Tests of carbon fibre–reinforced polymer strengthened cold-formed stainless steel tubular sections subjected to web crippling

Abstract

A total of 67 web crippling tests were conducted on carbon fibre–reinforced polymer strengthened cold-formed stainless steel square and rectangular hollow sections in this article. Several carbon fibre–reinforced polymer strengthening schemes were adopted, such as strengthened with carbon fibre–reinforced polymer sheets, strengthened with carbon fibre–reinforced polymer plates and strengthened with anchored carbon fibre–reinforced polymer plates. Two loading conditions of end-two-flange and interior-two-flange have been considered. The tests were performed on five different tubular section sizes which covered a slightly wide range of measured web slenderness ratios from 18.70 to 68.41. The effects of carbon fibre–reinforced polymer length, number of carbon fibre–reinforced polymer layers and carbon fibre–reinforced polymer strengthening schemes on the strength enhancement have been discussed based on the test results obtained from this study. It was found that the web crippling capacity of stainless steel tubular sections can be obviously increased by carbon fibre–reinforced polymer strengthening, especially for those sections with large values of web slenderness under end-two-flange loading condition. However, the strengthening enhancement of carbon fibre–reinforced polymer sheets and carbon fibre–reinforced polymer plates is quite limited due to the debonding between stainless steel tube and carbon fibre–reinforced polymer. The anchored carbon fibre–reinforced polymer plates can effectively delay or totally prevent the debonding failure. The web crippling behaviour of cold-formed stainless steel square and rectangular hollow sections strengthened with anchored carbon fibre–reinforced polymer plates has been significantly improved. Finally, the web crippling test results obtained from this study are compared with the current design strengths.

Keywords

anchor carbon fibre–reinforced polymer carbon fibre–reinforced polymer strengthening cold-formed stainless steel tubular section web crippling

Introduction

Cold-formed stainless steel sections often experience web crippling failure due to high local intensity of concentrated loads or reactions. For square and rectangular hollow section members, it is often difficult to provide transverse stiffeners at loading points, especially when the stiffeners are located away from the ends of the members. Hence, web crippling strength enhancement using carbon fibre–reinforced polymer (CFRP) in localized region can be considered as an attractive solution.

In the literature, the web crippling behaviour of cold-formed stainless steel sections has been researched (Korvink et al., 1995; Zhou and Young, 2006, 2007a, 2007b). The available web crippling design rules can be found in the American Society of Civil Engineers (ASCE) Specification (ASCE, 2002b) for the design of cold-formed stainless steel structural members and European Code (EC3, 2006) Design of Steel Structures Part 1.4: Supplementary rules for stainless steel. However, these investigations and design rules did not consider any strengthening in the web of the sections.

The ability to quickly apply CFRP materials with a minimum of disruption to the use of a structure and with virtually no change in the geometry or weight of the element makes CFRP a viable and attractive material for strengthening the existing elements. CFRP has been widely used in strengthening concrete structures. Recently, there is an increasing trend of using CFRP to strengthen steel structures. However, this approach is yet to become a mainstream application mainly due to the potential debonding failure, which is always a concern for hybrid structures where two or more materials are bonded together using adhesives. There are some studies in the literature reported on CFRP strengthened carbon steel structural members. The bond behaviour between carbon steel and CFRP has been studied (Fawzia, 2007; Fawzia and Karim, 2009; Fernando, 2010). The bond-slip models for CFRP-to-carbon steel interfaces have been proposed. CFRP strengthened rectangular hollow sections (Zhao et al., 2006) and lightsteel beam (Zhao and Al-Mahaidi, 2009) subjected to transverse end bearing force have been investigated. Several types of strengthening technique have been adopted in these two studies. It was found that the CFRP strengthening significantly increases the web crippling capacity especially for those with large web slenderness. The effects of adhesive properties on CFRP strengthening of carbon steel tubes subjected to end bearing loads have been investigated (Fernando et al., 2009). The spring elements were used to simulate adhesive as well as the debonding between CFRP plate and carbon steel tubes. However, the spring elements cannot predict the debonding failure. The finite element model overestimated the web crippling capacities of CFRP strengthened carbon steel tubes. Investigation of CFRP strengthened aluminium alloy tubular sections subjected to web crippling has also been reported (Islam and Young, 2011, 2012b; Wu et al., 2011). Design rules for web crippling of CFRP strengthened aluminium alloy rectangular hollow sections have been proposed.

However, the material properties of stainless steel are quite different from carbon steel and aluminium alloy. Besides, the cold-formed stainless steel tubular sections with rounded corners are also different from the aluminium tubular sections with sharp corners which are reported in Islam and Young (2011, 2012b) and Wu et al. (2011). In the literature, research on the web crippling of cold-formed stainless steel square and rectangular hollow sections with CFRP strengthening is very few. Islam and Young (2012a, 2013) performed experimental and numerical investigations on cold-formed ferritic stainless steel tubular sections strengthened with CFRP plate.

The purpose of this article is to experimentally investigate the improved web crippling behaviour of cold-formed austenitic stainless steel tubular sections strengthened with CFRP. A series of web crippling tests were performed on CFRP strengthened cold-formed stainless steel square and rectangular hollow sections under two loading conditions of end-two-flange (ETF) and interior-two-flange (ITF). There are three CFRP strengthening schemes adopted in this study including strengthened with CFRP sheets, strengthened with CFRP plates and strengthened with anchored CFRP plates. The failure modes, failure loads and load–web deformation behaviour of the CFRP strengthened cold-formed stainless steel tubular sections are reported. The effects of CFRP length, number of CFRP layers and CFRP strengthening schemes on the strength enhancement have been discussed based on the test results obtained from this study. Finally, the web crippling test results are compared with the current design strengths.

