Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012
An In – Built Trial Mechanism of Providing Permanent ‘Sound Proofing and Thermal Insulation’ In Buildings Using Steel Shear Bolsters In Sandwiched Reinforced Cement Concrete Slabs and Beams V. Akshay, Senior Engineer, Larsen & Toubro – Construction Division, Rajashree Cement Works, Unit – IV, Malkhed Road, Karnataka, India Email: firstname.lastname@example.org, email@example.com Abstract – This paper proposes to provide a permanent ‘combo’ in-built solution to two major problems in buildings without maintenance issues – Sound proofing and Thermal Insulation. While conventional eco – hating techniques of sound proofing in buildings utilize porous saw dust boards, coir mats and carpets, thermal insulation is done by coatings of toxic external paints, This paper proposes a eco – friendly theory in which sand is used for sound proofing and aluminium sheets as heat sinks sandwiched between two layers of Reinforced Cement Concrete in roof slabs and beams. This paper also evolves with the idea of modifying brick manufacture to counter the above mentioned issues with a positive approach. The theory proves to be of better efficiency as is it is in-built and permanent. The concept of Reinforced Cement Concrete design is coupled with the concept of steel sections to achieve structural stability of the ‘sandwiched’ slabs and beams. Details involving design procedures of such sandwiched Reinforced Cement Concrete slabs and beams with shear bolsters using steel plates forms the essence of this paper. A case study comparing the economies of sound proofing and thermal insulation using traditional Limit state design of RCC and that of the proposed sandwich theory is also enumerated. Index Terms – Limit State Design, RCC, Sandwich Theory, Shear Bolsters, Sound and Heat Insulation, Cost Calculator
I. INTRODUCTION It has become an immense necessity in this noisy world to provide sound proofing and thermal insulation in homes, schools, hospitals and office buildings at economical rates offering the same or better efficiency without causing any damage to the environment by artificial means of cooling and/or non – eco friendly sound proofing techniques. Utilizing traditional sound proofing solutions such as wooden coir mats and foams adds additional problems in terms of maintenance and dims lighting in interiors resulting in negative contribution to Global Warming. If roof slabs, beams and walls could be sealed completely from sound and heat with an in – built solution, interiors would be cooler and more peaceful. For achieving this, it is proposed to utilize the ‘Sandwiching’ Theory inspired from a Sandwich itself. The designs and details are enumerated in the first portion of the paper followed by its functioning and a case study in the second portion. 51 © 2012 ACEE DOI: 02.ADCS.2012.1. 513
A. Concept of Reinforced Cement Concrete Sandwiched Beams and Slabs The proposed sandwiched beam section (composite Reinforced concrete section) is detailed as shown in figure 1. In the following pages, Reinforced cement concrete shall be denoted by RCC. (NA in figure indicates Neutral Axis)
Figure.1. Proposed Sandwich Beam Section
The design of such Sandwiched beams out rightly defies basic assumptions in the Limit state design of RCC members as mentioned in the code . For a sandwiched section, 1. Plane sections do not remain plane after bending. 2. Sections are not homogenous. 3. The portions of the section above and below the Neutral Axis do not stay in fixed position in space with respect to each other defying transfer of stresses from the top fiber concrete to bottom fiber steel. 4. Section may slip and separate as the sand bath in between can be assumed to possesses neither bending or shear strength. To counter these effects, the Limit state design of collapse needs to be considered as mentioned below. a. Limit state of Flexure in which the concrete above neutral axis takes care of bending compressive stresses while Steel below the neutral axis resists bending tensile stresses (As per initial assumption)1 The steel stirrups/ plate bolsters in beams/ slabs serve the purpose of preventing section slip between the compression and tensile zones and allow for transfer of flexural forces from the top fiber to the bottom fiber.
