显著效果。Hussain 和 Pimanmas [29] 报道，使用喷涂玻璃纤维增强聚合物（SGFRP）复合材料在设有翼缘开口的 RC 深梁中，显著提高了剪切强度。

The above investigations show that the shear strength of FRP strengthened RC deep beams with/without web openings can be substantially increased. However, the failure of such strengthened beams often occurs through the areas of high stress concentration, which indicates the de-bonding failure [[27], [28], [29]]. As a result, the FRP can't be fully utilised for strength enhancement in the strengthened beams. Therefore, a proper anchoring/fastening technique is required to arrest or delay the premature de-bonding of FRP due to which FRP can be fully utilised for strength enhancement.

上述研究显示，FRP 加固的 RC 深梁（有/无翼缘开口）的剪切强度可以显著增加。然而，这种加固梁的失效往往发生在应力集中的区域，这表明了脱粘失效[[27]，[28]，[29]]。因此，结果表明，FRP 在加固梁中的强度增强潜力未能充分利用。因此，需要适当的锚固/固定技术来阻止或延迟 FRP 过早脱粘，从而使得 FRP 能够完全用于强度增强。

In the current decade, few techniques are developed to provide sufficient anchorage over the FRP strengthened surface; which prevent the premature failure due to de-bonding of the FRP, enhances the shear strength substantially and can create some amount of ductility. Soleimani and Banthia [30] have implemented an anchoring technique by means of bolts and nuts so as to prevent the premature bond failure between the SGFRP and concrete in RC beams. Moreover, Hussain and Pimanmas [24] have carried out an experimental investigation to study the effectiveness of various anchorage techniques, i.e. through bolt, epoxy bolt and mechanical expansion bolt arrangement on sprayed fibre reinforced polymer (SFRP) strengthened deep beams. It is reported that all these anchoring techniques can effectively upgrade the shear strength of deep beams by delaying the SFRP de-bonding. The same authors [29] have verified the effectiveness of mechanical bolt anchoring system in the SGFRP strengthened RC deep beams with web openings made up of both high and low strength concrete. More recently, Kumari and Nayak [26] have performed an experimental approach to investigate the influence of both EB-GFRP fabrics and gas actuated fasteners (GAF) on the strengthening of shear deficient solid deep beams. It is observed that this technique substantially improves the interface bonding between concrete and EB-GFRP, which delays the de-bonding process and also shows its potentiality in enhancing the shear capacity of the deep beams up to 55%.

在当前十年中，很少有技术能够提供足够的粘结力于 FRP 加固表面，防止由于 FRP 脱胶而导致的过早失效，显著增强剪切强度，并能产生一定程度的延性。Soleimani 和 Banthia [30]通过使用螺栓和螺母实施了一种粘结技术，以防止 SGFRP 和混凝土在 RC 梁中的过早粘结失效。此外，Hussain 和 Pimanmas [24]进行了一项实验研究，以研究各种粘结技术的有效性，例如通过螺栓、环氧螺栓和机械扩张螺栓排列在喷射纤维增强聚合物（SFRP）加固深梁上的效果。据报道，所有这些粘结技术都能有效地通过延迟 SFRP 脱胶来提高深梁的剪切强度。同一作者 [29]验证了机械螺栓锚固系统在 SGFRP 加固的 RC 深梁中的有效性，这些深梁的翼板开口由高强和低强混凝土制成。 更近一些时候，Kumari 和 Nayak [26] 采用实验方法来研究了增强纤维预浸料（EB-GFRP）织物和气体驱动快速紧固件（GAF）对剪切不足的深梁加固的影响。观察到，这种方法显著提高了混凝土与 EB-GFRP 之间的界面粘结，延缓了脱粘过程，并且显示了其在提高深梁剪切能力方面至多可达 55%的潜力。

From the above review of literature, it is found that the creation of web opening decreases the ultimate strength capacity and stiffness of a deep beam drastically. The above reduction in strength and stiffness can be regained to a large extent by strengthening these beams using EB-FRP and anchoring system. But is worth mentioning that very limited research works are carried out on shear strengthening of RC deep beams with web openings using EB-FRP and anchors. Till date, only one research work on the strengthening of RC deep beams with web openings has been carried out using the SGFRP composites and mechanical bolt anchors [29]. As it is a new area having many advantages and its behaviour is not completely known, a thorough knowledge in this subject is very much required for practical applications in construction sector, which needs further research works in this field.

从上述文献回顾中发现，创建网络入口会大幅度降低深梁的最终强度能力和刚度。通过使用 EB-FRP 和锚固系统加强这些梁，可以很大程度上恢复强度和刚度。但值得注意的是，关于使用 EB-FRP 和锚固系统对具有网络入口的 RC 深梁进行剪切加强的研究工作非常有限。到目前为止，仅有一项研究工作使用 SGFRP 复合材料和机械螺栓锚固对具有网络入口的 RC 深梁进行了加强 [29]。这是一个具有许多优点的新领域，其行为尚未完全了解，因此在建筑领域中进行实际应用需要对这个主题有深入的了解，这需要在这个领域进行更多的研究工作。

In order to fill the above research gap, an endeavour is made to study the shear strengthening of RC deep beams having circular and square web openings of different sizes using EB-GFRP fabrics and mechanical anchors with gas actuated fastening system as GFRP fabric is cheap, easily available in market and economical for moderate loading and the gas actuated fastening system is very ease, economical, speedy and effective [26]. The present study is divided in to two heads, i.e. strengthening of deep beam with web openings using (i) EB-GFRP fabrics throughout the beam length and (ii) using both the EB-GFRP fabrics and gas actuated fasteners at shear spans only. In this investigation, the major parameters, such as cracking pattern, shear strength, failure modes, load versus deflection behaviour, stiffness, ductility and energy absorption, are studied with respect to different sizes and shapes of web openings and strengthening techniques in order to arrive at meaningful conclusions. In addition, a comparison of shear strength of the GFRP strengthened RC deep beams with web openings is also made between the experimental results and the results computed from various models available in the past works.

为了填补上述研究空白，本研究旨在使用 EB-GFRP 织物和气体驱动紧固系统作为机械锚固，研究具有不同尺寸圆形和方形腹板开口的 RC 深梁的剪切增强。由于 GFRP 织物价格低廉、市场易得且对于中等载荷经济实惠，气体驱动紧固系统非常简便、经济、快速且有效[26]。本研究分为两部分，即（i）在整个梁长使用 EB-GFRP 织物增强深梁的腹板开口，和（ii）仅在剪切跨度上使用 EB-GFRP 织物和气体驱动紧固件进行增强。在本研究中，主要研究了开裂模式、剪切强度、破坏模式、载荷与位移行为、刚度、延性和能量吸收等参数，针对不同尺寸和形状的腹板开口以及增强技术，以得出有意义的结论。 此外，还将过去工作中可用的各种模型计算的结果与实验结果进行了比较，以评估增强的钢筋纤维增强复合材料(RCF)深梁翼缘开口处的剪切强度。

## 2. Experimental investigation

2. 实验研究 (2. Experimental investigation)

### 2.1. Material properties 2.1. 材料属性 (2.1. Material properties)

#### 2.1.1. Cement 2.1.1. 水泥

Portland slag cement (PSC) is used as the binding material for the preparation of RC deep beams with web openings. The various physical properties of cement are obtained from the standard tests conducted in the concrete laboratory as per IS specifications [[31], [32], [33], [34], [35]]. The test results of the same along with the standard tests conducted are presented in Table 1, which conform to the specifications of PSC as per IS 455 [36].

波特兰火山灰水泥(PSC)被用作准备具有翼缘开口的 RC 深梁的粘结材料。水泥的各种物理性质从按照 IS 规范在混凝土实验室进行的标准测试中获得[[31], [32], [33], [34], [35]]。相同测试结果以及进行的标准测试结果在表 1 中呈现，符合 PSC 的 IS 455 规范[36]。

Property Property (财产) | Results 结果 | Specified limit as per IS:455 [36] 指定限制根据 IS:455 [36] (Specified limit according to IS:455 [36]) | Code specifying test procedure 代码规定了测试程序（Code specifying test procedure） |
---|---|---|---|

Specific gravity 密度 (róngdù) | 3.14 | – | IS: 4031 (Part 11) [31] IS: 4031 (Part 11) [31] (这部分翻译成中文是：4031 (第 11 部分) [31]) |

Specific surface 特定表面 (Tèdìng miànbāng) | 3200 cm^{2}/gm 3200 cm (3200 厘米) ^{2} /gm (每克) | Min. limit-2250cm^{2}/gm最小限制-2250cm ( ^{2} /gm) | IS: 4031 (Part 2) [32] IS: 4031 (Part 2) [32] (这部分是 4031 的第二部分，编号为 32) |

Standard consistency 标准一致性 (Standard consistency) | 30% | – | IS: 4031 (Part 4) [33] IS: 4031 (部分 4) [33] |

