Question

A bridge is made with segments of concrete 91 m long (at the original temperature). If the linear expansion coefficient for concrete is 1.2 × 10−5(◦C)−1, how much spacing is needed to allow for expansion for an increase in temperature of 56◦F? Answer in units of cm.

Answer 1

The spacing needed to allow for expansion for a temperature increase of 56°F on the bridge is approximately 3.53 cm.

Step-by-step explanation:

To determine the spacing needed for expansion of the bridge due to an increase in temperature, we can use the linear expansion coefficient of concrete and the change in temperature. The linear expansion coefficient for concrete is given as 1.2 × 10-5 (°C)-1. First, we need to convert the increase in temperature from 56°F to °C using the conversion formula °C = (°F-32) x 5/9. This gives us an increase in temperature of 31.11°C. Next, we can calculate the change in length of the bridge using the formula ΔL = αLΔT, where ΔL is the change in length, α is the linear expansion coefficient, L is the original length of the bridge segment, and ΔT is the change in temperature.

Let's calculate the change in length:
ΔL = (1.2 × 10-5 (°C)-1) × (91 m) × (31.11°C)
ΔL = 0.035267 m
To convert the change in length to centimeters, we multiply by 100:
ΔL = 3.5267 cm

Therefore, the spacing needed to allow for expansion for a temperature increase of 56°F is approximately 3.53 cm.

Answer 2

Step-by-step explanation:

It is given that,

Length of bridge, L = 91 m

The linear expansion coefficient for concrete is,
`\alpha=1.2* 10^(-5)\ ^(\circ)C^(-1)`

Change in temperature,
`\Delta T=56^(\circ)F=13.33^(\circ)\ C`

Let
`\Delta L` is the increase in length. The formula is given by :

`\Delta L=L\alpha \Delta T`

`\Delta L=91\ m* 1.2* 10^(-5)\ ^(\circ)C^(-1)* 13.33^(\circ)\ C`

`\Delta L=0.0145\ m`

or

`\Delta L=1.45\ cm`

So, the expansion in the bridge is 1.45 cm. Hence, this is the required solution.