Compressive Membrane Action in RCC Slabs

Department of Civil Engineering NED University of Engineering and Technology

Karachi, Pakistan

Seminar on

Compressive Membrane Action in RCC Slabs CE-503: Advanced Reinforced Concrete

November, 2010

Submitted By

Sadaf Fatima CE-05

M-Engg, Batch 2009-10

Submitted To

Prof. Dr. S.F.A. Rafeeqi

Compressive Membrane Action in RCC Slabs

NED UET, Karachi Page 1

Contents 1

List of Figures 2

Introduction 4

Impetus of Research 5

Types of Reinforced Concrete Slab Construction 6 Approaches to Analysis and Design of Slab System 7 Membrane Action 8 Experimental Research 11 Treatment in Design Codes 16 Considering Membrane Action in Design 17 Conclusion 19 References 20



List Of Figures

Figure-1: Beam-Less Slab Figure-2: Beam Slab Figure-3: Axial forces developed in laterally restrained slab: a) slab subjected to transverse loading, b) slab elongates upon cracking, c) restrained elongation induces axial compression. Figure-4: Schematic Load-Deflection curve of a slab with full edge restraint (Park 1964) Figure-5: Load-Deflection curve for slabs Figure-6: Comparison of slab strength results (Taplin and Hon) Figure-7: Comparison of load carrying capacity with code predictions (Alam, Amanat, Seraj)



To my husband Shariq,

my son Sameer,

my daughter Rania,

my mother-in-law,

for their never ending support, love and patience throughout the period of

accomplishing this task, without which I would never have gotten this far,

my teacher and advisor Dr. S. F. A. Rafeeqi,

whose teachings have awaken in me the passion to learn more, and has

encouraged me to work hard consistently and who has reminded me and

my fellow engineers, our role, being an engineer towards our society,

And above all,

my beloved mother,

for her prayers and

the strength of body and soul she has endowed me with,

by upbringing me the way she did.



Introduction Reinforced concrete slabs are one of the most common structural engineering elements. Their behavior strongly depends on the support condition and interaction of slab with the surrounding structure. If the edges of slabs are restrained against lateral movement by stiff boundary elements, compressive membrane forces are induced in the plane of slab when, as the slab deflects, changes of geometry cause the slab edges to move outward and to react against the bounding elements. The compressive forces so induced enhance the flexural strength of slab sections at the yield lines which will cause the ultimate load of the slab to be greater than the ultimate load calculated using Johansen’s theory of yield lines. This action enhances not only the flexural capacity of slabs, but also their punching capacity in case of beamless slabs. At larger deflections, the slab edges tend to move inward, and, if the edges are laterally restrained, tensile membrane forces are induced that may enable the slab to carry significant load by catenary action of the reinforcing steel. The three factors, membrane action, flexural behavior and punching shear are interdependent. The type and degree of membrane action will depend on the loading ,support conditions and the shape (both plan and cross sections) of the slab. The flexural strength is generally improved in a compressive membrane field. The punching shear strength will decrease as the amount of cracking due to flexure increases. Therefore, as membrane action improves the flexural strength, it also aid the punching strength, unless the shear failure load is much below the flexural failure load. The presence of compressive membrane action has been recognized for many decades now, but its obvious benefits are not fully utilized in design and assessment codes.



Impetus of Research The objective of this research is to investigate the influence of compressive membrane action on the behavior of RCC slabs.



Types of Reinforced Concrete Slab Construction RCC slabs have taken many forms with the development of methods of construction, economics, stability of particular slab system as per requirement and advancement in methods of analysis of slabs. Slabs are mainly categorized in two general categories;

1- Beamless Slabs 2- Slabs supported on beams on all four sides.

