a steel beam is 12.0 m long when installed at 23 degrees celsius.Find the change in the beam's length if the temperature changes from -32.0 degrees celcius to 55 degrees celcius?
Cooling from 23ºC to -32ºC
ΔL1= α•L•ΔT1 =12•12•10^-3•[23-(-32)]=
=12•12•10^-3•55= 7.92•10^-3 m
Heating from 23ºC to +55ºC
ΔL2= α•L•ΔT2 =12•12•10^-3•[55-23]=
=12•12•10^-3•32= 4.61•10^-3 m
Chamge in the beam’s length is
ΔL=ΔL1+ ΔL2=7.92•10^-3+ 4.61•10^-3=
=1.253•10^-2 m.
To find the change in the beam's length, you need to use the coefficient of linear expansion for steel. The coefficient of linear expansion represents how much a material expands or contracts for each degree of temperature change.
Here are the steps to calculate the change in the beam's length:
1. Find the coefficient of linear expansion for steel: The coefficient of linear expansion for steel is typically around 12 x 10^(-6) per degree Celsius.
2. Calculate the initial length change: Multiply the initial length of the beam (12.0 m) by the coefficient of linear expansion (12 x 10^(-6) per degree Celsius) and by the initial temperature change (-32.0 degrees Celsius - 23 degrees Celsius = -55 degrees Celsius). The negative sign indicates that the beam will contract due to the decrease in temperature.
Length change = 12.0 m * 12 x 10^(-6) per degree Celsius * -55 degrees Celsius
3. Calculate the final length change: Multiply the initial length of the beam (12.0 m) by the coefficient of linear expansion (12 x 10^(-6) per degree Celsius) and by the final temperature change (55 degrees Celsius - 23 degrees Celsius).
Length change = 12.0 m * 12 x 10^(-6) per degree Celsius * (55 degrees Celsius - 23 degrees Celsius)
4. Calculate the total change in length: Add the initial length change and the final length change to get the total change in length.
Total change in length = Length change (initial) + Length change (final)
Therefore, to calculate the change in the beam's length, you need to evaluate the above equations.