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 b. Limit state of Shear in which the section is assumed to have zero shear capacity. 2 – Legged or 4 – Legged Steel stirrups in beams (and steel plate bolsters in slabs which shall be enumerated later) should be able to completely resist shear stresses without contribution from concrete. c. Side face reinforcement of nominal amount has to be provided in beams to ensure that plane sections remain plane after bending. The sand bed should not extend to the ends of the member and should leave side covers. All other assumptions for flexural design can be applied in the design. The relationship between compressive stress distribution in concrete and the strain in concrete, stress and strain curves as well as stress block parameters can be adopted in the same manner as mentioned in the code. A revision of partial safety factor may be done to a greater value on the basis of experimental results. II. INCORPORATION
In general, a one – way slab is designed for a beam of width 1000 mm and depth equal to the thickness of the slab . In most cases, slabs are designed only for Limit State of Flexure while it is found that owing to the large width considered for design, it is safe in shear. Yet, in the proposed Sandwiched slabs, it has been assumed that the shear capacity of the section is zero. Similar to the utilization of vertical stirrups in beams, there is a need for provision of additional accessories in the section in order to completely resist shear. Two – Legged and Four – Legged stirrups cannot be used successfully in slabs owing to large spans in both directions. In such cases, the concept of steel I – sections can be incorporated into RCC slab design. I – sections with long webs have substantial success in resisting shear . The RCC slab is designed purely to resist only flexural stresses whereas steel I – sections incorporated into the slab shall be designed to resist only shear and torsion. Local Buckling is not an issue with I – sections in slabs and hence steel sections can be made thinner and longer into optimum size so as to provide greatest shear resistance. Instead of I - sections, vertical steel plates at all cross – sections are positioned where shear failure is likely to occur. These vertical steel plates can be labeled ‘Steel Shear Bolsters’ owing to their function. They need to be ‘roughed up’ on their surface to provide a strong bond between the plates and concrete. Utilization of vertical plates instead of Rolled I - sections reduces cost of fabrication and self – weight. An instance of Steel Shear Bolsters incorporated in the one – way slab is shown in figure 2.The end supports are L – beams in this case, whose shear is resisted by vertical stirrups alone while steel shear bolsters are used for the same in the above one – way slab. Each shear bolster would be designed to support shear arising due to live and dead load on the slab adjacent to the bolster on either side.
© 2012 ACEE DOI: 02.ADCS.2012.1.513
Figure. 2. Plan Of Bottom Reinforcement Of Proposed One – Way Slab
For instance, if ‘x’ is the spacing between two shear bolsters, forces arising due to live load and dead load on a width ‘x’ per metre length on either side of the bolster would be the governing shear force for designing the dimensions of the steel plate/ bolster.
Figure. 3. Left Portion (Section) Of Proposed One – Way Sandwich Slab
III. THEORY INCORPORATION IN TWO – WAY SLABS The steel shear bolsters would form a grid system in case of a two – way slab is as shown in figure 4.The grids form
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 larger panels at the centre of the slab where shear is low and bending moments are high.The shear bolsters need to be designed in each direction separately and the grid – set of bolsters can be pre – fabricated and brought to the site on the day of construction. This facilitates quicker construction. It can be incorporated even in continuous one – way, two – way slabs and beams but the designer has to ensure that the sand bed and Aluminium sheet is always present in the tensile zone. The shift of position of sand bed from the bottom zone to the top zone in case of continuous slabs has to be gradual from the point of contra flexure. This however, involves a risk factor and more research into the same has to be carried out before ascertaining its structural safety.
Figure. 5. 3 – D Sectional View Of Proposed Stuffed Brick
in larger strength.A compromise needs to be reached in the ratio of matrix to surrounding in order to get optimum effect in terms of strength, sound proofing and thermal insulation. 20x10x10 cm is the standard size of a brick . Hence the total load coming on a standard first class brick at failure adopting the load per sq mm at failure as 10 N = 10 x 200 x 100 = 200 kN Considering the equilibrium of the brick system neglecting Aluminium, we have p1A1 + p2A2 = P ————————— (1) p1 = Maximum stress resisted by the cement portion A1 = Area of cement portion of brick p2 = Maximum stress resisted by Sand portion A2 = Area of sand portion of brick P = Total load resisted by brick Assume that the strength exhibited by the cement portion of the brick manufactured by 43 grade cement with fly ash is 35 MPa. Hence, by trial and error, if 30% of the sectional area of the brick is occupied by the cement portion, then p1A1 = 35 x (30/100) x200 x100 = 180 kN Sand within the hollow portion is purposely kept porous to facilitate sound proofing. Yet, with optimum compaction, a small amount of compressive resistance is exhibited by the portion of sand in brick to achieve total load resisted by the brick, P H” 200 kN which is almost equivalent to that of a first class brick. The grade of cement, the amount of fly ash, the overall size of brick and proportioning of matrix and surrounding can be varied to achieve better strength and greater sound proofing.Aluminium plates are on the expensive side; hence utilization of these on the outer face of the brick would be sufficient for optimum thermal insulation. The thickness of the plates can be kept as small as possible, as they do not contribute towards strength of the brick and only are present for thermal insulation. Two or three layers ofAluminium foils on the hollow inner of the brick also serves the same purpose in an economical way. Therefore, any apprehensions regarding the brittleness of hollow bricks can be cleared by introducing the concept of ‘Stuffing’ in bricks to produce multiple advantages.
