Introduction to Reinforced Concrete - Worked Examples

A beam carries service dead load $D=20\,\text{kN/m}$ and service live load $L=15\,\text{kN/m}$. For this gravity-only introductory case, determine the governing factored load from $1.4D$ and $1.2D+1.6L$.

For normal-weight concrete with $f'_c=28\,\text{MPa}$, estimate $E_c$ using the simplified normal-weight expression and determine $n=E_s/E_c$ with $E_s=200{,}000\,\text{MPa}$.

A rectangular section has $b=300\,\text{mm}$, $h=500\,\text{mm}$, and $f'_c=28\,\text{MPa}$. Estimate its cracking moment using $\lambda=1.0$ and the gross uncracked section.

A normal-weight concrete beam is $300\,\text{mm}$ wide by $500\,\text{mm}$ deep. If the project preliminary load model uses $\gamma_c=24\,\text{kN/m}^3$, estimate the beam self-weight per meter.

Sand-lightweight concrete has $f'_c=28\,\text{MPa}$. For the stated course calculation, use $\lambda=0.85$ and estimate $f_r$.

Using $E_s=200{,}000\,\text{MPa}$, calculate the idealized yield strain for reinforcement with $f_y=420\,\text{MPa}$ and $f_y=520\,\text{MPa}$.

A tension-controlled flexural section has nominal moment strength $M_n=450\,\text{kN}\cdot\text{m}$. For the adopted NSCP 2015 / ACI 318-14 flexural basis, use $\phi=0.90$ and determine the design strength.

A roof beam has service dead load $D=12\,\text{kN/m}$ and roof live load $L_r=8\,\text{kN/m}$, with ordinary floor live load absent. Compare $1.4D$ with $1.2D+1.6L_r$ for this stated case.

A coastal reinforced-concrete beam will be exposed to airborne salt and intermittent wetting. The contractor proposes a calcium-chloride accelerator solely to obtain faster early strength. Identify the appropriate engineering response from the durability principles in the lesson.