Strain Energy Formula
Strain energy is the energy stored in a body as a result of deformation. It is represented by the symbol U. It鈥檚 unit of measurement is J. The dimensional formula of strain energy is given by [M1L2T-2]. The strain energy per unit volume strain energy density or the area under the stress-strain curve towards the site of deformation. The formula for strain energy is equal to half the product of the compression factor and force applied to the body.
Formula
U = 1/2 脳 F 脳 未
where,
未 is the compression factor,
F is the force applied on the body.
In terms of Young鈥檚 modulus, stress and volume of the body, the formula is given by,
U = 蟽2/2EV
where,
蟽 is the value of stress,
E is the Young鈥檚 modulus,
V is the volume of body.
When stress 蟽 is proportional to strain 系, the strain energy formula is equal to half the product of stress, strain and volume of the body.
U = 1/2 脳 蟽 脳 系 脳 V
where,
蟽 is the stress,
系 is the strain,
V is the volume of body.
Sample Problems
Problem 1. Calculate the strain energy if a force of 1200 N compresses the body by 3 m.
Solution:
We have,
F = 1200
未 = 3
Using the formula we have,
U = 1/2 脳 F 脳 未
= 1/2 脳 1200 脳 3
= 1800 J
Problem 2. Calculate the strain energy if a force of 1000 N compresses the body by 4 mm.
Solution:
We have,
F = 1000
未 = 4 脳 10-3
Using the formula we have,
U = 1/2 脳 F 脳 未
= 1/2 脳 1000 脳 4 脳 10-3
= 2 J
Problem 3. Calculate the strain energy if the stress of 500 Pa is applied on a body of volume 270 cu. m. The value of Young鈥檚 modulus is given as 120 Pa.
Solution:
We have,
V = 270
蟽 = 500
E = 120
Using the formula we have,
U = 蟽2/2EV
= (500 脳 500)/(2 脳 120 脳 270)
= 3.85 J
Problem 4. Calculate the strain energy if the stress of 160 Pa is applied on a body of volume 90 cu. m. The value of Young鈥檚 modulus is given as 50 Pa.
Solution:
We have,
V = 90
蟽 = 160
E = 50
Using the formula we have,
U = 蟽2/2EV
= (160 脳 160)/(2 脳 50 脳 90)
= 2.84 J
Problem 5. Calculate the strain energy if the stress of 35 Pa is applied on a body of area of 12 sq. m and length of 4 m. The value of Young鈥檚 modulus is given as 25 Pa.
Solution:
We have,
A = 12
l = 4
蟽 = 35
E = 25
Calculate the volume V of the body.
V = Al
= 12 (4)
= 48 cu. m
Using the formula we have,
U = 蟽2/2EV
= (35 脳 35)/(2 脳 25 脳 48)
= 0.51 J
Problem 6. Calculate the strain energy if the stress of 60 Pa and strain of 2 脳 10-6 are applied on a body of volume 100 cu. m such that the stress is proportional to strain.
Solution:
We have,
蟽 = 60
系 = 2 脳 10-6
V = 100
Using the formula we have,
U = 1/2 脳 蟽 脳 系 脳 V
= 1/2 脳 60 脳 2 脳 10-6 脳 100
= 6 脳 10-3 J
Problem 7. Calculate the strain energy if the stress of 250 Pa and strain of 7 脳 10-3 are applied on a body of volume 400 cu. m such that the stress is proportional to strain.
Solution:
We have,
蟽 = 250
系 = 7 脳 10-3
V = 400
Using the formula we have,
U = 1/2 脳 蟽 脳 系 脳 V
= 1/2 脳 250 脳 7 脳 10-3 脳 400
= 350 J