Figure. 4. Plan Of Bottom Reinforcement Of A Proposed Two – Way Sandwiched Slab
IV. SOUND AND HEAT INSULATION INCORPORATED IN WALLS THROUGH STUFFED CEMENT/FLY ASH BRICKS A similar strategy can be applied to bricks in walls, however, without compromising on compressive strength.Since bricks used for sound proof walls would generally be First class bricks with an average compressive strength of 10 MPa, proposed ‘Sandwich’ bricks or ‘Stuffed’ bricks also need to exhibit same or better strength characteristics.The 3-D sectional view of the proposed stuffed brick is shown in figure 5. Greater the hollow portion, greater would be the sand content allowed, larger would the length of Aluminium plates and greater would be effect of sound proofing and thermal insulation. On the contrary, larger space of the section occupied by cement/ fly ash would result © 2012 ACEE DOI: 02.ADCS.2012.1. 513
V. MECHANISM OF SOUND PROOFING AND T HERMAL INSULATION IN BUILDINGS USING SANDWICH THEORY Sand is one of the best sound proofing mediums which can be used in construction at highly economical rates in comparison to traditional techniques. Transfer of sound 53
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 waves from one medium to another takes place when there is a continuous medium in between them. When the continuous medium is interrupted at regular intervals by a porous medium, Sound waves fail to flow and sound insulation is achieved. An experiment was conducted to test sound absorption.Two tuning forks were inserted into a sand bed at close intervals (15 cm) and one of them was strongly disturbed. There was no transfer of vibrations into the adjacent fork. However, on fixing two tuning forks to a concrete floor at the same distance apart, the second tuning fork vibrated 10 seconds after the first tuning fork vibrated.
VI. CASE STUDY The following case presents a comparative study between economies of construction of a 7m x 3m simply supported one – way slab present in a single long room atop the terrace of a one – storey residential home in Secunderabad designed by the conventional limit state design of RCC members (as per IS 456:2000) and by the proposed sandwich theory. The rates used for comparison are based on construction materials in Hyderabad. A. Design of Basic RCC slab 7m x 3m by Limit State method (as per IS 456:2000) using Fe415 steel and M15 concrete Since L/ b > 2, it is a one – way slab and load will be transferred to the supports along the shorter span. Considering a 1 m strip parallel to its shorter span. Minimum depth of slab D =L/ (α x β x γ x δ x λ) Let α = 20, β = 1, γ = 1, δ = 1 and λ = 1 Therefore, on substitution, D = 3000/ 20 = 150 mm Adopt overall depth of slab D = 175 mm and effective depth d = 150 mm. Dead load of slab = 0.175 x 1 x 25 = 4.375 kN/m Superimposed load = 4 kN/m (Assumed value) Total load = 8.375 kN/m Factored load for load factor as 1.5, wu= 8.375 x 1.5 = 12.56 kN/m Maximum Bending Moment (BM) at centre of shorter span = (wul2) / 8 Effective span of slab, l = 3 + d = 3 +.15 = 3.15 m Therefore, BM = 12.56 x 3.152/8 = 15.58 kN-m Maximum Shear Force = (wulc)/ 2 = 12.56 x 3/2 = 18.84 kN Where lcis the clear span between supports. Checking Depth of Slab: As per IS 456:2000, to check for minimum depth of the slab, we use the equation, BM = 0.138 σckbd2 σck= 15 MPa (for M15 concrete) Substituting values of BM, σ ck and b in the above equation, we get d = 87 mm Adopt new values of slab depths as D = 150 mm and d = 125 mm. Area of tension steel is determined by the equation BM = 0.87σyAt [d – (σyAt)/ (σckb)] Substituting all values in the above equation, we determine the area of tensile steel for the under – reinforced section as At = 377 mm2 Provide 10 mm bars @ 200 mm c/c giving actual area of tensile steel = 392.5 mm2 Bend alternate bars at L/7 from the face of support where moment reduces to half of its maximum value. Temperature reinforcement at 0.15% of the gross concrete area will be provided in the longitudinal direction = 0.0015 x 1000 x 150 = 225 mm2 Use 6 mm MS bars @ 100 mm c/c giving total area = 28 x 1000/ 100 = 280 mm2> 225 mm2
Figure. 6. Mechanism Of Thermal Insulation And Sound Dissipation Through Roofs And Walls Of An Interior Room (One – Way Slab)
Aluminium is known as one of the best thermal insulators. Aluminium foils are known worldwide to keep food hot for long durations, disallowing temperature to escape into surroundings. If outside heat is disallowed from entering interiors by placing Aluminium barriers, interiors would remain cool for longer periods reducing need for artificial cooling requirements. Even if Air conditioners were used in such rooms, the thermostat would ensure lower usage of power by retaining cool temperatures in the interior for longer periods. The mechanism of sound proofing and thermal insulation works as shown in Figure 6 on application of the ‘Sandwich’ Theory. To avoid complexities, columns have been assumed inert in transferring both sound and heat. Sand is also a heat dissipating agent, though in a smaller magnitude when compared to Aluminium. For instance, villagers use sand beds on top of their flooring to separate their stoves from the floor to prevent heat transfer. Thus, by using the ‘Sandwich’ Theory, the interiors are virtually sealed from noise and external heat.
