A concrete sidewalk is constructed between two buildings on a day when the temperature is 25 0C. The sidewalk is 6 m long and consists of two slabs each 3 m in length and of negligible thickness. What would be amount of buckling (displacement) upwards that will occur in the slabs if the temperature increases to 38 0C. Assume that the buildings don’t move and the slabs move directly upwards from the joint when they expand.

To determine the amount of buckling (displacement) that will occur in the slabs due to temperature change, we can use the formula:

ΔL = α * L * ΔT

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

First, let's calculate the change in temperature:

ΔT = T2 - T1

Where:
- T2 is the final temperature (38°C)
- T1 is the initial temperature (25°C)

ΔT = 38°C - 25°C
ΔT = 13°C

Next, we need to find the thermal expansion coefficient of concrete. The thermal expansion coefficient for concrete can vary depending on its composition, but a rough estimate is around 10 x 10^-6 per °C.

Now we can calculate the change in length for each slab using the formula mentioned earlier:

ΔL = α * L * ΔT

For the first slab (3 m in length):

ΔL1 = (10 x 10^-6) * 3 m * 13°C
ΔL1 = 0.00039 m

For the second slab (3 m in length):

ΔL2 = (10 x 10^-6) * 3 m * 13°C
ΔL2 = 0.00039 m

Since the slabs are connected at the joint, the total displacement (buckling) will be the sum of the displacements for each slab:

Total displacement = ΔL1 + ΔL2
Total displacement = 0.00039 m + 0.00039 m
Total displacement = 0.00078 m

Therefore, the amount of buckling (displacement) that will occur in the slabs is approximately 0.00078 meters.