Experimental Compressive Assessment of Different Stiffened Plate Welding Configurations

Abstract

The application of fillet welding in the shipbuilding industry is essential for composing different structural components such as stiffened plates and panels, which are the sub-structural elements of the entire hull. The connection between the base plating and its reinforcement members as stiffeners may be found in different fillet welding configurations such as continuous and intermittent chain welding. The application of each welding configuration may differ according to the importance of the structural component, its location and the acting load. The aim of the present work is to experimentally evaluate the ultimate compressive capacity of a stiffened plate with different base plating thicknesses and a welded stiffener using different fillet welding configurations. The results are presented in the form of different relationships between axial force–vertical/lateral displacement relationships and corresponding collapse modes. Discussion and analysis of results are performed for a deep understating of both the local and global behaviour of the stiffened plate, accounting for the absorbed energy within the elastic regime and up to the ultimate limit, with developed regression formulations. Also, a comparison between the experimental results and existing empirical formulations is performed, showing a good agreement and reasonable behaviour.

1. Introduction

The basic structural components of marine structures, especially ships, are plates, either unstiffened or stiffened. To satisfy the stiffening criteria, additional structural members may be attached as stiffeners using welding techniques, or plates are corrugated in special ways, i.e., corrugated bulkheads. Welding as a connecting technique induces both geometrical imperfection and residual stresses, and both affect the global response of the structure, especially the ultimate load-carrying capacity.

Fu et al. [1] experimentally evaluated and numerically validated the effect of welding sequence on the subsequent residual stresses and distortion. It was observed that concentration of transverse residual stresses at the middle is affected by the welding sequence, where the double-side sequence (both sides are welded at the same time) induces less stresses. Also, the distortion magnitude is higher in case of single-side welding (one side welded first and then the second one) than double-side welding. Therefore, for practical application, the double-side sequence is recommended.

Fu et al. [2] performed both experimental tests and numerical simulation to investigate the effect of different material models on both residual stress and induced distortion and concluded that the material model has a remarkable effect on both parameters. Zhang and Wang [3] numerically examined the effect of different boundary conditions on both residual stresses and the distortion of welded stiffened panels and stated that the symmetrical boundary conditions significantly affect the distortion amplitude with less effect on the induced residual stresses. Yi et al. [4] measured welding-induced residual stress using the X-ray diffraction method in addition to a 3D thermo-elastic–plastic finite element model for a full-scale stiffened plate structure.

Saad-Eldeen et al. [5] performed distortional analysis of welded stiffened plates considering two welding configurations to attach the stiffener: continuous and intermittent chain fillet welding. It was reported that for continuous welding, the number of consumed electrodes increases linearly as the plating thickness increases, with no effect on electrode consumption in cases of intermittent chain welding. Also, the ratio of welding time between continuous and intermittent welding decreases as the plate thickness increases.

The existence of initial imperfections and residual stresses affect the pre-buckling and post-buckling regimes, respectively, and decrease the ultimate strength of stiffened steel plates and marine structures in general. Several empirical expressions and simplified approaches have been developed to assess the ultimate strength of plated structures, such as the work performed by Faulkner [6] for the effective width concept and the effect of residual stress. Guedes Soares [7,8] assessed the influences of the uncertainties in plate buckling and proposed a design formulation for specific types of ship plating.

Chen and Guedes Soares [9,10] performed three-dimensional thermo-elasto-plastic analysis to detect the residual stress distribution and the resultant imperfections of stiffened plates. It was noticed that as the stiffener height increases, the effect on reducing the asymmetry of the plate distortion increases. Also, the existence of residual stresses reduces the longitudinal strength of the stiffened plate by 5–7%. Furthermore, short welding passes from the middle of the plate to the edge induce lower distortion and residual stress than long passes.

Paik and Thayamballi [11] empirically derived a simplified equation for predicting the ultimate compressive strength of longitudinally stiffened steel panels, as a function of both plate and column slenderness. Khedmati et al. [12] studied the effect of different welding procedures—continuous, chain and staggered intermittent fillet welding—on the ultimate strength of stiffened plates. It was observed that the strength of the stiffened plate may be sorted in descending order according to the method of stiffener attachment as continuous, staggered and chain intermittent fillet welding.