© 2012 ACEE DOI: 02.ADCS.2012.1. 513
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 Check for Shear The slab is safe in shear as nominal shear stress developed is less than shear strength of concrete for the percentage tensile steel provided. Development Length Since development length is not a major criterion for comparison between the two theories, we shall not delve into details. The code requires that bars must be carried into the supports by at least Ld /3 . The design is complete with respect to collapse.
Let d1 = 95 mm (providing cover at the top to prevent corrosion) Let us adopt structural steel of Grade St 52 giving a Yield stress of 360 MPa for steel shear bolsters each extending for a length 6.8 m providing 100 mm side covers at the ends. Adopt 4 mm thickness of steel shear bolsters. Therefore, Vp = (95 x 4 x 360) / = 79 kN > 70.65 kN OK! Thus, provide 5mm thick, 95 mm depth steel plates as steel shear bolsters for a length of 6.75m at a spacingof 125 mm near supports. Increase the spacing to 200 mm near mid span for a distance of 1.5 m. The design is complete with respect to collapse.
B. Design of Basic RCC slab 7m x 3m by Sandwich theory using Fe415 steel and M15 concrete Design for flexure shall be carried out in the same manner as it has been in the previous case. Amount of tensile reinforcement is provided in same amount with same effective depth. Do not provide any temperature reinforcement as steel shear bolsters take care of the same. Determination of Neutral Axis Force of compression = 0.36 σckbx = 0.36 x 15 x 1000 x = 5400x N Force of tension = 0.87 σy At = 0.87 x 415 x 392.5 = 141712.125 N Therefore, on equating the above forces, we get depth of neutral axis as x = 26.24 mm < 0.48d OK! Provide 4 mm thickness Aluminium sheet and 20 mm thickness sand bed at a depth of 30 mm from top. Thus the distance of top compression fiber from the bottom of sand bed = 54 mm. Design for Shear It is assumed that shear capacity of the section is nil. Design of shear bolsters and its spacing is done by adopting guidelines from the code. Maximum Factored Shear Force = 18.84 kN The nominal plastic shear resistance under pure shear is given by Vp = Av fyw/ Where Av = shear area, and fyw= yield strength of the material of plate For plates, shear area = A = d1 x t Where d1 is the depth of steel shear bolster and t is its thickness. The factored design shear force, V, in a beam due to external actions shall satisfy V Vd Where Vd= design strength = Vp/ γmo(for pure shear) The partial safety factor against shear failure resistance, governed by ultimate stress is 1.25. Thus, Vpshould exceed the product of factored shear force and 1.25 Therefore, Vp 23.55 kN for critical section. Yet, the steel shear bolster is required to resist shear from all sections at a distance ‘(spacing)/2’ on either side of the bolster. Assume that the total shear resisted by the shear bolster for a spacing of 125 mm near supports is thrice Vp i.e. 70.65 kN. 3Vp is also taken in consideration for transfer of stress from top to bottom. © 2012 ACEE DOI: 02.ADCS.2012.1. 513
VII. A COMPARISON OF MATERIALS OF THE DESIGNED SLAB (FOR CLEAR SPAN) BY UTILIZING BOTH T HEORIES TABLE I. MATERIAL REQUIREMENTS AS PER I S: 456 AND AS PER SANDWICH T HEORY
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 Summary: (Difference In Quantities Between Sandwich Theory Of Design And IS 456: 2000 Method)Difference In Concrete Requirement = -0.504 cu.mDifference in Steel requirement (Fe415 bars) = - 0.0061 cu.mDifference in Steel requirement (Grade St 52) = 0.0646 cu.mDifference in Sand requirement (apart from that required for concrete) = 0.42 cu.mDifference in Aluminium requirement = 0.084 cu.m(Negative sign indicates lesser material required in Sandwich technique)
