Problem: A one-way simply supported slab spans $L = 4.5 \text{ m}$. Determine the minimum thickness $h$ to avoid deflection calculations. $f_y = 420 \text{ MPa}$.

Problem: Design a one-way slab to carry a live load of $4 \text{ kPa}$ and superimposed dead load of $2 \text{ kPa}$ on a simply supported span of $4 \text{ m}$. $f'_c = 28 \text{ MPa}$, $f_y = 420 \text{ MPa}$. Use $h=150 \text{ mm}$.

Problem: A two-way slab panel is $4 \text{ m} \times 5 \text{ m}$ (short span $S=4$, long span $L=5$). Supported on all sides, discontinuous edges. Calculate the positive moment in the short direction. $w_u = 12 \text{ kPa}$.

Problem: A one-way solid slab with an effective depth $d = 120 \text{ mm}$ supports a uniform factored load $w_u = 15 \text{ kPa}$. The slab spans $4.0 \text{ m}$ between the centerlines of its simple supports. Determine if the slab's concrete shear capacity $\phi V_c$ is adequate without stirrups. Use $f'_c = 25 \text{ MPa}$.

Problem: Determine if the Direct Design Method (DDM) can be used to analyze a two-way flat slab floor system consisting of 3 continuous spans in each direction. The panels are $6 \text{ m}$ by $5 \text{ m}$. The unfactored live load is $3.0 \text{ kPa}$ and the unfactored dead load (including self-weight) is $4.5 \text{ kPa}$.

Problem: An open-plan retail store was built using a flat plate concrete floor system (a two-way slab resting directly on columns without drop panels or column capitals). The floor was originally designed for a live load of $4.8 \text{ kPa}$. Decades later, a tenant placed densely packed heavy library shelving ($12 \text{ kPa}$) around several interior columns. The slab suddenly dropped around one column, leaving the column punching through the floor. Diagnose the structural failure.

Problem: Following an initial punching shear failure at a single column in an underground parking garage, the entire floor slab progressively collapsed, pulling down the columns next to it, and triggering a chain reaction across the entire structure. Explain why the failure propagated so extensively and how modern codes prevent this.