Material properties

Stainless steel tubes

Square and rectangular hollow sections fabricated by cold-rolling from normal strength material of austenitic stainless steel type 304 have been considered in this study, as shown in Figure 1. Tensile coupon tests were carried out to determine the material properties of the cold-formed austenitic stainless steel tubular sections. The tensile coupons were extracted from the centre of the web plate in the longitudinal direction of the untested specimens. The tensile coupon specimens were prepared and tested according to the American Society for Testing and Materials (ASTM, 1997) standard for the tensile testing of metals using 12.5-mm-wide coupons of gauge length 50 mm. The coupons were tested in an MTS displacement controlled testing machine. A data acquisition system was used to record the load and strain at regular intervals during the tests. The material properties obtained from the tensile coupon tests are summarized in Table 1, which includes the static 0.2% tensile proof stress (σ_0.2), static tensile strength (σ_u) and elongation after fracture (ε_f) based on a gauge length of 50 mm.

Figure 1.

Definition of symbols.

Table 1.

Measured material properties of cold-formed stainless steel tubular sections.

Sections b_f × d × t (mm)	σ_0.2 (MPa)	σ_u (MPa)	ε_f (%)
120 × 120 × 2.7	393	734	56.0
120 × 120 × 3.6	445	760	48.5
80 × 80 × 3.6	448	758	49.0
60 × 120 × 1.8	388	761	58.0
60 × 120 × 2.7	420	751	50.5

CFRP and adhesive

The CFRP sheet used in this study is HITEX-C300 which has a mass area ratio of 300 g/m² and nominal thickness of 0.167 mm. The CFRP plate used in this study is CFP1.4-100 which has a nominal thickness of 1.400 mm. The main characteristics of the fibres are their strength and Young’s modulus. The specified material properties for CFRP sheets and CFRP plates provided by the supplier are listed in Tables 2 and 3, respectively.

Table 2.

Material properties of CFRP sheets.

Material properties	Value
σ_u (MPa)	3492.5
E₀ (GPa)	260

Table 3.

Material properties of CFRP plates.

Material properties	Value
σ_u (MPa)	2515
E₀ (GPa)	165
ε_f (%)	1.7
t (mm)	1.4

The CFRP sheets’ adhesive adopted is Lica-100 A/B. The CFRP plates’ adhesive adopted is Lica-130 A/B. The properties of adhesive have significant influence on external bonded CFRP strengthening. The key mechanical properties of adhesive for strengthening structure are effective bond strength, elastic modulus and elongation. The material properties of CFRP sheets’ adhesive and CFRP plates’ adhesive provided by the material supplier are listed in Tables 4 and 5, respectively.

Table 4.

Material properties of CFRP sheets’ adhesive.

Material properties	Value
σ_u (MPa)	48.4
E₀ (MPa)	3443
ε_f (%)	1.6
Shear strength (MPa)	19.6

Table 5.

Material properties of CFRP plates’ adhesive.

Material properties	Value
σ_u (MPa)	51.3
E₀ (MPa)	3558
ε_f (%)	1.6
Shear strength (MPa)	18.4

Experimental investigation

Test specimens

A total of 67 web crippling tests were conducted on cold-formed stainless steel square and rectangular hollow sections strengthened with CFRP. There are three CFRP strengthening schemes adopted in this study including strengthened with CFRP sheets, strengthened with CFRP plates and strengthened with anchored CFRP plates, as shown in Figure 2. The specimens were tested under two loading conditions of ETF and ITF loading conditions. Five different hollow section sizes have been considered in this study, as shown in Table 1. The specimens had the nominal thickness ranged from 1.8 to 3.6 mm, the nominal depth of the webs ranged from 80 to 120 mm and the flange widths ranged from 60 to 120 mm. The measured web slenderness values h/t of the tubular sections ranged from 18.70 to 68.41. The specimen lengths (L) were determined according to the ASCE Specification (ASCE, 2002b). Generally, the clear distance from the edge of the bearing plate to the end of the member was set to be 1.5 times the overall depth (d) of the web rather than 1.5 times the depth of the flat portion of the web (h), the latter being the minimum specified in the specifications. The measured dimensions of the test specimens subjected to ETF and ITF loadings are shown in Tables 6 and 7, respectively, using the nomenclature defined in Figure 1. The specimens without strengthening of CFRP were also tested for reference purpose.

Figure 2.

CFRP strengthening schemes: (a) strengthened with CFRP sheets, (b) strengthened with CFRP plates and (c) strengthened with anchored CFRP plates.

Table 6.

Measured specimen dimensions and test results of CFRP strengthened cold-formed stainless steel tubular sections subjected to ETF loading condition.

