تجزیه و تحلیل رفتار سازه در مقیاس کامل فولاد دیواره نازک پانل های ساختاری سرد محوری بارگذاری شده در شرایط آتش سوزی تست شده

This paper presents a theoretical analysis to predict lateral deflections and failure times of six full-scale cold-formed thin-walled steel structural panels, tested under in-plane loads and exposed to fire attack on one side. The main objectives of this study are to investigate the effects of thermal bowing deflection and to check the relative merits of using either ENV 1993-1-2 or a modified version of ENV 1993-1-3 to perform design calculations for axially loaded steel studs under non-uniform temperature distributions. In general, the design of steel studs should also consider the effect of shift of neutral axes in both principal directions of the cross-section at elevated temperatures. However, such calculations can be rather time-consuming. Therefore, a secondary objective of this study is to assess how to effectively and accurately deal with this aspect in routine design calculations. It can be seen that thermal bowing deflections will have substantial effect on the fire resistance of steel structural panels exposed to fire on one side. However, for design calculations, it is not necessary to consider the effect of increasing thermal bowing deflections due to axial compression and reducing elastic modulus of steel at elevated temperatures. Both ENV 1993-1-2 and ENV 1993-1-3 may be used in design calculations of the ultimate load of this type of construction. It appears that ENV 1993-1-3 gives slightly better agreement with test results, but ENV 1993-1-2 is easier to implement because it does not require additional calculations of effective areas of thin-walled cross-sections at non-uniform elevated temperatures. The effect of shift of the minor axis is very small on the prediction of panel failure times and can be ignored to simplify routine design. Neutral axis shift of the major axis has some effect and may change the panel failure position from at the mid-height to the support. However, ignoring this neutral axis shift seems to give the best agreement to test results in term of panel failure location and panel failure times.