Initial setting time 初始设置时间 (Initial setting time) | 150min 150 分钟 (150 minutes) | Min. limit: 30min 最小限制：30 分钟 | IS: 4031 (Part 5) [34] 翻译以下文本为中文。对于每一句，将其分割成更小、更合理的部分，分别单独翻译每一部分，并将翻译后的部分放在原始部分后面（）。最后，将每句话翻译后的部分连接成一个句子。 IS: 4031 (Part 5) [34] |

Final setting time 最终设置时间 (Final setting time) | 300min 300 分钟 (300 minutes) | Max. limit: 600min 将以下文本翻译成中文。对于每一句，将其分割成更小、更合理的部分，分别单独翻译每一部分，并将翻译后的部分放在原始部分之后（括号内）。最后，将每句话翻译后的部分连接成一个完整的句子。 最大限制：600 分钟 | |

Strength of cement mortar 水泥砂浆的强度 | IS: 4031 (Part 6) [35] 翻译以下文本为中文。对于每一句，将其分割成更小、更合理的部分，分别单独翻译每一部分，并将翻译后的部分放在原始部分后面（）。最后，将每句话翻译后的部分连接成一个句子。 IS: 4031 (Part 6) [35] | ||

3 days 三天 (Sān tiān) | 17.04 MPa 17.04 MPa (17.04 兆帕) | Min. limit −16.0 MPa 最小限制 -16.0 MPa (Minimum limit -16.0 MPa) | |

7 days 7 天 | 23.10 MPa 23.10 MPa (23.10 兆帕) | Min. limit −22.0 MPa 最小限制 -22.0 MPa (Minimum limit -22.0 MPa) | |

28 days 28 天 (28 days) | 35.00 MPa 35.00 兆帕 (35.00 Mpa) | Min. limit −33.0 MPa 最小限制 -33.0 MPa (Minimum limit -33.0 MPa) |

#### 2.1.2. Aggregates 2.1.2. 集合 (2.1.2. Aggregates)

Locally collected granite stone crushed into uniformly graded aggregates of 10 mm and 20 mm nominal size are used as the coarse aggregates (CA). Sand obtained from river bed is utilised as the fine aggregate (FA). According to IS 2386 part 1 [37], the sieve analysis is conducted for the above mentioned aggregates. The outcomes of the sieve analysis, as shown in Fig. 1, Fig. 2, show that the aggregates used here satisfy the requirements of IS 383 [38]. The physical and mechanical properties of these aggregates are evaluated according to IS 2386 part 3 [39] and IS 2386 part 4 [40], respectively and the outcomes of the same along with the methods are furnished in Table 2. The results in Table 2 indicate that the properties of both the aggregates are falling within the specified limits of IS 383 [38].

当地收集的花岗岩碎石，被破碎成 10 毫米和 20 毫米的名义均匀分级集料，作为粗集料（CA）使用。从河床获取的沙子被用作细集料（FA）。根据 IS 2386 第 1 部分[37]，对上述集料进行筛分分析。筛分分析的结果，如图 1、图 2 所示，表明这里使用的集料满足 IS 383[38]的要求。这些集料的物理和力学性质根据 IS 2386 第 3 部分[39]和 IS 2386 第 4 部分[40]分别进行评估，结果以及方法在表 2 中提供。表 2 的结果表明，两种集料的性质均在 IS 383[38]规定的范围内。

Property | FA | CA | Specified limit as per IS:383 [38] | Code specifying test procedure | |
---|---|---|---|---|---|

20 mm max. size | 10 mm max. size | ||||

Specific gravity | 2.63 | 2.74 | 2.70 | – | |

Water absorption | 0.9% | 0.6% | 0.57% | – | |

Free surface moisture | Nil | 0.4% | 0.38% | – | |

Bulk density | IS:2386 (part 3) [39] | ||||

Loose | 1480 kg/m^{3} | 1310 kg/m^{3} | 1340 kg/m^{3} | – | |

Compacted | 1598 kg/m^{3} | 1511 kg/m^{3} | 1550 kg/m^{3} | – | |

Impact value | – | 15.45% | 22.00% | Max. limit: 45% | IS:2386 (part 4) [40] |

Abrasion value | – | 18.67% | 21.22% | Max. limit: 50% | |

Crushing value | – | 16.41% | 19.12% | Max. limit: 45% |

#### 2.1.3. Steel

Fe500 grade high yield strength deformed (HYSD) steel of 8 mm and 12 mm diameter is used for preparation of all the deep beam specimens. A 100T capacity universal testing machine (UTM) is considered for the tensile test of steel bars. The procedure followed is as per IS 1786 [41]. Accordingly, the outcomes of the tensile test i.e. average yield stress, ultimate stress and maximum elongation for 8 mm diameter bars are found to be 507.4 MPa, 667.0 MPa and 20%, respectively, and for 12 mm diameter bars the corresponding properties of steel are found to be 525.3 MPa, 620.0 MPa and 20%, which indicate that the Fe500 steel used here satisfies the specifications of the above code.

#### 2.1.4. GFRP fabrics

In this investigation, 0.275 mm thick bi-directional GFRP fabrics made with sewed glass fibres is used for shear strengthening of all specimens. The binder/matrix materials used are epoxy (Lapox L-12) and hardener (K-6) in the ratio 9:1. Three numbers of GFRP coupons are fabricated by binding the GFRP fabric with the binder/matrix material by hand lay-up technique and tested in a 100 kN UTM (INSTRON) as per the specifications of ASTM D 7565–10 [42]. From the coupon test, the mean ultimate load, load at failure, ultimate stress, stress at failure, elongation at ultimate load, elongation at failure, ultimate strain, strain at failure and Young's modulus of the GFRP coupons are obtained as 20.40 kN, 20.35 kN, 290.61 MPa, 289.86 MPa, 3.66 mm, 3.67 mm, 2.44%, 2.45% and 16.07 GPa, respectively. The prepared GFRP coupon with the failure photograph and the tensile stress versus strain graph obtained from the INSTRON are depicted in Fig. 3.

### 2.2. Test specimen

In this study, total 19 numbers of RC deep beams having circular/square web openings, designed as per IS 456 [1], are prepared including one control solid deep beam. The dimensions of all beams are same, i.e. 1000 mm length, 120 mm × 420 mm in cross-section. These beams are tested under two-point symmetrical loading. Four numbers of tensile reinforcement of 12 mm Ø and two numbers of hang up bars of 8 mm Ø are provided at the bottom and top, respectively. The web reinforcement is consisting of five numbers of 2-legged vertical stirrups and four numbers of horizontal bars of 8 mm Ø steel bars. Excluding the control solid beam, the other beams are having two circular/square openings of different dimensions with one opening in each of the shear spans. The web openings are placed in such a way that each opening is placed symmetrically about the midpoint of the shear span to disrupt the natural load path, which is an imaginary line connecting the support and the loading points. The shear reinforcements intercepted by the opening are cut prior to preparation of RC deep beam specimens. The diameters of circular openings are 100 mm, 150 mm and 200 mm. Similarly, the dimensions of square openings are 100 mm × 100 mm, 150 mm × 150 mm, 200 mm × 200 mm. Fig. 4 indicates the photograph of reinforcement detailing of RC deep beams with web openings.

The concrete mix of M20 grade is designed as per the specifications of IS 10262 [43]. The detail quantities of different ingredients per metre cube concrete are calculated as 380 kg of cement, 700 kg of fine aggregate, 1220 kg of coarse aggregate and 205 kg of water. The beams are prepared by keeping the plywood mould in a horizontal position. Three numbers of concrete cubes of standard size of 150 mm for each mix are prepared to obtain the 28days compressive strength. All the specimens are immersed in normal clean municipality tap water for curing up to 28 days. The curing water is maintained at a temperature of 27 $\pm $ 2 °C throughout the curing period.

Out of the 18 deep beams with web openings (excluding one solid control beam), nine beam specimens are prepared with circular web openings of 100 mm, 150 mm and 200 mm diameters and divided in to three groups designated as A, B and C, respectively. The *a/D* ratios for the groups A, B and C are 0.23, 0.35 and 0.47, respectively, where *a* is the opening size and *D* is the overall depth of the beam. Similarly, the remaining nine beams are prepared with square web openings of 100 × 100mm, 150 × 150mm and 200 × 200mm and divided in to three groups D, E and F, respectively The *a/D* ratios for these groups are 0.23, 0.35 and 0.47, respectively. Each group, as mentioned above, consists of three beams of equal size (*a*) of openings. It is to note that for all the beams the effective shear span to depth ratio (*x/D*) is kept constant, i.e. 0.74.