Saad-Eldeen et al. [13] analysed both initial and post-collapse deformed shapes of 36 steel plates that are parts of scaled box girders and proposed a plate slenderness criterion for predicitng the post-collpase shape. Tekgoz et al. [14] numerically investigated the effect of residual stresses on the strength of stiffened plates, accounting for different plating thicknesses, welding sequences and heat characteristics. It was reported that the increase in the plate thickness increased the vertical distortion and compressive residual stress and decreased the compressive strength. Also, the parameter with the greatest effect on the stiffener distortion is the welding sequence.

Zhang and Khan [15] carried out intensive numerical analysis for plates, including stiffened plates, and developed a semi-empirical expression to predict the ultimate compressive strength of stiffened steel panels. Kim et al. [16] proposed an empirical formulation for estimating the ultimate strength of stiffened panels with column slenderness of $0.5\le \lambda <5$. Kim et al. [17] presented a technical review on the developed expressions for assessing the ultimate strength of stiffened panels subjected to axial compressive loading. They also conducted an intensive numerical simulation for stiffened panels with average imperfection amplitude, without considering residual strength effects.

Li et al. [18] analysed the effect of residual stresses on the ultimate strength of stiffened panels, considering two scenarios; in the first scenario, only the plate had residual stress, and in the second scenario, residual stresses existed in both the plate and stiffener. It was reported that the strength reduction is about 6% and 8.5%, respectively. Also, an increased contribution of stiffener residual stress to strength reduction occurs when the final collapse mode is controlled by beam-column buckling and not plate buckling.

Mun and Ri [19] estimated the ultimate strength of intermittently welded stiffened plates using a proposed simplified method, in which the span of the welded specimen is divided into welded and non-welded segments. The results are in good agreement with other published numerical results. Tatsumi and Kageyama [20] investigate the effect of initial distortion components (shape and amplitude) on the ultimate strength of thin and thick plates. It was reported that the strength of thin plates is highly affected by the distortion components and vice versa for thick plates, which may reach their ultimate strength with small deviations.

Park et al. [21] included the combined effect of local dents, fracture damage, initial imperfections and residual stress on the residual strength of box girders under four-point bending. Saad-Eldeen et al. [22] numerically studied the effect of weld toe shape and material models on the strength of slightly corroded box girders; the simulation of welding as an existing area increases the strength by 5%, where the effect of weld toe shape may be neglected. Also, a modified elasto-plastic material model has been proposed accounting for the residual stress effect.

Guedes Soares and kmiecik [23] investigated the effect of boundary conditions on the strength of square plates. It was reported that the plate slenderness plays an important role in identifying such an effect, where significant effects arise for slender plates.

Such stiffened plates may exist in marine structures in other forms besides stiffened plates with multiple openings, and their strength according to the acting loads is an essential issue; therefore, Saad-Eldeen and Garbatov [24] performed a series of experimental tests and analysed both local and global responses. It was reported that for these structural elements under compressive loading, it is better to be designed according to the residual cross-sectional area rather than the resting volume.

The aim of the present study is to carry out an experimental capacity assessment of welded stiffened plates of different fillet welding configurations to add an additional step in understanding the behaviour of such structural components due to the lack of information regarding the ultimate strength of stiffened plates and panels with intermittent chain fillet welding.

2. Experimental Compressive Collapse Test Procedure

The experimental work included testing of welded stiffened plate specimens, with an attached stiffener using two different fillet weld configurations for such attachment. The test is conducted under uniaxial compressive loading to assess the ultimate load carrying of these specimens and investigate the effect of the welding configurations on the carrying capacity as well as the collapse mode. Firstly, the specimens are prepared for such testing by attaching the stiffener using two different welding configurations. Secondly, the induced weld distortion after heat relief is measured. Thirdly, the compressive collapse test is conducted using a universal testing machine in the vertical position.

2.1. Material and Specimen Preparation

The tested specimens are composed of square steel plates with one attached flat bar stiffener, welded together using different fillet welding geometrical configurations. Both the plate and attached stiffener are made of mild shipbuilding steel of Lloyd’s Register material grade LR-A with the following mechanical properties: yield and tensile strength of 341 MPa and 487 MPa, with elongation of 39%, considering the gauge length of 5.65√S₀, where S₀ is the intact cross-sectional area of the tensile test coupons, as described by Saad-Eldeen et al. [5], where the chemical compositions of the used material are given in

Table 1. Main material chemical compositions of LR-A.