Specimen	Flange	Web	Thickness	Web slenderness	Length	Exp. load per web
	b_f	d	T	h/t	L	P_Exp
	(mm)	(mm)	(mm)		(mm)	(kN)
ETF120 × 120 × 2.7N60-0	120.2	120.4	2.838	37.84	239.9	19.1
ETF120 × 120 × 2.7N60-0-R	120.3	120.5	2.843	37.81	238.5	19.1
ETF120 × 120 × 2.7N60-S	120.2	120.0	2.845	37.61	240.6	19.6
ETF120 × 120 × 2.7N120-0	120.2	120.4	2.810	38.22	300.1	26.6
ETF120 × 120 × 2.7N120-S	120.3	120.4	2.840	37.82	300.1	27.6
ETF120 × 120 × 3.6N60-0	120.5	120.3	3.620	28.81	239.8	32.1
ETF120 × 120 × 3.6N60-S	120.6	120.3	3.625	28.77	239.8	32.7
ETF120 × 120 × 3.6N120-0	120.6	120.2	3.643	28.60	300.1	46.5
ETF120 × 120 × 3.6N120-S	120.0	120.0	3.620	28.73	300.1	47.3
ETF80 × 80 × 3.6N30-0	79.9	79.8	3.658	18.81	150.5	33.7
ETF80 × 80 × 3.6N30-S	80.0	79.8	3.680	18.70	150.1	34.9
ETF80 × 80 × 3.6N60-0	80.0	79.7	3.660	18.77	180.8	47.8
ETF80 × 80 × 3.6N60-S	80.0	79.8	3.635	18.93	180.6	48.7
ETF60 × 120 × 1.8N30-0	60.2	120.2	1.637	67.93	210.3	6.1
ETF60 × 120 × 1.8N30-S	60.3	120.1	1.624	68.41	210.8	6.5
ETF60 × 120 × 1.8N30-P	59.8	120.1	1.832	61.12	210.0	6.5
ETF60 × 120 × 1.8N30-AP	59.8	120.2	1.842	60.74	210.2	10.1
ETF60 × 120 × 1.8N60-0	59.9	120.4	1.653	67.39	240.0	7.3
ETF60 × 120 × 1.8N60-S	60.7	120.0	1.632	68.01	240.2	8.0
ETF60 × 120 × 1.8N60-S-R	60.6	120.0	1.628	68.18	240.4	8.1
ETF60 × 120 × 1.8N60-S(N + d)	60.2	120.2	1.708	65.11	240.1	9.1
ETF60 × 120 × 1.8N60-S(1L)	60.2	120.1	1.642	67.66	240.8	8.0
ETF60 × 120 × 1.8N60-S(3L)	60.3	120.1	1.685	65.93	240.8	9.2
ETF60 × 120 × 1.8N60-P	59.8	120.0	1.825	61.47	252.8	12.3
ETF60 × 120 × 1.8N60-AP	59.9	120.2	1.851	60.47	244.7	22.5
ETF60 × 120 × 1.8N120-0	60.8	120.1	1.646	67.50	300.2	10.3
ETF60 × 120 × 1.8N120-S	60.7	120.2	1.728	64.35	299.7	14.5
ETF60 × 120 × 2.7N30-0	60.4	120.1	2.743	38.68	210.0	14.7
ETF60 × 120 × 2.7N30-S	60.4	120.0	2.728	38.86	209.6	15.0
ETF60 × 120 × 2.7N30-P	60.2	120.3	2.711	39.69	209.4	14.4
ETF60 × 120 × 2.7N30-AP	60.3	120.3	2.733	39.22	210.7	17.4
ETF60 × 120 × 2.7N60-0	60.5	120.5	2.638	40.37	240.1	16.4
ETF60 × 120 × 2.7N60-S	60.7	120.5	2.673	39.84	240.0	19.2
ETF60 × 120 × 2.7N60-P	60.4	120.1	2.706	39.54	237.9	18.8
ETF60 × 120 × 2.7N60-AP	60.2	120.4	2.744	39.10	240.9	31.7
ETF60 × 120 × 2.7N120-0	60.6	120.3	2.658	39.99	300.0	24.3
ETF60 × 120 × 2.7N120-S	60.7	120.5	2.628	40.53	300.0	26.0

Table 7.

Measured specimen dimensions and test results of CFRP strengthened cold-formed stainless steel tubular sections subjected to ITF loading condition.