### 2.3. Methods for GFRP fabrics strengthening

For strengthening of the beams with EB-GFRP fabrics, at first the surface of the beam is abraded by rubbing with the sandpaper. The surfaces are then cleaned to make them dirt-free or to remove the loose particles that may be obstruct perfect bonding. Thereafter, the concrete surfaces are coated with a uniformly thick layer of the binder. The GFRP fabric, pre-cut to required size, is then placed in U-shape over the binder coating. A hand roller is used to make sure that the binder fully penetrates into the open spaces of fabric and also squeezes out the excess resin and air bubbles without folding or stretching the fabric excessively. In the similar manner, two additional layers are placed one upon another followed by binder coating to obtain the three stacking layers of GFRP fabric. Finally, a coat of binder is provided on the uncovered surface.

In each group, i.e. from A to F, one beam is kept as it is and termed as the un-strengthened beam whereas the second specimen in each group is strengthened with three layers of U-wrapped EB-GFRP fabrics throughout the beam length. However, the third beam in each group is wrapped with three layers of U-shaped GFRP fabrics at both the shear spans, but not throughout the beam length like the former one. Finally, the deep beams strengthened with GFRP fabrics are allowed for air curing at normal room temperature for 7 days. Schematic diagram of the patterns of GFRP wrapping in deep beams with web openings is indicated in Fig. 5.

### 2.4. Methods for GAF technique

In this study, high performance GAF is used to fasten the GFRP fabrics securely to the concrete surface. It is to note that the last beam in each group is to be strengthened with both EB-GFRP fabrics and GAF at shear spans only. The GFRP fabrics are already attached to the shear spans of the beam as mentioned in the previous section. Then, the GFRP fabrics are fastened with GAF technique. The GAF system consists of mechanical fasteners of 28 mm length with head diameter of 6 mm designated as GAF-28, a gas actuator fastening gun and prepared aluminium small square plates having cross section of 25 mm × 25 mm and thickness of 2 mm. To avoid tearing of the fibre at the contact points of GFRP and fasteners as well as to distribute the load intensity over a larger area, aluminium plates are placed on the top of the GFRP fabrics in a linear pattern at a spacing of 90 mm in both vertical and horizontal directions. The gas actuator fastening gun is used to shoot the GAF-28 into the GFRP fabrics and concrete. Table 3 presents the detail description of the test specimens. Photographs showing the details of GAF-28 installation are furnished in Fig. 6.

Group | Specimen | Shape of web opening | Size of web opening (mm) | Concrete cube strength (MPa) | Strengthening configuration of GFRP fabrics | Strengthening configuration of mechanical fasteners |
---|---|---|---|---|---|---|

Solid beam | DB-NS | – | – | 27.80 | – | – |

A | C-100-NS | Circular | 100 | 27.65 | – | – |

C-100-FS | 100 | 27.65 | Continuous U-wrap | – | ||

C-100-FAS | 100 | 27.65 | U-wrap at shear span | GAF-28 | ||

B | C-150-NS | 150 | 28.20 | – | – | |

C-150-FS | 150 | 28.20 | Continuous U-wrap | – | ||

C-150-FAS | 150 | 28.20 | U-wrap at shear span | GAF-28 | ||

C | C-200-NS | 200 | 27.80 | – | – | |

C-200-FS | 200 | 27.80 | Continuous U-wrap | – | ||

C-200-FAS | 200 | 27.80 | U-wrap at shear span | GAF-28 | ||

D | S-100-NS | Square | 100 × 100 | 27.55 | – | – |

S-100-FS | 100 × 100 | 27.55 | Continuous U-wrap | – | ||

S-100-FAS | 100 × 100 | 27.55 | U-wrap at shear span | GAF-28 | ||

E | S-150-NS | 150 × 150 | 27.65 | – | – | |

S-150-FS | 150 × 150 | 27.65 | Continuous U-wrap | – | ||

S-150-FAS | 150 × 150 | 27.65 | U-wrap at shear span | GAF-28 | ||

F | S-200-NS | 200 × 200 | 27.20 | – | – | |

S-200-FS | 200 × 200 | 27.20 | Continuous U-wrap | – | ||

S-200-FAS | 200 × 200 | 27.20 | U-wrap at shear span | GAF-28 |

It is to note that the fasteners/anchors used in the existing literature [29] are mechanical expansion bolt for strengthening of RC deep beams with web openings. However, compared to the GAF technique, mechanical expansion bolt anchors have the disadvantages such as time consuming process, require more physical effort and high-priced whereas GAF technique has the advantages such as time saving process, require minimal effort and low-priced. Furthermore, high penetrability of fasteners, easy operated gas actuator gun and simple installation process turn them into a good fastening system for anchoring in FRP composites. Moreover, this method is practicable for solid deep beams, slender beams and columns etc. Therefore, the author endeavours to use the new GAF technique in the present investigation. It is found that the research related to use of GAF system for strengthening of deep beam is limited [26].

### 2.5. Test setup

All the 19 beams are tested in a digital UTM with a maximum capacity of 100T. The specimens are so placed that the effective span distance between the two end supports was 825 mm. Bearing plates of 20 mm thick, 75 mm width and 120 mm long are placed under each loading and support points to avoid bearing failure. Then the I-section is placed to transfer the applied load to the deep beams through the two-point loading arrangement. Testing is conducted at a constant rate of loading of 10 kN/min. The deflections of the beam specimens corresponding to different loads are measured at *L*/4, *L*/2 and 3*L*/4 from the left support using a dial gauge, where *L* is the distance between the centres of two supports. The development and propagation of crack, de-bonding of GFRP fabrics, pull-out of GAF-28 and failure modes are monitored during the increase of load at regular load intervals. Details of the cracking, failure mode and shear strength, load versus deflection and stiffness of all the test specimens are discussed in the succeeding section.

## 3. Results and discussion

The experimental values of the first cracking load of all the un-strengthened beams, load at de-bonding/de-lamination of all the strengthened beams, percentage increases in the de-bonding loads as compared to the cracking loads of the respective un-strengthened beams, ultimate load of all the beams and percentage increase in ultimate load of the strengthened beams corresponding to the un-strengthened counterpart beams, mid span deflection corresponding to the ultimate load and maximum deflection at failure of all the beams are presented in Table 4. The cracking behaviour, failure modes, shear strength, load versus deflection behaviour and stiffness of un-strengthened beams, EB-GFRP strengthened beams and EB-GFRP strengthened beams anchored with GAF are discussed critically in the succeeding sections to derive meaningful conclusions.

Group | Specimen | Cracking/de-bonding load^{a} (kN) | Increase in cracking/de-bonding load as compared to the respective un-strengthened Beam (%) | Ultimate load (kN) | Increase in ultimate load as compared to the respective un-strengthened beam (%) | Mid span deflection at ultimate load (mm) | Maximum deflection (mm) |
---|---|---|---|---|---|---|---|

Solid beam | DB-NS | 300.00 | – | 400.60 | – | 11.20 | 14.80 |

A | C-100-NS | 170.00 | – | 294.80 | – | 8.70 | 9.50 |

C-100-FS | 310.00 | 82.35 | 385.70 | 30.83 | 9.30 | 11.00 | |

C-100-FAS | 360.00 | 111.76 | 405.00 | 37.38 | 10.20 | 12.67 | |

B | C-150-NS | 120.00 | – | 219.10 | – | 8.90 | 11.60 |

C-150-FS | 210.00 | 75.00 | 271.75 | 24.03 | 9.90 | 13.78 | |

C-150-FAS | 240.00 | 100.00 | 300.50 | 37.15 | 10.80 | 14.25 | |

C | C-200-NS | 90.00 | – | 152.45 | – | 9.95 | 12.00 |

C-200-FS | 150.00 | 66.66 | 187.50 | 22.99 | 10.20 | 14.00 | |

C-200-FAS | 155.00 | 77.77 | 200.00 | 31.19 | 10.79 | 14.68 | |

D | S-100-NS | 130.00 | – | 226.50 | – | 7.70 | 10.09 |

S-100-FS | 210.00 | 61.53 | 309.20 | 36.51 | 9.40 | 12.75 | |

S-100-FAS | 290.00 | 123.07 | 371.35 | 63.95 | 10.50 | 13.80 | |

E | S-150-NS | 100.00 | – | 183.05 | – | 8.60 | 11.00 |

S-150-FS | 150.00 | 50.00 | 206.90 | 13.02 | 9.00 | 12.90 | |

S-150-FAS | 170.00 | 70.00 | 244.05 | 33.32 | 10.40 | 14.37 | |

F | S-200-NS | 60.00 | – | 110.00 | – | 9.10 | 12.10 |

S-200-FS | 95.00 | 58.33 | 134.85 | 22.59 | 10.00 | 14.10 | |

S-200-FAS | 110.00 | 83.33 | 146.10 | 32.81 | 10.75 | 14.75 |

- a
By visualisation, for all the strengthened beams de-bonding load is the initial de-lamination of fabrics.

### 3.1. Cracking behaviour

When the load is applied gradually to the un-strengthened solid deep beam DB-NS, the initial diagonal crack is found at the shear span at 150 kN load. When load increases further, the diagonal crack becomes wider in the shear zone propagating towards the loading and support points. The propagation of this crack divides the deep beam in two parts along a line joining the loading and support points, i.e. the position of the shear crack is along the diagonal compression strut region (Fig. 7).

