Concrete sidewalks are always laid in sections, with gaps between each section. For example, the drawing shows three identical 2.4-m sections, the outer two of which are against immovable walls. The two identical gaps between the sections are provided so that thermal expansion will not create the thermal stress that could lead to cracks. What is the minimum gap width necessary to account for an increase in temperature of 33 C°?

To calculate the minimum gap width necessary to account for the increase in temperature, we need to know the coefficient of linear expansion of the material used for the sidewalk. The coefficient of linear expansion represents how much a material expands or contracts per degree Celsius.

Let's assume that the coefficient of linear expansion for the material used in the sidewalk is α (alpha).

The formula to calculate the change in length due to thermal expansion is given by:
ΔL = α * L * ΔT

Where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L is the original length, and
ΔT is the change in temperature.

In this case, we have 2.4m sections, so L=2.4m, and ΔT=33°C.

To calculate the minimum gap width, we want to find ΔL, which represents the expansion of the sidewalk section.

ΔL = α * L * ΔT
ΔL = α * 2.4m * 33°C

Now, we need to determine the value of α.

Different materials have different coefficients of linear expansion, so without knowing the specific material, we cannot determine the exact value. However, let's assume a typical value for α, which is 12x10^(-6) 1/°C for concrete.

Using this value, we can now calculate the minimum gap width necessary:
ΔL = α * 2.4 m * 33°C
ΔL = (12x10^(-6) 1/°C) * 2.4 m * 33°C
ΔL = (12 * 2.4 * 33 * 10^(-6)) m

Calculating this value will give us the change in the length of one section due to thermal expansion. Since there are two identical gaps, the minimum gap width necessary would be half of the calculated value.

Gap width = (ΔL) / 2

Please note that this calculation is based on the assumption of a coefficient of linear expansion of 12x10^(-6) 1/°C for concrete. If the actual material used has a different coefficient, the calculation may vary. It is always recommended to consult the material specifications or engineering guidelines for accurate values.

To determine the minimum gap width necessary to account for thermal expansion in the concrete sidewalk, we need to consider the coefficient of thermal expansion of concrete and the temperature change.

The coefficient of thermal expansion (α) represents the amount of expansion per unit length when the temperature increases by 1°C. For concrete, the typical coefficient of thermal expansion is around 10 x 10^-6 per °C.

To calculate the thermal expansion of the concrete sidewalk, we can use the formula:
ΔL = α * L * ΔT

Where:
ΔL is the change in length of the concrete section
α is the coefficient of thermal expansion of concrete
L is the original length of the concrete section
ΔT is the temperature change

In this case, we have a temperature change of 33°C. Let's assume the length of each concrete section is 2.4 meters.

For the sections against immovable walls, no gaps are necessary as those sides are fixed. So, we will focus on the gaps between the sections.

Using the formula, the change in length of each section due to the temperature change can be calculated as:
ΔL = α * L * ΔT = 10 x 10^-6/°C * 2.4 meters * 33°C

ΔL = 7.92 x 10^-4 meters (approximately)

Since there are two gaps between the three sections, the total change in length for the gaps would be:
Total ΔL = 2 * ΔL = 2 * 7.92 x 10^-4 meters

Total ΔL = 1.584 x 10^-3 meters

Therefore, the minimum gap width necessary to account for the increase in temperature of 33°C would be approximately 1.584 millimeters.

ΔL = αLΔT

ΔL = 12•10⁻⁶•3•2.4•33 = 2.85•10⁻³ m
ΔL/2 = 2.85•10⁻³ /2 = 1.425•10⁻³ m