Experimental, analytical and numerical studies on concrete encased trapezoidally web profiled cold-formed steel beams by varying depth-thickness ratio

Abstract

Concrete encased with trapezoidally corrugated web profiled cold-formed steel beams are used worldwide to improve resistance toward fire and corrosion, higher load carrying capacity as well as significant increase in the bending stiffness by encasing concrete on the beam portion. The present work gives a detailed description on the experimental, analytical and numerical investigation on the flexural behavior of concrete encased trapezoidally corrugated web profiled cold-formed steel beams which were simply supported at both ends and subjected to two point symmetric loading. The flexural behavior of such structure has been experimentally tested to failure under pure bending. To find the effect of concrete encasement in the web, 12 experiments were conducted by two different series. Beams having three different web corrugation angles of 0°, 30°, and 45° with two different web depth-thickness (d_w/t_w) ratios of 60 and 80 were tested. Experimental results such as load-deflection relationship, ultimate capacity, load-strain relationship, moment-curvature curves, ductility and failure mode indices of the specimens are presented. From the static bending tests the concrete encased trapezoidally corrugated web beam showed improved moment carrying capacity, ductility behavior and the resistance to transverse deflections in comparison to concrete encased with plain web beam. Especially for the beams with concrete encased 30° trapezoidally corrugated web having (d_w/t_w) ratio 60 and 80, the loading capacity was improved about 54% and 67.3% and the ductility also increased about 1.6 and 3.6 times, when compared to concrete encased beams with plain web. This research should contribute to the future engineering applications on seismic resistant structures and efficient usage of concrete encased with cold-formed steel beams by exhibiting its super elasto-plastic property. The analytical and numerical results showed good agreement with the experimental results at yield load, which indicates that the proposed analytical equations can be applied in predicting flexural strength accurately for such concrete encased trapezoidally corrugated web profiled cold-formed steel beams.

Keywords

concrete encased beam / trapezoidally corrugated web / loading capacity / super elasto-plastic

Introduction

Two types of structural steel member’s namely hot-rolled sections and cold-formed sections are being used in the construction industry. Use of hot rolled steel sections in structures is widely used in construction industry. But in case of light and moderate loaded structures as well as for the members with short span lengths, the utilization of hot rolled steel members leads to overloading and uneconomical. To overcome this flaw, a new form of steel known as cold-formed section has come into rehearsal. Cold-formed members are traditionally used as secondary bearing members such as purlins for lightly loaded roofs. Since 1990, there is an increasing use of cold-formed steel sections as primary bearing members in low to medium rise buildings.

Built-up beam is a beam with corrugated web and flange plates. The loss of stability of the web before reaching the plastic limit will be avoided by the profiles of web. When the beam length exceeds a given threshold value, the corrugated web becomes unstable and tends to buckle laterally. But, corrugated web encased with concrete could be used as an effective lateral restraint. Engineers have understood that webs with corrugation extremely intensify their stability against local buckling and thus their efficiency in structural design is optimized. Therefore, the web corrugation acts as the replacement for the web stiffeners. Furthermore, the significant cost reduction is accompanied by using thinner web, which could save the cost up to 30% while compared with webs with and without stiffeners [¹].

The use of encased beam in buildings will increase its moment carrying capacity and ductility of the composite construction. When a steel beam is encased with concrete in the web portion throughout the entire length, it is called beam with encased web. The concrete between the flange of the beam results in several advantages, such as corrosion resistance, high fire resistance and high load carrying capacity, as well as a significant increase in the bending stiffness compared to a normal steel beam. Therefore, it is recommended that concrete must be poured ahead the corrugated web profile mutually low yield strength or minimum thickness to avoid buckling occurrence earlier than yielding of steel web by He et al. [²].