	C ×10−2	Si ×10−2	Mn ×10−2	P ×10−3	S ×10−3	Al ×10−3
Min.						20
Max.	21	50	2.5 × C	35	35

. The geometrical configurations of the stiffened plate are as follows: the length (L) and breadth (B) of the plate are 500 mm, with different plating thicknesses (t_p) of 6 mm, 8 mm and 10 mm; see Figure 1 and

Table 2. Geometrical configurations of the tested specimens.

ID	L, mm	B, mm	tp, mm	hw, mm	tw, mm
SP-6C	500	500	6	80	10
SP-8C			8
SP-10C			10
SP-6I			6
SP-8I			8
SP-10I			10

SP is a stiffened plate specimen. C and I are welding configurations, C for continuous and I for intermittent chain welding.

. The web height (h_w) and web thickness (t_w) of the stiffener are 80 mm and 10 mm, respectively. The selected geometrical configurations of the tested specimen, especially the aspect ratio, is based on many research articles, such as the work performed by Chen and Guedes Soares [9,10]. Based on the plate slenderness (β) definition given in Equation (1), the slenderness values for the specimens are 3.39, 2.54 and 2.03, while the column slenderness values (λ) according to Equation (2) are 0.33, 0.36 and 0.38, respectively.

$$\beta ={\displaystyle \frac{B}{tp}}\sqrt{{\displaystyle \frac{\sigma y}{E}}}$$

(1)

$$\lambda ={\displaystyle \frac{L}{\pi r}}\sqrt{{\displaystyle \frac{\sigma y}{E}}}$$

(2)

where $\sigma y$is the material yield stress, E is the modulus of elasticity, the radius of gyration is $\sqrt{{\displaystyle \raisebox{1ex}{$I$}\!\left/ \!\raisebox{-1ex}{$A$}\right.}}$, I is the second moment of area and A is the cross-sectional area.

2.2. Welding Procedure

The specimens are fabricated in the Port Said Shipyard that is owned by the Suez Canal Authority (EGYPT) using manual shielded metal arc welding. The welding process is carried out with a current of 180–200 amperes, voltage of 40–50 volts and speed of 2.4–2.6 mm/s, using welding electrode E6013 of 4 mm diameter approved by LR’S Grade 2Y. Two fillet welding configurations are considered to attach the stiffener, continuous and intermittent, as described in Figure 1. The intermittent weld characteristics of weld length (w) and weld gap (g) presented in Figure 1 are 80 mm and 130 mm, respectively, according to the Polish Register of Shipping [25]. The welding procedure is performed using two welding passes with the sequence defined in Figure 1. The four edges of the specimen are free during welding, without any imposed constraints.

Figure 2 presents the welded stiffened plate using continuous (left) and intermittent chain fillet welding (right). To ensure the quality of welding before conducting the compressive test, all specimens are examined using the magnetic particle test (MT) according to the testing standard IACS UR W33 [26] and ISO 17638:2016 [27]. The device used is permanent yoke with particles type-colour MR^@ 76 s-black, contrast type-colour MR^@ 72- white and cleaner type MR^@ 85, respectively, with cleaned surface condition. The MT shows that all specimens are free of cracks, as reported in Figure 3.

After finishing the welding procedure and letting the specimens sit at room temperature for several days, the induced imperfection amplitudes due to welding were measured along the breadth (B) of the plating. The measured values were recorded and plotted for each specimen as presented in Figure 4 for each group, with continuous (left) and intermittent chain fillet welding (right). For example, for the stiffened plate specimens with a base plating thickness of 10 mm and continuous welding (SP-10C), the induced imperfection amplitude is asymmetric, with 6 mm in the right portion and 5 mm in the left portion; see Figure 4 (left). On the other hand, the amplitudes of the stiffened plate with a base plating thickness of 10 mm and intermittent chain welding (SP-10I) are also asymmetric, with 9 mm in the right portion and 2 mm in the left portion; see Figure 4 (right). The recorded induced imperfection amplitudes for the six specimens are given in Figure 4 and

Table 3. Measured induced imperfection amplitudes in mm.