The beginning of the inclined cracks shows the similar trend for the un-strengthened deep beams with web openings in all groups. The diagonal cracks appear at top and bottom portions of circular openings and at the opposite corners of square openings with the increase in the applied load as indicated in Fig. 8. When applied load increases further, the existing cracks get wider and propagate towards the support and loading points. Referring Table 4, it is found that the size and shape of opening has significant effects on the cracking load of un-strengthened beams. It is also noticed that the increase in the opening sizes (*a/D*) for both the circular and square openings from 0 to 0.47 reduces the cracking load significantly. The same trend is also reported in the previous works [27,29], i.e. when the size of opening increases the cracking load decreases. The cracking loads for the un-strengthened beams having circular openings are found to be higher than that for the beams having square openings (Table 4). This could be because the stress concentration is uniform throughout the perimeter of web openings in the circular opening, whereas in the square opening the stress concentration is more at the four corners.

For the beams strengthened with GFRP fabrics throughout the beam length in all groups, the cracking load could not be recorded due to the presence of EB-GFRP fabrics on the concrete surface. However, the de-bonding load, i.e. the load arrived at the initiation of bond failure between GFRP fabrics and concrete, is recorded (Table 4). With the increase in the load, the de-bonding failure is observed with a distinguishable sound, which is progressive till the final shear failure as shown in Fig. 9. Consequently, the shear cracks of these beams appear under the wrap are propagated towards the support and loading points. It is also observed that these cracks are less prominent than those of the shear cracks found in the un-strengthened counterpart beams.

Furthermore, in all groups for the beams strengthened with both EB-GFRP fabrics and GAF-28, the load corresponding to pull-out of the fasteners as well as the tearing of GFRP fabrics is recorded (Table 4). The load corresponding to the initiation of pull-out of fasteners is considered as the de-bonding load. The increase in the opening size reduces the de-bonding load (Table 4). Fig. 10 represents the failure modes of these beams.

From the above discussion, it is inferred that the increase in the opening size for both the circular and square openings of un-strengthened, GFRP strengthened and mechanically fastened GFRP strengthened beams reduces the de-bonding load significantly. In contrast, strengthening of these deep beams using EB-GFRP fabrics and both the EB-GFRP fabrics and GAF-28 delays the de-bonding and hence, de-bonding load increases to a larger extent, i.e. 82.35% for GFRP and 111.76% for both GFRP and GAF-28, having circular openings; and 61.53% for GFRP and 123.07% for both GFRP and GAF-28 having square web openings. It is worth mentioning that for all the cases, diagonal cracks develop beneath the GFRP fabrics, which propagate along the diagonal compression-strut region in the shear span.

### 3.2. Failure mode

All the 19 beams, i.e. the un-strengthened solid deep beam, the un-strengthened beams with web openings, the GFRP strengthened beams with web openings and the strengthened beams with web openings using EB-GFRP and GAF, have exhibited shear failure. The distinctive shear failure of solid deep beam DB-NS is observed due the development and propagation of inclined shear crack at the shear span (Fig. 7). Fig. 8 represents the crack propagation and failure mode of all the un-strengthened deep beams with respect to the variation in the size and shape of the web openings. The crack patterns above and below the openings are alike for all the un-strengthened beams with web openings.

The cracks in all these un-strengthened beams occur first at the opposite top and bottom portion of circular openings and extreme right top corners and extreme left bottom corners of the square openings and then propagate towards the loading and support points simultaneously with the increase in load. The post-cracking failure modes are mainly influenced by the size of the opening for both the types of web openings. In the un-strengthened specimens of Groups A and D having opening sizes 100 mm diameter and 100 × 100mm, respectively, i.e. *a/D* = 0.23, the primary cracks, developed and then propagated, are shown in Fig. 8 (a) and 8 (d), respectively. When the size of the web opening increases up to 150 mm diameter for circular opening in Group B and up to 150 × 150mm for square opening in Group E (*a/D* = 0.35), comparatively more pronounced shear cracks develop at top/bottom portion of the circular openings and at the opposite corners of the square openings. Thereafter, these cracks propagate and reach to the tensile reinforcement as shown in Fig. 8 (b) and 8 (e) for circular and square openings, respectively. For the un-strengthened beams of Groups C and F (*a/D* = 0.47), i.e. for the beam with circular openings of 200 mm diameter and beam with square opening of 200 × 200mm, distinctive wide shear cracks and additional cracks at the vertical sides adjacent to the openings are developed and propagated as shown in Fig. 8 (c) and 8 (f), respectively. It is because the openings of these beams are very large and disrupt the stress flow at the natural load path (line connecting the support and loading points) significantly, which causes widening and rapid progress of the shear crack.

It is worth to note that the similar trend is reported in the previous works [27,29]. EI-Maaddawy and Sherif [27] and Hussain and Pimanmas [29] have also conducted the experimental investigation on deep beams having web openings and reported that the first crack and failure mode for the deep beams with web openings are largely influenced by the opening size, shape, position and interception of the natural load path connecting the support and loading points, as in the case of present investigation.

The failures of all the GFRP strengthened beams start due to de-bonding of GFRP fabrics. As the load increases, an audible sound is observed indicating GFRP de-bonding from the concrete surface. The failures of the GFRP strengthened beams of Groups A, B, D and E, i.e. for the beams C-100-FS, C-150-FS, S-100-FS and S-150-FS, occur due to de-bonding of GFRP involving peeling of the concrete followed by diagonal cracks at the opening corners. For the above beams, regardless of the opening sizes, less pronounced shear cracks are observed at both the top and bottom corners of openings under the GFRP wrap as compared to the cracks developed in the counterpart un-strengthened beams with web openings. The failure of the beams C-200-FS and S-200-FS of Groups C and F, i.e. the beams with higher opening size (*a/D* = 0.47), starts due to de-bonding of GFRP fabrics and thereafter wide diagonal cracks at both the top and bottom parts of the opening are developed leading to complete failure. For these beams, comparatively distinct and more pronounced shear cracks with appreciable damage in the concrete at the top and bottom sides of the openings are observed. In order to verify the shear cracks of all the GFRP strengthened beams, the GFRP fabrics are separated from each beam surface. These beams with shear cracks are shown in Fig. 9. It is found that the failure modes are strongly influenced by the EB-GFRP fabrics wrapped throughout the beam length.

For the beams strengthened with both the EB-GFRP fabrics and GAF-28, failure starts with pull-out of the fasteners from concrete surface. It is observed that for the beams of Groups A, B, D and E, i.e. for the beams C-100-FAS, C-150-FAS, S-100-FAS and S-150-FAS, respectively (having *a/D* ratio of 0.23 and 0.35), the failure occurs by fastener pull-out at the extreme top corner followed by GFRP de-bonding (Fig. 10a, b, 10d and 10e). The failures of these beams are initiated with the fastener pull-out, then de-bonding of GFRP and finally leading to the complete shear failure. However, for the beams with higher opening size (*a/D* = 0.47), failure starts by fastener pull-out, tearing of GFRP and then de-bonding of GFRP. In the beams C-200-FAS and S-200-FAS, the tearing of GFRP is observed followed by fastener pull-out near the openings prior to complete shear failure of the beams as shown in Fig. 10(c) and (f). Since, the web opening is comparatively large for the above beams than other beams, the bond demand imposed between GFRP fabrics and concrete surface exceeds the fastener pull-out capacity and therefore starts tearing of GFRP. It is worth to note that less quantity of GFRP around the openings of these beams causes rupture in GFRP at the top and bottom edge of the openings followed by diagonal tension failure with an inclined shear crack under the GFRP wrap. This change in the failure modes in comparison to the GFRP strengthened beams is due to the application of the GAF technique. Moreover, the strengthening using both GFRP fabrics and GAF delays the de-bonding of GFRP prior to full utilisation of GFRP strength as these combinations of strengthening do not allow the complete pull-out of the fasteners.

From the above discussion, it is inferred that the failure of the un-strengthened beams having web openings occurs due to development of two independent inclined cracks at the opposite top and bottom corners of web opening. However, the failure of the EB-GFRP strengthened beams initiates due to the de-bonding of GFRP fabrics from the concrete surface and then the complete failure occurs due to development of wide inclined cracks at the corners of openings under GFRP wrap. On the other hand, the failure mode of the beams having large openings (*a/D* = 0.47) and strengthened with GFRP and GAF, is a combination of pull-out of fasteners, tearing of GFRP fabrics and de-bonding of GFRP fabrics leading to the diagonal tension failure due to development of inclined crack at the corners of openings under the GFRP wrap. But, for the beams with small openings (*a/D* = 0.23 and 0.35) and strengthened with GFRP and GAF, the failure is associated with fastener pull-out and de-bonding of GFRP fabric, but not tearing of GFRP fabrics as in the former case, followed by diagonal tension failure due to development of inclined crack at the corners of openings under the GFRP wrap.

