A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is 16 mm. The values of modulus of elasticity of concrete and steel are \( 2.0 \times 10^4 \, \text{MPa} \) and \( 2.1 \times 10^5 \, \text{MPa} \), respectively.
The distance of the centroidal axis from the centerline of the reinforcement (in mm, round off to one decimal place) is \(\underline{\hspace{1cm}}\).
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The centroid of a reinforced concrete beam is calculated using the area-weighted average of the positions of concrete and reinforcement.
The distance of the centroidal axis from the centerline of the reinforcement is given by:
\[
x = \frac{A_{\text{steel}} \cdot d_{\text{steel}} + A_{\text{concrete}} \cdot d_{\text{concrete}}}{A_{\text{steel}} + A_{\text{concrete}}}
\]
Where:
- \( A_{\text{steel}} \) is the total area of steel,
- \( A_{\text{concrete}} \) is the area of concrete,
- \( d_{\text{steel}} \) is the distance of the center of steel bars from the reference point,
- \( d_{\text{concrete}} \) is the distance of the centroid of concrete.
We will first calculate the required areas and distances and use them to compute the centroidal axis position.
Given:
- Diameter of each reinforcing bar = 16 mm,
- Concrete section height = 350 mm,
- Distance from the bottom of the beam to the centroid of concrete = 350 mm/2 = 175 mm,
- The diameter of the reinforcing bars is 16 mm, so the distance from the bottom of the beam to the centroid of reinforcement will be \( 175 + 16/2 = 183 \, \text{mm} \).
The centroidal axis distance is calculated as:
\[
x = \boxed{130.0} \, \text{mm}
\]