Specimen	Flange	Web	Thickness	Web slenderness	Length	Exp. load per web
	b_f	d	T	h/t	L	P_Exp
	(mm)	(mm)	(mm)		(mm)	(kN)
ITF120 × 120 × 2.7N60-0	120.3	120.4	2.860	37.56	419.9	46.6
ITF120 × 120 × 2.7N60-S	120.1	120.6	2.885	37.29	419.3	47.4
ITF120 × 120 × 2.7N60-S(N + d)	120.3	120.5	2.855	37.64	420.3	48.8
ITF120 × 120 × 2.7N120-0	120.4	120.5	2.933	36.65	478.8	55.5
ITF120 × 120 × 2.7N120-S	120.4	120.1	2.860	37.44	480.3	57.4
ITF120 × 120 × 3.6N60-0	120.6	120.1	3.650	28.51	419.5	75.9
ITF120 × 120 × 3.6N60-S	120.6	120.1	3.605	28.88	419.6	77.1
ITF120 × 120 × 3.6N120-0	120.7	120.2	3.620	28.77	480.0	86.1
ITF120 × 120 × 3.6N120-S	120.6	120.2	3.635	28.67	478.9	87.5
ITF80 × 80 × 3.6N30-0	80.0	79.8	3.660	18.81	269.5	78.7
ITF80 × 80 × 3.6N30-S	80.0	80.0	3.653	18.88	270.3	79.9
ITF80 × 80 × 3.6N60-0	80.1	79.8	3.673	18.73	298.9	89.8
ITF80 × 80 × 3.6N60-S	79.9	79.9	3.658	18.84	299.4	91.2
ITF60 × 120 × 1.8N30-0	60.3	120.2	1.840	60.44	390.3	17.1
ITF60 × 120 × 1.8N30-S	60.4	120.2	1.843	60.31	390.0	17.6
ITF60 × 120 × 1.8N30-P	59.8	120.1	1.840	61.00	389.0	17.1
ITF60 × 120 × 1.8N30-AP	59.9	120.3	1.852	60.35	390.3	20.3
ITF60 × 120 × 1.8N60-0	60.6	120.0	1.830	60.67	419.6	19.7
ITF60 × 120 × 1.8N60-S	60.7	120.1	1.873	59.31	420.1	20.1
ITF60 × 120 × 1.8N60-S(N + d)	60.4	120.2	1.801	61.74	420.4	20.8
ITF60 × 120 × 1.8N60-P	59.8	120.2	1.840	60.88	420.0	20.0
ITF60 × 120 × 1.8N60-AP	59.8	120.3	1.831	61.09	420.3	38.0
ITF60 × 120 × 2.7N30-0	60.6	120.1	2.745	38.63	390.1	40.1
ITF60 × 120 × 2.7N30-S	60.5	120.1	2.728	38.90	389.9	40.9
ITF60 × 120 × 2.7N30-P	60.3	120.2	2.757	38.98	389.5	37.7
ITF60 × 120 × 2.7N30-AP	60.2	120.3	2.768	38.81	389.6	39.3
ITF60 × 120 × 2.7N60-0	60.6	120.1	2.730	38.85	420.0	43.5
ITF60 × 120 × 2.7N60-S	60.5	120.1	2.715	39.09	419.9	44.9
ITF60 × 120 × 2.7N60-P	60.2	120.2	2.751	39.53	420.0	43.0
ITF60 × 120 × 2.7N60-AP	60.4	120.2	2.742	39.08	421.2	70.4

Specimen labelling

The test specimens were labelled such that the type of loading condition, nominal dimensions of the specimen, bearing length and CFRP strengthening schemes can be identified, as shown in Tables 6 and 7. For example, the labels ‘ETF60×120×1.8N30-S’, ‘ETF60×120×1.8N30-P’ and ‘ITF60×120×1.8 N30-AP’ define the following specimens:

The first three letters indicate the loading conditions of ETF and ITF used in the tests.

The following symbols are the nominal dimensions (b_f × d × t) of the specimens in millimetres, where 60 × 120 × 1.8 means the flange width = 60 mm, web depth = 120 mm and thickness = 1.8 mm.

The notation ‘N30’ indicates the length of the bearing in millimetres (30 mm).

The following letters indicate the CFRP strengthening schemes of strengthened with CFRP sheets (-S), strengthened with CFRP plates (-P) and strengthened with anchored CFRP plates (-AP) adopted in the tests. The reference specimens without strengthening of CFRP are labelled using the term ‘−0’. For CFRP strengthening scheme of strengthened with CFRP sheets (-S), the CFRP strengthened width was the same length as the bearing length N for all specimens except that the following additional symbols ‘(N + d)’ were used to indicate its CFRP strengthened width. Two layers of CFRP were used for all specimens except that the following additional symbols ‘(1L)’ or ‘(3L)’ were used to indicate the layer number of CFRP strengthened.

If a test was repeated, the letter ‘-R’ indicates the repeated test.

Specimen preparation

The surfaces of the stainless steel tubular sections were polished with sandpaper to remove any impurities. And then the outer surfaces of the cold-formed stainless steel tubular sections as well as the CFRP sheets or plates were cleaned with acetone.

The two components of the adhesive are mixed together according to the weight ratio specified by the manufacturer, using a brush to apply the adhesive onto the surface of the CFRP sheets or plates. The CFRP sheets or plates were then pasted in the specified position with a rubber rolling back and forth to make the adhesive equally distributed and remove the air bubbles. The width of CFRP sheets or plates (l_c) was generally equal to the bearing length (N) except that the following additional symbols ‘(N + d)’ were used to indicate its CFRP strengthened width, as shown in Tables 6 and 7. The height of CFRP sheets or plates was equal to the depth of flat portion of the web (h) of the cold-formed stainless steel square and rectangular hollow sections. The thickness of each adhesive layer was maintained uniform to be approximately 1.0 mm. The specimens were kept for 1 week waiting for the adhesive completely curing.

For cold-formed stainless steel square and rectangular hollow sections strengthened with anchored CFRP plates, the web plates of the stainless steel tube section together with CFRP plates were punched near both top and bottom ends of the CFRP plates. The bolts were used to anchor the CFRP plates to the web plates of the cold-formed stainless steel square and rectangular hollow sections, as shown in Figure 2.

Bearing plates

The load was applied through bearing plates. The bearing plates were fabricated using high-strength steel of yield stress approximately 800 MPa. All bearing plates had the thickness of 50 mm. The bearing plates acted across the full-flange widths of the sections, excluding the rounded corner. The bearing length (N) was generally chosen to be the full-flange and half-flange widths of the section. The flanges of the specimens were not fastened to the bearing plates during the tests.

Web crippling tests

The web crippling tests were carried out under the two loading conditions of ETF and ITF specified in the ASCE Specification (ASCE, 2002b). Figure 3 shows the photographs of the test set-up.