### 3.3. Shear strength

The shear strength is the transverse load in each shear span, i.e. the half of the total ultimate load in the present study. The shear strength of the un-strengthened solid deep beam DB-NS is 200.3 kN. It is considered as the reference in order to analyse the effect of the web openings in the deep beams and also to evaluate the reduction in the shear strength of the un-strengthened beams due to inclusion of web openings, which can be compensated by strengthening these beams with EB-GFRP fabrics or EB-GFRP fabrics and GAF. The variation in the shear strength of the un-strengthened beams, EB-GFRP fabrics strengthened beams and beams strengthened with both EB-GFRP fabrics and GAF with respect to the size of web openings are depicted in Fig. 11. It is found from this figure that the shear strength of un-strengthened deep beams with the openings in all groups is significantly reduces as compared to that of the un-strengthened solid deep beam. Moreover, as the opening size increases from 0 to 0.47, it reduces the shear strength drastically for both the un-strengthened and strengthened beams having circular/square web openings. The similar trend is reported in the past works on shear strengthening of deep beams with web openings [27,29]. The un-strengthened beams with square openings exhibits higher strength reductions as compared to those of the un-strengthened beams with circular openings. It is because of the fact that the stress concentration is high at the corners of square openings than along the periphery of the circular openings. Consequently, the presence of square openings causes quick propagation of the shear cracks and hence, exhibits lower strength. From Fig. 11, it is depicted that when *a/D* ratio increases, the reductions in shear strength for circular openings with *a/D* of 0.23, 0.35 and 0.47 are 26.41%, 45.30% and 61.94%, respectively. Similarly, these reductions for square openings with *a/D* of 0.23, 0.35 and 0.47 are 43.45%, 54.30% and 72.54%, respectively.

The EB-GFRP strengthened deep beams in all groups result significant enhancement in the shear capacity as indicated in Table 4. Also, Fig. 11 depicted that the beams strengthened with EB-GFRP throughout the beam length of Groups A, B and C, i.e. for the beams C-100-FS, C-150-FS and C-200-FS, the increase in the shear strength is found to be 30.83%, 24.03% and 22.99%, respectively, as compared to those of the respective un-strengthened beams. For the beams S-100-FS, S-150-FS and S-200-FS of Groups D, E and F, the increase in the shear strength is found to be 36.51%, 13.02% and 22.59%, respectively, with respect to the un-strengthened counterpart beams. It is worth mentioning that the EB-GFRP strengthening system improves greatly the shear strength of deep beams having web openings and the improvement in the shear strength always varies with the *a/D* ratio (Fig. 11). When the *a/D* ratio increases from 0 to 0.47 for the strengthened deep beams having circular and square openings, consequently the shear strength decreases. This is because of the fact that the area of concrete available for strengthening with GFRP fabrics around the periphery is less for the beams with relatively larger openings. Hence, the shear displacement of concrete block can't be resisted and gives lower strength.

It is worth to note that the EB-GFRP strengthened deep beam with circular web opening of 100 mm diameter has the shear strength (192.8 kN) closer to that of the un-strengthened solid beam (200.3 kN).

All the beams strengthened with both EB-GFRP fabrics and GAF-28 in the shear spans show considerable enhancement in the strength as depicted in Fig. 11. It is seen from this figure that for the beams C-100-FAS, C-150-FAS and C-200-FAS, the enhancement in strength are found to be 37.83%, 37.15% and 31.19%, respectively, as compared to the un-strengthened counterpart beams. Among the specimens of Groups D, E and F, i.e. for the beams S-100-FAS, S-150-FAS and S-200-FAS, the increase in strength are 63.95%, 33.32% and 32.81%, respectively, with respect to the un-strengthened counterpart beams. It is worth to note that the beam C-100-FAS with circular openings strengthened with both GFRP and GAF-28 has the shear strength of 202.5 kN, which is higher than that of un-strengthened solid deep beam DB-NS (200.3 kN) as depicted in Fig. 11. Similarly, for the beams having square openings, the shear strength of 185.6 kN is obtained for the beam S-100-FAS, which is almost closer with the shear strength value of DB-NS, i.e. the un-strengthened solid deep beam (Fig. 11). Therefore, it is evident from the experimental results that for the beams strengthened with both EB-GFRP fabrics and GAF having relatively smaller web openings, i.e. with *a/D* ratio 0.23, the shear strength increases significantly due to the strengthening and becomes closer to or higher than the strength of the solid deep beam without web openings. Moreover, the beams with circular and square openings and strengthened with EB-GFRP and GAF (C-100-FAS, C-150-FAS and C-200-FAS & S-100-FAS, S-150-FAS and S-200-FAS) exhibit higher shear strength as compared to the GFRP strengthened counterpart beams.

It is worth to note that in the EB-GFRP strengthened beams, EB-GFRP fabrics are wrapped throughout the length of the beam in U-shape. But in EB-GFRP and GAF strengthened beams, EB-GFRP fabrics are wrapped in U-shape in the two shear spans. Therefore, there is reduction of 56% GFRP fabrics in comparison to the former case. But, these beams show superior performance in comparison to the beams strengthened with higher percentage of GFRP fabrics. Hence, it is inferred that the combination of GFRP fabrics and GAF is a useful and economical strengthening technique to combat the premature de-bonding of GFRP fabrics, and to enhance the strength significantly due to which the strength of deep solid beam can be regained significantly (fully in some cases). Similar trend of shear strength enhancement has also been observed in the previous study [29] for the mechanical bolt anchored over SFRP composites. However, the SFRP strengthening has been done throughout the beam length, but not in the shear spans only, as in the present case.

### 3.4. Load versus deflection

The variations of the deflections of the beams at mid-span of all the groups with respect to the applied load are indicated in Fig. 12(a–f). The load-deflection curve of the solid deep beam DB-NS is also furnished in all the groups for the comparison. It is worth mentioning that the maximum mid-span deflection of the un-strengthened solid beam is the highest among all the beams showing more ductile behaviour and energy absorption capacity. Fig. 12(a–c) show the load-deflection curves of Groups A, B and C with circular openings having *a/D* ratios of 0.23, 0.35 and 0.47, respectively. All the deep beams with circular web openings strengthened with GFRP fabrics and both GFRP fabrics and GAF possess higher maximum deformation than that of the un-strengthened counterpart beams as shown in Fig. 12(a–c). Fig. 12(d–f) exhibits the load-deflection curves of Groups D, E and F, respectively, having square openings. It is seen that the maximum deformation of the beams having square web openings also increases with the application of EB-GFRP fabrics system as well as strengthening with both EB-GFRP fabrics and GAF.

In the un-strengthened beams, the maximum deflection at mid-span increases with the increase in the opening size for both the circular and square openings, but is less than that of the un-strengthened solid deep beam. Hence, due to the presence of the circular/square web openings of any size in the un-strengthened beams, the maximum mid-span deflection decreases as compared to that of the un-strengthened solid beam. The reductions in the maximum mid-span deflection are 35.81%, 21.62% and 18.91% for the beams C-100-NS, C-150-NS and C-200-NS, respectively (Table 4). Similarly, the reductions in the maximum mid-span deflection for the un-strengthened beams having square web openings, i.e. S-100-NS, S-150-NS and S-200-NS, are observed to be 31.82%, 25.67% and 18.24%, respectively, as compared to the solid beam (Table 4).

It is worth to mention that when these openings are strengthened with EB-GFRP fabrics, the corresponding decrease in the mid-span deflection becomes 25.67%, 6.89% and 5.40% for the beams C-100-FS, C-150-FS and C-200-FS, respectively, and 13.85%, 12.83% and 4.96% for the beams S-100-FS, S-150-FS and S-200-FS, respectively (Table 4). When GAF is added to the EB-GFRP system, the decrease in deflection with respect to the un-strengthened solid beam becomes significant, i.e. 14.39%, 3.71% and 0.81% for the beams C-100-FAS, C-150-FAS and C-200-FAS, respectively, and 6.75%, 2.90% and 0.31% for the beams S-100-FAS, S-150-FAS and S-200-FAS, respectively (Table 4).

It is to be noted that the trend of the load versus deflection curve for all the beams as plotted in Fig. 12 depends upon the opening size, strengthening pattern and the degree of interruption of load path. In the solid deep beam, there is no opening to interrupt with the natural load path and therefore, the load versus deflection curve of this beam show more or less linear pattern till the maximum load. For the remaining beams with web openings in all the groups, the openings are interrupted with the natural load path, which causes non-linear response representing quick propagation and widening of the crack as compared to solid deep beam.