Shao and Wang [³] studied the behavior of novel type of I-girder which composed of a flat-plate flange, a concrete-filled tubular flange with a corrugated web. It was established that, the conventional I-girder which failed by global buckling and the girder having concrete-filled tubular flange using a corrugated web had improved huge bending and torsional stiffness. Nonlinear finite element analysis were carried out to find out the performance of bridge girders by the whole of corrugated webs withstand to fatigue loading by Ibrahim et al. [⁴]. It was found that the fatigue life of bridge girders by the whole of trapezoidally corrugated webs were more than the conventionally stiffened plate girders.

Abbas et al. [⁵,⁶] extended a theoretical expression of the linear elastic bending performance of girder with corrugated web subjected to static symmetric loads and concluded that the theoretical results showed very good agreement with the experimental results. Chan et al. [⁷] and Khalid et al. [⁸] investigated the beams with plain web, horizontally and vertically corrugated webs by finite element package and it was observed that webs with vertical corrugation has superior flexural capacity than those mutually plain and horizontally corrugated webs. Pasternak and Kubieniec [⁹] carried out experimental investigation on girders with sinusoidally corrugated webs and it was establish that the failure due to web buckling was prevented by the sinusoidal corrugation.

Several research on the behavior of trapezoidally corrugated web profiled hot-rolled steel beams under shear has been done: analytically, experimentally and numerically [¹⁰–¹²], to investigate the shear carrying capacity and they have concluded that their carrying shear capacity from corrugated web gives a better prediction than plain web. Figure 1 shows the profile of trapezoidally corrugated web. He et al. [¹³] carried out the analytical and experimental investigation on the flexure behavior of composite I-girder with concrete encased corrugated web under hogging moment. It was found that the bending strength at ultimate and ductility were improved virtually 20% and 3 times, respectively, in concrete encased I-girder corrugated steel. Divahar and Joanna [¹⁴–¹⁷] investigated the comparison between plain web, corrugated web and encased corrugated web and it was found that the encased corrugated web shows relatively good performance.

Recently, Ungureanu and Dubina [¹] has carried out an experiment on studying the performance of built-up beams by a trapezoidally corrugated cold-formed profiled steel web back-to-back channel section. It was found that the beam capacity was almost similar, but for deeper corrugation, the deflection increased with reduction in stiffness.

Literature studies claim a large number of investigations on the behavior of trapezoidally corrugated web profiled hot-rolled steel beams under flexure [³,¹³,¹⁸–²⁰] and shear [²,¹⁰–¹²,²¹,²²]. But literatures related to the study on concrete encased trapezoidally corrugated web profiled cold-formed steel beams web under flexure is limited. To arrive at a better understanding of the level of uncertainty associated with the actual experimental observations, numerical models representing the material properties and structural configuration of the experimental conditions simulated using ANSYS workbench and the proposed analytical equations that demonstrates the boundary conditions and respective behavior of the system were developed and used to validate.

In this context, this paper presents an experimental, analytical and numerical study on the bending behavior of concrete encased trapezoidally corrugated web profiled cold-formed steel beams by varying the depth-thickness (d_w/t_w) ratio.

Experimental investigation

Test specimens

Three series of different specimens were fabricated and the behavior by testing under pure bending with simply supported end condition. One is a conventional concrete encased cold-formed steel beam having plain web with flat-plate flanges (EPWB) and the other two are concrete beams encased trapezoidally corrugated web having 30° and 45° corrugations angles with flat-plate flanges (ECWB 30° and ECWB 45°), respectively. The cross sections specimens were 150 mm × 100 mm × 2.5 mm and 200 mm × 100 mm × 2.5 mm with 2 m span. Flanges and web were connected by intermittent welds of 4 mm thick at the nodal points. To prevent the bearing failure at the loading point, stiffeners of 2.5 mm thick were provided at the loading points and at supports. Three layers of concrete was placed in the web portion, each layer was vibrated using needle vibrator. After that the surface of the paste was smoothed with a trowel and cured in a water for 28 d by wet gunny bags. The concreting was done on one side of beam and left to set for one day and the similar procedure was followed for the other side of beam.

