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Topic I

The document discusses the strain energy of an axially loaded bar with a slowly changing or constant cross-section. It provides equations that show strain energy is proportional to the square of the axial load, the length of the bar, and inversely proportional to the cross-sectional area and modulus of elasticity. It also notes that bars that are easier to distort will store more strain energy.

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Er Venkat
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67 views1 page

Topic I

The document discusses the strain energy of an axially loaded bar with a slowly changing or constant cross-section. It provides equations that show strain energy is proportional to the square of the axial load, the length of the bar, and inversely proportional to the cross-sectional area and modulus of elasticity. It also notes that bars that are easier to distort will store more strain energy.

Uploaded by

Er Venkat
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Axial Load

 Consider a bar with a slowly changing cross-section that is loaded centroidally.

 The internal load at x from one end is N , and the normal stress is N / A . using Eq. (6-
4) the strain energy is:

2 N2
 U i   x dV   2
dV 
V 2E V 2EA

 The volume dV can be expressed as Adx and:

 L
N2
Ui   2AE
dx (6-10)
  0

 If the cross-sectional area is constant:

 N 2L
Ui  (6-11)
2AE

 Note:

o L , Ui  

o A, Ui 

 o E , Ui 

 o i.e. something that is easy to distort will store more strain energy.

 

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