ID	Left Portion	Middle	Right Portion
SP-6C	+8	0	+5
SP-8C	+6	0	+6
SP-10C	+5	0	+6
SP-6I	+2	0	+9
SP-8I	+2	0	+4
SP-10I	+1.5	0	+2

.

2.3. Static Compressive Test Set-Up

Compressive collapse tests were carried out at the Structure and Concrete Research Laboratory of the Faculty of Engineering, Port Said University, using a universal testing machine with a capacity of 2000 kN, according to the testing standard ASTM E9-19 [28]. The welded specimen was controlled by two thick supports (upper and lower) with a central gap to ensure the fitting of the attached stiffener; see Figure 5 (left), where the other two unloaded edges are free. The load was transmitted from the machine to the specimen through the thick supports to satisfy the condition of uniform distribution along the specimen short edge, as presented in Figure 5. Two mechanical displacement transducers were fitted at distances a and b of 250 mm and 125 mm, respectively, as described in Figure 5, to record the lateral displacement during the test. The test was performed using displacement control at a rate of 0.016 mm/s until reaching the ultimate load-carrying capacity. During the test, both vertical displacement and applied load were recorded, where the lateral displacement was recorded by the additional mechanical transducers. The tested specimens are categorised into two groups: Group 1 contains the welded specimens using continuous fillet welding: SP-6C, SP-8C and SP-10C. Group 2 includes the specimens welded using intermittent chain welding: SP-6I, SP-8I and SP-10I.

3. Compressive Test Results

The results presented here are for two groups of specimens, with six specimens in total, and for each group, the only variable is the base plating thickness. The results are presented in the form of different relationships between axial force–vertical/lateral displacement relationships and corresponding collapse modes.

3.1. Group 1 Specimens with Continuous Welding

In this group, the experimental results of the compressive test for specimens SP-6C, SP-8C and SP-10C are presented. For the first specimen, SP-6C, the load shortening curve is presented in Figure 6, where the registered ultimate load-carrying capacity is 882.65 kN, with developed shortening displacement of 3.47 mm. Before final collapse occurs, the structural response of the stiffened plate passes through three different phases—elastic buckling, post-buckling and post-collapse—and for each phase, the registered capacity and the corresponding shortening displacement are defined. In the elastic buckling phase, the specimen reacts as one unit until the local response to the applied load is triggered in the right portion of the plate, represented by downward deformation up to an acting load of 255.35 kN and shortening displacement of 0.73 mm. By increasing the acting load, the left portion of the plate reacts in the opposite direction with upward lateral deformation until reaching the capacity of 685.02 kN and shortening of 2.06 mm, which is the end of the elastic limit. After crossing the elastic limit (whole plate buckling), and in increasing the acting load, each structural component starts to react individually, represented by permanent downward deformation of the plate in the right portion, as may be seen in Figure 7, with registered negative lateral displacement of 2.05 mm (Figure 6 (right)). Due to plate failure (left and right portions), the whole load is transferred directly to the nearest supporting member, which is the stiffener. As the load increased, the downward deformation of the plate increased, which forced the adjacent stiffener to deform outward (out of plane—see Figure 7), until reaching the ultimate capacity of 882.65 kN, with corresponding shortening displacement of 3.47 mm. After that, the global failure of the stiffened plate occurred (post-collapse) with a collapse rate of 20.02 kN/mm. Therefore, the failure sequence of SP-6C occurs in the following order, as plotted in Figure 8 (left): sub-plate (right portion), sub-plate (left portion) and stiffener failure. After finishing the collapse test, the amplitude of the final collapse mode is measured along the plate length (between the upper and lower clamp—see (Figure 8 (right)), showing that asymmetric severe deformation occurs at ±50 mm around the midspan of the stiffened plate, with global downward deformation in the right portion and upward deformation in the left portion.

The second specimen in this group is SP-8C, which has 8 mm base plating thickness, with the same geometrical configurations as SP-6C. The resultant force–displacement relations and related collapse mode are presented in Figure 9 and Figure 10. It is obvious that the specimen withstands 970 kN, with shortening displacement at ultimate load of 5.43 mm (Figure 9a). The response of SP8-C started with upward elastic buckling of the left portion near the upper edge, followed by downward buckling of the right portion at almost the same location as occurred in the left portion, as may be seen by the lateral displacement of both transducers (see Figure 9b,c), until reaching the end of the elastic response at 830.40 kN. With increasing the acting load, both portions responded with large lateral displacement, with higher magnitude in the right portion than the left portion, which forced the supporting stiffener to withstand the acting load up to the ultimate capacity of 970 kN, with shortening and lateral displacement in the left and right portion of 5.43 mm, 8.22 and −11.23 mm, respectively. This large deformation forced the stiffener to react with large out-of-plane deformation towards the right potion, which forced the specimen to lose its stiffness with a progressive collapse shape, as presented in Figure 10.