The material properties of the concrete and cold-formed steel were all obtained from standard tests before the static flexural tests were carried out. For the cold-formed steel material, tension test was conducted according to ASTM 370 [²³] standards. The common values of tensile stress f_u, the yield stress f_y and the modulus of elasticity E, are shown in Table 1. For the concrete material M30 grade was used, its compressive strength tests was measured at different ages as per the procedure specified in IS:516-1959 [²⁴] and the measured value f_ck is 31 MPa with a mix ratio of 1:1.86:3.07 (cement: FA: CA) with w/c ratio of 0.40. The detailed configuration of the specimens are shown in Fig. 2.

Test instrumentation

The test set-up for the experiment was shown in Fig. 3. The flexural strength of the invented specimens was measured according to the ASTM specifications using 40 tones capacity hydraulic jack includes a loading frame. The load was applied at the rate of 2 kN/min until the ultimate failure of the specimens. The hydraulic jack is located above the mid-span of axis of the specimens, and so that a beam is subjected to point loading. The applied loads were monitored using a load cell and loading beam transferred two-point loads at L/3 distance from the supports. To avoid the lateral deflection and tilting of the specimen, lateral clamping of web was obligated at the supports of the specimen. The beams were tested roller support at the right end and hinged support at left end having an effective span of 1.8 m.

Results and discussions

Load-deflection relationship

As seen in Fig. 3, six LVDTs are used to measure the deflection at some critical positions. Figures 4, 5(a)–5(f) show the load-deflection development at 5 places of the bottom flange with the increase of the concentrated load. For the beams with 150 mm depth (d_w/t_w = 60), the average load carrying capacity for the specimens with plain web EPWB 0° has failed at 46 kN with an average vertical deflection of 20€mm. Similarly, the average load carrying capacity for other two specimens with corrugated web ECWB 30° and ECWB 45° was failed at 60.7 and 57 kN. The measured ultimate load of the specimens ECWB 30° is 100.2 kN was slightly larger than the specimens ECWB 45° is 99.9 kN and the average vertical deflection of the specimens ECWB 30° is 45.2 mm slightly smaller than the specimens ECWB 45° is 45.95 mm. Correspondingly, for the beams with 200 mm depth (d_w/t_w = 80), the average load carrying capacity of encased plain web specimens EPWB 0° was failed at 68.65 kN with an average vertical deflection of 21.5 mm. Similarly, the average load carrying capacity for other two specimens with corrugated web ECWB 30° and ECWB 45° was failed at 74.65 and 72.55 kN. The measured ultimate load of the specimens ECWB 30° is 114.85 kN slightly larger than the specimens ECWB 45° is 111.95 kN and the average vertical deflection of the specimens ECWB30° is 45.5 mm slightly smaller than the specimens ECWB 45° is 47.15 mm. It is observed that the specimens with ECWB 30° was having slightly larger load carrying capacity with smaller deflection when compared other specimens ECWB 0° and ECWB 4°. The confinement from corrugated profile and concrete is good, shall can increase in strength of the ECWB 30° and ECWB 45° specimens.

Ultimate capacity of the specimens

Ultimate load carrying capacity with corresponding maximum deflection of tested specimens is given in Table 2. The measured ultimate load of the specimens ECWB 30° is slightly higher than the specimens ECWB 45° and the average vertical deflection of the specimens ECWB 30° is slightly smaller than the specimens ECWB 45°. The beams with d_w/t_w = 60 (150 mm depth), the loading capacity of the specimens ECWB 30° is 1% more than the specimens ECWB 45° and it is 54% additional than the specimens EPWB 0°.

Correspondingly, for the beams with d_w/t_w = 80 (200 mm depth), the loading capacity of the specimens ECWB 30° is 2.5% more than the specimens ECWB 45° and it is 67.3% additional than the specimens EPWB 0°. Figure 6 shows the ultimate load against central deflection of the EPWB 0°, ECWB 30°, and ECWB 45° specimens.