Figure-1: Beam-Less Slab

Figure-2: Beam Slab



Beamless Slabs One of the advantages of beamless slabs is that they are easier to construct due to simplicity in the formwork. Design is usually governed by the shear strength at columns. Deflection is also a major concern under heavy loading (See Figure-1). Slabs Supported On Beams If severe deflection limits are imposed, two-way slab will introduce moderately stiff beams which will reduce deflection more than largest column capital. Beams are also easily reinforced for shear. They are used in structures which are to resist large horizontal loads by frame action as they provide greater lateral stiffness because of both the presence of the beams and the greater efficiency of the beam-column connections (See Figure-2). Approaches to Analysis and Design of Slab System There are numbers of approaches to analysis and design of reinforced concrete slab systems. These various approaches are elastic theory, limit analysis theory and modifications to elastic theory and limit analysis theory as in ACI Code. Elastic Theory Analysis The distribution of moments and shear found by elastic theory is such that,

1- The equilibrium conditions are satisfied at every point in the slab. 2- The boundary conditions are complied with. 3- Stress is proportional to strain, i.e., bending moments are proportional to

curvature.

Examples are direct design method, equivalent frame method. Limit Analysis Limit Analysis recognizes that because of plasticity, redistribution of moments and shears away from elastic theory distribution can occur before the ultimate load is reached. However, yield line theory does not take account of membrane effects in the slab, which are often present in reinforced concrete slabs at the ultimate load as a result of boundary conditions and the geometry of deformations of slab segments.



Membrane Action Consider the behavior of a reinforced concrete slab under transverse load, shown in Figure-3. As the slab deflects under the load, the concrete on the tension face cracks and the reinforcement is stretched. Typically, the strains on the tension face will be considerably greater in magnitude than those on the compression face.

Figure-3: Axial forces developed in laterally restrained slab: a) slab subjected to transverse loading, b) slab elongates upon cracking, c) restrained elongation induces axial compression.



The net tensile strain resulting at the slab mid-depth causes the slab to expand, producing outward horizontal displacements at the slab ends. The tendency to expand will be prevented, to some degree, by the lateral stiffness of supporting columns, beams, or walls. Adjoining slab panels will also form an extremely stiff diaphragm which will oppose the expansion of the loaded slab. As a result, compressive membrane force will be induced in the loaded slab owing to restrained expansion. The compressive force, in turn, produces an increase in the nominal flexural capacity of the slab section. This mechanism is known as membrane action and can lead to significant increases in the load carrying capacity of slab. In more advanced stages, of deformation, the concrete may crush completely leaving only the reinforcement to act as a tensile net. This second stage behavior is termed as Catenary Action.

Figure-4: Schematic Load-Deflection curve of a slab with full edge restraint (Park 1964)



Figure-4 shows the load –central deflection curve of a uniformly loaded two-way rectangular reinforced concrete slab with laterally restrained edges. One can distinguish 3 phases: Phase-1, From A to B: As the load is increased from A to B, the yield line pattern develops, and with the help of compressive membrane forces, the slab reaches its enhanced ultimate load at B. The introduction of compressive membrane forces in the slab can be thought of as being due to jamming of the slab segments between boundary restraints, which causes the slab strips to arch from boundary to boundary. The induced compressive membrane force in slab results in an enhancement of the flexural strength of slab section. Phase-2, From B to C: As the deflection increases beyond B, the load carried by the slab decreases rapidly because of a reduction in compressive membrane force .As C is approached, the membrane forces in the central region of slab change from compression to tension. Phase-3, From C to D: Beyond C the slab carries load by the reinforcement acting as a plastic tensile membrane with full depth cracking of the concrete over the central region of slab due to the large stretch of the slab surface. The slab continues to carry further load with an increase in deflection until at D, the reinforcement begins to fracture or some other component in the system fails. The load at B will be referred to as ultimate load.