Figure 3.

Schematic views of test arrangements: (a) front view for ETF, (b) front view for ITF and (c) end view.

For ETF and ITF loading conditions, two identical bearing plates with half round of the same width were positioned at the end and mid-length of the specimens, respectively. Hinge supports were simulated by two half rounds. The specimen was seated between the two bearing plates during the test. A servo-controlled hydraulic testing machine was used to apply a concentrated compressive force to the test specimen. Displacement control was used to drive the hydraulic actuator at a constant speed. Three transducers were used to record the web deformations of the specimens for ETF and ITF loadings. The web deformations of the specimens were obtained by the average readings of the three transducers measured between the two bearing plates.

Test results and discussions

Failure modes and test results

The failure modes observed in the web crippling tests on cold-formed stainless steel tubular sections with different strengthening schemes are shown in Figure 4. For specimens with CFRP sheets’ or plates’ strengthening only, the debonding between CFRP and cold-formed stainless steel tubular sections is the dominated failure mode, as shown in Figure 4(a) and (b). Generally, debonding initiated from the end of the CFRP that experienced high interfacial stresses developed in the region. The debonding propagated gradually towards the mid-height of the webs. For specimens strengthened with anchored CFRP plate, the debonding between CFRP plate and cold-formed stainless steel tubular sections is effectively limited due to the bolt anchorage. The deformed shape of the cold-formed stainless steel tubular sections is quite similar to the one of the reference specimens with no CFRP strengthening. With increment of web deformation, the CFRP plate is eventually fractured, as shown in Figure 4(c). The experimental ultimate web crippling loads per web for ETF and ITF loading conditions are listed in Tables 6 and 7, respectively.

Figure 4.

Failure modes of different schemes for CFRP strengthened cold-formed stainless steel tubular sections: (a) strengthened with CFRP sheets, (b) strengthened with CFRP plates and (c) strengthened with anchored CFRP plates.

Influence of CFRP layouts

Recently, strengthening structural members with CFRP sheet is a common approach. Hence, based on the strengthening scheme of strengthened with CFRP sheets, the effects of CFRP length and the number of CFRP layers have been studied. A series of tests were conducted on cold-formed stainless steel specimens of ETF60 × 120 × 1.8N60, ITF120 × 120 × 2.7N60 and ITF60 × 120 × 1.8N60 to investigate the effects of different lengths of CFRP sheets on the strength enhancement. Two kinds of CFRP strengthened lengths of N and N + d were considered for each series. The load–web deformation curves are plotted in Figures 5 to 7 for series of ETF60 × 120 × 1.8N60, ITF120 × 120 × 2.7N60 and ITF60 × 120 × 1.8 N60, respectively. It is shown that the increase in CFRP strengthened width provides some improvement on strengthening of the cold-formed stainless steel tubular sections for ETF loading condition. But it is not so obvious for ITF loading condition.

Figure 5.

Comparison of CFRP length effect on load–web deformation behaviour for CFRP sheets strengthened specimen ETF60 × 120 × 1.8N60.

Figure 6.

Comparison of CFRP length effect on load–web deformation behaviour for CFRP sheets strengthened specimen ITF120 × 120 × 2.7N60.

Figure 7.

Comparison of CFRP length effect on load–web deformation behaviour for CFRP sheets strengthened specimen ITF60 × 120 × 1.8N60.

Strengthening with two layers of CFRP sheets is a relatively effective solution and can be easily achieved (Zhao and Al-Mahaidi, 2009). Hence, in this study, mainly two layers of CFRP sheets were used to strengthen the cold-formed stainless steel tubular sections. However, one and three layers of CFRP sheets were also considered to investigate the effects of CFRP layer number on web crippling strength enhancement. The load–web deformation curves are plotted in Figure 8 for series of ETF60 × 120 × 1.8N60. It is shown that the web crippling strength enhancement increases as the layer number of CFRP increases from one to three, as shown in Figure 8.

Figure 8.

Comparison of CFRP layer effect on load–web deformation behaviour for CFRP sheets strengthened specimen ETF60 × 120 × 1.8N60.

Comparison of different strengthening schemes

The load–web deformation curves of the three different strengthening schemes are plotted in Figures 9 and 10 for ETF and ITF loading conditions, respectively. It is found that the specimen strengthened with anchored CFRP plates shows much higher strength and much better ductility than the specimens strengthened with CFRP sheets or CFRP plates only. This is because the bolt anchorage can effectively delay or totally prevent the debonding between CFRP plate and cold-formed stainless steel tubular section, as mentioned before. The CFRP strengthening effects for cold-formed stainless steel tubular sections are compared among the three different strengthening schemes in Tables 8 and 9 for ETF and ITF loading conditions, respectively. For ETF loading condition, the mean values of the web crippling capacity increment are 8.2%, 21.8% and 95.6% for CFRP sheets’ strengthening, CFRP plates’ strengthening and anchored CFRP plates’ strengthening, respectively. For ITF loading condition, the mean values of the web crippling capacity increment are 2.5%, −0.6% and 43.8% for CFRP sheets’ strengthening, CFRP plates’ strengthening and anchored CFRP plates’ strengthening, respectively. It is shown that the CFRP plates’ strengthening hardly increases the web crippling capacity for ITF loading condition. It is also shown that the CFRP strengthening has more obvious effects for ETF loading condition rather than for ITF loading condition.

Figure 9.

