Design of composite slabs with prepressed embossments using small-scale tests
4.2 Numerical comparison
All the results are related to a reference slab of 2 m span and 1.08 m width. A comparison of the results from bend-ing tests and design methods can be seen in the first part of Table 1. Results using small-scale test data are displayed in the other parts of the table. Finally, the magnitude of the plastic bending moment considering full composite ac-tion is shown.
The Slip-Block Test is older and simpler than the New Simplified Method. However, the bending resistance obtained from the Slip-Block Test is similar to that of the
m-k and partial connection methods. The bending resis-tance obtained using the New Simplified Method is less conservative, especially when the friction contribution above the support is included.
All the test results are obtained using the test setup corresponding to the Slip-Block Test, which may influence the results. Another important factor influencing results is that embossment geometry, mainly the distance from the longitudinal edge of the trapezoidal sheeting, differed from officially declared geometry. Therefore, a sensitivity study is a very convenient tool for a better understanding and comparison of the methods [18]. The effect of the se-lected input parameters (shear resistance τmax, maximum slip before failure smax and friction above support m) on the bending resistance can be observed in Fig. 15. Here, the bending resistance corresponding to τmax= 0.127 MPa and smax = 3 mm without considering friction above the support is taken as a reference value. The sensitivity of the shear resistance of mechanical interlock Hriband the sen-sitivity of the coefficient of friction m in the Slip-Block Table 1. Comparison of results of tests and design methods considering simply supported slab (2 m span) converted to a corresponding uniformly distributed load per unit area
ultimate bending moment corresponding uniform load
[kNm] [kN/m2]
results of vacuum loading tests 21.84 40.45
results of four-point bending tests 19.51 36.13
m-k method (data from manufacturer) [7] 12.98 24.03
partial connection method (data from manufacturer) [7] 16.43 30.42
Slip-Block Test 13.12 24.30
New Simplified Method 16.58 30.79
New Simplified Method + friction above support 17.76 32.89
Slip-Block Test + cast screws 22.72 42.08
New Simplified Method + cast screws 24.71 45.75
partial connection method + cast screws 23.06 42.70
New Simplified Method + inserted wedges 19.84 36.57
plastic bending moment (full composite action) 32.21 59.65
Fig. 14. State of embossments after testing with a) changing vertical clamping force, b) constant clamping force and wooden wedge blocks inserted as additional end restraints
a) b)
Test can be observed in Fig. 16. The reference value is cal-culated using Hrib= 64.74 kN/m and m = 0.46 in this case.
It is obvious that the resulting bending resistance is influ-enced much more by changes in the shear resistance of the mechanical interlock in both methods.
5 Conclusions
Small-scale shear tests on composite slabs represent a less expensive alternative to full-scale bending tests. Two de-sign methods based on small-scale tests results were cho-sen to compare: the Slip-Block Test method and the New Simplified Method.
The Slip-Block Test gives the designer specific infor-mation about the contribution of friction and mechanical interlock to the resulting shear bearing capacity. The test procedure is more intensive than most other small-scale test procedures because the magnitude of the vertical clamping force is changed during the testing of each spec-imen. On the other hand, the corresponding design method is simple and transparent. The loading procedure can be modified so that the clamping force is gradually in-creased instead of dein-creased. It is more effective and
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ables several loading series to be performed per specimen.
A disadvantage is that the values obtained from the tests correspond to higher magnitudes of slip, whereas in a real situation, lower values of slip are dominant.
The New Simplified Method describes slab behav-iour in three phases. An iterative mathematical model is needed to calculate section properties and find the solu-tion. The solution is based on the strength of concrete in tension, equality of curvatures and force equilibrium at the critical section. The method is more sophisticated and describes the real behaviour of the slab, also before reach-ing the ultimate bendreach-ing moment. Moreover, it supplies in-formation about curvature corresponding to calculated moment resistance, and so the deflection of the slab can be calculated as well. However, design using the New Sim-plified Method is generally more complicated and less transparent in comparison to the Slip-Block Test method, which could be an obstacle in practical usage. Compari-son of ultimate moments calculated using these methods and data from small-scale tests with the same arrangement show that the New Simplified Method is less conservative.