Experimental Research Effects on Flexural Capacity Perhaps, the most dramatic demonstration of membrane action was made by Ockleston (1955). The floor slabs in a 10-year old three storey reinforced concrete structure were intentionally loaded to destruction. The lightly reinforced two-way slab panels were 135mm thick, 4.9m x 4.1m in plan, and bounded by main and secondary beams. The slabs were designed for a dead load of 3.2 kN/m2 and a superimposed floor load of 3.4 kN/m2. Upon gradual loading, the floor did not collapse until the total load reached 40.4 kN/m2, representing a factor of safety of 6.12. The structural aspects pertaining to the 1978 collapse of a warehouse structure in Niagra Falls were examined in a paper (Vecchio and Collins 1990). The collapsed structure was the Kimberley Clark Warehouse building, a four-storey reinforced concrete structure with flat-slab floors supported on columns with capitals. Its floors were designed for a dead load of 4.8kN/m2 and a superimposed live load of 6.0kN/m2, thus the total design load was 10.8kN/m2. In time, the third floor of the building came to be used as a storage site for nickel materials. At the time of collapse, the total load imposed over several entire bays of the third floor was estimated to be in excess of 48kN/m2. It is a disputed issue as to whether overloading of the floor, or the effects of a fire burning directly beneath, caused collapse. Nevertheless, the floor demonstrated a factor of safety against collapse of 4.5 relative to design loads. It was surmised that this high strength reserve was developed primarily through the influence of compressive membrane action in the slabs. In a test conducted by Gamble et al., on a ¼ scale model of a nine panel (3x3) reinforced concrete slab and beam floor, when the interior panel alone was subjected to a uniformly distributed live load, the supporting beams failed when the load was approximately twice the ultimate load predicted by Johansen’s yield line theory. This slab was in the tensile membrane stage, as the mid span deflection was about twice the slab thickness, and tensile cracks penetrated the full thickness of the slab in the central portion of the panel. Vecchio and Tang conducted test on two large-scale slab strip specimens consisted of 100mm thick, 1500mm wide slab strip built integral with two stub columns 200x200 mm in cross section with 100mm thick drop panel provided at each column. Transverse edge beams were included at the ends to facilitate the desired support conditions. The results demonstrated the influence of membrane action in reinforced concrete slabs. Axial forces induced because of membrane action served to increase the flexural stiffness and load-carrying capacity of slab by about 30 to 40% relative to an unrestrained slab. However, test results also



indicated that geometric non-linearity effects had also a significant influence over capacity. The high axial forces induced, coupled with large slab deflections at ultimate load, created large secondary moments which partially negated the beneficial influence of membrane action. Two ¼ scale models of a reinforced concrete nine-panel (3x3) flat slab system supported by four interior columns and by a continuous wall around perimeter have been tested under uniform static and dynamic loading by Criswell, and showed a 30% increase in the ultimate load due to compressive membrane forces from the restraint of the boundry walls. Comparison of this test result with the load enhancement obtained by Ockleston, Lienbenberg and Gamble et al. illustrates that the increase in ultimate load due to membrane action is more significant for slab-and-beam systems than for flat slab systems. In a paper presented by G.S.T. Armer (1968) on the ultimate load test of slabs by strip method, it was shown that in slabs having relatively higher reinforcement ratio, it was possible to increase load beyond the limiting state without collapse resulting. The applied load was then carried by a combination of flexural and compressive membrane action. This was not possible in the slab with low reinforcement ratio because of its low moment capacity.( See Figure-5) As shown in Figure-5, the main difference between two slabs is their behavior after the limiting (maximum) compressive membrane action has been generated by the partial restraint of the edge beams. In a paper by Taplin and Hon, a method for assessing typical beam-and-slab bridge decks taking into account the compressive membrane action, is described and experimental results are compared with capacity predicted by code. (See Figure-6)



Figure-5: Load-Deflection curve for slabs.