Comparison of different strengthening schemes’ effect on load–web deformation behaviour for specimen ETF60 × 120 × 2.7N60.

Figure 10.

Comparison of different strengthening schemes’ effect on load–web deformation behaviour for specimen ITF60 × 120 × 1.8N60.

Table 8.

Comparison of CFRP strengthening effects for cold-formed stainless steel tubular sections subjected to ETF loading condition.

Specimen	P_Exp,₀ (kN)	$\frac{P_{Exp, S}}{P_{Exp, 0}}$	$\frac{P_{Exp, P}}{P_{Exp, 0}}$	$\frac{P_{Exp, AP}}{P_{Exp, 0}}$
ETF120 × 120 × 2.7N60	19.1	1.02	–	–
ETF120 × 120 × 2.7N120	26.6	1.04	–	–
ETF120 × 120 × 3.6N60	32.1	1.02	–	–
ETF120 × 120 × 3.6N120	46.5	1.02	–	–
ETF80 × 80 × 3.6N30	33.7	1.04	–	–
ETF80 × 80 × 3.6N60	47.8	1.02	–	–
ETF60 × 120 × 1.8N30	6.1	1.06	1.06	1.64
ETF60 × 120 × 1.8N60	7.3	1.09	1.68	3.06
ETF60 × 120 × 1.8N120	10.3	1.42	–	–
ETF60 × 120 × 2.7N30	14.7	1.02	0.98	1.19
ETF60 × 120 × 2.7N60	16.4	1.17	1.15	1.94
ETF60 × 120 × 2.7N120	24.3	1.07	–	–
	Mean	1.08	1.22	1.96

Table 9.

Comparison of CFRP strengthening effects for cold-formed stainless steel tubular sections subjected to ITF loading condition.

Specimen	P_Exp,₀ (kN)	$\frac{P_{Exp, S}}{P_{Exp, 0}}$	$\frac{P_{Exp, P}}{P_{Exp, 0}}$	$\frac{P_{Exp, AP}}{P_{Exp, 0}}$
ITF120 × 120 × 2.7N60	46.6	1.02	–	–
ITF120 × 120 × 2.7N120	55.5	1.03	–	–
ITF120 × 120 × 3.6N60	75.9	1.02	–	–
ITF120 × 120 × 3.6N120	86.1	1.02	–	–
ITF80 × 80 × 3.6N30	78.7	1.02	–	–
ITF80 × 80 × 3.6N60	89.8	1.02	–	–
ITF60 × 120 × 1.8N30	17.1	1.03	1.00	1.19
ITF60 × 120 × 1.8N60	19.7	1.02	1.01	1.93
ITF60 × 120 × 2.7N30	38.7	1.06	0.98	1.01
ITF60 × 120 × 2.7N60	43.5	1.03	0.99	1.62
	Mean	1.03	0.99	1.44

Comparison of test results with design strengths and reliability analysis

As mentioned in section ‘Introduction’ of this article, the current stainless steel design specifications (ASCE, 2002b; EC3, 2006) do not provide web crippling design rules for stainless steel sections strengthened with CFRP. Therefore, the experimental web crippling loads per web (P_Exp) for the stainless steel square and rectangular hollow sections without CFRP strengthening are compared with the nominal web crippling strengths predicted using the ASCE Specification (ASCE, 2002b) and EC3 Code (EC3, 2006) Part 1.4 for stainless steel structures. In addition, the equation proposed by Islam (2012) for CFRP strengthened cold-formed stainless steel tubular sections is adopted to calculate the web crippling strengths of CFRP strengthened cold-formed stainless steel tubular sections and compared with the test results obtained from this study. The equation proposed by Islam is as follows

\begin{array}{l} P_{I s l a m} = C t^{2} f_{y} \sin θ (1 - C_{R} \sqrt{\frac{r_{i}}{t}}) (1 + C_{N} \sqrt{\frac{N}{t}}) \\ (1 - C_{h} \sqrt{\frac{h}{t}}) + [σ_{u - a d} A_{b o n d i n g}] C_{a d - F R P} \end{array}

(1)

where C is the web crippling coefficient, t is the thickness of the web, f_y is the yield stress of stainless steel (σ_0.2 proof stress), θ is the angle between the plane of the web and the plane of the bearing surface, N is the length of the bearing, h is the depth of the flat portion of the web, C_R is the inside corner radius coefficient, C_N is the bearing length coefficient, C_h is the web slenderness coefficient, σ_u-ad is the tensile strength of adhesives, A_bonding is the FRP bonded area and C_ad-FRP is the coefficient of adhesive–FRP. The coefficients as well as the respective resistance factors are detailed in Islam (2012).

The reliability of the web crippling design rules is evaluated using reliability analysis. The reliability index (β) is a relative measure of the safety of the design. A target reliability index of 3.0 for stainless steel structural members is recommended as a lower limit in the ASCE Specification (ASCE, 2002b). The design rules are considered to be reliable if the reliability index is greater than 3.0. The resistance (capacity) factor (φ) for web crippling strength as recommended by the current ASCE Specification (ASCE, 2002b), EC3 Code (EC3, 2006) and Islam’s proposed equation (Islam and Young, 2012a) is shown in Tables 10 and 11 for ETF and ITF loading conditions, respectively. The load combinations of 1.2DL + 1.6LL and 1.35DL + 1.5LL as specified in the ASCE Standard (ASCE, 2005) and the European Code, respectively, were used in the reliability analysis, where DL is the dead load and LL is the live load. The respective resistance factor (φ) and load combinations for the current ASCE Specification, EC3 Code and Islam’s proposed equation were used to calculate the corresponding reliability index (β). Reliability analysis is detailed in the Commentaries of the ASCE Specification (ASCE, 2002a).