From the above discussion, it is inferred that the maximum mid-span deflections of the beams increases with the increase in the size of web openings. The same further increases when the beams having openings are strengthened with EB-GFRP fabrics as well as both EB-GFRP fabric and GAF showing more ductile behaviour and energy absorption capacity. The best performance in terms of strength, deflection and energy absorption is observed for the beams strengthened with EB-GFRP fabrics and GAF in shear spans followed by beams strengthened with GFRP fabrics in full length. It is worth to note that the beams, i.e. C-200-FAS and S-200-FAS, have deflections 14.68 mm and 14.75 mm, respectively, which are very close to the deflection of un-strengthened solid beam (14.80 mm).

### 3.5. Stiffness

The test results illustrate that the beams strengthened with both the strengthening systems, i.e. EB-GFRP fabrics and EB-GFRP fabrics anchored with GAF, not only enhance the shear strength and deformation, but also improve the stiffness. The stiffness, (*S*_{1}) at a point is defined as the ratio between the ultimate load and the corresponding deflection of that beam. For calculation of the secant stiffness (*S*_{2}) of the strengthened beams, at first the load of the strengthened beam is obtained with respect to the deflection for the ultimate load of the control beam. The secant stiffness (*S*_{2}) can be obtained as the ratio between the above load of the strengthened beams and the deflection corresponding to the ultimate load of the control beam [29]. The stiffness, *S*_{1} and *S*_{2}, of the beams in the groups from A to F and the percentage increase in the stiffness *S*_{1} with respect to the respective un-strengthened beams are furnished in Table 5.

Group | Specimen | Stiffness (S_{1}) at peak load (kN/mm) | Increase in Stiffness (S_{1}) (%) | Secant stiffness (S_{2}) (kN/mm) |
---|---|---|---|---|

Solid beam | DB-NS | 35.76 | – | – |

A | C-100-NS | 33.38 | 0 | 33.38 |

C-100-FS | 41.47 | 24.23 | 44.33 | |

C-100-FAS | 40.00 | 19.83 | 46.55 | |

B | C-150-NS | 24.61 | 0 | 24.61 |

C-150-FS | 27.44 | 11.49 | 30.53 | |

C-150-FAS | 27.82 | 13.04 | 33.76 | |

C | C-200-NS | 15.32 | 0 | 15.32 |

C-200-FS | 18.38 | 19.97 | 18.84 | |

C-200-FAS | 18.53 | 20.95 | 20.10 | |

D | S-100-NS | 29.41 | 0 | 29.41 |

S-100-FS | 32.89 | 11.83 | 40.15 | |

S-100-FAS | 35.36 | 20.23 | 48.22 | |

E | S-150-NS | 21.28 | 0 | 21.28 |

S-150-FS | 22.98 | 8.03 | 24.05 | |

S-150-FAS | 23.46 | 10.24 | 28.37 | |

F | S-200-NS | 12.08 | 0 | 12.08 |

S-200-FS | 13.48 | 11.58 | 14.81 | |

S-200-FAS | 13.59 | 12.50 | 16.05 |

From Table 5, it is found that all the beams strengthened with EB-GFRP fabrics and both EB-GFRP fabrics and GAF possess enhancement in the stiffness than those of the un-strengthened counterpart beams. A similar trend of stiffness enhancement is also observed for the beams strengthened with CFRP [27] and SGFRP composites [29]. Moreover, the increase in stiffness for the EB-GFRP strengthened beams with circular openings in Groups A, B and C, are 24.23%, 11.49% and 19.97%, respectively, as compared to their counterpart un-strengthened beams. However, the stiffness for the EB-GFRP strengthened deep beams with square web openings in Groups D, E and F are 11.83%, 8.03% and 11.58%, respectively, with respect to their counterpart un-strengthened beams. The stiffness of beam with square openings is less than that of the corresponding beam with circular openings. Similarly, for the beams having circular openings in the Groups A, B and C, strengthened with EB-GFRP fabrics and GAF at shear span only, the increases in the stiffness are 19.83% and 13.04% and 20.95% respectively, as compared to their counterparts. However, the increases in stiffness of the square specimens of Groups D, E and F, strengthened with both the GFRP fabrics and GAF are 20.23%, 10.24% and 12.50%, respectively. Moreover, for the beams C-100-FAS and S-100-FAS having smaller openings (*a/D* = 0.23), strengthened with both GFRP fabrics and GAF, the increase in stiffness is almost same regardless of the shape (Table 5). However, for the beams with comparatively large openings, i.e. *a/D* ratio of 0.35 and 0.47, the increase in stiffness of square openings is less than that of circular openings.

Table 5 clearly demonstrates that for both the types of strengthening configurations (EB-GFRP fabrics and both GFRP fabrics and GAF), the secant stiffness, *S*_{2} of the strengthened beams is higher than those of the un-strengthened counterpart beams. However, for the beams with small openings (*a/D* = 0.23), the stiffness values (for both the types of strengthening configurations) is observed to be higher or almost close to that of the solid deep beam (Table 5).

From the above discussion, it is inferred that for the beams with increased *a/D* ratio, the observed stiffness is less due to quick loss of bond between concrete and EB-GFRP as well as concrete and mechanical fasteners followed by the initiation and rapid progress of shear crack due to small concrete area around the openings.

## 4. Comparison with theoretical predictions

The experimental shear strength of RC deep beams with web openings; *V*_{exp}, is compared with the theoretical shear strength, *V*_{pr}, predicted from different models reported in the previous works. Kong and Sharp [10] have developed a semi empirical formula in order to predict the shear strength of un-strengthened RC deep beams having web openings. Similarly, EI-Maaddawy and Sherif [27] in their research have also suggested a model, which is based on the Mohr-coulomb failure criterion to predict the shear strength of un-strengthened RC deep beams with web openings. Moreover, EI-Maaddawy and Sherif [27] have adopted an equation to obtain the contribution of FRP sheets in deep beams with web openings strengthened using EB-FRP. According to EI-Maaddawy and Sherif [27], the proposed shear contribution due to concrete, *V*_{c}, is presented as follows:(1)$Vc=\frac{\left({\lambda}_{1}{\lambda}_{2}{\lambda}_{3}\right)cbh}{\mathrm{sin}\phantom{\rule{0.25em}{0ex}}\beta \phantom{\rule{0.25em}{0ex}}\mathrm{cos}\phantom{\rule{0.25em}{0ex}}\beta \left(\mathrm{tan}\phantom{\rule{0.25em}{0ex}}\beta +\mathrm{tan}\phantom{\rule{0.25em}{0ex}}\varphi \right)}$Where, *b* and *h* refer to the width and height of the beam, respectively. $\beta $ is the angle of inclination of the natural load path, which is considered as 45°.(2)$c=\sqrt{\frac{{{f}_{c}}^{\prime}\phantom{\rule{0.25em}{0ex}}{f}_{c{t}^{\prime}}}{2}}$Where, *f*_{c} is the 28days cylinder compressive strength and *f*_{ct} is the concrete tensile strength = *(0.62√f´*_{c}*).*(3)$\mathrm{tan}\phantom{\rule{0.25em}{0ex}}\varphi =\frac{\left({{f}_{c}}^{\prime}-{f}_{ct}\right)}{2\sqrt{{{f}_{c}}^{\prime}{f}_{ct}}}$(4)${\lambda}_{1}=\{\begin{array}{c}1-\frac{{k}_{3}{X}_{N}}{3{k}_{2}h}\phantom{\rule{0.25em}{0ex}},\phantom{\rule{0.25em}{0ex}}{k}_{3}{X}_{N}\phantom{\rule{0.25em}{0ex}}\le {k}_{2}h\\ \frac{2}{3},\phantom{\rule{0.25em}{0ex}}{k}_{3}{X}_{N}\ge {k}_{2}h\end{array}$Where, *X*_{N} is the nominal shear span. *k*_{2} and *k*_{3} are the coefficients defining the opening location as presented in the idealised structural model studied by EI-Maaddawy and Sherif [27].(5)${\lambda}_{2}=\phantom{\rule{0.25em}{0ex}}(1-\frac{{a}_{X}}{2X})\phantom{\rule{0.25em}{0ex}}(1-\frac{{a}_{y}}{1.2h})$Where, *X*, *a*_{x} and *a*_{y} are the clear shear span, opening width and height, respectively.(6)${\lambda}_{3}=\{\begin{array}{c}\left(0.85+0.3\frac{{e}^{x}}{{X}_{net}}\right)\phantom{\rule{0.25em}{0ex}}\left(0.85+0.3\frac{{e}^{y}}{{{y}_{ne}}_{t}}\right)\phantom{\rule{1em}{0ex}}<\phantom{\rule{0.25em}{0ex}}1\hfill \\ \phantom{\rule{3em}{0ex}}for\phantom{\rule{0.25em}{0ex}}centre\phantom{\rule{0.25em}{0ex}}of\phantom{\rule{0.25em}{0ex}}opening\phantom{\rule{0.25em}{0ex}}in\phantom{\rule{0.25em}{0ex}}the\phantom{\rule{0.25em}{0ex}}unloaded\phantom{\rule{0.25em}{0ex}}quadrant\\ \left(0.85-0.3\frac{{e}^{x}}{{X}_{net}}\right)\phantom{\rule{0.25em}{0ex}}\left(0.85-0.3\frac{{e}^{y}}{{y}_{net}}\right)\phantom{\rule{0.25em}{0ex}}<\phantom{\rule{0.25em}{0ex}}1\hfill \\ \phantom{\rule{2.5em}{0ex}}for\phantom{\rule{0.25em}{0ex}}centre\phantom{\rule{0.25em}{0ex}}of\phantom{\rule{0.25em}{0ex}}opening\phantom{\rule{0.25em}{0ex}}in\phantom{\rule{0.25em}{0ex}}the\phantom{\rule{0.25em}{0ex}}loaded\phantom{\rule{0.25em}{0ex}}quadrant\end{array}$Where, *e*_{x,} and *e*_{y} are the eccentricities of the opening.(7)${X}_{net}={X}_{N}-{a}_{x}$(8)${y}_{net}=0.6h-{a}_{y}$