Cold-formed thin-walled (CF-TW) steel lipped channels are the predominant sections used as load bearing wall studs in light-weight steel construction. Under fire conditions, because of their thinness, CF-TW steel sections heat up quickly resulting in fast reduction in their stiffness and strength. However, if gypsum boards are combined with thin-walled steel channels to form steel stud walls, the fire resistant performance of the steel structure will improve since the gypsum boards can protect the steel studs from fire exposure, thus delaying temperature rises in the steel studs. Achieving sufficient fire resistance to prevent or delay the spread of fire and to ensure building integrity so that occupants can safely evacuate and fire fighters perform their duties is a major issue when using CF-TW steel wall panels as load-bearing walls. At present, although some analytical studies have been performed to predict the structural performance of CF-TW steel panels subjected to the standard fire condition [2], [3] and [6], the fire-resistance rating of load-bearing CF-TW steel wall panels are still assigned based on the results of standard full-scale furnace tests [3], [4], [5] and [7]. Among a few available analytical studies, Gerlich [3] presented a design model to determine the critical failure temperature of CF-TW steel studs. The model is based on the AISI design manual [1] and adopts the reduction factors for the yield strength and modulus of elasticity of steel given by Klippstein [4]. The purposed design checks are equation(1) View the MathML sourceσ=PA−P[e(ΔT)+e(M)]W≤Fy,Tforthehotflange Turn MathJax on equation(2) View the MathML sourceσ=PA+P[e(ΔT)+e(M)]W≤Fy,Tforthecoolflange Turn MathJax on where P is the applied compression force; A is the gross cross-sectional area of the steel stud; e(ΔT) is the mid-length deflection due to thermal effects; e(M) is the mid-length deflection due to bending moment; W is the elastic modulus about the stronger axis of the cross-section and Fy,T the yield stress of the steel stud at temperature T. This approach does not consider local buckling of CF-TW steel studs. Alfawakhiri and Sultan [2] also presented a structural analysis model for CF-TW steel wall studs subject to non-uniform temperatures. In their model, they assumed that flexural–torsional or weak axis buckling failure was prevented by adequate lateral restraints. Also there was no temperature variation in the vertical direction along the stud but there were temperature gradients across the stud section from one side to the other of the stud panel. Therefore, under a compression load and non-uniform temperatures, thermal bowing deflections will be induced. Based on elastic behaviour, they gave the total lateral deflection of the stud as equation(3) y(x)=ν+ν0=(φβ−2−e)[tan(0.5βL)sin(βz)+cos(βz)−1]y(x)=ν+ν0=(φβ−2−e)[tan(0.5βL)sin(βz)+cos(βz)−1] Turn MathJax on where refer to Fig. 1, β=P/(EI*); ϕ(=αΔT/bw) is the thermal bowing curvature; ΔT is temperature difference across the stud section; L is the stud height; I* is temperature dependent elasticity-modulus-weighted moment of inertia of the gross stud section about the neutral axis parallel to flanges; E is the modulus of elasticity of steel at room temperature; ey is an eccentricity that is dependent on non-uniform stiffness distribution at ends, loading condition and boundary condition of the stud and is given by equation(4) ey=(1−KR)φβ−2ey=(1−KR)φβ−2 Turn MathJax on where KR is a reduction coefficient which has a value of 0.6.After the lateral deflections have been determined, the following two equations are used to predict the column ultimate failure load equation(5) View the MathML sourceETE(PAe*+P[ey−y(x)]SeH*)≤FyH,atsupports Turn MathJax on equation(6) View the MathML sourceECE(PAe*+Py(x)SeC*)≤FyC,atmidheight Turn MathJax on in which, E T is the elastic modulus of steel at temperature T H of the hot side; E C is the elastic modulus of steel of the cold side at temperature T C; F yH is the yield stress of steel at temperature T H; F yC is the yield stress of steel at temperature T C; View the MathML sourceAe* is the temperature dependent elasticity-modulus-weighted effective stud cross-section area in compression; and View the MathML sourceSeH∗ and View the MathML sourceSeC∗ are the temperature dependent elasticity-modulus-weighted effective stud cross-section elastic modulus in bending with compression in the hot flange at supports and cold flange at mid-height, respectively. Wang and Davies [6] carried out a theoretical study using the design equations in [9] to calculate the fire resistance of thin-walled cold-formed members. They found that the ambient temperature approach was suitable for adoption under fire conditions, however, design calculations should take into account reductions in the strength and stiffness of steel at elevated temperatures, the additional bending moments due to thermal bowing and shift in the neutral axis. Neither Gerlich [3] nor Wang and Davies [6] consider the magnification of thermal bowing deflections due to axial compression. This paper presents a different approach that considers thermal bowing deflections and their magnifications as in [2], local and global buckling as in [6] based on [9]. However, it differs from the aforementioned methods in the following ways: • It considers the combination of bi-axial bending and axial compression. • It includes partial plasticity when checking the stud load carrying capacity. The proposed design calculation method will be compared against results of six full-scale fire tests on CF-TW steel panels, which have recently been conducted by the authors [10]. Afterwards, various simplifications will be introduced to the proposed method to reduce the complexity of the calculation method while maintaining its accuracy.

This paper has presented a calculation method to predict the elastic lateral deflections and failure times of steel studs in wall panels exposed to fire from one side. Two design methods, ENV 1993-1-2 and the modified ambient temperature design method ENV 1993-1-3, were used. The predicted results were compared with the test results. The following conclusions can be drawn: • The thermal bowing deflection has substantial effect on the fire resistance of steel panels exposed to fire on one side. However, for design calculations, it is not necessary to consider the effect of magnified thermal bowing deflections due to reducing elastic modulus of steel at elevated temperature. • Both ENV 1993-1-2 and ENV 1993-1-3 may be used for design calculations of the ultimate load of this type of construction. It appears that ENV 1993-1-3 gives slightly better agreement with test results, but ENV 1993-1-2 is easier to implement because it does not require additional calculations for effective areas of thin-walled cross-sections at non-uniform elevated temperatures. • The effect of a shift of the minor axis is very small and it can be ignored to simplify routine design. The neutral axis shift of the major axis has some effect and may change the predicted panel failure position from at mid-height to the support. However, ignoring this neutral axis shift seems to give the best agreement with test results in terms of the predicted panel failure location and panel failure times. Therefore it may be ignored. • The elevated temperature calculation methods are extremely complex and an alternative method should be sought.