Problem: A beam with $b_w=300 \text{ mm}$, $d=500 \text{ mm}$ is subjected to a factored shear force $V_u = 250 \text{ kN}$. Concrete $f'_c = 28 \text{ MPa}$ (normal weight). Check if the section is adequate without stirrups. If not, determine the required $V_s$.

Problem: Using the result from Example 1 ($V_s = 198.4 \text{ kN}$), design the spacing for 10mm diameter U-stirrups ($A_v = 2 \times 78.5 = 157 \text{ mm}^2$). $f_{yt} = 275 \text{ MPa}$.

Problem: A rectangular beam ($b=400$, $h=600$) is subjected to a factored torque $T_u = 5 \text{ kN-m}$. $f'_c = 28 \text{ MPa}$. Determine if torsion reinforcement is required.

Problem: Determine the maximum allowable spacing $s_{max}$ for vertical U-stirrups in a beam with $b_w = 300 \text{ mm}$, $d = 500 \text{ mm}$. The required shear strength from steel is $V_s = 150 \text{ kN}$, $f'_c = 28 \text{ MPa}$, and $f_{yt} = 275 \text{ MPa}$.

Problem: A solid rectangular beam ($b=400 \text{ mm}, h=600 \text{ mm}$) is subjected to a factored shear $V_u = 200 \text{ kN}$ and factored torsion $T_u = 40 \text{ kN-m}$. Calculate the critical limits to verify if the section size is adequate to resist combined shear and torsion before designing reinforcement. $f'_c = 30 \text{ MPa}$, clear cover = $40 \text{ mm}$.

Problem: A deep beam carrying heavy concentrated loads near its supports developed severe cracks propagating at a 45-degree angle from the support towards the load point. The beam failed suddenly without yielding of the flexural reinforcement. Diagnose the failure mechanism.

Problem: An edge (spandrel) beam in a parking garage began to twist excessively, showing wide spiral cracking along its length. The main flexural rebar and stirrups were spaced closely, but the stirrups were open U-shapes. Explain why the failure occurred despite having "enough" stirrup area.

Problem: For a beam with $b_w=300 \text{ mm}$, $d=450 \text{ mm}$, and $f'_c = 28 \text{ MPa}$, the required shear reinforcement to carry the factored load is $V_s = 150 \text{ kN}$. Check the ACI 318 maximum spacing limit for the stirrups. Assume 10mm diameter U-stirrups ($A_v = 157 \text{ mm}^2$) with $f_{yt} = 420 \text{ MPa}$.