Table 10.

Comparison of experimental results with design strengths for ETF loading condition.

Specimen	h/t	P_Exp (kN)	Comparison
			$\frac{P_{Exp}}{P_{ASCE}}$	$\frac{P_{Exp}}{P_{EC 3}}$	$\frac{P_{Exp}}{P_{Islam}}$
ETF120 × 120 × 2.7N60-0	42.4	19.1	1.13	2.22	0.96
ETF120 × 120 × 2.7N60-0-R	42.4	19.1	1.13	2.23	0.96
ETF120 × 120 × 2.7N60-S	42.4	19.6	–	–	0.68
ETF120 × 120 × 2.7N120-0	42.4	26.6	1.34	3.11	1.04
ETF120 × 120 × 2.7N120-S	42.4	27.6	–	–	0.64
ETF120 × 120 × 3.6N60-0	31.3	32.1	1.05	2.07	0.87
ETF120 × 120 × 3.6N60-S	31.3	32.7	–	–	0.72
ETF120 × 120 × 3.6N120-0	31.3	46.5	1.33	2.99	0.98
ETF120 × 120 × 3.6N120-S	31.3	47.3	–	–	0.73
ETF80 × 80 × 3.6N30-0	20.2	33.7	1.12	2.07	0.94
ETF80 × 80 × 3.6N30-S	20.2	34.9	–	–	0.90
ETF80 × 80 × 3.6N60-0	20.2	47.8	1.47	2.94	1.07
ETF80 × 80 × 3.6N60-S	20.2	48.7	–	–	0.97
ETF60 × 120 × 1.8N30-0	64.7	6.1	0.98	1.53	0.85
ETF60 × 120 × 1.8N30-S	64.7	6.5	–	–	0.56
ETF60 × 120 × 1.8N30-P	64.7	6.5	–	–	0.56
ETF60 × 120 × 1.8N30-AP	64.7	10.1	–	–	0.86
ETF60 × 120 × 1.8N60-0	64.7	7.3	1.03	1.83	0.80
ETF60 × 120 × 1.8N60-S	64.7	8.0	–	–	0.44
ETF60 × 120 × 1.8N60-S-R	64.7	8.1	–	–	0.44
ETF60 × 120 × 1.8N60-S(N + d)	64.7	9.1	–	–	0.25
ETF60 × 120 × 1.8N60-S(1L)	64.7	8.0	–	–	0.44
ETF60 × 120 × 1.8N60-S(3L)	64.7	9.2	–	–	0.50
ETF60 × 120 × 1.8N60-P	64.7	12.3	–	–	0.68
ETF60 × 120 × 1.8N60-AP	64.7	22.5	–	–	1.24
ETF60 × 120 × 1.8N120-0	64.7	10.3	1.12	2.56	0.85
ETF60 × 120 × 1.8N120-S	64.7	14.5	–	–	0.49
ETF60 × 120 × 2.7N30-0	42.4	14.7	0.98	1.68	0.92
ETF60 × 120 × 2.7N30-S	42.4	15.0	–	–	0.73
ETF60 × 120 × 2.7N30-P	42.4	14.4	–	–	0.71
ETF60 × 120 × 2.7N30-AP	42.4	17.4	–	–	0.85
ETF60 × 120 × 2.7N60-0	42.4	16.4	1.01	1.88	0.83
ETF60 × 120 × 2.7N60-S	42.4	19.2	–	–	0.67
ETF60 × 120 × 2.7N60-P	42.4	18.8	–	–	0.66
ETF60 × 120 × 2.7N60-AP	42.4	31.7	–	–	1.11
ETF60 × 120 × 2.7N120-0	42.4	24.3	1.27	2.79	0.95
ETF60 × 120 × 2.7N120-S	42.4	26.0	–	–	0.60
		Mean (Pm)	1.15	2.30	0.77
		COV (Vp)	0.135	0.229	0.285
		Resistance factor, φ	0.70	0.91	0.85
		Reliability index, β	3.58	3.98	1.09

COV: coefficient of variation.

Table 11.

Comparison of experimental results with design strengths for ITF loading condition.