Figure-6: Comparison of slab strength results (Taplin and Hon)



Effects on Punching Shear Capacity As demonstrated by Armer (1968), the enhancement effects of compressive membrane action on the punching load of a slab under a concentrated loading, if they could be taken into account in analysis, would probably lead to considerable benefits in economy. Further research was encouraged to attempt to simulate boundary conditions more closely than those tests carried out in past. This conclusion was reached after a study of number of tests carried out at Queen’s university, Belfast, on quarter scale models and in light of the findings made by Armer. An experimental study was conducted by A.K.M. Jahangir, KM Amanat and SM. Seraj on the punching shear behavior of concrete slabs. The experiments comprised of tests on restrained as well as unrestrained, 15 slab specimens, with variation of flexural reinforcement and slab thickness. Edge restraint was provided by means of edge beams of various dimensions to mimic the behavior of continuous slabs. All the models underwent punching type of failure with their inherent brittle characteristics and failed at a load much higher than those predicted by the design codes. It was found that the ultimate punching shear capacity and behavior of slab samples are dependent on restraining action of slab edges, flexural reinforcement ratio, slab thickness and span-to-depth ratio. It was also noted that cracking pattern were fine and large in number in case of strongly restrained slabs. On comparing the test results with different code predictions, it appears that, ACI 318 (2005) is most conservative in calculating punching shear capacity of slabs. The experimental load capacity was averagely 1.8 times higher than that calculated by ACI code. Whereas, CEB-FIP (1990) code was found to be less conservative than ACI 318, BS 8110 and CAN3-A23.3.( See Figure-7)



Figure-7: Comparison of load carrying capacity with code predictions (Alam, Amanat, Seraj)



Treatment in Design Codes In design and assessment codes, the flexural strength of reinforced concrete slabs is usually determined using an elastic analysis and the ultimate strength of the cross-section. The yield line theory developed by Johansen can also be used to determine the ultimate strength of a reinforced concrete slab. These theories have a common limitation, in that compressive membrane action within the slab cannot be taken into account. The Ontario Highway Bridge Design Code first introduced provisions for compressive membrane action in 1979. This code (and later editions including Canadian Highway Bridge Design code) contains an empirical deck slab design method for slab on girder bridges that reduces amount of steel required in concrete slab decks. The code allows this to be done only if certain restrictions on span length, slab thickness, detailing of diaphragms and connection between slab and beam are met. In 2002, the United Kingdom Highways Agency published guidelines for the use of compressive membrane action in bridge decks. This allows for both simplified and rigorous analysis to utilize the beneficial effects of membrane action where adequate deck slab restraint exists. Some of the present-day code provisions usually specify the punching shear strength as a function of compressive strength of concrete alone. Thus, these codes do not take adequate account of possible role of specimen size and edge restraint. As concluded in a study by Alam, Amanat and Seraj, Present code methods underestimate the punching load capacity of slabs as the code provisions are based on tests conducted on simply supported slabs with their edges unrestrained.



Considering Membrane Action in Design Wood and Park were two of the earliest researchers to develop analytical methods to assess the strength of reinforced concrete slabs where compressive membrane action exists. The theoretical formulations have generally been based on plasticity theory. Because of the complexity of this approach, many assumptions and simplifications have been required in those analyses. This lead to formulations that, while being fundamentally and theoretically important, did not provide accurate predictions of the strength and loading behavior methods. To use these methods in practical situations, knowledge of the surround stiffness that exists for the slab is required. Various researchers have come up with analytical methods to account compressive membrane action in designing of reinforced concrete slabs. Taplin and Hon have presented a method to design one-way bridge deck slabs (Ref. 7).Park and Gamble have described analytical methods to determine capacity of reinforced concrete slab with different configurations and edge restraints (Ref. 1). Kulkarni and Desayi have presented a method to analyze membrane action in fixed orthotropic circular slabs (Ref.8). To investigate the possibility of incorporating membrane action in design, a ¼ scale model of a reinforced concrete nine-panel (3x3) slab and beam floor system was tested by Hopkins and Park. The center panel had been designed for an ultimate load of twice the Johansen’s yield line theory and the beams were designed to carry the enhanced ultimate load, and the resulting axial forces. The floor reached the anticipated ultimate load, but it was found that in such a design, it could be difficult to ensure that crack widths and deflections at service load were not excessive. The use of compressive membrane action allows the designer of continuous slab-and-beam floors to reduce the amount of reinforcement in the panels to less than that required by Johansen’s yield line theory. For the same ultimate loads and the concrete dimensions, there will be more steel in the beams supporting the panels designed to include membrane action than in the beams supporting the panels designed by Johansen’s theory, however, since extra steel will be required for tie reinforcement. A floor that has been designed by Johansen’s yield line theory to carry a particular ultimate load on all panels can, in fact, carry on some panels an ultimate load much greater than the design ultimate load, provided that the surrounding panels are lightly loaded, since the steel in lightly loaded adjacent beams and panels can be used to develop the compressive membrane action in the heavily loaded panels.



