Rahman, Q.

Sennah, K.

English

Missouri University of Science and Technology (Missouri S&T): Scholars' Mine

Missouri University of Science and Technology Scholars' Mine International Specialty Conference on Cold-Formed Steel Structures (2008) - 19th International Specialty Conference on Cold-Formed Steel Structures Oct 14th, 12:00 AM Experimental Study on Web Crippling of Lapped Cold-formed Steel Channels Subjected to Interior Two-flange Loading Q. Rahman K. Sennah Follow this and additional works at: https://scholarsmine.mst.edu/isccss  Part of the Structural Engineering Commons Recommended Citation Rahman, Q. and Sennah, K., "Experimental Study on Web Crippling of Lapped Cold-formed Steel Channels Subjected to Interior Two-flange Loading" (2008). International Specialty Conference on Cold-Formed Steel Structures. 2. https://scholarsmine.mst.edu/isccss/19iccfss/19iccfss-session4/2 This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in International Specialty Conference on Cold-Formed Steel Structures by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu. 205  Nineteenth International Specialty Conference on Cold-Formed Steel Structures St. Louis, Missouri, U.S.A, October 14 & 15 2008     Experimental Study on Web Crippling of Lapped Cold-Formed Steel Channels Subjected To Interior Two-Flange Loading   Q. Rahman1; K. Sennah2; and S. Fox3   Abstract  This investigation focused on the effects of lapped channels on the web crippling capacity of cold-formed steel members. The current design recommendations in North America Specifications specifies expressions for web crippling strength of different joist geometries in case of exterior end and concentrated load locations. However, it does not permit an increase in web crippling capacity when lapped cold-formed steel channels are subjected to interior two-flange loading. This may be attributed to the lack of experimental data on web crippling strength at interior support locations. Thus, the objective of the current research is to generate experimental data for CFS channels where both flanges of channel members are lapped at the interior support location and being loaded simultaneously. This paper summarizes the results of investigation. Test specimens were loaded to failure and load history and the failure pattern were recorded. Recommendations for further testing were drawn to establish design equations for web crippling strength of lapped CFS channels at interior support location when subjected to two flange loading. The test specimen used for the investigation is single web C-section.     1Graduate Student, Civil Engineering Dept., Ryerson University, 350 Victoria St, Toronto, ON, Canada M5B 2K3, qrahman@ryerson.ca 2Professor, Civil Engineering Dept., Ryerson University, 350 Victoria St, Toronto, ON, Canada, M5B 2K3, ksennah@ryerson.ca 3General Manager, Canadian Sheet Steel Building Institute (CSSBI), 652 Bishop St.N, Unit 2A, Cambridge, ON, Canada, N3H 4V6, Canada, sfox@cssbi.ca  206  Introduction   Web crippling is a form of localized buckling that occurs at points of transverse concentrated loading or supports of thin walled structural members. Cold-formed channels that are unstiffened against this type of loading are susceptible to structural failure caused by web crippling [2]. Web crippling may occur when there is no end or load stiffener in cold-formed steel members under concentrated force or reaction [7]. The computation of the web crippling strength by means of theoretical analysis is quite complex, as it involves a large number of factors, such as the initial imperfection of web element, local yielding in the region of load application, instability of the web element, and other factors. Hence, the current design rules found in most specifications for cold-formed steel structures are empirical in nature and may not adequately account for sections outside the range of variables tested [2]. Due to the appearance of new materials and the improvement of cold-forming techniques, the material strength and sheet thickness of such channels may be increased. Thus, the applicability of the current web crippling design rules needs to be investigated [7]. This study focused on an interior two flange loading condition with the specimen load capacity governed by a web crippling failure. Fig. 1 illustrates the necessary conditions for an interior two flange loading.   