Abstract:
A system for walls and structural slabs is disclosed. It consists of units of a pre-case reinforced concrete element has a special form design, fabrication methods and utilisation. The element has a circular section, variable lengths and flat surface on the top and bottom sides ( 2 ). It has a sectional area of 4170 sq mm. The optimum preferred dimensions of the cross section are 64 mm high and 75 mm wide ( 1 ). The element has an optimum shape that reduces the materials used yet provides the structural performance required. When stacked vertically between two structural framing columns, the elements form non-load-bearing walls system( 3 ). The elements form structural diaphragm when horizontally laid side by side in a butt-jointed manner, supported on both ends by means of structural framing beams. Plain concrete topping to the necessary thickness is cast over the diaphragm/elements, forming an integral reinforced concrete structural slab system ( 4 ). The elements are fabricated mechanically or manually. Manual fabrication using PCV moulds produces individual elements of various lengths. Machine fabrication allows production of jointed elements forming slabs of various widths and lengths.

Description:
TECHNICAL FIELD OF THE INVENTION 
   The present invention relates to a reinforced concrete element. 
   BACKGROUND OF THE INVENTION 
   Reinforced concrete elements are generally used as building construction material for walls and slabs. 
   The predominant techniques used in reinforced concrete construction are mostly based on previously set models. The technical research on reinforced concrete as a building construction material is extensive with particular emphasis placed on its physical performance. Most of the applications in the field utilise heavy equipment, extensive amounts of formwork or a combination of both. Advanced technical know how is required but may not be readily available. All of these factors result in prohibitive or redundant costs. 
   Unfortunately, reinforced concrete is expensive. These costs are due to factors such as: cost of technical expertise, cost of design, supervision and skilled labour; cost of materials and material handling; equipment and labour; formwork and related labour; and construction time. 
   It would therefore be desirable to have a reinforced concrete element which is designed such that it maximises the benefits of the material and concurrently reduces costs. 
   OBJECT OF THE INVENTION 
   It is an object of the present invention to overcome or ameliorate some of the disadvantages of the prior art or at least to provide a useful alternative. 
   SUMMARY OF THE INVENTION 
   There is firstly disclosed herein an elongated pre-cast concrete element, said element having: 
   longitudinally extending upper and lower generally parallel surfaces that enable the element to be stacked with like elements when horizontally oriented; and 
   longitudinally extending convex side surfaces joining the upper and lower surfaces. 
   There is further disclosed herein a wall structure including a plurality of elements, each element being an element as hereinbefore defined, wherein the elements are stacked so each element is generally horizontally oriented. 
   The present invention, at least in a preferred embodiment preferably achieves the following: the elimination of formwork for reinforced concrete slabs resulting in a direct cost saving and a positive environmental impact; the elimination of mandatory use of heavy equipment, intensive labour and advanced technical expertise; the substantial reduction in capital investment as a result of major savings achieved through the use of the elements alternative building material; and substantial reduction in the time required for fabrication and construction of walls and slabs. 
   Therefore, the present invention is preferably a pre-designed, pre-cast reinforced concrete element that is characterised by its cross sectional form. In an individual form, the elements can be utilised for other purposes such as walls of a building structure, partition walls, fencing, planters, tree support posts, pavements, retaining walls, etc. 
   The present invention is yet further preferably easy to transport and handle without the use of heavy equipment. 
   Preferably, the present invention is economical to fabricate and build and is generally maintenance free. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A preferred embodiment of the invention will now be described, by way of example only, with reference to the accompanying drawings, wherein: 
       FIGS. 1   a  and  1   b  are cross-sectional views of two alternate embodiments of the element according to the present invention; 
       FIGS. 1   c  and  1   d  are cross-sectional view of moulds for the construction of the elements shown in  FIGS. 1   a  and  1   b  respectively; 
       FIG. 1   e  is a side view of an element; 
       FIGS. 1   f  and  1   g  are side views of a series of elements in accordance with  FIGS. 1   a  and  1   b  forming a slab; 
       FIG. 1   h  is a side view of a series of elements in accordance with  FIG. 1   a , forming a free standing wall; 
       FIG. 1   i  is a side view of a series of elements in accordance with  FIG. 1   a , forming a wall where the elements are cemented together; 
       FIG. 1   j  is a side view of a series of elements in accordance with  FIG. 1   a , forming a plastered wall; 
       FIG. 2  is a perspective view of a series of elements in accordance with  FIG. 1   a ; 
       FIG. 3  is a partial 3-dimensional view of a house showing use of a series of elements; and 
       FIG. 4  is a partial 3-dimensional cut away view of the roof of the house of FIG.  3 . 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   In  FIGS. 1A ,  1 I to  1 J and  2  there is depicted a preferred elongate pre-cast concrete element  5 . The element  5  has longitudinally extending upper and lower generally parallel surfaces  10 ,  15  that enable the elements  5  to be stacked as shown, for example, in  FIGS. 1I  to  1 J vertically to form a wall. The element  5  further includes longitudinally extending convex side surfaces  20  joining the upper and lower surfaces  10 ,  15  to define a cross-section  17 . A longitudinal passage  25  is located centrally and extends between the end surfaces  12 ,  13  and is adapted for receipt for a reinforcing bar such as a reinforced steel bar  30 . 
   The convex sides  20  are designed to provide excellent load bearing capabilities. The preferred cross section  17  of the element  5  has dimensions 64 mm high and 75 mm wide resulting in a cross sectional area  17  of the element  5  of 4170 square millimetres. The length of the element  5  can be any length, but generally between 100 mm and 5000 mm. Advantageously, the width and height of the cross section  17  can be varied to suite the required increase or decrease in the bearing capacity of the element  5 . Accordingly, construction using the elements allows an optimal combination between the element cross sectional dimensions and its bearing capacity, with the only constant being the cross sectional design  17 . These can be determined by the following: 
   Structural Parameters and Analysis of the Element Under Different Conditions 
   The design of the element  5  considers the loads and stresses from the following stages:
         Handling   Cast of concrete topping   Full service loading in its permanent location       

