Problem: A reinforced concrete beam supports a dead load of $20 \text{ kN/m}$ and a live load of $15 \text{ kN/m}$. Calculate the critical factored design load $w_u$.

Problem: Calculate the modulus of elasticity of normal weight concrete with $f'_c = 28 \text{ MPa}$. Also determine the modular ratio $n$, which is used in Working Stress Design (WSD) and deflection calculations.

Problem: A plain concrete beam (without reinforcement) has a width of 300mm and height of 500mm. $f'_c = 28 \text{ MPa}$. Calculate the cracking moment $M_{cr}$.

Problem: A column supports the following service loads: $D = 1000 \text{ kN}$, $L = 600 \text{ kN}$, $W = 400 \text{ kN}$, and $E = 500 \text{ kN}$. Determine the governing ultimate factored load $U$ for the column design.

Problem: During construction, cylinders cast from a concrete pour on the second floor yielded a 28-day compressive strength ($f'_c$) of 15 MPa, well below the specified 28 MPa. Analyze the potential consequences and required actions.

Problem: A contractor mistakenly substituted Grade 40 (276 MPa) steel with high-strength, low-ductility steel (with no clear yield plateau and low elongation at rupture) in a seismic moment frame. Evaluate the theoretical implications for structural safety.

Problem: A reinforced concrete column has a calculated theoretical nominal axial strength ($P_n$) of $3500 \text{ kN}$. If the column is spiral-reinforced, calculate its reliable design strength ($\phi P_n$).

Problem: Calculate the theoretical yield strain ($\epsilon_y$) for Grade 60 ($414 \text{ MPa}$) and Grade 75 ($520 \text{ MPa}$) reinforcing steel. Use the standard modulus of elasticity.

Problem: A $250 \text{ mm} \times 400 \text{ mm}$ beam is made of sand-lightweight concrete. Calculate its self-weight (dead load) per meter length. Assume the density of sand-lightweight concrete is $18 \text{ kN/m}^3$. What is the corresponding modification factor ($\lambda$) for strength calculations?

Problem: A roof beam is subjected to a dead load of $12 \text{ kN/m}$ and a roof live load ($L_r$) of $8 \text{ kN/m}$. Determine the governing factored load $U$.