It is observed from the Fig. 6 that 30° encased corrugated web specimens with 200 mm depth have performed well and shows higher load carrying capacity as well as super elasto-plastic of encased corrugated web beams increases utility of it in the earthquake resistant design of building structures.

Load-strain behavior of the specimens

Figures 7, 8, and 9 show the load-strain curves and comparison of load-strain relationship for the EPWB 0°, ECWB 30°, and ECWB 45° specimens. The beams having 150 mm depth (d_w/t_w = 60), the measured maximum strain value in the bottom surface and top surface for the beam with plain web at ultimate load varies from 880µ (µ=10⁻⁶) to 900µ and 868µ to 910µ correspondingly and for the beams with 30° corrugated web it varies from 2055µ to 2992µ and 2539µ to 2566µ similarly and for the beams with 45° corrugated web it varies from 2201µ to 2240µ and 2587µ to 2597µ, respectively.

Correspondingly, for the beams having 200 mm depth (d_w/t_w = 80), the measured maximum strain value in the bottom surface and top surface for the beam with plain web at ultimate load varies from 1382µ to 1406µ and 1638µ to 1560µ correspondingly and for the beams with 30° corrugated web it varies from 2444µ to 2467µ and 3157µ to 3175µ similarly and for the beams with 45° corrugated web it varies from 2347µ to 2401µ and 3047µ to 3101µ, respectively. Table 3 shows the summary of compressive and tensile strain for the encased beam specimens. It is observed that the ECWB 30° and ECWB 45° specimens has higher longitudinal compressive strain when comparison to the EPWB 0° specimens.

Ductility

The structure undergoes large deflection with losing its strength is called ductility. Ductility (µ_D) is measured in terms of ductility factor which is expressed as the ratio of ‘displacement at ultimate load’ (Δ_u) to the ‘displacement at yield load’ (Δ_y). The ultimate load is taken as the 80% of the peak load.

Table 4 shows the average ductility ratio (\overline{\mu }_D) of the specimens. The beams with 150 mm depth (d_w/t_w = 60), the EPWB 0° and ECWB 45° specimens recorded an average ductility ratio of 4.72 and 7.07, while the ECWB 30° specimens recorded an average ductility ratio of 7.60 which is nearly 1.6 and 1.075 times more than the EPWB 0° and ECWB 45°. Correspondingly, for the beams having 200 mm depth (d_w/t_w = 80), the EPWB 0° and ECWB 45° specimens recorded an average ductility ratio of 2.42 and 8.42, while the ECWB 30° specimens recorded an average ductility ratio of 8.71 which is nearly 3.6 and 1.035 times more than the EPWB 0° and ECWB 45°.

This increase in ductility shows higher ductility of the concrete encased trapezoidally corrugated web profiled cold-formed steel beams can be attributed to the confinement provided to the concrete by the corrugated profile and it is found that the concrete encased trapezoidally corrugated web profiled cold-formed steel beams behaved in a ductile manner when compared with concrete encased plain web profiled cold-formed steel beams.

Behavior and failure mechanism

Figures 10 and 11 shows the failure pattern of all the test specimens. It was observed that all the specimens EPWB 0°, ECWB 30°, and ECWB 45° failed due to flexural stress in concrete. The specimens experienced crack initiated from soffit. Most of the cracks were observed in between the two-point loading region and few cracks were also formed near the supports. The propagation of cracks can be modeled and further observed in future work by using the phase field model by Zhou et al. [²⁵–²⁹].

Analytical study

Flexural capacity and deflection of concrete encased plain web profiled cold-formed steel beams

The flexural strength is stress at failure in bending. It represents the highest stress experienced within the material at its moment of yield. Concrete encasing prevented local as well as overall buckling of cold formed steel, which ensure by improving flexural bending capacity of section and the ductility. Based on experimental results of the concrete encased web some assumptions are proposed for analytical model to predict bending moment.

1)The flange attains its yield stress at the ultimate state.