   The element is designed utilising the requirements of the ACI- 318  code of practice. 
   The reinforcement percentage in the section is calculated as per the following equation: 
       Mu   =     φ   ⁢           ⁢   fy   ⁢           ⁢       As   ⁡     (     d   -       1   2     ⁢     Asfy     a   ⁢           ⁢   0.85   ⁢           ⁢     fc   ′             )       *           
 
   Mu=Ultimate moment capacity 
       As   =     ρ   ⁢     bd   100           
 
   ρ=steel percentage 
   fy=steel yield strength 
   fc′=concrete cylindrical strength at 28 days 
   φ=0.9 
   Deflection limitations as governed by the limits stipulated in ACI- 318  Code of Practice, Chapter 9. Other criteria like general detailing, cover to reinforcement etc. are as per ACI- 318 , Chapter 7. Local code requirements can be implemented keeping the ACI requirements as the minimum acceptable. 
   Notes:
         “a” is the upper and lower flat surfaces  10 ,  15  dimension of the element  5 .   “As” is the area of steel section used in reinforcement  30  of the element  5 .   “d” is the direction from the bottom of steel reinforcement  30  to the element upper surface  10 .       

   A number of structural design tables have been formulated to provide alternatives of cross sectional dimensions, reinforcement, lengths and load bearing capacity. The tables located herein on pages 12 to 16 enable the user to choose the optimum dimensions of the cross section  17  and the length of the element  5 . From the tables it can be seen that the linear metre weight of a single element, the load bearing capacity, the square metre cost are prime factors dictating the choice of the required dimensions. 
   In a preferred embodiment, steel bars  30  can be used as reinforcing bars for the reinforcement of the element  5 . The diameter of the steel bars  30  and the passage  25  could vary from 6 mm to 12 mm depending on the desired length of the bar and the required bearing capacity. In mechanized production pre-stressed steel reinforcement can be used, in which case the span and bearing capacity of the element can be increased without any addition in the raw material. 
   The elements are preferably able to be handled without the need for heavy equipment. The following table is based on a specific gravity of 2350 kg/cubic meter and illustrates the weights per length of a preferred form of the elements. 
   
     
       
             
             
             
           
         
             
                 
                 
             
             
                 
               Length 
               Weight in kg 
             
             
                 
                 
             
           
           
             
                 
               0.50 meter long 
               04.90 
             
             
                 
               1.00 meter long 
               09.80 
             
             
                 
               1.50 meter long 
               13.70 
             
             
                 
               2.00 meter long 
               18.60 
             
             
                 
               2.50 meter long 
               24.50 
             
             
                 
               3.00 meter long 
               29.40 
             
             
                 
               3.50 meter long 
               34.30 
             
             
                 
               4.00 meter long 
               39.20 
             
             
                 
               4.50 meter long 
               44.10 
             
             
                 
               5.00 meter long 
               49.00 
             
             
                 
                 
             
           
        
       
     
   
   These elements also preferably have crushing strengths varying between 25 K e.g. for walls to 40 K as in roof slabs. In this regard, the physical characteristics of the ingredients; sand, gravel, cement, water and the weather temperature are basic contributors to the mix. In most cases, the crushing strength of the concrete will be the decisive factor in identifying the various proportions of the mix. The Table below sets out the concrete mix used for building the pilot project. 
   
     
       
             
           
             
             
             
           
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Concrete Mix Design For The Pilot Project 
             
           
        
         
             
                 
               Type of concrete 
               K40 
             
             
                 
               Type of cement 
               OPC. 
             
             
                 
               Type of mix 
               PRODUCTION 
             
           
        
         
             
                 
                 
                 
               Spec 
               SSD 
                 
               Water 
               Correct 
             
             
                 
               Aggregate 
               Vol. 
               Gravel 
               Weight 
               Natural 
               Absorp 
               Weight 
             
             
               Materials 
               % - SSD 
               Ltrs 
               vma 
               kg 
               Moist % 
               % 
               kg 
             
             
                 
             
           
        
         
             
               Cement 
                 
               143 
               3.15 
               450 
                 
                 
               450 
             
             
               Water 
                 
               185 
               1 
               185 
                 
                 
               173 
             
             
               Admixture 
                 
                 
               1.11 
               12.77 
                 
                 
               13 
             
             
               Air 
                 
               10 
             
             
               Fine Aggregate 
                 
               268 
               2.61 
               700 
               5 
               1 
               728 
             
             
               (Sand) 
             
             
               Coarse Aggregate 
             
             
               ¾″ 
                 
                 
               2.7 
                 
                 
               1.5 
             
             
               ½″ 
                 
               196 
               2.7 
               530 
                 
               1.5 
               522 
             
             
               ⅜″ 
                 
               204 
               2.7 
               550 
                 
               1.5 
               542 
             
             
               TOTAL 
               100% 
               1018 
                 
               2428 
                 
                 
               2428 
             
             
                 
             
           
        
       
     
   
