How to calculate Young's Modulus from a graph?

Question

I have a graph of Extension against Force applied for a steel wire. I need to know how to calculate the Young's Modulus of the wire from this. The questions simply says "Explain how you would use the graph to determine the Young's Modulus of the wire", so i don't actually have to do the calculation.

Answer 1

Young's modulus = stress/strain

Stress = force / cross sectional area

Strain = extension/original length

so



Y.M. = Force/Extension * Original Length/[cross sectional area]



but Force/Extension = 1/[gradient of your curve]



so Young's Modulus = Original length/(gradient * c.s.area)

Answer 2

Young Modulus Graph

Answer 3

There are 3 thoughts for this: preliminary tangent modulus - the slope of a line tangent to the curve on the commencing place Tangent modulus at a particular rigidity - slope of the line at a factor on the curve below the yield rigidity Secant modulus - slope of a line secant to the curve passing which passes in direction of the commencing place and a factor on the curve below the yield rigidity Your question or your professor would desire to have presented some practise related to which of those to apply for a curved diagram, because of the fact the end results of each and every technique are diverse, have diverse purposes, and diverse ones are favourite for various components. Concrete, case in point, in many instances makes use of the secant modulus reminiscent of 50% of the basically actual power. I recommend making use of the preliminary tangent modulus, and putting forward that for the duration of your answer/calculations. verify your textbook for further information, because it would additionally incorporate something to show you in direction of what the question needs. EDIT: Bomba, the 0.2% tension is usually only utilized for determining a yield power, yet not for the elastic modulus itself.

Answer 4

the Young's Modulus is the slope (S) of effort x deformation graphic. This Modulus only is been worth in the elastic zone (straight line). It is not valid on the plastic zone.



Given a data set:



S = [ n∑xy - (∑x)(∑y) ] / (n∑x² - (∑x)²)



x axis: unitary deformation, adimensional

y axis: Effort (N/m2, Mpa)



Good Luck.