A sensitivity study indicates that friction above the sup-port has a smaller influence on the bending resistance Fig. 15. a) Influence of shear strength tmaxon bending resistance, b) influence of assumed level of maximum slip before failure smax on bending resistance in New Simplified Method
Fig. 16. a) Influence of shear resistance Hribof mechanical interlock on bending resistance, b) influence of coefficient of friction m on bending resistance in Slip-Block Test method
a) b)
b) a)
J. Holomek/M. Bajer/J. Barnat/P. Schmid · Design of composite slabs with prepressed embossments using small-scale tests than the shear resistance in both methods. Both design
methods enable additional end restraints to be taken into account.
The performance of small-scale tests may still pre-sent a significant uncertainty. The results exhibit a large scatter, especially for the magnitude of the shear force be-fore reaching slip in the case of constant clamping force or for low values of slip in the case of changing clamping force. The features that ought to be specified are, for ex-ample, optimal loading speed and conditions for casting and placing the specimens for the test setup.
Two types of easily assembled end restraints are com-pared in this paper: cast screws and inserted wooden wedges. Adding a sufficient number of screws enables the bearing capacity of the sheeting with low bond to be easily enhanced – even up to full composite action. A disadvan-tage is that it changes the behaviour of the slab from duc-tile to brittle. The ductility of the screws can be slightly in-creased by allowing their heads to protrude from the slab.
Inserting wooden wedges comes from the idea that the shear bearing capacity of the indentations in concrete is usually unused, as can be observed from visual compar-isons. By filling the ribs in the area above the support it is possible to prevent the sheeting from separating from the concrete surface. The loadbearing capacity of a slab with prepressed embossments can be effectively increased in this way. Inserting wooden wedges increases the shear bearing capacity while preserving ductile behaviour.
Acknowledgements
This paper has been worked out under the project No. LO1408 “AdMaS UP – Advanced Materials, Struc-tures and Technologies”, supported by Ministry of Educa-tion, Youth and Sports under the “National Sustainability Programme I” and under the project FAST-J-13-1918 and FAST-S-13-2077.
Notation
Ap cross-sectional area of sheeting Ac cross-sectional area of concrete
Aequ cross-sectional area of equivalent section Ea modulus of elasticity of steel
Fl longitudinal shear resistance of sheeting
Hrib rib resistance per unit length due to mechanical interlock
Ia,eq,y moment of inertia of equivalent section Ls shear span length
Lsf limiting length for full composite action Mlim,1 limiting bending moment for phase I Mlim,2 limiting bending moment for phase II Mlim,3 limiting bending moment for phase III
Nc longitudinal shear force in partial composite action
Ncf longitudinal shear force in full composite action Ru ultimate vertical reaction at end support per unit
width of slab
Vl additional longitudinal shear resistance from end anchoring
b slab width
b1 length of slip block specimen
br average steel rib spacing
dp distance from top of sheeting to centroid of effec-tive area of steel sheeting
fy yield strength
x + Lc shear span length (including length beyond sup-port)
z vertical coordinate of cross-section gVS partial safety factor
φlim,1 limiting curvature for phase I
φlim,f,0 limiting curvature calculated from maximum ten-sile strain before cracking (phase II)
φlim,sl,0 limiting curvature calculated using shear resis-tance of sheeting (phase II)
μ coefficient of friction
σa longitudinal stress in sheeting σb longitudinal stress in concrete
τmax maximum longitudinal shear strength for New Simplified Method
τu,Rk longitudinal shear strength for partial connection method (characteristic value)
References
1. Patrick, M., Poh, W.: Parameters affecting the design and be-haviour of composite slabs. IABSE reports, Zurich, 60, 1990, pp. 220–225.
2. Maekawa, K., Okamura, H., Pimanmas, A.: Non-Linear Me-chanics of Reinforced Concrete. CRC Press, 2003, p. 768.
3. Ferrer, M., Marimon, F., Crisinel, M.: Designing cold-formed steel sheets for composite slabs: An experimentally validated FEM approach to slip failure mechanics. Thin-Walled Struc-tures, vol. 44, No. 12, Elsevier, 2001, p. 1261–1271.