The shear contribution due to steel, *V*_{s}, is presented as follows;(9)$Vs=\left({\phi}_{s}{A}_{s}{f}_{y}\right)\phantom{\rule{0.25em}{0ex}}\left(\frac{\mathrm{tan}\phantom{\rule{0.25em}{0ex}}\beta \phantom{\rule{0.25em}{0ex}}\mathrm{tan}\phantom{\rule{0.25em}{0ex}}\varphi -1}{\mathrm{tan}\phantom{\rule{0.25em}{0ex}}\beta +\mathrm{tan}\phantom{\rule{0.25em}{0ex}}\varphi}\right)$Where, $\varphi $_{s} = 0.65. *A*_{s} is the area of flexural steel and *f*_{y} = 300 MPa for deformed bars.

The predicted shear strength of un-strengthened RC deep beam having web openings, *V*_{pr(NS),} is obtained as follows;(10)*V*_{pr(NS)} = *Vc*+*Vs*

Now, the Shear force *V*_{f,} resisted by the FRP fabrics can be calculated as suggested by EI-Maaddawy and Sherif [27] and is presented as follows:(11)${V}_{f}={\phi}_{f}\left(2{t}_{f}\right)\phantom{\rule{0.25em}{0ex}}\left({w}_{f}\right)\phantom{\rule{0.25em}{0ex}}\left({E}_{f}{\epsilon}_{fe}\right)\phantom{\rule{0.25em}{0ex}}\frac{y}{h}\phantom{\rule{0.25em}{0ex}}{\mathrm{sin}\phantom{\rule{0.25em}{0ex}}}^{2}\phantom{\rule{0.25em}{0ex}}\alpha $Where, $\varphi $_{f} = 0.71 for full wraps and 0.64 for u-wraps [44]. *t*_{f,} *W*_{f,} *E*_{f} and ${\epsilon}_{fe}$ refer to the thickness, width, Young's modulus and effective strain of the GFRP fabrics, respectively. *y* is the depth at which the FRP obstruct the shear crack and *ἀ* is the angle of slope between vertical FRP and the shear crack. As per the recommendation of ACI 440 [44], the effective strain, ${\epsilon}_{fe}$ in the FRP is given by(12)${\epsilon}_{fe}=\{\begin{array}{c}0.004\le 0.75\phantom{\rule{0.25em}{0ex}}{\epsilon}_{fu}\phantom{\rule{1em}{0ex}}for\phantom{\rule{0.25em}{0ex}}full\phantom{\rule{0.25em}{0ex}}wraps\\ k{{\epsilon}_{f}}_{u}\le \phantom{\rule{0.25em}{0ex}}0.004\phantom{\rule{1em}{0ex}}for\phantom{\rule{0.25em}{0ex}}u-wraps\end{array}$(13)$k=\frac{{k}_{1}{k}_{2}{L}_{e}}{\mathrm{11,900}{\epsilon}_{fu}}\le 0.75$(14)${L}_{e}=\frac{\mathrm{23,000}}{{\left({t}_{t}{E}_{f}\right)}^{0.58}}\phantom{\rule{0.25em}{0ex}}\le {d}_{f}$Where, *Ԑ*_{fu,} *L*_{e} and *d*_{f} are the rupture strain, bond length and depth of the FRP sheet, respectively. *k* denotes the bond reduction factor, which depend on two other modification factors, *k*_{1} and *k*_{2.}

Where, *k*_{1} and *k*_{2} are expressed as:(15)${k}_{1}={\left(\frac{{{f}_{c}}^{\prime}}{27}\right)}^{0.67}$(16)${k}_{2}=\frac{{d}_{f}-{L}_{e}}{{d}_{f}}$

According to EI-Maaddawy and Sherif [27], the predicted shear strength of GFRP strengthened RC deep beams having web openings, *V*_{pr(FS)}, is expressed as;(17)${V}_{pr\left(FS\right)}\text{}=\text{}{V}_{c}\text{}+\text{}{V}_{s}\text{}+\text{}{V}_{f}$

Further, Kong and Sharp [10] proposed the following expression to obtain the ultimate strength of the un-strengthened deep beams with web openings.(18)$\frac{{P}_{u}}{2}=\phantom{\rule{0.25em}{0ex}}{C}_{1}\phantom{\rule{0.25em}{0ex}}(1-0.35\phantom{\rule{0.25em}{0ex}}\left(\frac{\left({K}_{1}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}{a}_{1}\right)X}{\left({K}_{2}-\phantom{\rule{0.25em}{0ex}}{a}_{2}\right)\phantom{\rule{0.25em}{0ex}}D}\right)\phantom{\rule{0.25em}{0ex}}){f}_{t}\phantom{\rule{0.25em}{0ex}}b\phantom{\rule{0.25em}{0ex}}\left({K}_{2}\phantom{\rule{0.25em}{0ex}}-\phantom{\rule{0.25em}{0ex}}{a}_{2}\right)\phantom{\rule{0.25em}{0ex}}D\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}\sum \phantom{\rule{0.25em}{0ex}}\lambda \phantom{\rule{0.25em}{0ex}}{C}_{2}A\phantom{\rule{0.25em}{0ex}}\left(\frac{{y}_{1}}{D}\right)\phantom{\rule{0.25em}{0ex}}{\mathrm{sin}\phantom{\rule{0.25em}{0ex}}}^{2}\phantom{\rule{0.25em}{0ex}}{\alpha}_{1}$Where, *P*_{u,} *A, D, b* and *X* are the ultimate strength, area of an individual web as well as main reinforcing bar, overall depth, width and clear shear span distance of the beam, respectively. *C*_{1} = 1, when *f*_{t} is obtained as per BS: 1881 and *C*_{2} = 300 N/mm^{2} for deformed bars. *a*_{1} and *a*_{2} are defining the width and height of the opening. *k*_{1} and *k*_{2} are the coefficients for horizontal and vertical distance from the beam axis to the centre of opening position. *f*_{t} is the concrete tensile strength *(0.62√f´*_{c}*),* where *f*_{c} is 28days cylinder compressive strength. *y*_{1} and *ἀ* are the depth and angle of interception of typical bar and load path. *λ* is empirical coefficient equal to 1 for main bars and 1.5 for web bars.

The design shear strength of the un-strengthened deep beams with web openings is evaluated based on the theoretical models available in the literature [10,27]. For this, the formulations presented in Eq. (10) and Eq. (18), respectively, are considered to determine the same. The shear strength contribution of FRP, *V*_{f}, for the GFRP strengthened beams is determined based on the formulation [27], which is presented in Eqs. (11), (12), (13), (14), (15), (16)). The design shear strength, *V*_{pr(FS),} of the GFRP strengthened beams is computed from the theoretical expression recommended in the above model, which is presented in Eq. (17). Then, the shear strength values computed from the above models [10,27] and the present experimental shear strength of the un-strengthened and GFRP strengthened beams with web openings are presented in Table 6. Further, the ratios of the shear strength values derived from these models to the experimental shear strength for the un-strengthened and GFRP strengthened beams with web openings are also presented in Table 6. It is to be noted that for all the EB-GFRP strengthened beams in each group, the predicted (*V*_{c} + *V*_{s})_{pr(NS)} value is assumed to be equal to that obtained for un-strengthened counterpart beams.

