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

Thermal Stress & Strain so 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

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

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 0.4-0.9x10-5 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 5.110-5 Glass 1.2-2.7x10-5 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

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)

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

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

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