Modulus of Elasticity vs Modulus of Rigidity |Elastic Modulus vs Shear Modulus

Modulus of Elasticity vs Modulus of Rigidity |Elastic Modulus vs Shear Modulus 

Modulus of elasticity and modulus of rigidity are two properties of matter. These properties are very important in designing and implementing mechanical and structural designs. These concepts are very important in understanding the proper mechanics and statics of solid systems. To have a clear understanding in fields such as engineering and physics, a clear understanding in these concepts is required. In this article, we are going to discuss what modulus of elasticity and modulus of rigidity are, their applications, definitions of modulus of elasticity and modulus of rigidity, their differences and finally the difference between these two.

Modulus of Rigidity (Shear Modulus)

Shear stress is a deformation force. When a force is applied tangential to a solid surface, the solid tends to “twist”. For this to happen, the solid must be fixed, so that it cannot move in the direction of the force. The unit of shear stress is Newton per meter squared or commonly known as Pascal. We know that Pascal is also the unit of pressure. However, the definition of pressure is the force normal to the surface divided by the area, whereas the definition of shear stress is the force parallel to the surface per unit area. Torque acting upon a fixed object can also produce shear stress. By definition, not only solids but also fluids can have a shear stress. Objects have a property called the shear modulus, which tells us how far will the object twist for a given shear stress. This depends on the shape, size, material and temperature of the object. Shear stress of constructions and automobile engineering plays a main role in designing and implementing the design.

Modulus of Elasticity

Elasticity is a very useful property of matter. It is the ability of the materials to return to their original shape after any external forces are removed. It is observed that the force required to keep an elastic rod stretched is proportional to the stretched length of the rod. Modulus of elasticity is the tendency of an object to deform elastically when an external force is applied. The definition of the elastic modulus is the ratio of stress to the strain. The stress is the restoring force caused by the deformation of the molecules. Stress is given as a pressure. Strain is the ratio of the deformed length to the original length of the object. Strain is a dimensionless quantity. Therefore, modulus of elasticity also has the dimensions of stress, which is Newton per square meter or Pascal.

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What is actually poisson's ratio.. Read it u will learn something most important

Poisson's ratio is defined as the negative of the ratio of the lateral strain to the axial strain for a uniaxial stress state. If a tensile load is applied to a material, the material will elongate on the axis of the load ﴾perpendicular to the tensile stress plane﴿,

Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio. Poisson's ratio, also called Poisson ratio or the Poisson coefficient, or coefficient de Poisson, is usually represented as a lower case Greek nu, n. 









Note: Poisson's Ratio has no units

Poisson's ratio is sometimes also reffered to as the ratio of the absolute values of lateral and axial strain. This ratio, like strain, is unit less since both strains are unit less.

For stresses within the elastic range, this ratio is approximately constant. For a perfectly isotropic elastic material, Poisson's Ratio is 0.25, but for most materials the value lies in the range of 0.28 to 0.33.

Generally for steels, Poisson's ratio will have a value of approximately 0.3. This means that if there is one inch per inch of deformation in the direction that stress is applied, there will be 0.3 inches per inch of deformation perpendicular to the direction that force is applied.


In other words poission ratio indicates the fraction by which a material is deformed by the action of compressive  or tensile(elongating) force in one of its perpendicular direction...

the best example to understand its physical effect is when u stretch a rubber band,it increases its length and at the same time,its diameter decreases , amount of decrement is given by poisson's ratio wrt its elongation

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Characteristic strength of concrete

Characteristic strength of concrete is one of the important properties of concrete which indeed unanimously by design engineeror any other person involved in the construction sector.

The compressive strength of concrete is given in terms of the characteristic compressive strength of 150 mm size cubes tested at 28 days (fck)- as per Indian Standards (ACI standards use cylinder of diameter 150 mm and height 300 mm). The characteristic strength is defined as the strength of the concrete below which not more than 5% of the test results are expected to fall.

This concept assumes a normal distribution of the strengths of the samples of concrete.

                               

Normal Distribution curve on test specimens for      determining compressive strength

The above sketch shows an idealized distribution of the values of compressive strength for a certain number of test specimens. The horizontal axis represents the values of compressive strength in MPa. The vertical axis represents the number of test samples for a

particular compressive strength. This is also termed as frequency.

The average of the values of compressive strength (mean strength) from the graph is 40 MPa. The characteristic strength (fck) is the value in the x-axis below which 5% of the total area under the curve falls. From the graph we can clearly say that 30 MPa is the characteristic strength of the given concrete mix. The value of fck is lower than fcm (40 MPa- mean strength) by 1.64σ, where σ is the standard deviation of the normal distribution.

So we can say the given concrete mix has a characteristic strength of 30 MPa or it is a M30 grade mix.

   M- Mix

* Note: For a 95% confidence level k=1.64 , hence k value varies on the confidence level of the experiment

Definition:

Characteristic strength of concrete is the strength of concrete specimens casted and tested as per given code of practice and cured for a period of 28 days; 95% of tested cubes should not have a value less than this value.

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