The principal benefit of this project is to develop more liberal design expression for the joist lap at support, thereby potentially making cold formed steel framing more economical. In addition, this work will give the design professional and building code officials added confidence in the reliability of steel joist construction. The current web crippling design guidelines do not permit an increase in capacity when lap is present. This investigation will enhance these guidelines by providing a modification to the interior two flange web crippling design equation to account for the lap.             Fig.1 Interior Two Flange Loading Condition  207  Current Design Equation  At university of waterloo in 1993 Prabakaran performed an extensive statistical analysis of the web crippling capacity of cold formed steel section. Based on his research he developed a unified equation for the web crippling capacity of cold-formed steel section. This equation (1) is used in North American Specifications for determination for web crippling resistance.  ⎟⎟⎠⎞⎜⎜⎝⎛ −⎟⎟⎠⎞⎜⎜⎝⎛ +⎟⎟⎠⎞⎜⎜⎝⎛ −θ=thC1tNC1tRC1sinFCtP hNRy2n               (1) Where  Pn = nominal web crippling strength C = regression analysis coefficient  Ch = web slenderness coefficient  CN = bearing length coefficient  CR = inside bend radius coefficient  Fy = yield strength  h = flat dimension of the web measured in the plane of the web  N = bearing length (lap length) R = inside bend radius  t = web thickness  θ = angle between the plane of the web and the plane of the bearing surface  Experimental Study   An experiment study performed at the Ryerson University, studied the web crippling capacity of a single web section loaded under an interior two flange condition with a variance in a lap length at support. Following is the summary of the test performed.  Test Specimen   The specimens consisted of edge-stiffened “C” section. (Fig 2) The sections have average yield stress of 53ksi (370Mpa). A nominal depth of web ranging from 8” (203mm) to 10” (254mm), and thickness of channel ranging from 0.068” (1.7mm) to 0.045” (1.14mm). The key cross sectional parameters for each tested cross-section are summarized in Table 1.    208                   Fig. 2 Typical C-Section   Bearing Plate  The loads were applied by means of bearing plates. All bearing plates were machined to specified dimensions. The thickness of bearing plates was 0.5” (12.7mm). The bearing plates were designed to act across the full flange width of the channels. The length of bearing plate was equal to the lap length (N). The flanges of the channel specimens were restrained by the bearing plate.  Specimen Labelling  Total 24 specimens were tested. Each specimen was labeled such that the depth, thickness and lap length could be identified from the label. For example, the labels “10C14 250” define the following specimens. • The first two letters shows the over all depth of the web in “inches”. • The letter “C” shows that specimen cross section is “C”. • The next two digits show the thickness of section in “gauge”. • The last three digits shows the lap length in “inches”  Material Properties  The material properties of the test specimens were determined by tensile coupon test. For each section tested, the three coupons were taken from the center of the  209  Table 1. Typical “C” Section Properties  N (in) 2.5 3.625 6 2.5 3.625 6 2.5 3.625 6 2.5 3.625 6 Fy (ksi) 51.80 51.80 51.80 54.70 54.70 54.70 53.16 53.16 53.16 56.50 56.50 56.50 df (in) 0.787 0.787 0.787 0.708 0.708 0.708 0.708 0.708 0.708 0.708 0.708 0.708 R (in) 3.38 3.38 3.38 2.77 2.77 2.77 2.77 2.77 2.77 1.78 1.78 1.78 B (in) 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 t (in) 0.067 0.067 0.067 0.056 0.056 0.056 0.055 0.055 0.055 0.047 0.047 0.047 h (in) 9.52 9.52 9.52 9.68 9.68 9.68 7.63 7.63 7.63 7.75 7.75 7.75 D (in) 10 10 10 10 10 10 8 8 8 8 8 8 Specimen  10C14   10C16   8C16   8C18  210  web plate in the longitudinal direction of the undisturbed specimens. The tensile coupons were prepared and tested according to American Society of Testing and Materials (ASTM A370, 2005). To measure the actual thickness of specimen the galvanized coating was removed by hydrochloric acid solution. The averages of three coupon tests for each specimen were used in the formula. Table2 shows the material mechanical properties of tested specimens.  