Constitutive Laws of the Reinforced Concrete Beam with the Onyx Waste Aggregate

Onyx waste as additional aggregate in a concrete mix will enhance the compressive strength and elasticity modulus of the concrete material, eventually resulting in the change of behavior and strength of the concrete beam structure and also skew the constitutive law of reinforced concrete structure plan, especially in a reinforced concrete beam. The magnitude of stress tensile coefficient of tensile block used as a reference for reinforced concrete beam structure plan will also differ. This study compared cylinder beam and reinforced concrete beam made from the Tulungagung onyx waste aggregate materials with cylinder beam and reinforced concrete beam made from crushed stone waste according to the established rules. The test results showed the difference in concrete strength, level of elasticity modulus and stress tensile coefficient of the tensile block. The difference of β1 coefficient shown in the outcome of the tensile analysis of the test blocks was 1.14% for concrete made from normal aggregate and 0.3% for concrete made from onyx waste aggregate. Keywordconstitutive law, RC beam, onyx waste

ASTM C469 -02 [3] explained the calculation of elasticity modulus chord (Ec) as: with : S 2 = 0,4 fc' S 1 = stress in association to the longitudinal strain ε 2 = longitudinal strain of 0,4 fc' C. Stress and strain curvature of concrete Many studies have been done to develop a formula to achieve better stress and strain curve. The equation of stress and strain curve of concrete studied by Popovics [4] and Thorensfeldt et al. [5] gave us stress strength of 15 to 125 MPa. The correlation between the resulting stress (fc) and the determined strain is as below: ( 2 ) with : fc' = maximum stress on test cylinder (psi) εo = strain level in maximum stress n = curve adjustment factor = Ec/(Ec-E'c) Ec = concrete elasticity modulus E'c = fc'/ εo k = factor determining the elevation of the curve; for εc/ εoless than or similar to one then k = 1 ;forεc/ εo>1 then k = 0.67 . All in psi. D. Equivalent block stress of concrete Tae yi [6] explained that Koenen (1866) is the first person demonstrating the theory of ultimate flexure capacity failure. He hypothesized that the stress distribution on the plane of a reinforced concrete beam is linear and uniform. Emperger (1904), and later modified by Whitney (1942), proposed an equivalent square to simplify the calculation of stress distribution theory. The distribution value of pressure stress block that occur on reinforced concrete beam surfaces forms the parabolic curve. To calculate the volume of pressure stress block by the form of parabolic is difficult, in which the parabolic pressure stress block curve is replaced by equivalent square shaped-stress block as a way to easily estimate the pressure stress without reducing the accuracy of the calculation.
The parameter beam for equivalent stress, as explained by Tae Yi [6], is shown in Figure 1 (fc')  k2  =Length ratio between maximum compressive fibril with the resultant of compressive strength toward  neutral line  k1 =Ratio between the curvature and rectangular surface E. Flexure strength of reinforced concrete beam According to Wang [7], parameters used for determining the nominal strength of square surface given only steel reinforcement consists of the width of the surface (b), the effective height of the block (d) and the area of steel reinforcement (As). The value of the reinforced area (As) has resulted from a combination of all reinforced area. Concrete mantle (d') functioned as the protector of reinforcing structure toward burn and external factors. Generally, the strain strength of concrete is abandoned as it usually contributes only 10% of all pressure strength. The distribution of tensile and stretch of the reinforced concrete beam (square) can be idealized as

IV. RESULTS AND DISCUSSION
A. Compressive strength and elasticity modulus of concrete A total of 40 cylinder test objects are used in the concrete pressure strength test, 20 objects each for concrete with coarse pebble aggregate and concrete with coarse onyx aggregate. To get the concrete strain value, while in the process, a strain measurement tool (extensometer) is applied to the cylinder. Its function is to achieve maximum strain while the concrete reaches fc' (εo). Maximum strain (εo) is used as a parameter that applied in the analysis of equivalent compressive strain of each test object.
Modulus elasticity of normal concrete and onyx concrete is calculated from the data of stress and strain experienced from pressure strength test, where the data is collected from every load addition of 10 KN. After the data is received, the next step is to put the data into a curve graph according to the fixed load addition. Therefore we can get a good parameter of modulus elasticity analysis as in ASTM C469. Following is the pressure strength value and modulus elasticity for each of normal concrete and onyx concrete: BN: 35 722 727 702 and Average BO of 32,9227106,79 MPa. B. Flexure strength of experimental reinforced concrete beam To get the data of reinforced concrete block strength experimentally, a test of flexure strength is done to a total of 20 reinforced concrete blocks, where ten blocks are of concrete with coarse pebble aggregate (normal concrete) and another 10 of concrete blocks with coarse onyx aggregate. The test is run when the blocks are 28 days old and have been cured, measuring 25 x 15 x 200 cm, using a single reinforced system and two loading points to get the pure flexure strength. The test is done for every 200 kg of load additions.
Deflection of blocks was measured using LVDT tool that was placed in the middle of block's length. The test was run until there is 20% depreciation of the former ultimate load.
In analyzing a new block compressive stress equivalent, we need a data as per formula to get the new stress-strain value. The data required are fc' (compressive strength of 28-days old concrete), ε0 (the maximum strain of concrete strength), εcu(ultimate concrete strain)and Ec(concrete modulus elasticity). Data collected from the reinforced concrete beam testing was summarized in table 1-4. The comparison result between analysis calculation and observation result of the reinforced concrete beam was concluded in table 5-6 Experimental flexure strength value that has been discussed in the previous chapters will be compared with the analytical flexure strength value, using the evaluated value of block compressive stress equivalent. The analytical calculation using the new β1 value with block measured at 15 x 20 x 200 cm and other test object details equal to reinforced concrete block experimentally. Following is the analytical value of the flexure strength:  After we get the flexure strength value experimentally from the test result of each reinforced concrete block using the normal coarse aggregate and onyx waste, we tried to compare it to the flexure strength value of reinforced concrete block analytically using the β1 value that has been modified following the value modification according to the new stress-strain diagram area. The result as follows : reinforcement is 172625,75 kg.cm. It is higher than the flexure strength value of reinforced concrete block with onyx waste aggregate that is 168300 kg.cm. This is due to some factors, such as bigger value of compressive strength and modulus elasticity in the normal concrete. 3. The value of block compressive strength equivalent (β1) with normal aggregate is higher, measured at 0,874, while the value of β1 in concrete with onyx waste aggregate is 0,868. This proves that the higher compressive strength in concrete is not necessarily resulting in lesser β1 value, but also influenced by the value of modulus elasticity and a maximum strain of both concrete types.