2)The cold-formed steel web and the encased concrete acts monolithically and thus the compressive strain along the height of the web reduces linearly.

3)The contribution of cracked concrete in tension to flexure strength is ignored when the tensile strength up to crack resistance.

Figure 12 shows the analysis loading of pure bending and notations for materials plastic section.

The flexural capacity (P_yield )and maximum deflection (δ) of concrete encased plain web profiled cold-formed steel beams subjected to pure bending is given by,

(1)P_{\mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}={\displaystyle \frac{\mathrm{6}{M}_{\mathrm{p}\mathrm{l}}}{L_{\mathrm{e}\mathrm{f}\mathrm{f}}}},

(2a)M_{\mathrm{p}\mathrm{l}}=M_{\mathrm{p}\mathrm{l},\mathrm{a}}-{\displaystyle \frac{\mathrm{2}{f}_{\mathrm{y}\mathrm{a}}{t}_{\mathrm{w}}{(\mathrm{0.5}{h}_{\mathrm{1}}-e_{\mathrm{p}\mathrm{l}})}^{\mathrm{2}}}{\mathrm{2}}}+{\beta }_{\mathrm{R}}\mathrm{2}{b}_{\mathrm{1}}{e}_{\mathrm{p}\mathrm{l}}(\mathrm{0.5}{e}_{\mathrm{p}\mathrm{l}}+\mathrm{0.5}{h}_{\mathrm{1}}-e_{\mathrm{p}\mathrm{l}}),

(2b)M_{\mathrm{p}\mathrm{l},\mathrm{a}}={\displaystyle \frac{f_{\mathrm{y}}.I_{\mathrm{z}}}{y}},

(2c)f_{\mathrm{y}\mathrm{a}}={\displaystyle \frac{f_{\mathrm{y}}}{{\mathit{\gamma }}_{\mathrm{w}}}},

(2d)e_{\mathrm{p}\mathrm{l}}={\displaystyle \frac{\mathrm{2}{f}_{\mathrm{y}\mathrm{a}}{t}_{\mathrm{w}}(h_{\mathrm{1}}/\mathrm{2})}{\mathrm{2}{f}_{\mathrm{y}\mathrm{a}}{t}_{\mathrm{w}}+\mathrm{2}{b}_{\mathrm{1}}{\beta }_{\mathrm{R}}}},

(2e){\beta }_{\mathrm{R}}=f_{\mathrm{c}\mathrm{k}}/{\mathit{\gamma }}_{\mathrm{w}},

(3)I_{\mathrm{z}}=I_{\mathrm{z}\mathrm{a}}+I_{\mathrm{z}\mathrm{c}\hspace{0.17em}\hspace{0.17em}\mathrm{r}\mathrm{e}\mathrm{d}},

(4a)I_{\mathrm{z}\mathrm{a}}={\displaystyle \frac{B{D}^{\mathrm{3}}-b{d}^{\mathrm{3}}}{\mathrm{12}}},

(4b)I_{\mathrm{z}\mathrm{c}\hspace{0.17em}\hspace{0.17em}\mathrm{r}\mathrm{e}\mathrm{d}}=I_{\mathrm{z}\mathrm{c}}.{\displaystyle \frac{E_{\mathrm{c}}}{E_{\mathrm{s}}}},

(4c)I_{\mathrm{z}\mathrm{c}}=e_{\mathrm{p}\mathrm{l}}{\displaystyle \frac{{(b-t_{\mathrm{w}})}^{\mathrm{3}}}{\mathrm{12}}},

(5)\delta ={\displaystyle \frac{Pa}{\mathrm{48}EI}}[\mathrm{3}{L}^{\mathrm{2}}-\mathrm{4}{a}^{\mathrm{2}}].