   Turning now to the mode of production of the element  5 , manual and mechanised methods are presently contemplated. The manual production is well suited for a limited production of the elements. For an individual, wishing to construct his/her own home unit, the means and the process of production are dependent upon moulds  40 , shown in  FIGS. 1   c  and  1   d  and are made out of material that allows multiple use and minimal deterioration. 
   Elements  5  could be produced as follows: procurement or fabrication of moulds  40 ; arranging moulds in batteries: placing reinforcing bars  30 ; mixing concrete; placing concrete in the mould  40  and vibrating as per standards; casting the reinforced concrete; curing and storing. As, preferably, the invention is intended to minimize the cost of reinforced concrete elements, it is important that the mould material is obtainable and that moulds fabricated from such material can be readily used without deterioration. The most suitable materials found for the purpose are GRC or GRP or PVC or polyethylene moulds cast to the form. The PVC or polyethylene moulds are made in one piece and, because the mould is flexible, it allows casting of formwork without disturbing the moulds and/or the elements and easy removal of the mould after use. 
   Generally, moulds  40  are arranged on specially prepared level casting floors, reinforcement is set in position, concrete is mixed and then cast into the moulds. Small size vibrators may be used to vibrate the concrete. The concrete should be retained in the moulds for a period of about three days, during which time the concrete will be cured. The elements could then be removed from the moulds and stacked for future use. The moulds can then be rearranged for another cast 
   If reinforcement is required the reinforcing bars are laid in the mould and suspended in the required position by means of thin tie wires (not shown) or other suitable means. The wires keep the reinforcing bars properly positioned while the concrete mix is poured. The reinforcing bars should protrude beyond the ends of the moulds. The reinforcing could also be added later by casting a recess as in the preferred embodiment. 
   Another presently contemplated mode of production is the mechanized mode where the elements are produced on mass in a factory. Any practical length and width is possible only being limited by the length and width of the machines and the casting bed. The factory setup can be similar to the production line of hollow core slabs. The same principles of mixing, handling and casting of concrete apply. That is, it can be a concrete extrusion operation. The reinforcing bars for the element can be either normal tension bars or pre-stressed bars. In the preferred embodiment of this invention normal reinforcing bars are used. In the case of mass production for wide scale commercial purposes, the elements can be produced in slabs of various widths and lengths. The slabs can range from 1 meter in length up to 5 meters and the width is anywhere between 0.6 meters wide to 2 meters wide. All dimensions will generally be limited only by the deflection allowable in relation to the length of the slabs. The elements can be stacked in a storage yard and sold on order. This allows spontaneous delivery of required material thus contributing to substantial reduction in construction time. 
   There are two main uses presently contemplated for the elements  5 ; constructing walls  50  and structural slabs  55 . In the first case, and as shown in  FIGS. 1   h  to  1   j , the elements  5  can be assembled with or without mortar/cement  45 , depending on the final treatment of the walls  50 . For the slabs  55 , as shown in  FIG. 1   g , the elements  5  can be built on structural frames  57  and either cast in place, pre-cast or a steel frame. After arranging the elements  5  in place, a concrete topping  59  (see  FIGS. 3 and 4 ) could be poured to the thickness required. Further, as shown in  FIGS. 1B and 1G  the upper surface may be rounded 60. 
   As shown in  FIGS. 1   h  to  1   j , when constructing wall  50  the elements  5  stacked vertically, with or without mortar  45 . The elements  5  can be restrained on both horizontal ends by concrete columns  65  as shown in  FIGS. 3 and 4 . The elements  5  are then laid therebetween, either dry or with mortar  45  one on top of the other. In this arrangement, the upper surface  10  on top of the element  5  will act as a base for the following element  5 . Dry construction of the elements  5  in walls  50  will usually include plaster  62  on the outside in order to weather tighten the walls  50 . Further, casting the concrete framing columns  65  on site after building the elements  5  will allow an integral structural bonding between the elements  5  and the frame. This adds substantial structural rigidity to the building frame. If, however, the columns  65  are built in situ ahead of the elements  5 , then the elements  5  will have to be bonded to the columns  65  by means of mortar  45 . Enough space for this procedure can be provided by placing a pre-moulded groove  69  in the column to allow for the bonding mortar. 
   In embodiments including housing construction, windows  70  may be opened in the wall  50  simply by casting the elements  5  to the specific dimensions required to allow the window opening to be formed. The elements can be cut to size on site or better pre-fabricated to the required lengths. No special framing system is required for the windows and no lintels will be needed. The elements once plastered will produce the required window frame thickness. Depending on the insulation standards required for the building, the necessary insulation material is constructed. Alternatively if the insulation of the exterior is not required, the inner face may be left without any treatment and/or may be plastered to produce a good internal finish face with plaster and paint as per the standard practice. Depending upon the design requirements, the exterior walls can be clad with marble, stone, granite, bricks or can be plastered and painted. 
   It is also foreshadowed that elements can be used as internal partitions too. Further, about 15 millimetres of plaster on each side of the partition will produce a 100 mm thick partition wall. 
   If considering structural slabs  55 , as shown in  FIGS. 1   e  to  1   g , based on the slab plans and the finishing beneath the slabs, the length and the reinforcement of the elements  5  are decided; all fabrication of the elements should be to the pre-designed, required length. Moreover, cutting the elements to the required length on site is easy and can be achieved by means of an electric disc saw. The elements  5  are laid horizontally to the full length and width of the slab area. If the clear span between the two end supports of the element is more than 2.5 metres, an intermediary support should be temporarily provided until the plain concrete slab topping  59  of the elements  5  is poured and cured. 
   Further to the above, the elements  5  can be used in fencing posts and runners; warehouse wall closure; warehouse roof trusses; shoring panels closing between vertical structural supports; pavements substructures; and fruit trees groves and vineyards, however, they are not limited to only these uses. 
   As cost is important in the construction industry the following table and figures draw a comparative analysis between the elements of the present invention at least in a preferred embodiment and other concrete products, emphasising the economic implications. 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE A 
             
           
           
             
                 
             
             
               Walls and Slab Analysis 
             
           
        
         
             
                 
                 
               Square 
               Steel Rein- 
                 
             
             
               Description 
               Linear Metre 
               Metre 
               forcement 
               US$ 
             
             
                 
             
             
               Concrete and 
               0.00417 mc/ 
               Walls 0.063 
               @6 mm 
               6.78/sqm of 
             
             
               steel content in 
               lm 
               cm/sqm 
               0.226 kg/lm 
               Walls 
             
             
               one element. 
                 
               Slabs 0.055 
               3.01 kg/sm. 
               107.20/cm 
             
             
                 
                 
               cm/sqm 
               54.87 kg/cm 
               of Walls 
             
             
               1 cubic metre 
               240 lm. 
               Walls @ 
               @8 mm 
               10.00/sqm 
             
             
               concrete. 
                 