4. European Convention for Constructional Steelwork (ECCS):
Design Manual for Composite Slabs, No. 87, Brussels, 1995.
5. ANSI/SDI T-CD-2011: Test Standard for Composite Steel Deck – Slabs. Steel Deck Institute, 2012, available at http://www.sdi.org/publications-2/standards/
6. CSTB Technical report Cofraplus 60, 3/03-390, PAB, ARCELOR Group, 32 rue Gambetta BP 62, F-59264 On-naing, 2004, pp. 27–34.
7. Cofraplus 60. Statické tabulky, Arval ArcelorMittal Con-struction Solutions, Biskupsky´ dvu°r 7, 110 00 Praha 1, Czech Republic, available at: http:// ds. arcelor mittal. com / construc-tion/arval_easterneurope/10642/10643/language / CZ 8. Melcher, J.: Full-Scale Testing of Steel and Timber
Struc-tures: Examples and Experience, Structural Assessment – The Role of Large and Full Scale Testing, K. S. Virdi et al.
(eds.), E&FN SPON, London, 1997, pp. 301–308.
9. European Convention for Constructional Steelwork (ECCS):
Longitudinal Shear Resistance of Composite Slabs: Evalua-tion of Existing Tests, Brussels, 1998.
10. Holomek, J., Bajer, M.: Experimental and Numerical Investi-gation of Composite Action of Steel Concrete Slab. Procedia Engineering, Elsevier, vol. 40, 2012, pp. 143–147.
11. Abdullah, R.: Experimental Evaluation and Analytical Mod-eling of Shear Bond in Composite Slabs. Dissertation, Vir-ginia Polytechnic Institute & State University, Blacksburg, 2004.
12. Patrick, M., Bridge, R.: Review of Concepts Concerning Bond of Steel Decking. 12th Intl. Specialty Conf. on Cold-Formed Steel Structures, St. Louis, Missouri, 1994.
13. Patrick, M., Poh, W.: Controlled test for composite slab design parameters. IABSE reports, Zurich, 60, 1990, pp. 227–231.
14. Crisinel, M., Marimon, F.: A new simplified method for the design of composite slabs. Journal of Constructional Steel Research, 60, 2004, pp. 481–491.
15. Patrick, M., Bridge, R.: Partial shear connection design of composite slabs. Engineering Structures, vol. 16, No. 5, 1994, pp. 348–362.
16. Crisinel, M., Edder, P.: New Method for the Design of Com-posite Slabs. ComCom-posite Construction in Steel and Concrete V, 2006, pp. 166–177.
17. Guignard, P., Schumacher, A., Crisinel, M.: Etude des dalles mixtes et développement d’une méthode de calcul basée sur la relation moment-courbure. ICOM REPORT, Lausanne, 2003.
18. Kala, Z., Kala J.: Sensitivity Analysis of Stability Problems of Steel Columns using Shell Finite Elements and Nonlinear Computation Methods. Proc. of 17th Intl. Conf. on Engi-neering Mechanics, Svratka, Czech Republic, 2011, pp.
271–274.
Josef Holomek, PhD student Institute of Metal & Timber Structures Faculty of Civil Engineering
Brno University of Technology
Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147330
[email protected] (corresponding author)
148
J. Holomek/M. Bajer/J. Barnat/P. Schmid · Design of composite slabs with prepressed embossments using small-scale tests
Structural Concrete (2015), No. 1
Pavel Schmid, Assoc. Professor Institute of Building Testing Faculty of Civil Engineering Brno University of Technology
Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147491
Miroslav Bajer, Assoc. Professor Institute of Metal & Timber Structures Faculty of Civil Engineering
Brno University of Technology
Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147311
Jan Barnat, Assistant
Institute of Metal & Timber Structures Faculty of Civil Engineering
Brno University of Technology
Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147305
Structural Concrete 16 (2015), No. 1 149