JOB # 6DETERMINATION OF PRINCIPAL STRAIN AND STRESS USING STRAIN ROSSETE TECHNEIQUE.

APPARATUS:

Model beam Strain rossete (g.f=2.05) Strain meter 45v dc bettery Pressure cell Vernier calliper Measuring tape Connecting wires

RELATED THEORY

PRINCIPLE STRESSES :

Stresses On The Principle Plain Are Principle Stresses.

PRINCIPLE STRAIN :

strain due to principle stresses.The extreme values of normal strain at any point in the material are called principal strains.Major principal strain = ε1 = εmax

Minor principal strain = ε2 = εmin

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DIFFERENCE BETWEEN PRINCIPLE PLANE & PRINCIPLE AXES.

Principal planes are the two dimensional surfaces where normal stresses achieve their extremevalues and shear stresses are zero.(σx = max, σy = max or σmax or min & τxy = 0 )But principal axes are imaginary lines where 2nd moment of area achieve it’s extreme values andproduct moment of inertia is zero.(Ixx = max, Iyy = max, Ixy = 0 )

STRAIN ROSETTE:

Definition:Combination of at least three strain gauges cemented/pasted in three different directions onthe surface of structural components to determine the complete state of stress and strains.

DESCRIPTION:

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So in this way we have three equations and three unknowns εx εy γxy. So the equations canbe solved for these three values.

COMPLETE STATE OF STRESS:When we know all the following parametersσx, σy, τxy, σ1, σ2, θp, θs, τmax, τminthen this is known as complete state of stress.

COMPLETE STATE OF STRAIN:When we know all the following parametersεx, εy, γxy, ε1, ε2, θp, θs, γmax, γminthen this is known as complete state of strain.

TYPES:Usually there are four types of strain rosettes available in the market.

45° Strain Rosette. 60° Strain Rosette. 120° Strain Rosette. 4-element Strain Rosette.

45° STRAIN ROSETTE:“A strain rosette having included angle of 45° between two consecutive elements”.

θa = 0° θb=45° θc=90°εx = εa

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εy = εcεxy = εa+εc-2εb

60° Strain Rosette :“A strain rosette having included angle of 60° between two consecutive elements”. It is also called Equilateral Strain Rosette.

120°

Strain Rosette (Delta Strain Rosette):“A strain rosette having included angle of 60° between two consecutive elements”.It is also called Delta Strain Rosette or

Equiangular Strain Rosette

4-element Strain Rosette:The Strain Rosette having four strain gauges/elements is called 4-element stain rosette.

ADVANTAGES:

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We can have a counter check of the computed values of coordinate strains (Precision)

Graphical solution for Strain Rosette (Mohr Circle):

Set up a vertical axis to represent ε = 0(which will subsequently be the semi shear strainaxis)

Draw three lines parallel to the above axis at the appropriate distance representing thevalues (positive or negative) of εa, εb and εc.

On the middle lines of these three (representing the middle value of the three strains) mark a point P representing the origin of the rosette.

Draw the rosette configuration at the point P but lining up gauge c along its verticalordinate.

Project the directions of gauges a and b to cut their respective vertical ordinates at Q and R.

Construct perpendicular bisectors of PQ and PR; where these intersect is the centre of thestrain circle, O.

Draw the circle on this centre, which of course should pass through the points P, Q and R. Insert the horizontal strain abscissa through O.

Join O to Q, R and S, where S is the other intersection of the circle with the middle vertical line.

The lines OQ, OR and OS represent the three gauges on the circle where 2α and 2β are the angles between OR and OQ, and OQ and OS, respectively.

From the circle read off as requires the principal strains ε1, ε2 or the chosen co-ordinatedirection strains εx, εy, γxy.

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