               15.80 sq m./ 
               0.40 kg/lm 
               Slabs 
             
             
                 
                 
               cm Slabs @ 
               5.35 kg/sq 
               180.00/cm in 
             
             
                 
                 
               18.00 sq m/ 
               m. 
               Slabs includ- 
             
             
                 
                 
               cm 
               97.556 kg/ 
               ing 80 mm/ 
             
             
                 
                 
                 
               cm 
               sqm thick- 
             
             
                 
                 
                 
                 
               ness concrete 
             
             
                 
                 
                 
                 
               topping of 
             
             
                 
                 
                 
                 
               plain con- 
             
             
                 
                 
                 
                 
               crete topping 
             
             
               1 cubic metre 
               Not appli- 
               12.50 units 
               Not appli- 
               11.00/sq m. 
             
             
               in concrete 
               cable 
               13.40/cm 
               cable 
             
             
               blocks 
             
             
               10*20*40. 
             
             
               1 cubic metre 
               Not appli- 
               8.33 sq m/ 
                 
               196.8.00/cm 
             
             
               in reinforced 
               cable 
               cm 
                 
               23.60/sq m. 
             
             
               concrete slab, 
             
             
               average thick- 
             
             
               ness 12 cm. 
             
             
                 
             
           
        
       
     
   
   Upon analysis of the above table it can be seen that, walls constructed using the elements of the present invention cost 61.60% of the standard 100 mm thick sand cement blocks and slabs cost 42.37% of the standard 120 mm thick reinforced concrete slabs. 
   The cost analysis of one cubic meter displayed in the table (cost is calculated on basis of Kuwait market prices) was calculated as follows: 
   
     
       
             
             
             
           
         
             
                 
                 
             
           
           
             
                 
               Concrete material 
               $42.00 
             
             
                 
               Reinforced steel 55 kg. @ $249/Metric Ton 
               $13.69 
             
             
                 
               Allow for casting, curing and transport to site 
               $15.00 
             
             
                 
               Allow for site handling and construction in walls 
               $15.00 
             
             
                 
               Sub-total cost/cubic Metre: 
               $85.69 
             
             
                 
               Add 25% for overhead and profit 
               $21.42 
             
             
                 
               Total cost/cubic metre 
               $107.20. 
             
             
                 
                 
             
           
        
       
     
   
   Further differences with the present invention is that normal block work construction is a “wet” trade whilst the present invention is a “dry” trade. This minimises the messiness on sites and will save on water consumption. Most block work requires plastering. The elements of the present invention can stay without plaster on the interior, for example, when providing for low cost housing, and still maintain an aesthetically acceptable look. Further, block work requires seven days curing time before it is allowed to be plastered whilst the elements can be plastered instantly. Still further, the transportation and mechanical handling costs are also reduced when simply considering that light and less material will be transported. 
   Further, when constructing slabs the labour rate for carpenters forming slabs is estimated at a minimum of US$42.80 per cubic metre and this is eliminated with the elements of the present invention. The need for wood and other sundries for formwork at US$ 18 per cubic metre is also preferably eliminated. A minimum of 30% of the concrete used in similar span solid slabs will be reduced by one third, yielding a saving in concrete quantity and in reinforcement of US$35.00/cubic metre. Total direct saving of labour, formwork and the reduction in quantities in slab concrete and reinforcement steel is US$95.80. This will produce a yield saving of approximately 64% of the prevailing cost of cubic metre of concrete of the classical slab system. 
   In consideration of the substantial direct savings mentioned above, there is an indirect saving effect that results from the reduction in the concrete and reinforcement quantities and the dead load. A proportional reduction to the foundation and the framing structure will result from the elimination of dead weights on walls and on slabs. This will yield a minimum saving of 25% of the concrete and reinforcement value for the foundations and the framing of the structure. It is contemplated that there would be US$15.00 per cubic metre in the foundation and the framing system. 
   As reinforced concrete is globally considered one of the most utilised material in the construction industry and is also expensive to acquire in its final form, people in the low-income bracket would be substantially advantaged to use such a product. 
   The element of the present invention is directed towards a segment of the world&#39;s population by giving them a cost-effective and economically viable solution in order to address the cost issues and the difficulties involved in advanced technology. It does not eliminate all the problems but makes the solution much more attainable by the end user. It provides a standard solution to the construction of walls and slabs in any standard structure and in particular modular structures. The fact that the formwork for slabs, and in many parts of the world for wall construction, is relatively eliminated, a major saving on the use of wood for concrete construction purposes is achieved. This, on its own merit, will reflect positively on the issue of world forestry depletion. 
   Although the invention has been described with reference to specific examples, it would be appreciated by those skilled in the art that the invention may be embodied in many other forms. 
   
     
       
             
           
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
               section properties 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               diame 
               7.51 
             
             
                 
               depth 
               6.4 
             
             
                 
                 
             
           
        
         
             
               x 
               y 
               dA 
               dA.x 
               dA.x2 
             
             
                 
             
             
               0.00 
               0.00 
               0.0 
               0.0 
               0.0 
             
             
               0.16 
               2.17 
               0.3 
               0.1 
               0.0 
             
             
               0.32 
               3.03 
               0.5 
               0.2 
               0.0 
             
             
               0.48 
               3.67 
               0.6 
               0.3 
               0.1 
             
             
               0.64 
               4.19 
               0.7 
               0.4 
               0.3 
             
             
               0.80 
               4.63 
               0.7 
               0.6 
               0.5 
             
             
               0.96 
               5.02 
               0.8 
               0.8 
               0.7 
             
             
               1.12 
               5.35 
               0.9 
               1.0 
               1.1 
             
             
               1.28 
               5.65 
               0.9 
               1.2 
               1.5 
             
             
               1.44 
               5.91 
               0.9 
               1.4 
               2.0 
             
             
               1.60 
               6.15 
               1.0 
               1.6 
               2.5 
             
             
               1.76 
               6.36 
               1.0 
               1.8 
               3.2 
             
