Elastic deflections are the immediate deflections that occur only once during service period. It is not a time function i.e., there is no specific time when immediate deflections come into action. Mathematically immediate deflections can be expressed as;
- EI is the flexural rigidity of the reinforced concrete beam
- f is a function that depends on loads, span length and the arrangement of supports.
For a uniformly loaded simple beam, f can be evaluated by using a mathematical formula;
Same type of equations can be easily computed for various other supports like cantilever, fixed on both ends, fixed from one end, both end continuous, one end continuous etc. The problem occurs during the calculation of flexural rigidity EI. This is because of the two totally different materials i.e., concrete and a steel. Both vary in material properties and as well as in behavior.
Generally, elastic modulus of concrete is evaluated. As steel is more elastic than concrete, it shows elasticity like rubber. So, if the material fails then it only occurs due to concrete inelastic behavior. Therefore, during the calculation of elastic modulus, we will use only of concrete instead of the combined elastic modulus.
A mathematical expression for calculation of Elastic modulus for concrete having compressive strength ranges to about 6000 Psi.
For concrete having compressive strength up to 3000 Psi. Elastic modulus can be evaluated by using;
Similarly, gross moment of inertia can be calculated very easily. By using the expression
Now after calculating put the values in the formula and get the value of immediate deflection in flexural members and find a remedial solution.
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