Stress-strain curve for various mix proportioned concrete are shown in Fig. Though concrete is not an elastic material in true sense, yet within limits it is considered an elastic material. Thus the relation between the modulus of elasticity of concrete and its strength depends on age. The deflection of a concrete slab under a Falling Weight Deflectometer (FWD) ... Key word: Maize, bending stress, modulus of elasticity, shearing stress, specific shearing energy. Secondly it is difficult to determine tangent modulus with accuracy as the tangent to the curve is drawn by the eye judgment. Disclaimer 8. Capacities of reinforced concrete masonry determined by the strength design method are included in Strength Design of Concrete Masonry Walls for Axial Load and Flexure, TEK 14-11B (ref.3). [gravityform id="1" title="false" description="false" ajax="true"]. The bulk modulus (K) is like Young's modulus, except in three dimensions. Uses. Hence three methods can be used to determine the modulus of elasticity. This method is very useful to determine the quality of concrete, when it is subjected to alternate freezing and thawing. The stress will be obtained by dividing the load by the area of cross-section of the specimen. Video Included, What are the Causes of Cracks in Reinforced Concrete Slab? for normal weight concrete. Privacy Policy 9. Please note that the higher the E-module, the higher peak stresses will become! In addition to compute deflections which are required to be limited under the serviceability requirements in all structures. All Rights Reserved. Finally, knowledge of the modulus of elasticity of high strength concrete is very important in avoiding excessive deformation providing satisfactory serviceability and avoiding the most cost-effective designs. It has been observed that even under short term loading concrete does not behave as an elastic material. The modulus of elasticity is determined by subjecting a cylinder of 15 cm diameter and 30 cm length or 15 cm cube to uniaxial compression usually in U.T.M. This failure of bond at the interface increases at a faster rate than that due to applied stress. The strain of wet concrete is found less than for dry concrete, hence the modulus of elasticity is higher for wet concrete than for dry concrete. Higher value 16.3% is observed for lower strength i.e., 21 MPa and 7.5% increase for 70 MPa strength, while the strength of wet concrete is found less than dry concrete. Sign Up to The Constructor to ask questions, answer questions, write articles, and connect with other people. As it is the case for the compressive strength, Young's modulus … Before uploading and sharing your knowledge on this site, please read the following pages: 1. This is one reason that bones can be long and relatively thin. Bone is a remarkable exception. Concrete modulus of elasticity based on Indian standard can be calculated using the following expression: It is highly crucial to define modulus of elasticity of concrete in the design of concrete structure. Sorry, you do not have permission to ask a question, You must login to ask question. Elastic modulus of concrete can be classified into two main groups as: The strains obtained as above are plotted against stress and a curve is obtained as shown in Fig. Content Guidelines 2. 15.4. It has been observed that richer mixes have higher modulus of elasticity of concrete i.e., higher the amount of cement; higher the modulus of elasticity. In this method either the resonant frequency through a specimen of concrete or pulse velocity travelling through the concrete is measured. Concrete Technology, Concrete, Properties, Elasticity, Modulus of Elasticity of Concrete. The terms elastic modulus or Young’s modulus of elasticity can be applied strictly to linear relationship i.e., straight part of stress strain curve. This may be due to the fact that for stronger concretes its gel is also stronger, hence there is less strain for a given load. The linear analysis of elements, which is based on elastic theory, is used in some cases to satisfy requirements of ultimate and serviceability limit state such as in the design of pre-stressed concrete structures. The shear or modulus of rigidity (G) describes shear when an object is acted upon by opposing forces. Become VIP Member. Creep also does not significantly affect the initial tangent modulus. Definition of Modulus of Elasticity 2. It is represented by the slope of a line drawn from the origin to any point C on the curve. Thus a non-destructive method of testing known as dynamic method is adopted for determining the modulus of elasticity. The modulus of elasticity of concrete is used in the calculations of structural deformations. This method is most practical and is in most general use as it represents the actual deformation at the selected point and no uncertainties are involved in its determination. 15.5. f’c = Compressive strength of concrete. ... MODULUS OF ELASTICITY. Prohibited Content 3. In case of concrete, it deforms on the application of load, but this deformation does not follow any set rule. Similarly the curve of stress-strain of cement paste alone shows a fairly good straight line. The American Concrete Institute. It is represented by the slope of a tangent to the stress-strain curve drawn passing through the origin. At the time of design of a reinforced concrete structure, it is assumed that the bond between concrete and steel is perfect and the stress in steel is ‘m’ times the stress in concrete, where m is the ratio of modulus of elasticity of steel and concrete. Higher strengths give higher value of modulus of elasticity. Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary First Printing August 2011 ISBN 978-0-87031-744-6 American Concrete Institute® It is a measure of volumetric elasticity, calculated as volumetric stress divided by volumetric strain. Structural components still must be able to withstand dead and live loads without collapse even though the rise in temperature causes a decrease in the strength and modulus of elasticity for concrete and steel reinforcement. A stress-strain curve is drawn with the help of values of stress and strain obtained. For light weight concrete relation is-, It has been observed that for the same stress-strength ratio, the stronger the concrete, higher the strain, On the contrary stronger the concrete higher the modulus of elasticity. The concrete composite is then in the range of 30 to 50 GPa. Hence the degree of nonlinear behaviour is also very small. A spring is an example of an elastic object - when stretched, it … Determination of Modulus of Elasticity 3. Which means that the higher the E-module in concrete, the … The designed MST-BAR® deliver extremely high bond strength with concrete (x3 of the one with the steel) while providing the highest stiffness in a material. It can also be defined as the change of stress with respect to the elastic strain and may be computed by the following relation. Modulus of Elasticity of Concrete- Determination and Importance in Design, Calculation of Elastic Modulus of Concrete, 1. fcu,28: concrete compressive strength at 28 days. Ec = Modulus of elasticity of concrete. units is determined from the relation-, If length of specimen is measured in mm and density Ï in kg/m3 then-, The value of dynamic modulus of elasticity can also be determined from the relation-, Ed = Ïv2 [(1 + µ)(1 â 2µ)/(1 â µ)]. Country (b) The greater the volume of aggregate, the higher the modulus of elasticity of concrete. ... What are the Causes of Cracks in Reinforced Concrete Slab? We would like to show you a description here but the site won’t allow us. The concrete damaged plasticity model assumes that the reduction of the elastic modulus is given in terms of a scalar degradation variable d as E = ( 1 - d ) E 0 , where E 0 is the initial (undamaged) modulus of the material. Modulus of elasticity E cm The elastic deformation properties of reinforced concrete depend on its composition and especially on the aggregates. The value of modulus of elasticity Ec determined by actual loading of concrete is known as static modulus of elasticity. Stress-Strain Relationship of Aggregate and Cement Paste: The curve drawn between stress and strain of aggregate alone is found a fairly good straight line. The load on cylinder increased till it reaches to 1/3rd of cube strength plus 7 kg/cm2. The value of strain is calculated by dividing the gauge readings by gauge length. Ec = modulus of elasticity of concrete (5000 x SQRT(f ck) N/mm 2) As the modulus of elasticity of concrete changes with time, age at loading etc the modular ratio also changes accordingly. VIP members get additional benefits. Modulus of elasticity for all grades of steel is taken as Es = 29 x 10 6 psi. In other words, it reflects the ability of concrete to deflect elastically.
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