1. Thermal Stress and Strain
Prof. Marlon Flores Sacedon
Department of Mathematics and Physics
College of Arts and Sciences
Visayas State University, Visca
Baybay City, Leyte, Phiippines

2. Thermal Stress & Strainso A F
If the length is to be constant, the total fractional change in length must be zero.
Tensile Stress F
(thermal stress) Lo
Where:
F = Tensile force, (N)
A = cross-section area, (m2)
Y = Young’s Modulus, (Pa or N/m2)
= coef. of linear expansion, (K-1)
= change in tempersture, (K)
Tensile Strain

3. Approximate Young’s Modulus
Substance
Young’s Modulus, Y
(Pa)
Aluminum
7.0x1010
Brass
9.0x1010
Copper
11x1010
Crown glass
6.0x1010
Iron
21x1010
Lead
1.6x1010
Nickel
Steel
20x1010

4. MFS Coefficients of Linear Expansion Coefficients of Volume Expansion
Material
[K-1 or (Co)-1]
Aluminum
2.4x10-5
Brass
2.0x10-5
Copper
1.7x10-5
Glass
x10-5
Invar
0.09x10-5
Quartz
0.04x10-5
Steel
1.2x10-5
Material
[K-1 or (Co)-1]
Aluminum
7.2x10-5
Brass
6.0x10-5
Copper
Glass
x10-5
Invar
0.27x10-5
Quartz
0.12x10-5
Steel
3.6x10-5
Ethanol
75x10-5
Carbon Disulfide
115x10-5
Glycerine
49x10-5
Mercury
18x10-5
MFS

5. Example 1: An aluminum cylinder 10 cm long, with a cross-section area of 20 cm2, is to be used as a spacer between two steel walls. At 17.2 oC it just slips in between the walls. When it warms to 22.3oC, calculate the stress in the cylinder and the total force it exerts on each wall, assuming that the walls are perfectly rigid and a constant distance apart.
Substance
Young’s Modulus, Y
(Pa)
Aluminum
7.0x1010
Brass
9.0x1010
Copper
11x1010
Crown glass
6.0x1010
Iron
21x1010
Lead
1.6x1010
Nickel
Steel
20x1010
F = 0
Area A=20cm2
Lo=10cm
@ T1=17.2 oC
F > 0
Stress is - 8.6x106 Pa
Negative sign indicates compression
Lo=10cm
@ T2=22.3 oC
F = -1.7x104 N (compression)

6. Seat Work1: a) A wire that is 1
Seat Work1: a) A wire that is 1.50 m long at 20oC is found to increase in length by 1.9 cm when warmed to 420oC. Compute its average coefficient of linear expansion for this temperature range. b) The wire is stretched just taut (zero tension) at 420oC. Find the stress in the wire if it is cooled to 20oC without being allowed to contact. Young’s modulus for the wire is 20.x1011 Pa.
Substance
Young’s Modulus, Y
(Pa)
Aluminum
7.0x1010
Brass
9.0x1010
Copper
11x1010
Crown glass
6.0x1010
Iron
21x1010
Lead
1.6x1010
Nickel
Steel
20x1010
1.50 m
@ 20oC
0.019 m
@ 420oC
Ans
1.519 m
@ 420oC
1.519 m
F>0
@ 20oC

7. Assignment
1) A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120oC to 10oC?
Answer: 4.0x104 N
2) Steel train rails are laid in 12.0 m-long segments placed end-to-end. The rails are laid on a winter day when their temperature is -2.0oC. a) How much space must be left between adjacent rails if they are to just touch on a summer day when their temperature is 33.0oC? b) If the rails are originally laid in contact, what is the stress in them on a summer day when their temperature is 33.0oC?
Answer: a) 5.0x10-3 m; b) 8.4x107 Pa

8. eNd