Also, steel placed in beams for earthquake or wind loading could be utilized to carry some additional gravity loading alone. Although advantage can be taken of compressive membrane action during the design of new structures, it is in the assessment of existing structures that the greatest benefit can be gained. There are existing reinforced concrete buildings that have inadequate ultimate strength when assessed for increased loading in case of change of usage purpose of building. A common response to this problem is to strengthen the floor slab. Alternative approach is to make an assessment of the ultimate strength of slab allowing for the beneficial effect of compressive membrane action.



Conclusion

1- The load carrying capacity of reinforced concrete slabs is enhanced by compressive membrane action depending on the column layout, span to depth ratios, reinforcement ratio in slab and boundary restraints.

2- The slab-and-beam floors with only alternate panels loaded could carry extremely high ultimate loads on the loaded panels.

3- The incorporation of membrane action in design is most efficient when use

can be made of steel placed in beams for alternative loading cases to provide tie reactions for the membrane forces in the panels.

4- Geometric non-linearity effects can have a significant influence over load carrying capacity. High axial forces induced due to boundary restraints coupled with large slab deflections at ultimate load can create large secondary moments which can partially negate the beneficial effects of membrane action.

5- By obtaining a more accurate assessment of the true strength of the existing reinforced concrete slabs, the need for strengthening may be removed.

6- Punching shear strengths observed from tests conducted on restrained reinforced concrete slabs have found to be higher than predictions of present-day code provisions. Further experimental research on a wide range of slab is, of course, needed to consolidate findings.



References

1- Robert Park, William L. Gamble, “Reinforced Concrete Slabs”,2nd edition,1999.

2- F.J Vecchio, K. Tang, “Membrane action in reinforced concrete slabs”, CAN. J. CIV. ENG. Vol. 17, 1990.

3- Geoffrey Decan, Luc Taerwe, “Concrete beams and slabs”, Joint workshop of COST Actions TU0601 and E55, Slovenia, 2009.

4- Linus C.S. Lim, “Membrane action in fire exposed concrete floor systems”, thesis submitted for the partial fulfillment of the requirements for the PhD, Department of Civil Engineering, University of Canterbury, New Zealand, 2003.

5- A.K.M.Jahangir Alam, Khan Mahmud Amanat, Salek M. Seraj,BUET, Bangladesh, “An Experimental Study on Punching Shear Behaviour of Concrete Slabs”, Advances in Structural Engineering, vol 12, no.2, 2009.

6- G.S.T. Armer, “Ultimate load tests of slabs designed by the strip method”, Discussion on paper published. Proc. Instn civ. Engrs, 1968, 41(oct) 313-331.

7- Geoff Taplin, Maunsell Australia Pty Ltd, Alan Hon, Maintenance Technology Institute, Monach University, “ Compressive Membrane Action in Bridge Deck Slabs”.

8- Kulkarni and Desayi, “Effect Of Membrane Action On The Plastic Collapse Load Of Circular Orthotropic Slabs With Fixed Edges”, I n t . J. mech. Sci., Vol. 20, pp. 97-108. Pergamon Press 1978.

Compressive Membrane Action in RCC Slabs

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