             
               1.92 
               6.55 
               1.0 
               2.0 
               3.9 
             
             
               2.08 
               6.72 
               1.1 
               2.2 
               4.7 
             
             
               2.24 
               6.87 
               1.1 
               2.5 
               5.5 
             
             
               2.40 
               7.00 
               1.1 
               2.7 
               6.5 
             
             
               2.56 
               7.12 
               1.1 
               2.9 
               7.5 
             
             
               2.72 
               7.22 
               1.2 
               3.1 
               8.5 
             
             
               2.88 
               7.30 
               1.2 
               3.4 
               9.7 
             
             
               3.04 
               7.37 
               1.2 
               3.6 
               10.9 
             
             
               3.20 
               7.43 
               1.2 
               3.8 
               12.2 
             
             
               3.36 
               7.47 
               1.2 
               4.0 
               13.5 
             
             
               3.52 
               7.50 
               1.2 
               4.2 
               14.9 
             
             
               3.68 
               7.51 
               1.2 
               4.4 
               16.3 
             
             
               3.84 
               7.51 
               1.2 
               4.6 
               17.7 
             
             
               4.00 
               7.49 
               1.2 
               4.8 
               19.2 
             
             
               4.16 
               7.47 
               1.2 
               5.0 
               20.7 
             
             
               4.32 
               7.42 
               1.2 
               5.1 
               22.2 
             
             
               4.48 
               7.37 
               1.2 
               5.3 
               23.7 
             
             
               4.64 
               7.30 
               1.2 
               5.4 
               25.1 
             
             
               4.80 
               7.21 
               1.2 
               5.5 
               26.6 
             
             
               4.96 
               7.11 
               1.1 
               5.6 
               28.0 
             
             
               5.12 
               7.00 
               1.1 
               5.7 
               29.3 
             
             
               5.28 
               6.86 
               1.1 
               5.8 
               30.6 
             
             
               5.44 
               6.71 
               1.1 
               5.8 
               31.8 
             
             
               5.60 
               6.54 
               1.0 
               5.9 
               32.8 
             
             
               5.76 
               6.35 
               1.0 
               5.9 
               33.7 
             
             
               5.92 
               6.14 
               1.0 
               5.8 
               34.4 
             
             
               6.08 
               5.90 
               0.9 
               5.7 
               34.9 
             
             
               6.24 
               5.63 
               0.9 
               5.6 
               35.1 
             
             
               6.40 
               5.33 
               0.9 
               5.5 
               34.9 
             
             
                 
                 
               40.6 
               141.1 
               606.4 
             
             
                 
             
           
        
         
             
                 
               Area 
               40.6 
               cm2 
             
             
                 
               xbar 
               3.48 
               cm 
             
             
                 
               l xbar 
               115.6 
               cm4 
             
             
                 
               top w 
               5.33 
               cm 
             
             
                 
               w avr. 
               6.81 
               cm 
             
             
                 
               fc 
               240 
               kg/cm2 
             
             
                 
               beta 
               0.85 
             
             
                 
               Fy 
               4200 
               kg/cm2 
             
             
                 
               Ec 
               248646 
               kg/cm2 
             
             
                 
               n 
               8.04 
             
             
                 
               cover 
               2 
               cm 
             
             
                 
               Mcr 
               1024.9 
               kg-cm 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Maximum Element Span Before Cracking 
             
           
        
         
             
               diam 
               x 
               lcr 
               Muc 
               Mu 
               Ms 
               span 
               le 
               le/lg 
               defl. 
             
             
                 
             
           
        
         
             
               0.6 
               0.00 
               38.2 
               5649 
               3864 
               2760 
               576 
               39.5 
               0.34 
               2.1 
             
             
               0.8 
               0.00 
               64.7 
               5377 
               5964 
               3841 
               562 
               65.7 
               0.57 
               1.1 
             
             
               1.0 
               0.00 
               96.1 
               5111 
               7583 
               3651 
               548 
               96.5 
               0.83 
               0.7 
             
             
               1.2 
               0.00 
               131.4 
               4853 
               7960 
               3466 
               534 
               131.0 
               1.13 
               0.5 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               Variation of Reinforcement Steel Diameter, Concrete Topping, Element 
             
             
               Length, Allowable and Actual Deflection and Load Bearing Limit 
             
           
        
         
             
               diam 
               topp 
               span 
               Muc 
               Mu 
               Ms 
               ttl cap. 
               ld cap. 
               defl. 
               def lmt 
               LIMIT CPCTY 
             
             
                 
             
           
        
         
             
               0.6 
               5 
               500 
               27829 
               9208 
               6577 
               280.3 
               26.0 
               1.9 
               2.50 
               25.99 
             
             
               0.8 
               5 
               500 
               27220 
               15464 
               11046 
               470.6 
               216.4 
               3.1 
               2.50 
               122.96 
             
             
               1.0 
               5 
               500 
               26619 
               22427 
               16019 
               682.6 
               428.3 
               4.5 
               2.50 
               122.96 
             
             
               1.2 
               5 
               500 
               26024 
               29335 
               18589 
               792.1 
               537.8 
               5.2 
               2.50 
               122.96 
             
             
               0.6 
               6 
               500 
               34281 
               10277 
               7341 
               312.8 
               34.5 
               1.6 
               2.50 
               34.52 
             
             
               0.8 
               6 
               500 
               33605 
               17364 
               12403 
               528.5 
               250.2 
               2.7 
               2.50 
               207.19 
             
             
               1.0 
               6 
               500 
               32937 
               25396 
               18140 
               772.9 
               494.7 
               4.0 
               2.50 
               207.19 
             
             
               1.2 
               6 
               500 
               32275 
               33611 
               23053 
               982.3 
               704.0 
               5.1 
               2.50 
               207.19 
             
             
               0.6 
               7 
               500 
               41405 
               11346 
               8104 
               345.3 
               43.0 
               1.4 
               2.50 
               43.05 
             