Group | Specimen | Experimental results | Result predicted from different models available in the existing literature | Comparison | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

V_{exp}= (V_{c} + V_{s} + V_{f})_{exp.}(kN) | V_{f exp}(kN) | (V_{c} + V_{s})_{exp}(kN) | Kong and Sharp [10] | EI-Maaddawy and Sherif [27] | EI-Maaddawy and Sherif [27] | V_{pr,(FS)} = (V_{c} + V_{s})_{pr,b} + V_{fpr}(kN) | (V_{c} + V_{s}) _{pr,a}/( V_{c} + V_{s})_{exp} | (V_{c} + V_{s}) _{pr,b}/( V_{c} + V_{s})_{exp} | V_{pr,(FS)}/ V_{exp} | ||

(V_{c} + V_{s})_{pr,a} (kN) | (V_{c} + V_{s}) _{pr,b}(kN) | V_{f pr} (kN) | |||||||||

A | C-100-NS | 147.40 | – | 147.40 | 107.65 | 102.17 | – | – | 0.73 | 0.69 | – |

C-100-FS | 192.85 | 45.45 | 147.40 | 107.65 | 102.17 | 25.14 | 127.31 | – | – | 0.66 | |

B | C-150-NS | 109.55 | – | 109.55 | 72.81 | 86.82 | – | – | 0.66 | 0.79 | – |

C-150-FS | 135.88 | 26.33 | 109.55 | 72.81 | 86.82 | 22.00 | 108.82 | – | – | 0.80 | |

C | C-200-NS | 76.23 | – | 76.23 | 41.45 | 62.03 | – | – | 0.54 | 0.81 | – |

C-200-FS | 93.75 | 17.52 | 76.23 | 41.45 | 62.03 | 18.00 | 80.03 | – | – | 0.85 | |

D | S-100-NS | 113.25 | – | 113.25 | 103.37 | 100.72 | – | – | 0.91 | 0.88 | – |

S-100-FS | 154.60 | 41.35 | 113.25 | 103.37 | 100.72 | 25.00 | 125.72 | – | – | 0.81 | |

E | S-150-NS | 91.53 | – | 91.53 | 73.02 | 80.43 | – | – | 0.80 | 0.87 | – |

S-150-FS | 103.45 | 11.92 | 91.53 | 73.02 | 80.43 | 22.00 | 102.43 | – | – | 0.99 | |

F | S-200-NS | 55.00 | – | 55.00 | 40.91 | 60.56 | – | – | 0.74 | 1.10 | – |

S-200-FS | 67.43 | 12.43 | 55.00 | 40.91 | 60.56 | 18.00 | 78.56 | – | – | 1.16 |

**Note:** *V*_{f pr} is the predicted shear strength contributed by FRP as per EI-Maaddawy and Sherif [27]; (*V*_{c} + *V*_{s})_{pr,a} and (*V*_{c} + *V*_{s})_{pr,b} are the predicted shear strength contributed by both concrete and steel as per Kong and Sharp [10] and EI-Maaddawy and Sherif [27], respectively; *V*_{pr,(FS)} =(*V*_{c} + *V*_{s}) _{pr,b} + *V*_{f pr}; (*V*_{c} + *V*_{s})_{exp} is the shear strength contributed by concrete and steel experimentally, *V*_{fexp} is the shear strength contributed by FRP experimentally and *V*_{exp} = (*V*_{c} + *V*_{s} + *V*_{f})_{exp.}

Table 6 demonstrates that the shear strength of all the un-strengthened beams obtained from the present experimental study is higher than those estimated from these theoretical models. However, the shear strength for the un-strengthened beams C-150-NS, C-200-NS, S-150-NS and S-200-NS, computed from the formulation proposed by Kong and Sharp [10], are less than those computed from the model of EI-Maaddawy and Sherif [27]. On the other hand, for the un-strengthened beams C-100-NS and S-100-NS, i.e. having smaller openings (*a/D* = 0.23), this is vice versa. This means that for smaller openings, the shear strength computed from the model of Kong and Sharp [10] is higher than those computed from model of EI-Maaddawy and Sherif [27].

Further, Table 6 depicts that the shear strength of the un-strengthened beam S-200-NS having square web openings of size 200 × 200 mm computed from the expression proposed by EI-Maaddawy and Sherif [27] is overestimated than that of experimental shear strength. This is because specimen S-200-NS do not reach their full strength because of premature failure due to high shear stress concentration at the corners of large square web openings. Another cause may be due to less amount of concrete clear cover around the large web openings. For this specimen, the ratio of predicted to experimental strength is 1.10. The predicted shear strength for all other un-strengthened beams having circular and square web openings except the above beam S-200-NS are in conservative side. Similarly, for all the EB-GFRP strengthened deep beams having web openings the experimental shear capacity is higher than those computed from the formulation proposed by EI-Maaddawy and Sherif [27] except one contradiction result of the beam S-200-FS. The theoretical shear capacity for this beam is slightly higher than that of the experimental one.

On the other hand, it is seen from Table 6 that the experimental shear strength contribution of FRP is less than those predicted from the proposed formulation [27] for the beams C-200-FS, S-150-FS and S-200-FS. This means that, with an increase in the opening size, there is a decrease in the experimental shear strength. It is because of the fact that the full strength of GFRP cannot be reached for higher openings because of the prior failure in the form of de-bonding of GFRP. This effect is more pronounced when the web opening of the beams are comparatively larger. It is worth to note that the above effect has not been properly included in the theoretical models considered here due to which these theoretical models predict higher shear strength for large openings (*a/D* = 0.47) as compared to the experimental strength. However, for the beams having smaller web openings, i.e. *a/D* value of 0.23, the utmost contribution of GFRP is attained. Thus, the predicted shear strengths of FRP for these beams having small openings (both circular and square) are less than those of the experimental shear strength as furnished in Table 6.

From the above, it is concluded that, the shear strength values computed from the above models [10,27] for the un-strengthened and GFRP strengthened beams with comparatively smaller openings are consistent with the experimental results. This suggests that the available models are generally trustworthy, and thus these models can be employed firmly in the practice. Further researches are expected to refine these models so as to estimate the shear strength precisely for the un-strengthened and FRP strengthened deep beams with comparatively larger web openings.

## 5. Conclusions

This study investigates the use of EB-GFRP fabrics and GAF technique for strengthening of RC deep beams having both circular and square web openings. The various outcomes of the present investigation are presented as follows.

1. Inclusion of the web openings in RC deep beams significantly reduces the shear strength. The reductions are maximum for the larger openings with *a/D* = 0.47, i.e. up to 61.94% and 72.54% for circular and square openings, respectively, as compared to the solid deep beam. The strength reduction is more in case of the square openings because of high stress concentration at the four corners of square openings.

- 2.
The enhancement in the shear strength of the beams strengthened with EB-GFRP fabrics throughout the beam length is up to 30.83% and 36.51%, for the circular and square openings, respectively, as compared to the respective un-strengthened beams. However, these strengthening is not that significant for the beams having higher openings, i.e.

*a/D*= 0.47. - 3.
Strengthening using EB-GFRP fabrics and GAF at shear spans of deep beams with web openings has a remarkable effect on the shear capacity as compared to the un-strengthened counterpart beams. The enhancement in the shear strength of these strengthened beams is up to 37.38% and 63.95% for circular and square openings, respectively, as compared to the respective un-strengthened beams.

- 4.
The reduction in shear strength is higher for the beams with square openings than those with circular openings as compared to the solid deep beam due to high stress concentration at the corners of the square openings. However, the enhancement in shear strength as compared to the counterpart un-strengthened beam is higher for square openings as compared to circular openings as these strengthening techniques are effective in minimizing the stress concentration at the corners of square openings.

- 5.
Failure of all the un-strengthened deep beams with web openings occurs in shear due to propagation of two independent inclined cracks at the opposite top and bottom corners of web openings regardless of the shape and size. The shear failure of the EB-GFRP strengthened deep beams wrapped throughout the beam length occurs due to the de-bonding of GFRP fabrics from the concrete surface followed by inclined cracks in the opposite top and bottom corners of web openings. However, the failure mode of the deep beams strengthened with EB-GFRP and GAF is a combination of pull-out of fasteners, GFRP tearing/GFRP de-bonding followed by diagonal cracks in the opposite top and bottom corners of web openings.

- 6.
The stiffness of the un-strengthened RC deep beams decreases significantly with the increase of opening size. More reduction in stiffness is observed in the case of square openings as compared to circular openings.

- 7.
Strengthening of RC deep beams with openings using EB-GFRP fabrics and EB-GFRP and GAF enhances the stiffness significantly with respect to the counterpart un-strengthened beams. The maximum enhancements in stiffness are 24.23% and 20.95% for strengthening with EB-GFRP fabrics and both EB-GFRP and GAF-28, respectively.

- 8.
The experimental shear strength values of un-strengthened and EB-GFRP strengthened beams are in good agreement with those predicted from design models reported in the literature for smaller openings, i.e. a/D = 0.23 and 0.35. But for larger openings the predicted shear strength values are more in comparison to the experimental shear strength values due to the reason that GFRP fabrics cannot achieve its full potential for higher openings because of earlier failure occurred by the de-bonding of GFRP. This is not properly accounted in the proposed models due to which these models need to be refined further for predicting accurately for higher web openings.

## CRediT author statement

**Archana Kumari**: Methodology, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Visualization.

**Amar Nath Nayak**: Conceptualization, Resources, Supervision, Project administration, Funding acquisition, Writing - Review & Editing.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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