Flexure capacity of concrete encased trapezoidally corrugated web profiled cold-formed steel beams

The flexural capacity of concrete encased trapezoidally corrugated web profiled cold-formed steel beams subjected to pure bending is given by Eqs. (1a)–(1c), (2a)–(2e), (3), (4b), (4c) are similar like the section with concrete encased plain web. Calculating the moment of inertia for corrugated web steel section I_za, I_{top flange} and by Eqs. (6a)–(6c) and Eqs. (7a)–(7c) are used the computing the center of gravity (y) for corrugated web. The description of corrugation details and centroid for corrugated web as shown in Fig. 13.

(6a)I_{\mathrm{z}\mathrm{a}}=I_{\mathrm{t}\mathrm{o}\mathrm{p}\hspace{0.17em}\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}+I_{\mathrm{w}\mathrm{e}\mathrm{b}}+I_{\mathrm{b}\mathrm{o}\mathrm{t}\mathrm{t}\mathrm{o}\mathrm{m}\hspace{0.17em}\hspace{0.17em}\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}},

(6b)I_{\mathrm{t}\mathrm{o}\mathrm{p}\hspace{0.17em}\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}=I_{\mathrm{C}\mathrm{G}}+A_{\mathrm{1}}{h}_{\mathrm{1}}^{\mathrm{2}},

(6c)I_{\mathrm{w}\mathrm{e}\mathrm{b}}=\left[\mathrm{2}b{t}_{\mathrm{w}}{\left({\displaystyle \frac{h_{\mathrm{r}}}{\mathrm{2}}}\right)}^{\mathrm{2}}\right]+\left[{\displaystyle \frac{t_{\mathrm{w}}{h}_{\mathrm{r}}^{\mathrm{3}}}{\mathrm{6}\sin \varphi }}\right],

(6d)I_{\mathrm{b}\mathrm{o}\mathrm{t}\mathrm{t}\mathrm{o}\mathrm{m}\hspace{0.17em}\hspace{0.17em}\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}=I_{CG}+A_{\mathrm{3}}{h}_{\mathrm{3}}^{\mathrm{2}},

(7a)y_{\cos \mathrm{e}\mathrm{c}}={\displaystyle \frac{[b_{\mathrm{f}}{t}_{\mathrm{f}}{y}_{\mathrm{f}}+(h_{\mathrm{w}}/\mathrm{2}\left)t_{\mathrm{w}}{y}_{\mathrm{w}}\right]}{[b_{\mathrm{f}}{t}_{\mathrm{f}}+(h_{\mathrm{w}}/\mathrm{2}).t_{\mathrm{w}}]}},

(7b)y_{\mathrm{f}}={\displaystyle \frac{h_{\mathrm{w}}}{\mathrm{2}}},

(7c)y_{\mathrm{w}}{\displaystyle \frac{h_{\mathrm{w}}}{\mathrm{4}}},

where M_pl and M_pl,a represent the plastic moment and full plastic moment of the steel section, respectively, e_pl, f_ya, and β_R are the geometric properties according to the plastic compressive zone, design strength of steel and concrete; f_y, f_ck and are the yield stress of steel, grade of concrete and the partial safety factors for steel and concrete, respectively. I_z, I_zc, I_{zc red} and I_za is the moment of inertia of composed section, moment of inertia with respect to centroid, reduced moment of inertia of concrete, moment of inertia of steel for plain and corrugated web is given by Eqs. (5) and (6a). E_s and E_c is the modulus of elasticity of steel and concrete; L_eff is the effective span of the specimens; y is the center of gravity of the specimen for plain web and corrugated web is taken as D/2 and Eq. (7a), respectively. The values corrugation details α, a, b, c, d, t_w and L are describe in Fig. 1.

The flexure capacity P_yield can be evaluated in the following steps.

Step 1: Determining the moment of inertia of encased section I_z based on the material properties by Eq. (3).

Step 2: Computing M_pl,a based on the yield strength of steel, moment of inertia and center of gravity by Eq. (2b).

Step3:‚Obtaining the M_pl based on the plastic moment of inertia, geometric properties according to the plastic compressive zone, design strength of steel and concrete by Eq. (2a).