of maintenance = 40,472 Replacement for above mentioned traditional technique is required approximately in 12 years which adds to maintenance costs. Thus, by adopting Sandwiching technique the costs are recovered in a maximum of 5 years even if cheapest traditional sound proofing techniques are used. Utilizing ‘Stuffed Bricks’ shall further reduce maintenance costs incurred by sound proofing and thermal insulation using traditional ways. Further, the client is morally right as he disallows use of eco – hating materials. Advantages of the proposed ‘Sandwich’ Theory: a. It is in – built and permanent. Hence there is no issue of maintenance and heavy costs accompanying it. b. It is eco – friendly. It prevents felling of millions of trees for sound – proofing, usage of toxic heat insulating paints. c. Assures long – term economy. No compromise made on strength. d. No compromise made on head room space – Slabs and beams are of the same size as they would be without sandwiching. e. Stuffed bricks may be manufactured thinner than ordinary bricks, thus increasing room space.
VIII. COST CALCULATOR (AS PER RATES OF CONSTRUCTION MATERIALS IN HYDERABAD) TABLE III. COST D IFFERENCE TABLE BETWEEN IS: 456 AND SANDWICH T HEORY
IX. FUTURE PROSPECTS OF RESEARCH ON ‘SANDWICH’ THEORY The following points form the basis of future research on the proposed sandwich theory. a. It does not account for reversal of stresses b. Aluminium has a higher coefficient of linear expansion when compared to steel and concrete. c. The inertness of sand to resist loads is a cause for concern, a factor which may be considered risky for application as a Theory. d. Even though Steel Shear Bolsters will ensure sufficient resistance to deflection, Shrinkage and creep of concrete have not been accounted for in the design. e. Effect of lateral loads not considered CONCLUSION The need for new techniques in building construction is essential as traditional methods are more prone to eco – hazards. Yet, a new theory like the sandwich theory does pose technical challenges to a researcher, as mentioned in the previous item. The challenges that the theory poses shall be worked upon in the next portion of this research.
Approximate cost difference between Sandwich theory and IS 456:2000 method (excluding maintenance) = 36,317.681.1. A. Sound and Heat insulation costs using traditional methods (for slab designed as per IS 456:2000): Cost of 3 coats vinyl painting atop 7 x 3 m roof slab for heat insulation = 4320 (approximate) Cost of sound proofing using an industrial grade composite of two pound mass loaded vinyl and one inch polyether foam underneath 7 x 3 m roof using 3 sheets of the product = 11,408x 3 = 34,224 Total cost incurred = 34,224 + 4320 = 38,544 Adding 10% maintenance cost for 5 years, Total cost inclusive
© 2012 ACEE DOI: 02.ADCS.2012.1. 513
REFERENCES  Indian Standard code of practice for Plain and Reinforced Concrete (Fourth Revision), IS 456: 2000, Bureau of Indian Standards, New Delhi.  Ashok Jain K., Reinforced Concrete Limit State Design (6th Edition), Nem Chand & Bros, Roorkee, 2002, pp.287 – 295
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012  Duggal S.K., Design of Steel Structures (3 rd Edition), Tata McGraw Hill Education Private Limited, New Delhi, 2009, pp. 350, 354 – 357  Arora S.P. and Bindra S.P., The Text Book of Building Construction (4th Reprint), DhanpatRai Publications Ltd., New Delhi, 2007, pp.5.6 – 5.8  Dr. Punmia B.C., Ashok Kumar Jain and Arun Kumar Jain,
© 2012 ACEE DOI: 02.ADCS.2012.1.513
Mechanics of Materials, Laxmi Publications Ltd., New Delhi, 2006, pp.38 – 39  Indian Standard Code of Practice for General Construction in Steel (Third Revision), IS 800: 2007, Bureau of Indian Standards, New Delhi.  Subramanian N., Design Of Steel Structures (Fifth impression), Oxford University Press, New Delhi, 2010