<< Chapter < Page Chapter >> Page >

Check Your Understanding Does a given reading on a gasoline gauge indicate more gasoline in cold weather or in hot weather, or does the temperature not matter?

The actual amount (mass) of gasoline left in the tank when the gauge hits “empty” is less in the summer than in the winter. The gasoline has the same volume as it does in the winter when the “add fuel” light goes on, but because the gasoline has expanded, there is less mass.

Got questions? Get instant answers now!

Thermal stress

If you change the temperature of an object while preventing it from expanding or contracting, the object is subjected to stress that is compressive if the object would expand in the absence of constraint and tensile if it would contract. This stress resulting from temperature changes is known as thermal stress    . It can be quite large and can cause damage.

To avoid this stress, engineers may design components so they can expand and contract freely. For instance, in highways, gaps are deliberately left between blocks to prevent thermal stress from developing. When no gaps can be left, engineers must consider thermal stress in their designs. Thus, the reinforcing rods in concrete are made of steel because steel’s coefficient of linear expansion is nearly equal to that of concrete.

To calculate the thermal stress in a rod whose ends are both fixed rigidly, we can think of the stress as developing in two steps. First, let the ends be free to expand (or contract) and find the expansion (or contraction). Second, find the stress necessary to compress (or extend) the rod to its original length by the methods you studied in Static Equilibrium and Elasticity on static equilibrium and elasticity. In other words, the Δ L of the thermal expansion equals the Δ L of the elastic distortion (except that the signs are opposite).

Calculating thermal stress

Concrete blocks are laid out next to each other on a highway without any space between them, so they cannot expand. The construction crew did the work on a winter day when the temperature was 5 ° C . Find the stress in the blocks on a hot summer day when the temperature is 38 ° C . The compressive Young’s modulus of concrete is Y = 20 × 10 9 N/m 2 .


According to the chapter on static equilibrium and elasticity, the stress F / A is given by

F A = Y Δ L L 0 ,

where Y is the Young’s modulus of the material—concrete, in this case. In thermal expansion, Δ L = α L 0 Δ T . We combine these two equations by noting that the two Δ L s are equal, as stated above. Because we are not given L 0 or A , we can obtain a numerical answer only if they both cancel out.


We substitute the thermal-expansion equation into the elasticity equation to get

F A = Y α L 0 Δ T L 0 = Y α Δ T ,

and as we hoped, L 0 has canceled and A appears only in F / A , the notation for the quantity we are calculating.

Now we need only insert the numbers:

F A = ( 20 × 10 9 N/m 2 ) ( 12 × 10 −6 / ° C ) ( 38 ° C 5 ° C ) = 7.9 × 10 6 N/m 2 .


The ultimate compressive strength of concrete is 20 × 10 6 N/m 2 , so the blocks are unlikely to break. However, the ultimate shear strength of concrete is only 2 × 10 6 N/m 2 , so some might chip off.

Got questions? Get instant answers now!

Check Your Understanding Two objects A and B have the same dimensions and are constrained identically. A is made of a material with a higher thermal expansion coefficient than B . If the objects are heated identically, will A feel a greater stress than B ?

Not necessarily, as the thermal stress is also proportional to Young’s modulus.

Got questions? Get instant answers now!

Questions & Answers

What is vector
Ajibola Reply
Vector is a quantity having a direction as well as magnitude
tell me about charging and discharging of capacitors
Ahemen Reply
a big and a small metal spheres are connected by a wire, which of this has the maximum electric potential on the surface.
Bundi Reply
3 capacitors 2nf,3nf,4nf are connected in parallel... what is the equivalent capacitance...and what is the potential difference across each capacitor if the EMF is 500v
Prince Reply
four effect of heat on substances
Prince Reply
why we can find a electric mirror image only in a infinite conducting....why not in finite conducting plate..?
Rima Reply
because you can't fit the boundary conditions.
what is the dimensions for VISCOUNSITY (U)
what is thermodynamics
Aniket Reply
the study of heat an other form of energy.
heat is internal kinetic energy of a body but it doesnt mean heat is energy contained in a body because heat means transfer of energy due to difference in temperature...and in thermo-dynamics we study cause, effect, application, laws, hypothesis and so on about above mentioned phenomenon in detail.
It is abranch of physical chemistry which deals with the interconversion of all form of energy
what is colamb,s law.?
Muhammad Reply
it is a low studied the force between 2 charges F=q.q`\r.r
what is the formula of del in cylindrical, polar media
Birengeso Reply
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
what is flux
Bundi Reply
Total number of field lines crossing the surface area
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
what is temperature change
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
process whereby the degree of hotness of a body (or medium) changes
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
what was the temperature of the soft drink when it was removed ?
15 degree Celsius
15 degree
ok I think is just conversion
15 degree Celsius to Fahrenheit
0 degree Celsius = 32 Fahrenheit
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
I dont understand
the question said you should convert 15 degree Celsius to Fahrenheit
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
what is d final ans for Fahrenheit and Celsius
it said what is temperature change in Fahrenheit and Celsius
the 15 is already in Celsius
So the final answer for Fahrenheit is 59
what is d final ans for Fahrenheit and Celsius
what are the effects of placing a dielectric between the plates of a capacitor
Bundi Reply
increase the capacitance.
besides increasing the capacitance, is there any?
mechanical stiffness and small size
so as to increase the capacitance of a capacitor
also to avoid diffusion of charges between the two plate since they are positive and negative.
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
Anne Reply
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
Martin Reply
what is flux
Bundi, flux is the number of electric field crossing a surface area
you right
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
somebody help me answer the question above
Practice Key Terms 4

Get the best University physics vol... course in your pocket!

Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?