Step4:‚Calculating the flexural capacity P_yield by Eq. (1) in which M_pl is given by Eqs. (2a) and (2b).

Step5:‚The maximum deflection can be calculated by the flexural capacity P_yield by Eq. (1), moment of inertia of encased section I_z based on the material properties by Eq. (3), E_s is the modulus of elasticity of steel, and a is the 1/3 distance of the effective span.

Numerical study

Finite element model

The test specimens were modeled/simulated using the FEA software, ANSYS. The maximum deformation and the ultimate load of the concrete encased plain and trapezoidally corrugated web profiled cold-formed steel beams were from the analytical model. The models were simulated under experimental testing conditions like simply supported at the ends and one third loading. Obtained analytical results were compared with the experimental values. Displacement boundary conditions were assigned similar to the experimental set up so as to constrain the model to get a unique solution. The ends of the beams are restrained against displacement in vertical axis, whereas only one end is restrained against displacement in the horizontal axis. Also, at the support, the beams are not restrained against rotation on the axis perpendicular to the plane of the beam.

Modeling and loading

The Modeling of each specimen was carried out in three dimensions by using ANSYS Workbench software. 3D solid (SOLID 186) bodies with the hexahedral shape element were chosen to model the trapezoidally corrugated web profiled cold-formed steel beams and 3D solid (SOLID 65) element was used to simulate the concrete. The element can degenerate by combining some of nodes, to a tetrahedron, triangle or quadrilateral pyramid [³⁰–³⁸]. Figure 14 shows the 3D Solid Bodies. As per ASTM 370 [²³] standards coupon test were conducted to obtain the yield strength and modulus of elasticity of the material properties are given in Table 1.

Constitutive model for concrete and steel

Concrete in the encased beam has been Modeled as M30 grade concrete using ANSYS Workbench. The nonlinear model is adopted for the relationship between the stress (f_c) and strain (ε_c) of concrete in compression as shown in Fig. 15. As per IS:516:1959 [²⁴], compressive strength tests were conducted on specimens at different ages and the measured values are obtained. The modulus of elasticity of concrete E_c = 27.84 GPa, Ultimate static compressive strength of concrete f_ck = 31 MPa, mass density= 2400 kg/m³, and Poisson’s ratio v = 0.2 has mean considered. The ultimate concrete strain ε_cu is set at 0.004, considering the confined effect of the concrete encasement. The assumed stress-strain curve of steel is shown in Fig. 16. The stress- strain relation of steel is assumed to be a bilinear curve including the stain hardening effect on the both tension and compression side. As per ASTM 370 standards, coupon test was conducted to obtain the tensile strength, yield strength and modulus of elasticity of the material properties are given in Table 1.

Meshing the Geometry

Figure 17 shows the meshing of the concrete encased plain and trapezoidally corrugated web profiled cold-formed steel beams. After model creation, the most important step is meshing. Meshing a 3D solid body with SOLID 186, SOLID 65 and a 3D 20-node second-order structural solid element. ANSYS Meshing is automatically integrated with each solver within the ANSYS Workbench environment. The optimum mesh quantity is chosen by the solver of the Workbench using ‘smart size’ option and the mesh refinement is chosen as size 4 by Sangeetha and Aravind Raj [³⁹].

Numerical verification by experimental results

The deflected shape and load-deflection relationships of all the test specimens which were obtained from experimental and predicted by numerical are shown in Figs. 18(a)–18(f). The experimental investigation outputs are given as the input for the numerical investigation and it was observed that the deflections at the failure state corresponding to the maximum load in the numerical failure model are similar to the experimental results. Tables 5 and 6 lists the comparison of yield load and maximum deflection results from the experimental, analytical and numerical investigation on concrete encased plain and trapezoidally corrugated web profiled cold-formed steel beams. The yield load and maximum deflection predicted by numerical models agree well with that obtained from the experiments, in both failure modes and load-deflection curves.