             
               0.8 
               7 
               500 
               40662 
               19264 
               13760 
               586.3 
               284.0 
               2.4 
               2.50 
               284.05 
             
             
               1.0 
               7 
               500 
               39926 
               28364 
               20260 
               863.3 
               561.0 
               3.5 
               2.50 
               310.37 
             
             
               1.2 
               7 
               500 
               39197 
               37886 
               27061 
               1153.1 
               850.8 
               4.7 
               2.50 
               310.37 
             
             
               0.6 
               8 
               500 
               49202 
               12414 
               8867 
               377.8 
               51.6 
               1.2 
               2.50 
               51.58 
             
             
               0.8 
               8 
               500 
               48392 
               21164 
               15117 
               644.1 
               317.9 
               2.1 
               2.50 
               317.87 
             
             
               1.0 
               8 
               500 
               47588 
               31333 
               22381 
               953.6 
               627.4 
               3.1 
               2.50 
               434.01 
             
             
               1.2 
               8 
               500 
               46792 
               42161 
               30115 
               1283.2 
               956.9 
               4.2 
               2.50 
               434.01 
             
             
               0.6 
               9 
               500 
               57670 
               13483 
               9631 
               410.4 
               60.1 
               1.1 
               2.50 
               60.10 
             
             
               0.8 
               9 
               500 
               56793 
               23064 
               16474 
               702.0 
               351.7 
               1.9 
               2.50 
               351.70 
             
             
               1.0 
               9 
               500 
               55923 
               34302 
               24501 
               1044.0 
               693.7 
               2.8 
               2.50 
               579.66 
             
             
               1.2 
               9 
               500 
               55059 
               46436 
               33168 
               1413.3 
               1063.0 
               3.8 
               2.50 
               579.66 
             
             
               0.6 
               10 
               500 
               66811 
               14552 
               10394 
               442.9 
               68.6 
               1.0 
               2.50 
               68.63 
             
             
               0.8 
               10 
               500 
               65866 
               24964 
               17831 
               759.8 
               385.5 
               1.7 
               2.50 
               385.53 
             
             
               1.0 
               10 
               500 
               64929 
               37271 
               26622 
               1134.4 
               760.1 
               2.5 
               2.50 
               748.83 
             
             
               1.2 
               10 
               500 
               63998 
               50711 
               36222 
               1543.4 
               1169.2 
               3.4 
               2.50 
               748.83 
             
             
               0.6 
               5 
               450 
               27829 
               9208 
               6577 
               346.0 
               91.7 
               1.5 
               2.25 
               91.73 
             
             
               0.8 
               5 
               450 
               27220 
               15464 
               11046 
               581.0 
               326.8 
               2.5 
               2.25 
               263.19 
             
             
               1.0 
               5 
               450 
               26619 
               22427 
               16019 
               842.7 
               588.4 
               3.7 
               2.25 
               263.19 
             
             
               1.2 
               5 
               450 
               26024 
               29335 
               18589 
               977.8 
               723.6 
               4.3 
               2.25 
               263.19 
             
             
               0.6 
               6 
               450 
               34281 
               10277 
               7341 
               386.1 
               107.9 
               1.3 
               2.25 
               107.89 
             
             
               0.8 
               6 
               450 
               33605 
               17364 
               12403 
               652.4 
               374.2 
               2.2 
               2.25 
               374.18 
             
             
               1.0 
               6 
               450 
               32937 
               25396 
               18140 
               954.2 
               676.0 
               3.2 
               2.25 
               387.66 
             
             
               1.2 
               6 
               450 
               32275 
               33611 
               23053 
               1212.7 
               934.4 
               4.1 
               2.25 
               387.66 
             
             
               0.6 
               7 
               450 
               41405 
               11346 
               8104 
               426.3 
               124.0 
               1.1 
               2.25 
               124.05 
             
             
               0.8 
               7 
               450 
               40662 
               19264 
               13760 
               723.8 
               421.6 
               1.9 
               2.25 
               421.57 
             
             
               1.0 
               7 
               450 
               39926 
               28364 
               20260 
               1065.8 
               763.5 
               2.9 
               2.25 
               538.11 
             
             
               1.2 
               7 
               450 
               39197 
               37886 
               27061 
               1423.5 
               1121.3 
               3.8 
               2.25 
               538.11 
             
             
               0.6 
               8 
               450 
               49202 
               12414 
               8867 
               466.5 
               140.2 
               1.0 
               2.25 
               140.20 
             
             
               0.8 
               8 
               450 
               48392 
               21164 
               15117 
               795.2 
               469.0 
               1.7 
               2.25 
               468.97 
             
             
               1.0 
               8 
               450 
               47588 
               31333 
               22381 
               1177.3 
               851.1 
               2.5 
               2.25 
               716.64 
             
             
               1.2 
               8 
               450 
               46792 
               42161 
               30115 
               1584.2 
               1257.9 
               3.4 
               2.25 
               716.64 
             
             
               0.6 
               5 
               400 
               27829 
               9208 
               6577 
               437.9 
               183.6 
               1.2 
               2.00 
               183.63 
             
             
               0.8 
               5 
               400 
               27220 
               15464 
               11046 
               735.4 
               481.1 
               2.0 
               2.00 
               481.13 
             
             
               1.0 
               5 
               400 
               26619 
               22427 
               16019 
               1066.5 
               812.3 
               2.9 
               2.00 
               482.50 
             
             
               1.2 
               5 
               400 
               26024 
               29335 
               18589 
               1237.6 
               983.3 
               3.4 
               2.00 
               482.50 
             
             
               0.6 
               6 
               400 
               34281 
               10277 
               7341 
               488.7 
               210.5 
               1.0 
               2.00 
               210.46 
             
             
               0.8 
               6 
               400 
               33605 
               17364 
               12403 
               825.7 
               547.5 
               1.7 
               2.00 
               547.48 
             
             
               1.0 
               6 
               400 
               32937 
               25396 
               18140 
               1207.7 
               929.4 
               2.5 
               2.00 
               669.89 
             
