In the construction of a flyover, steel girders of length 12 m are used to place one after another. How much gap should be left between the two at their junction so that in summers whenpeak temperature is about `48^(@)C`, there should not be any compresion. Given that the construction is done in peak winters when temperature is `18^(@)C`. Given that the coefficient of linear expansion of steel is `1.1xx10^(-5).^(@)C^(-1)`.

Answer

To solve the problem, we need to determine the gap that should be left between two steel girders to prevent compression due to thermal expansion when the temperature rises from 18 °C to 48 °C.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Length of the steel girder (L) = 12 m
- Initial temperature (T1) = 18 °C
- Final temperature (T2) = 48 °C
- Coefficient of linear expansion of steel (α) = \(1.1 \times 10^{-5} \, °C^{-1}\)

2. **Calculate the Change in Temperature (ΔT):**
\[ \Delta T = T2 - T1 = 48 °C - 18 °C = 30 °C \]

3. **Calculate the Change in Length (ΔL):**
The formula for change in length due to thermal expansion is:
\[ \Delta L = L \cdot \alpha \cdot \Delta T \]
Substituting the values:
\[ \Delta L = 12 \, \text{m} \cdot (1.1 \times 10^{-5} \, °C^{-1}) \cdot (30 \, °C) \]

4. **Perform the Calculation:**
\[ \Delta L = 12 \cdot 1.1 \times 10^{-5} \cdot 30 \]
\[ \Delta L = 12 \cdot 3.3 \times 10^{-5} = 3.96 \times 10^{-4} \, \text{m} \]

5. **Determine the Required Gap:**
Since the expansion occurs equally in both girders, the gap required between the two girders is half of the total change in length:
\[ \text{Gap} = \frac{\Delta L}{2} = \frac{3.96 \times 10^{-4}}{2} = 1.98 \times 10^{-4} \, \text{m} \]

6. **Convert the Gap to Millimeters:**
\[ \text{Gap} = 1.98 \times 10^{-4} \, \text{m} = 0.198 \, \text{mm} \]

### Final Answer:
The gap that should be left between the two girders at their junction is approximately **0.198 mm**.