Steel expands 1 part in 100 000 for each 1°C increase in temperature. If the 1.5km main span of steel suspension bridge had no expansion joints, how much longer would it be for a temperature increase of 20°C?
Increase = a*(Tf-To)Lo =
10^-5*20*1.5 = 3.0*10^-4km.
To calculate the change in length of the steel bridge, we need to multiply the original length of the bridge by the expansion coefficient and the change in temperature.
Given:
Expansion coefficient: 1 part in 100,000 per 1°C
Original length of the bridge: 1.5 km
Change in temperature: 20°C
Step 1: Convert the length of the bridge to meters:
1.5 km = 1,500 meters
Step 2: Calculate the expansion coefficient for a 20°C temperature increase:
Expansion coefficient = (1/100,000) * 20 = 0.0002
Step 3: Calculate the change in length of the bridge:
Change in length = Original length * Expansion coefficient * Change in temperature
Change in length = 1,500 meters * 0.0002 * 20 = 60 meters
Therefore, the steel suspension bridge would be 60 meters longer for a temperature increase of 20°C.
To find out how much longer the steel suspension bridge would be for a temperature increase of 20°C, we need to calculate the expansion of the steel.
Given that steel expands 1 part in 100,000 for each 1°C increase in temperature, we can determine the expansion factor as follows:
Expansion factor = (1 part in 100,000 per 1°C) * (20°C)
Expansion factor = 20 parts in 100,000 = 0.0002
Now, we can calculate the additional length of the steel suspension bridge:
Additional length = Expansion factor * Original length
Additional length = 0.0002 * 1.5 km
Additional length = 0.0002 * 1500 m
Additional length = 0.3 meters
Therefore, the steel suspension bridge would be 0.3 meters longer for a temperature increase of 20°C.