The flexural strength for the concrete encased trapezoidally corrugated web profiled cold-formed steel beams has been carried out by experimental, analytical and numerical. Very good agreement between numerical, analytical and experimental ones at yield load have been obtained, in both load-displacement curves and failure mode. Which means the proposed analytical equations and numerical analysis can be applied in predict flexural strength accurately for such concrete encased trapezoidally corrugated web profiled cold-formed steel beams.

Parametric analysis

Concrete encased trapezoidally web profiled cold formed steel beams

A series of experimental, analytical and FE models were performed in the parametric study to examine the effects of corrugated web with different corrugated angles (0°, 30°, and 45°), varying depth of specimens (150 and 200 mm) and two different web depth-thickness (d_w/t_w) ratio (60 and 80).

Effect of trapezoidally web profiled

To determine the effect of trapezoidally web profiled, three series of different specimens were fabricated and tested EPWB, ECWB 30°, and ECWB 45°, respectively. The flexural experiments show that the ECWB 30° and ECWB 45° specimens has a higher load carrying capacity than the EPWB 0° specimens. Since confinement from corrugated profile and concrete is good, which increases the effective strength of concrete.

Effect of corrugation angle

Three different corrugation angles α (0°, 30°, and 45°) were considered as shown in Table 2. The specimens ECWB 30° has higher resisting moment due to which it was failed by local flange buckling alone not due to shear. Moreover, the ECWB 30° specimens increases the load carrying capacity, increased longitudinal compressive strain and higher ductility under bending.

Effect of depth of web

Two varying depth of the web (d_w) at 150 and 200 mm were also investigated. It can be observed that the yield load and maximum deflection is in linear proportion to the depth of web. Increase of the web depth will improves not only the flexure strength but also ductility.

Effect of different web depth-thickness (d_w/t_w) ratio

Two different web depth-thickness (d_w/t_w) ratio (60 and 80). The ECWB 30° and ECWB 45° specimens having (d_w/t_w) ratio 60 and 80 exhibited a ductility factor of 1.6 and 1.5 times and 3.6 and 3.5 times, when compared with EPWB 0° specimens and the results also found that the specimens ECWB 30° and ECWB 45° has more ductility.

Effect of with and without concrete encased trapezoidally corrugated web

Displacement ductility of trapezoidally corrugated beams without concrete encased with 30° and 45° corrugated webs are less than the specimens having without concrete encased plain web by Divahar and Joanna [⁴⁰]. Moreover, when compared with the specimens with concrete encased trapezoidally corrugated web it increases dramatically. This increase in ductility shows higher ductility of the concrete encased trapezoidally corrugated web profiled cold-formed steel beams can be attributed to the confinement provided to the concrete by the corrugated profile and it was observed that the concrete encased trapezoidally corrugated web profiled cold-formed steel beams has more ductility when compared with concrete encased plain web profiled cold-formed steel beams.

Conclusions

The bending behavior of EPWB 0°, ECWB 30°, and ECWB 45° has been carried out under two-point symmetric loading. The following conclusions were made from the investigation.

1)‚The flexural experiments showed that the ECWB 30° and ECWB 45° specimens has higher load carrying capacity, higher longitudinal compressive strain and higher ductility factor than the EPWB 0° specimens, since confinement from corrugated profile and concrete is good, strength of concrete was also increased and the ductility of the beam has been improved.

2)‚It was also seen that the increase of depth of web (d_w) improved both ductility as well as moment carrying capacity linearly. Increase of the web depth has improved the flexural strength.

3)‚The ECWB 30° specimens provide more load carrying capacity, increased longitudinal compressive strain and higher ductility under bending and obtained the super elasto-plastic of encased corrugated web beams increases utility of it in the earthquake resistant design of building structures.

4)‚It was found that the numerical and the analytical flexural strengths values had good agreement with the values obtained from the experimental results at yield load, which means the proposed analytical equations and numerical analysis can be applied to predict the flexural strength accurately for such concrete encased trapezoidally corrugated web profiled cold-formed steel beams.

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