             
               1.2 
               6 
               400 
               32275 
               33611 
               23053 
               1534.8 
               1256.6 
               3.2 
               2.00 
               669.89 
             
             
               0.6 
               7 
               400 
               41405 
               11346 
               8104 
               539.5 
               237.3 
               0.9 
               2.00 
               237.28 
             
             
               0.8 
               7 
               400 
               40662 
               19264 
               13760 
               916.1 
               613.8 
               1.5 
               2.00 
               613.84 
             
             
               1.0 
               7 
               400 
               39926 
               28364 
               20260 
               1348.9 
               1046.6 
               2.3 
               2.00 
               894.28 
             
             
               1.2 
               7 
               400 
               39197 
               37886 
               27061 
               1801.7 
               1499.4 
               3.0 
               2.00 
               894.28 
             
             
               0.6 
               8 
               400 
               49202 
               12414 
               8867 
               590.4 
               264.1 
               0.8 
               2.00 
               264.11 
             
             
               0.8 
               8 
               400 
               48392 
               21164 
               15117 
               1006.5 
               680.2 
               1.4 
               2.00 
               680.20 
             
             
               1.0 
               8 
               400 
               47588 
               31333 
               22381 
               1490.1 
               1163.8 
               2.0 
               2.00 
               1158.65 
             
             
               1.2 
               8 
               400 
               46792 
               42161 
               30115 
               2005.0 
               1678.7 
               2.7 
               2.00 
               1158.65 
             
             
               0.6 
               5 
               350 
               27829 
               9208 
               6577 
               571.9 
               317.7 
               0.9 
               1.75 
               317.68 
             
             
               0.8 
               5 
               350 
               27220 
               15464 
               11046 
               960.5 
               706.2 
               1.5 
               1.75 
               706.25 
             
             
               1.0 
               5 
               350 
               26619 
               22427 
               16019 
               1393.0 
               1138.7 
               2.2 
               1.75 
               845.51 
             
             
               1.2 
               5 
               350 
               26024 
               29335 
               18589 
               1616.4 
               1362.2 
               2.6 
               1.75 
               845.51 
             
             
               0.6 
               6 
               350 
               34281 
               10277 
               7341 
               638.3 
               360.1 
               0.8 
               1.75 
               360.06 
             
             
               0.8 
               6 
               350 
               33605 
               17364 
               12403 
               1078.5 
               800.3 
               1.3 
               1.75 
               800.26 
             
             
               1.0 
               6 
               350 
               32937 
               25396 
               18140 
               1577.4 
               1299.1 
               2.0 
               1.75 
               1137.05 
             
             
               1.2 
               6 
               350 
               32275 
               33611 
               23053 
               2004.7 
               1726.4 
               2.5 
               1.75 
               1137.05 
             
             
               0.6 
               7 
               350 
               41405 
               11346 
               8104 
               704.7 
               402.4 
               0.7 
               1.75 
               402.45 
             
             
               0.8 
               7 
               350 
               40662 
               19264 
               13760 
               1196.5 
               894.3 
               1.2 
               1.75 
               894.28 
             
             
               1.0 
               7 
               350 
               39926 
               28364 
               20260 
               1761.8 
               1459.6 
               1.7 
               1.75 
               1459.55 
             
             
               1.2 
               7 
               350 
               39197 
               37886 
               27061 
               2353.2 
               2050.9 
               2.3 
               1.75 
               1483.82 
             
             
               0.6 
               8 
               350 
               49202 
               12414 
               8867 
               771.1 
               444.8 
               0.6 
               1.75 
               444.83 
             
             
               0.8 
               8 
               350 
               48392 
               21164 
               15117 
               1314.6 
               988.3 
               1.0 
               1.75 
               988.30 
             
             
               1.0 
               8 
               350 
               47588 
               31333 
               22381 
               1946.2 
               1620.0 
               1.5 
               1.75 
               1619.95 
             
             
               1.2 
               8 
               350 
               46792 
               42161 
               30115 
               2618.7 
               2292.5 
               2.1 
               1.75 
               1890.28 
             
             
               0.6 
               5 
               300 
               27829 
               9208 
               6577 
               778.5 
               524.2 
               0.7 
               1.50 
               524.21 
             
             
               0.8 
               5 
               300 
               27220 
               15464 
               11046 
               1307.4 
               1053.1 
               1.1 
               1.50 
               1053.10 
             
             
               1.0 
               5 
               300 
               26619 
               22427 
               16019 
               1896.0 
               1641.8 
               1.6 
               1.50 
               1492.13 
             
             
               1.2 
               5 
               300 
               26024 
               29335 
               18589 
               2200.2 
               1945.9 
               1.9 
               1.50 
               1492.13 
             
             
               0.6 
               6 
               300 
               34281 
               10277 
               7341 
               868.8 
               590.6 
               0.6 
               1.50 
               590.57 
             
             
               0.8 
               6 
               300 
               33605 
               17364 
               12403 
               1468.0 
               1189.7 
               1.0 
               1.50 
               1189.73 
             
             
               1.0 
               6 
               300 
               32937 
               25396 
               18140 
               2147.0 
               1868.8 
               1.4 
               1.50 
               1868.77 
             
             
               1.2 
               6 
               300 
               32275 
               33611 
               23053 
               2728.6 
               2450.3 
               1.8 
               1.50 
               1969.20 
             
             
               0.6 
               7 
               300 
               41405 
               11346 
               8104 
               959.2 
               656.9 
               0.5 
               1.50 
               656.93 
             
             
               0.8 
               7 
               300 
               40662 
               19264 
               13760 
               1628.6 
               1326.4 
               0.9 
               1.50 
               1326.37 
             
             
               1.0 
               7 
               300 
               39926 
               28364 
               20260 
               2398.0 
               2095.8 
               1.3 
               1.50 
               2095.76 
             
             
               1.2 
               7 
               300 
               39197 
               37886 
               27061 
               3203.0 
               2900.7 
               1.7 
               1.50 
               2533.97 
             
