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Strain equation

  • Thread starter andrewh21
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  • #1
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Homework Statement


hi guys i have a sheet of i have the W,L and T a force and also the elastic modules etc
now my issue is i need to find the strain i have the stress etc but the is no extension figure given i have the usual strain equation e=x/l
can anyone point me in the right direction in regards to the equation [/B]


Homework Equations



e=x/l
strain= stress/e

The Attempt at a Solution


if my stress is 160 mpa and my gpa is 71 am i correct in strain = stress/e
160*10 to the power of 6/71*10 to the power of 9 =2.25 *10 to the power -2[/B]
 
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Answers and Replies

  • #2
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if my stress is 160 mpa and my gpa is 71 am i correct in strain = stress/e
160*10 to the power of 6/71*10 to the power of 9 =2.25 *10 to the power -2
 
  • #3
PhanthomJay
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You have denoted strain as e, and the modulus of Elasticity as e. That's confusing. Use E for youngs modulus. Then check your math. 160 MPa / 70 GPa equals ??
 
  • #4
The engineering strain is equal to the change in length of a specimen divided by the original specimen length. True strain can be manipulated so that: true strain = LN (instantaneous length of sample / original length of specimen)

The engineering stress is equal to the force applied to the body divided by the original cross-sectional area of the specimen. During a tensile stress, the length increases and therefore the cross-sectional area reduces within the necking region until fracture. Thus the material should actually experience an increase in stress. And so you use the true stress value, as opposed to the engineering stress. The true stress can be calculated by the force being applied at time, t, divided by the cross-sectional area of the specimen at that instant. This equation can be manipulated to express the true stress in terms of the engineering stress and and engineering strain.

Therefore the true stress = eng stress * (1 + eng strain) for tensile tests. For compression tests, the cross-sectional area increases and so the change in area affects the stress, demanding compensation in the following manner: true stress = eng stress * (1 - eng strain)

Using Hooke's law, the stress can be mathematically expressed as the product of the modulus of elasticity and strain. This is valid only for the elastic region of a stress-strain graph and not for plastic. Therefore, Young's modulus/modulus of elasticity is equal to stress divided by strain. This equation can be used for either true or engineering stress and strain.

In terms of your calculation and if it is only the strain you are interested in calculating, then the strain is indeed given by strain = stress / Young's modulus for any specimen exhibiting elastic behavior. The strain value you are trying to calculate is the corresponding value for when 160MPa of stress is experienced in the specimen. You should find your calculation to equal 2.25E-03.
 

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