Design of RCC Structures | Basic definitions and formulas
In this article, we will go through the basic definitions of Stress, strain, elastic materials and modulus of elasticity. This will be our first step towards understanding the design of “Singly reinforced sections”.
What is stress and how does it develop?
When an object is subjected to an external force, the object tends to build up internal resistance within itself (material). This resistance is termed as “stress”.
In short, stress can be defined as load per unit area.
Stress can be classified into four types:
- Compressive stress
- Tensile stress
- Bending stress
- Shear stress
Stress = Load/Area = W/A = N/mm2
Where, N = Newton
What is Strain?
To make it easier for you to understand, let’s merge the definition of stress with strain.
When an object is subjected to an external load, the internal resistance which is built up with the object itself is not enough to withstand the external load results into deformation of the object. This alteration or deformation of the object is called strain.
The formula for strain is given as follows:
Strain = Change in length/Original length
Strain has no unit.
What are elastic materials?
Elastic materials have the capacity to regain their original shape on removal of the load applied on the material.
When a rubber band is stretched, it deforms in shape but as soon as the pressure is released, the rubber band returns back to its original shape and size. This property of the material is called elasticity.
What is “Modulus of elasticity”?
We know that stress is directly proportional to strain within the elastic limit. The ratio of stress to strain is a constant which is denoted as k.
Stress/Strain = K
This constant is the measure of the elasticity of the material, hence called “modulus of elasticity”.
The formula for modulus of elasticity is given by,
E = modulus of elasticity = Stress/Strain = N/mm2
Denotations and their values:
- Modulus of elasticity for concrete = Ec = 2 x 105 N/mm2
- Modulus of steel = Es = 5700 (square root of fck) N/mm2
Where, fck = characteristic compressive strength of concrete
In our next article, we will discuss permissible stresses (steel, concrete) and modular ratio.