Based on the observations during the test and the recorded value of the load and relevant displacement, the failure sequence of specimen SP-8C occurred in the following order: sub-plate (left portion), sub-plate (right portion) and for stiffener failure; see Figure 11. From the final deformation amplitude measurements, it is obvious that the final collapse mode is asymmetric with severe deformation around ±50 mm around the midspan of the stiffened plate, as may be seen in Figure 11.

As the base plating thickness increases, the ultimate carrying capacity of the stiffened plate with the same stiffening configurations increases, where specimen SP-10C recorded an ultimate compressive capacity of 1109.05 kN, with a relative shortening displacement of 8.96 mm, as presented in Figure 12a. The response of the specimen started with upward elastic buckling of the right and left portions, represented by positive lateral displacement at the location of the transducer; see (Figure 12b,c). As the load increased, the elastic deformation increased up to an elastic load of 1054.74 kN with developed shortening of 3.58 mm and left and right lateral displacement of 6.36 mm and 3.09 mm, respectively. With more loading, the plate failed with a visible drop in the capacity, which forced the stiffener to react as a column element, showing hardening of its structural response, represented by a higher carrying capacity up to 1109.05 kN and displacement of 8.96 mm. Then, the stiffener failed near the upper clamp with outward deformation near the right portion, as visible in Figure 13.

The final collapse mode of SP-10C was almost symmetric with upward deformation in the two-plate portions, with shifted amplitude in the right portion. It has to be stressed that the higher deformation of the plate occurred around ±50 mm of the midspan of the stiffened plate, as reported in Figure 14, and the failure sequence of SP-10 C is as follows, with a collapse rate of 14.53 kN/mm: right portion, left portion and stiffener. It may be noticed that all specimens collapsed with visible deformation around ±50 mm of the midspan of the stiffened plate; this is because the structural integrity and continuity of the specimen acted as one unit with continuous fillet welding, as well as because of the welding quality checked by the NDT test.

3.2. Group 2 Specimens with Intermittent Chain Welding

The compressive test results for specimens SP-6I, SP-8I and SP-10I with a welded stiffener using the concept of intermittent chain welding are plotted. The test is carried out for a specimen with a base plating thickness of 6 mm (SP-6I) and the same configurations as in Group 1 except for the welding configurations. The ultimate load-carrying capacity recorded for the specimen is 816.44 kN, with developed shortening displacement of 3.42, mm as may be seen from Figure 15 (left). The plate reacts as one unit with preliminary downward buckling of the right portion near the lower clamp. With increasing the applied load, the left portion of the plate accommodates the acting load with irregular elastic bucking up to 700.05 kN and shortening displacement of 2.66 mm. As the load increases, the whole specimen starts to react plastically with permanent downward deformation of the plating near the lower end; see Figure 15 (right), Figure 16 and Figure 17 (right). This plate failure forces the stiffener to carry most of the load up to the maximum capacity of 816.44 kN and displacement of 3.42 mm. After that, the stiffener starts to lose its stability, represented by inward deformation of the stiffener towards the left portion exactly at the weld gap; see Figure 16.

Due to such progressive instability of the stiffeners, a crack at the toe of welding occurs and propagates as the load increases, which forces the specimen to lose its capacity. Therefore, the failure sequence of such a specimen is as follows, as shown in Figure 16 and Figure 17 (left): sub-plate (right portion), sub-plate (left portion), stiffener failure, and crack propagation at weld toe. According to the measured deformation amplitude (Figure 17 (right)), it is obvious that the final collapse mode is asymmetric with a higher plate deformation amplitude of 38 mm in the right portion near the lower clamp.