Table 2. Mechanical Properties   * Based on 2” gauge length           Specimen Test # t (in) Fy (ksi) Fu (ksi) % Elongation *   10C14   1 0.0678 51.90 68.50 34.5 2 0.0676 52.20 69.00 34.5 3 0.0677 51.40 68.50 34.0 Average 0.0677 51.80 68.70 34.3  10C16  1 0.0564 54.90 69.50 32.5 2 0.0562 54.30 70.10 33.0 3 0.0564 54.90 70.20 32.5 Average 0.0563 54.70 69.90 32.7  8C16  1 0.0555 53.20 69.70 34 2 0.0549 53.20 70.00 34 3 0.0552 53.10 70.00 34 Average 0.0552 53.16 69.90 34  8C18  1 0.0467 56.10 73.00 22 2 0.0476 56.80 73.20 22 3 0.0468 56.60 73.00 22 Average 0.0470 56.50 73.06 22 211  Test Procedure  The channel specimens were tested using interior two flange loading conditions (ITF) according to AISI specification. The test setup of ITF is shown in Fig 3. The channels at lapped was attached together with 4 self drilling screws size #10x1”. It should be noted that the two rows of screws are located at the third point of the web depth. Two identical bearing plates of the same width were placed top and bottom of channel at lap. Length of bearing plate was equal to length of lap. Channels’ sectional rotation at there ends were restrained by inserting their ends into a U-shape steel support system. In this case, the channel member is considered unbraced between this end rotational restraint and the interior support location. A 50 kip (222kN) capacity hydraulic jack was used to apply a compressive force to the test specimens over the interior support. Web lateral deflection and vertical movement of the channel top flange were recorded using LVDT’s. Each specimen was loaded incrementally till complete collapse. Failure was considered at the point at which the specimens could not accept a further load. Table 3. Shows the test results of all the tested specimen.   Fig 3. Schematic diagram of loading condition            Fig 4. Section at “A-A”  Fig 5. Section at lap 212                   (a)                    (b)  Fig 6. Specimen sample before test213                    (a)                   (b)  Fig 7. Specimen after failure 214  Table 3. Interior two flange loading Test Results   Development of New Coefficients  A nonlinear regression analysis was performed by using the unified web crippling expression to update the fastened case coefficients for single web “C” section subjected to ITF loading. For the regression analysis, the results of studies were analyzed using “MinRes” computer software. New proposed correction coefficients are shown in table 4.    Section Lap Length “N” (mm) Test #1 Pt1 (kip) Test #2 Pt2 (kip) Average Pt avg (kip)  10C14  2.5” 4.65 4.50 4.57 3.625” 4.63 5.17 4.90 6” 6.23 6.24 6.24  10C16  2.5” 2.84 3.20 3.02 3.625” 3.65 3.42 3.53 6” 5.06 5.40 5.22 8C16 2.5” 3.64 3.40 3.52 3.625” 4.12 4.15 4.14 6” 5.32 4.92 5.11 8C18 2.5” 2.62 2.86 2.74 3.625” 3.00 3.57 3.30 6” 3.60 3.94 3.76 215  Table 4. New Coefficients for Single Web Section  Notes: The above coefficient apply when h/t ≤172, N/t ≤127, N/h ≤ 0.78, R/t ≤ 1.97 and θ = 90°  Evaluation of Test Results  For the recommendation of this study, the recorded failure load for each specimen Pt was normalized by division of the corresponding design strength Pn. Pn was calculated by using equation 1 with new coefficient calculated. Pt/Pn values greater than unity for most of the specimens, meaning that the tested web-crippling values are greater than the predicted web-crippling values. This makes the analytical approaches conservative. The Pt/Pn ratio used for analysis of the test data. 00.10.20.30.40.50.60.70.80.911.11.21.30 1 2 3 4 5 6 7 8 9 10 11 12 13Test numberPt/Pn Fig 8. Pt/Pn for “C” Section Support and Flange Conditions Load Cases C CR CN Ch Fastened To Support  Stiffened Flanges Two Flange Loading Interior Lap 2.5 0.02 1.01 0.001 216    New Safety Coefficient  The objective of structural design and construction is to produce safe, serviceable, economic, durable and aesthetic structures. Structures must be able to withstand the loads acting on them during a reasonable lifetime. For cold formed steel member design there are two different methods, Limit State Design (LSD) and Allowable Stress Design (ASD). Based on a probabilistic concept, the structural safety can be measured in terms of a reliability index, β. The theory of probability can be applied to both design methods to achieve the same degree of structural safety.  Procedure for calculating both the resisting factor, φ, for load resistance factored design (LRFD), and the factor of safety, Ω, for allowable stress design (ASD), are well described in North American Specifications. The resistance factor φ and factor of safety Ω can be calculated as follows. Table 5. Shows the new proposed resistance factor and factor of safety.                                                       (2)          Ω = 1.6 / φ            (3)   Where C φ = Calibration coefficient and is equal to 1.52 for the United States and Mexico and 1.42 for Canada Mm = Mean value of material factor, “Mm = 1.10” Fm = Mean value of fabrication factor, “Fm = 1.00” Pm = Mean value of professional factor, “Pm = 1.0” βo = Target reliability index and is equal to 2.5 for structural members and 3.5 for connections for the United States and Mexico, and 3.0 for structural members and 4.0 for connections for Canada VM = Coefficient of variation of material factor “VM = 0.10”  VF = Coefficient of variation of fabrication factor “VF = 0.05” CP = Correction factor and is equal to (1+1/n)m/(m-2) for n ≥ 4, and 5.7 for n =       3  m = Degrees of freedom and is equal to (n-1) n = Number of tests VP = Coefficient of variation of test results, “VP = 10.94%” VQ = Coefficient of variation of load effect = 0.21 e = Natural logarithmic base (2.718)   ( ) 2Q2PP2F2M0 VVCVVmmm ePFMC +++β−φ=φ217  Table 5 Resistance Factors and Factors of Safety   Conclusions   A test program on cold-formed stiffened lapped channels subjected to web crippling has been presented in this paper. Channel specimens having an average nominal yield stress of 53ksi (370Mpa) were tested. The specimens were tested using interior two flange loading condition according to American Iron and Steel Institute (AISI 2001) specification for cold-formed steel structures. The concentrated load or reaction forces were applied by means of bearing plate. New proposed correction coefficient for equation 1 is shown in this paper. New proposed resistance factor and safety factor is also shown in this paper.  Acknowledgements   The authors are grateful to the Canadian Sheet Steel Building Institute (CSSBI) for providing all test specimens for this research. This research is part of the Master’s program of the first author. The financial support from Ryerson University to the first author in the form of Ryerson Graduate Scholarship is greatly appreciated.  Notation  C   Coefficient depending on the section type Ch   Web slenderness coefficient CN   Bearing length coefficient CR   Inside bend radius coefficient C.O.V.   Coefficient of variation D   Total depth of the Channel  Fy  Yield strength of steel h   Flat dimension of web measured in plane of web Support and Flange Conditions Load Cases Tests No. Mean Value C.O.V S136  AISI  Ω φ Ω φ Fastened To Support Stiffened Flanges Two Flange Loading Interior Lap 24 1.045 0.109 2.30 0.70 1.90 0.85 218  ITF   Interior Two Flange Loading N   Bearing length Pm   Mean Pn   Computed web crippling strength Pt   Web crippling strength in the test R   Inside bend radius t   Thickness of the web VP   Coefficient of variation β   Reliability index θ  Angle between the plane of the web and plane of bearing surface Ω   Factor of safety φ  Resistance factor  References  1. American Iron and Steel Institute (AISI). (2001). “North American Specification for the Design of Cold-formed Steel Structures Members”. Washington D.C. 2. Ben Young and Gregory J. Hancock. (2001). “Design of cold-formed channels subjected to web crippling” Journal of structural engineering, Vol. 127, No. 10, Oct 2001. 3. M.W. Holesapple and R.A. LaBoube. (2003). “Web crippling of cold formed steel beams at end supports”. Engineering Structures 25 (2003) 1211-1216, University of Missouri-Rolla, Rolla, Mo, USA. 4. R. LaBoube, and R. Schuster. 2002. “Standard test method for determining the web crippling strength of cold-formed steel members.” AISI Sponsored Report, American Iron and Steel Institute. 16p. 5. Wei-Wen Yu. “Cold formed steel design”. New York: John Wiley & Sons, 2000. 6. Wei-Xin Ren; Sheng-En Fang; and Ben Young. (2006). “Finite-Element simulation and design of cold-formed steel channels subjected to web crippling”. Journal of structural engineering, Vol. 132, No. 12. Dec 01, 2006. 7. W. Ren, S. Fang, and B. Young. (2006). “Finite-Element simulation and design of cold-formed steel channels subjected to web crippling.” ASCE Journal of Structural Engineering, 132(12): 1967-1975. 

Experimental Study on Web Crippling of Lapped Cold-formed Steel Channels Subjected to Interior Two-flange Loading

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Experimental Study on Web Crippling of Lapped Cold-formed Steel Channels Subjected to Interior Two-flange Loading

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