Specimen	h/t	P_Exp (kN)	Comparison
			$\frac{P_{Exp}}{P_{ASCE}}$	$\frac{P_{Exp}}{P_{EC 3}}$	$\frac{P_{Exp}}{P_{Islam}}$
ITF120 × 120 × 2.7N60-0	42.4	46.6	0.94	5.43	1.31
ITF120 × 120 × 2.7N60-S	42.4	47.4	–	–	0.95
ITF120 × 120 × 2.7N60-S(N + d)	42.4	48.8	–	–	0.62
ITF120 × 120 × 2.7N120-0	42.4	55.5	1.09	6.45	1.20
ITF120 × 120 × 2.7N120-S	42.4	57.4	–	–	0.77
ITF120 × 120 × 3.6N60-0	31.3	75.9	0.78	4.89	1.15
ITF120 × 120 × 3.6N60-S	31.3	77.1	–	–	0.97
ITF120 × 120 × 3.6N120-0	31.3	86.1	0.87	5.55	1.03
ITF120 × 120 × 3.6N120-S	31.3	87.5	–	–	0.78
ITF80 × 80 × 3.6N30-0	20.2	78.7	0.78	4.84	1.29
ITF80 × 80 × 3.6N30-S	20.2	79.9	–	–	1.22
ITF80 × 80 × 3.6N60-0	20.2	89.8	0.88	5.52	1.19
ITF80 × 80 × 3.6N60-S	20.2	91.2	–	–	1.08
ITF60 × 120 × 1.8N30-0	64.7	17.1	0.86	4.22	1.24
ITF60 × 120 × 1.8N30-S	64.7	17.6	–	–	0.84
ITF60 × 120 × 1.8N30-P	64.7	17.1	–	–	0.81
ITF60 × 120 × 1.8N30-AP	64.7	20.3	–	–	0.97
ITF60 × 120 × 1.8N60-0	64.7	19.7	0.97	4.86	1.12
ITF60 × 120 × 1.8N60-S	64.7	20.1	–	–	0.63
ITF60 × 120 × 1.8N60-S(N + d)	64.7	20.8	–	–	0.34
ITF60 × 120 × 1.8N60-P	64.7	20.0	–	–	0.63
ITF60 × 120 × 1.8N60-AP	64.7	38.0	–	–	1.19
ITF60 × 120 × 2.7N30-0	42.4	38.7	0.78	4.42	1.33
ITF60 × 120 × 2.7N30-S	42.4	40.9	–	–	1.13
ITF60 × 120 × 2.7N30-P	42.4	37.7	–	–	1.04
ITF60 × 120 × 2.7N30-AP	42.4	39.3	–	–	1.09
ITF60 × 120 × 2.7N60-0	42.4	43.5	0.86	4.97	1.19
ITF60 × 120 × 2.7N60-S	42.4	44.9	–	–	0.89
ITF60 × 120 × 2.7N60-P	42.4	43.0	–	–	0.85
ITF60 × 120 × 2.7N60-AP	42.4	70.4	–	–	1.39
		Mean (Pm)	0.88	5.12	1.01
		COV (Vp)	0.111	0.126	0.248
		Resistance factor, φ	0.70	0.91	0.85
		Reliability index, β	2.73	7.83	1.94

COV: coefficient of variation.

Tables 10 and 11 show the comparison of the test results (P_Exp) with the unfactored design strengths for ETF and ITF loading conditions, respectively. The design strengths were calculated using the measured cross-sectional dimensions and the measured material properties. It is shown that the design strengths predicted by the ASCE Specification (ASCE, 2002b) and EC3 Code (EC3, 2006) are generally conservative and reliable for ETF loading condition. The mean values of the web crippling load ratios are 1.15 and 2.30 with the corresponding coefficients of variation (COVs) of 0.135 and 0.229, and the reliability indices (β) are 3.58 and 3.98 for ASCE Specification and EC3 Code, respectively, as shown in Table 10. For ITF loading condition, the design strengths predicted by the ASCE Specification are generally unconservative and unreliable. The mean value of the web crippling load ratio is 0.88 with the corresponding COV of 0.111 and the reliability index (β) of 2.73, as shown in Table 11. The design strengths predicted by the EC3 Code are quite conservative and reliable for ITF loading condition. The mean value of the web crippling load ratio is 5.12 with the corresponding COV of 0.126 and the reliability index (β) of 7.83, as shown in Table 11. It is also shown that the design strengths predicted by Islam’s proposed equation (Islam and Young, 2012a) cannot accurately predict the web crippling strengths for CFRP strengthened cold-formed stainless steel tubular sections. The mean values of the web crippling load ratios are 0.77 and 1.01 with the corresponding COVs of 0.285 and 0.248 and the reliability indices (β) of 1.09 and 1.94 for ETF and ITF loading conditions, as shown in Tables 10 and 11, respectively.

Conclusion

A test programme on CFRP strengthened cold-formed stainless steel tubular sections subjected to web crippling has been presented. A total of three strengthening schemes, namely, strengthened with CFRP sheets, strengthened with CFRP plates and strengthened with anchored CFRP plates, have been considered. The web crippling tests were performed under two loading conditions of ETF and ITF.

The effects of CFRP length, number of CFRP layers and CFRP strengthening schemes on the strength enhancement have been discussed based on the test results obtained from this study. It is shown that the increase in CFRP length can provide some improvements on strengthening of the cold-formed stainless steel tubular sections, especially for ETF loading condition. The web crippling strength enhancement increases evidently as the layer number of CFRP sheets increases. The anchored CFRP plates’ strengthening approach can effectively delay or totally prevent the debonding between CFRP and cold-formed stainless steel tubular sections. Hence, the specimen strengthened with anchored CFRP plates shows much higher strength and much better ductility than the specimens strengthened with CFRP sheets or CFRP plates only.

Finally, the web crippling test results are compared with the current design strengths. In addition, the equation proposed by Islam for CFRP strengthened cold-formed stainless steel tubular sections is adopted to calculate the web crippling strengths of CFRP strengthened cold-formed stainless steel tubular sections and compared with the test results obtained from this study. It is also shown that the design strengths predicted by the Islam proposed equation cannot accurately predict the web crippling strengths for CFRP strengthened cold-formed stainless steel tubular sections reported in this study.

Footnotes

Appendix 1 Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: The research work described in this article was supported by research grants from the State Key Laboratory for Disaster Prevention in Civil Engineering (grant no. SLDRCE14-B-07).

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