For specimen SP-8I, the output results of the compressive test, presented as relationships between axial load and shortening/lateral displacement, are plotted in Figure 18. As the base plating thickness increases from 6 mm (SP-6I) to 8 mm (SP-8I), the load-carrying capacity increases from 816.44 kN to 852.80 kN, respectively. Also, the recorded shortening displacement related to the ultimate capacity increases from 3.42 mm to 4.58 mm, respectively; see Figure 18a. Furthermore, the lateral displacement measured using the attached displacement transducer at the right portion (Figure 18c) shows an increase in the downward deformation from 7.75 mm to 8.24 mm, respectively. In addition, for specimen SP-8I, the left transducer recorded upward lateral displacement of 1.82 mm at ultimate compressive load; see Figure 18b.

As the loading started, the whole specimen reacted globally, with initiation of visible downward and upward lateral elastic displacement in the right and left portions of the plate, respectively, as recorded by both transducers in (Figure 18b,c), up to 165 kN, with recorded shortening displacement by the testing machine of 0.63 mm. Such elastic response endured up to 780.40 kN and then the stiffener started to carry out the applied load up to an ultimate capacity of 852.80 kN, with relevant shortening of 4.58 mm, with a visible increase in lateral displacement in both plate portions, which recorded +1.83 mm and −8.24 mm for the left and right portions, respectively.

The excessive downward deformation in the right portion forces the stiffener to experience outward deformation towards the right portion, as may be seen from Figure 19. This instability of the stiffeners results in crack initiation in the welding toe at the beginning and end of the weld gab (see Figure 19), which facilitates the occurrence of collapse. As seen from Figure 19 and Figure 20, the final deformed shape is asymmetric with severe downward deformation in the right portion around ±50 mm around the midspan. Specimen SP-8I passes through different failure schemes before the final collapse occurs, which may be ordered as follows: sub-plate (right portion), sub-plate (left portion), stiffener failure with inward deformation, and crack propagation at weld toe.

The last specimen in the group with intermittent chain welding is SP-10I, for which the recorded ultimate carrying capacity is 1132 kN, with developed shortening displacement at ultimate load of 3.72 mm, as presented in Figure 21a. During the one-loading-cycle test, the right portion of the plate buckled elastically up to 287.6 kN, with visible lateral displacement at the location of the attached displacement gauge of 1 mm, which is almost the same at the right portion; see (Figure 21b,c). As the applied load increased, both plate portions near the upper clamp buckled upward (toward the stiffener), up to 1000 kN, which was confirmed by the registered lateral displacement of both transducers. After crossing the elastic phase, post-buckling of the plate occurred, with visible change in the slope in both axial load and shortening/later displacement relationships, until reaching the ultimate capacity of 1132 kN without any deformation or instability of the stiffener; see Figure 22. Then, the structural stability of the whole specimen decreased gradually, which may be defined as plate-induced failure. Therefore, for specimen SP-10I, the failure sequence involves plate failure in both portions at the same time with higher recorded amplitude after crossing the elastic limit (see Figure 21) and measured deformation after collapse; see Figure 23.

It has to be stressed that the final collapse shape for specimen SP-10 I is asymmetric from a deformation amplitude point of view, but the deformation direction is almost symmetric, as proven by the final positive (upward) measurement of the collapse shape described in Figure 23.

4. Discussion and Analysis

The experimental results of the tested stiffened plates with different welding configurations will be analysed and discussed in terms of resilience, absorbed energy up to ultimate compressive capacity and collapse rate.

Relationships between plate slenderness and the absorbed energy within the elastic regime as well as the effect of increasing the base plating thickness on the absorbed energy are presented in Figure 24. The plate slenderness is calculated according to Equation (1).

For both welding configurations, as the plate thickness increases (lower plate slenderness), the absorbed energy up to elastic limit (resilience) increases nonlinearly and the probability of buckling initiation decreases, the trend may be fitted to a power function; see (Figure 24, left). For specimens with continuous welding, the increased percentage of absorbed energy is not relative to the increase in plating thickness, which is the opposite for specimens with intermittent chain welding, and such deviation increases as the plate thickness increases, as presented in Figure 24, right. This difference may arise from the stiff connection of the attached stiffener with continuous welding, represented by higher electrode consumption, which is around two times that of intermittent chain welding, as reported in [5].