             
               0.6 
               8 
               300 
               49202 
               12414 
               8867 
               1049.5 
               723.3 
               0.4 
               1.50 
               723.29 
             
             
               0.8 
               8 
               300 
               48392 
               21164 
               15117 
               1789.3 
               1463.0 
               0.8 
               1.50 
               1463.00 
             
             
               1.0 
               8 
               300 
               47588 
               31333 
               22381 
               2649.0 
               2322.8 
               1.1 
               1.50 
               2322.75 
             
             
               1.2 
               8 
               300 
               46792 
               42161 
               30115 
               3564.4 
               3238.1 
               1.5 
               1.50 
               3193.52 
             
             
               0.6 
               5 
               250 
               27829 
               9208 
               6577 
               1121.0 
               866.7 
               0.5 
               1.25 
               866.74 
             
             
               0.8 
               5 
               250 
               27220 
               15464 
               11046 
               1882.6 
               1628.3 
               0.8 
               1.25 
               1628.33 
             
             
               1.0 
               5 
               250 
               26619 
               22427 
               16019 
               2730.3 
               2476.0 
               1.1 
               1.25 
               2476.03 
             
             
               1.2 
               5 
               250 
               26024 
               29335 
               18589 
               3168.2 
               2914.0 
               1.3 
               1.25 
               2763.51 
             
             
               0.6 
               6 
               250 
               34281 
               10277 
               7341 
               1251.1 
               972.9 
               0.4 
               1.25 
               972.86 
             
             
               0.8 
               6 
               250 
               33605 
               17364 
               12403 
               2113.9 
               1835.6 
               0.7 
               1.25 
               1835.65 
             
             
               1.0 
               6 
               250 
               32937 
               25396 
               18140 
               3091.7 
               2813.5 
               1.0 
               1.25 
               2813.46 
             
             
               1.2 
               6 
               250 
               32275 
               33611 
               23053 
               3929.2 
               3650.9 
               1.3 
               1.25 
               3605.36 
             
             
               0.6 
               7 
               250 
               41405 
               11346 
               8104 
               1381.2 
               1079.0 
               0.4 
               1.25 
               1078.97 
             
             
               0.8 
               7 
               250 
               40662 
               19264 
               13760 
               2345.2 
               2043.0 
               0.6 
               1.25 
               2042.96 
             
             
               1.0 
               7 
               250 
               39926 
               28364 
               20260 
               3453.2 
               3150.9 
               0.9 
               1.25 
               3150.89 
             
             
               1.2 
               7 
               250 
               39197 
               37886 
               27061 
               4612.3 
               4310.0 
               1.2 
               1.25 
               4310.03 
             
             
               0.6 
               8 
               250 
               49202 
               12414 
               8867 
               1511.3 
               1185.1 
               0.3 
               1.25 
               1185.09 
             
             
               0.8 
               8 
               250 
               48392 
               21164 
               15117 
               2576.5 
               2250.3 
               0.5 
               1.25 
               2250.28 
             
             
               1.0 
               8 
               250 
               47588 
               31333 
               22381 
               3814.6 
               3488.3 
               0.8 
               1.25 
               3488.32 
             
             
               1.2 
               8 
               250 
               46792 
               42161 
               30115 
               5132.7 
               4806.5 
               1.1 
               1.25 
               4806.49 
             
             
               0.6 
               5 
               200 
               27829 
               9208 
               6577 
               1751.6 
               1497.3 
               0.3 
               1.00 
               1497.31 
             
             
               0.8 
               5 
               200 
               27220 
               15464 
               11046 
               2941.5 
               2687.3 
               0.5 
               1.00 
               2687.29 
             
             
               1.0 
               5 
               200 
               26619 
               22427 
               16019 
               4266.1 
               4011.8 
               0.7 
               1.00 
               4011.82 
             
             
               1.2 
               5 
               200 
               26024 
               29335 
               18589 
               4950.3 
               4696.1 
               0.8 
               1.00 
               4696.08 
             
             
               0.6 
               6 
               200 
               34281 
               10277 
               7341 
               1954.9 
               1676.6 
               0.3 
               1.00 
               1676.61 
             
             
               0.8 
               6 
               200 
               33605 
               17364 
               12403 
               3303.0 
               3024.7 
               0.4 
               1.00 
               3024.72 
             
             
               1.0 
               6 
               200 
               32937 
               25396 
               18140 
               4830.8 
               4552.6 
               0.6 
               1.00 
               4552.55 
             
             
               1.2 
               6 
               200 
               32275 
               33611 
               23053 
               6139.3 
               5861.1 
               0.8 
               1.00 
               5861.08 
             
             
               0.6 
               7 
               200 
               41405 
               11346 
               8104 
               2158.2 
               1855.9 
               0.2 
               1.00 
               1855.91 
             
             
               0.8 
               7 
               200 
               40662 
               19264 
               13760 
               3664.4 
               3362.1 
               0.4 
               1.00 
               3362.15 
             
             
               1.0 
               7 
               200 
               39926 
               28364 
               20260 
               5395.5 
               5093.3 
               0.6 
               1.00 
               5093.29 
             
             
               1.2 
               7 
               200 
               39197 
               37886 
               27061 
               7206.7 
               6904.4 
               0.8 
               1.00 
               6904.44 
             
             
               0.6 
               8 
               200 
               49202 
               12414 
               8867 
               2361.5 
               2035.2 
               0.2 
               1.00 
               2035.22 
             
             
               0.8 
               8 
               200 
               48392 
               21164 
               15117 
               4025.8 
               3699.6 
               0.3 
               1.00 
               3699.58 
             
             
               1.0 
               8 
               200 
               47588 
               31333 
               22381 
               5960.3 
               5634.0 
               0.5 
               1.00 
               5634.02 
             
             
               1.2 
               8 
               200 
               46792 
               42161 
               30115 
               8019.9 
               7693.7 
               0.7 
               1.00 
               7693.65