After crossing the post-buckling phase and reaching the ultimate load-carrying capacity, the absorbed energy up to this point may be presented as a function of both effective plate slenderness and increased base plating thickness, as plotted in Figure 25. The effective slenderness is calculated according to the effective breadth concept, using Equation (3) given by Faulkner [6] for simply supported stiffened plates, where C₁ = 2 and C₂ = 1 are coefficients for simply supported stiffened plates.

$${\displaystyle \frac{b_{eff}}{b}}={\displaystyle \frac{C_1}{\beta }}-{\displaystyle \frac{C_2}{{\beta }^2}}for\beta \ge 1$$

(3)

As may be seen from Figure 25 (left), as the effective slenderness decreases, the deviation between the absorbed energy up to the maximum increases, which reflects the higher absorbed energy developed by continuously welded specimens than the intermittently welded ones. It has to be stressed that the change in the trend for specimen SP-10 I with less absorbed energy up to the maximum (Figure 25) is due to the plate-induced failure mode, without any visible damage to the attached stiffener (see Figure 21, Figure 22 and Figure 23), which facilitates the occurrence of failure with less shortening displacement in spite of the higher ultimate compressive capacity. Figure 25 (right) represents the effect of increasing the thickness of the base plating with respect to specimen SP-6C and SP-6I for each welding configuration on the percentage of absorbed energy up to the ultimate point for the same reference specimens. It is obvious that the trend is perfect for specimens with continuous welding regardless of the failure sequence for each specimen, in contrast with specimens with intermittent welding, i.e., SP-10I.

The relationship between the ultimate compressive strength as a function of plate slenderness for both welding configurations is presented in Figure 26 (left). It is obvious that the trend of the recorded capacity with respect to the corresponding slenderness for continuous welding is systematic and may be fitted as a polynomial function, as plotted in Figure 26 (left), with an increase in the capacity as the slenderness decreases. For specimens with intermittent welding, the trend is logical up to a slenderness of 2.54, but the failure sequence of specimen SP-10I results in a higher capacity, regardless of the weld configuration, as well as the occurrence of plate failure and plastic irregularities near the upper clamp, which interrupts the trend. The same behaviour may be noticed from the relationship between the percentage of capacity increment and increasing the base plating thickness; see Figure 26 (right). Therefore, more future tests may be performed to enhance the trend.

As may be seen from Figure 27 (left), as the plate slenderness decreases (higher plating thickness), the developed shortening displacement increases due to the increase in the load-carrying capacity for all specimens with different welding configurations, except specimen SP-10I, where the specimen collapsed due to plate-induced failure near the upper clamp with less shortening displacement and, consequently, lower absorbed energy up to the ultimate point, as given by Figure 25 (left).

As may be seen in Figure 4 (right), Table 3 and Figure 25 (right), all specimens with continuous welding are tested with upward initial imperfections, resulting from induced welding, but the recorded lateral displacement in the right portion up to ultimate load is not in the same direction for all specimens. For specimen SP-6C, the recorded lateral displacement was −2.05 mm (downward), which is in contrast to the upward initial imperfection of +5 mm; this may be due to the higher plate slenderness (3.39) of such a specimen and the failure sequence in which the initial buckling occurs in the right portion of the plate. The same change in behaviour occurred for SP-8C of slenderness (2.54), but with higher downward lateral displacement of −11.23 mm; the reason for that is the sequence and location of failure, where the sequence started in the left portion and then the right portion, with stiffener failure towards the right portion and near the upper clamp (see Figure 11), which enabled the specimen to carry out more load, with more developed lateral displacement. The opposite occurred for specimen SP-10C, where the direction of lateral displacement follows the upward initial imperfection, which indicates the ability of the lower slenderness (2.03) to dominate the final shape deformation with a higher carrying capacity. Regarding specimens with intermittent welding (Figure 25 (right)), it was observed that the change in the behaviour from upward imperfection to downward lateral deformation occurred for both specimens SP-6I and SP-8I as for the ones with continuous welding (SP-6C and SP-8C), in addition crack initiation at the weld toe, which facilitated the loss of structural capacity. Also, for lower slenderness (2.03) SP-10I, no changes in the deformation direction occurred, where the displacement transducer recorded positive lateral displacement of 4.90 mm. Therefore, it may be stated that for stiffened plate specimens with continuous and intermittent welding, the ability of plate slenderness to dominate the final collapse mode increases as the slenderness decreases. A comparison between the ultimate load-carrying capacity of the tested specimens and the empirical formulations (Equation (4) given by Paik and Thayamballi [11], Equation (5) by Zhang and Khan [15], and Equation (6) of Kim et al. [16] is presented in Figure 28.

$${\displaystyle \frac{\sigma u}{\sigma y}}={\displaystyle \frac{1}{\sqrt{0.995+0.936{\lambda }^2+0.170{\beta }^2+0.188{\lambda }^2{\beta }^2-0.067{\lambda }^4}}}$$

(4)

$${\displaystyle \frac{\sigma u}{\sigma y}}={\displaystyle \frac{1}{{\beta }^{0.28}\sqrt{1+{\lambda }^{3.2}}}}\mathrm{for}\lambda \le \sqrt{2}$$

(5)

$${\displaystyle \frac{\sigma u}{\sigma y}}={\displaystyle \frac{1}{0.8884e^{{\lambda }^2}}}+{\displaystyle \frac{1}{0.4121e^{\sqrt{\beta }}}}$$

(6)

The relationship is expressed in terms of the multiplication of β and λ and the ultimate load-carrying capacity. For continuously welded specimens (Figure 28 (left)), the empirical formulations showed a higher carrying capacity than the experimental one, which is logical due to the constraints imposed by the simply supported boundary conditions for the empirical formulations, which are different from the tested specimens, for which the unloaded edges are totally free. It may be noticed that for SP-6C ($\beta *\lambda =1.12),$ the three equations showed deviated results, where those of Zhang and Khan [15] and Kim et al. [16] are of higher and close values with respect to the experiment, but the one of Paik and Thayamballi [11] is of lower value. The reason for the better prediction by Zhang and Khan [15] and Kim et al. [16] is due to the conditional validity of both equations by a defined column slenderness (see Equations (5) and (6)), which agrees with the ones of the tested specimens of 0.33, 0.36 and 0.38 for SP-6C, SP-8C and SP-10C, respectively. Also, the higher slenderness of SP-6C of $\beta =3.39$ may affect the response.

To transform the empirical results of Equations (4)–(6) from continuous to intermittent chain welding, a proposed factor may be utilised as given in Equation (7), which is the ratio between the sum of the weld lengths ($\sum w$) and the sum of the weld gaps ($\sum g$), conditionally that $\sum w<\sum g$.

$${\left({\displaystyle \frac{Fu}{Fy}}\right)}_I={\left({\displaystyle \frac{Fu}{Fy}}\right)}_C*{\displaystyle \frac{\sum w}{\sum g}}$$

(7)

Figure 28 (right) presents the modified empirical results according to Equation (7) and experimental results for intermittent-chain-welded specimens. It is obvious that the results are comparable, especially with the formulations by Zhang and Khan [15] and Kim et al. [16], as discussed before for continuously welded specimens. It has to be stressed that more results are needed, either experimental or numerical, in order to enhance the trend.

5. Conclusions

The ultimate compressive capacity of welded stiffened steel plates using different fillet welding configurations was evaluated experimentally. The experimental results were presented and analysed; several concluding remarks and findings are listed as follows:

• For specimens with continuous welding, the higher deformation of the plate occurred around ±50 mm of the mid-span of the stiffened plate, while for intermittently welded specimens, the higher deformation is randomly located; this is due to the existing weld gaps that facilitate the occurrence of local buckling at any location as well as the cracks at the weld toe due to excessive deformation near the gaps, which is the opposite for continuously welded specimens.
• For both welding configurations, as the plate slenderness decreases, the absorbed energy up to the elastic limit increases nonlinearly. Also, the probability of buckling initiation decreases.
• As the effective plate slenderness decreases, the deviation in the absorbed energy up to the ultimate point between specimens with different welding configurations increases, which reflects the higher absorbed energy for continuously welded specimens than intermittently welded ones.
• Regression formulations are developed for ultimate compressive capacity as a function of plate slenderness for different welding configurations, and more future tests and numerical simulation may be performed to enhance the data fitting.
• For specimens with continuous and intermittent welding, the ability of plate slenderness to dominate the final collapse mode increases as the slenderness decreases.
• A comparison between the experimental results and empirical formulations is performed, showing that the results are comparable according to the imposed boundary conditions and column slenderness limitations.