Scenario: Designing a reinforced concrete beam for a high-rise building.

ASD Approach: Under ASD, the actual service loads (Dead + Live) are used, and the calculated stresses are kept below an allowable stress limit (which is a fraction of the material's yield strength). ASD does not explicitly account for the different degrees of uncertainty between dead loads (which are highly predictable) and live loads (which are highly variable).

LSD/LRFD Approach: LSD uses factored loads. Dead loads might have a lower factor (e.g., 1.2) because their weight is easily calculated, while live loads have a higher factor (e.g., 1.6) to account for unexpected overcrowding. The concrete and steel strengths are also reduced by resistance factors ($\phi$).

Conclusion: LSD provides a much more consistent level of safety across the entire structure. ASD might over-design structural members where the load is mostly predictable dead load, and potentially under-design members subjected to highly unpredictable live loads. LSD is the standard for modern concrete design.

Scenario: Sizing the concrete footing for a column.

Application: Even in modern practice where the superstructure (columns, beams) is designed using LSD/LRFD, the sizing of the foundation area (the footprint of the footing on the soil) is almost exclusively done using ASD. Geotechnical engineers provide an "Allowable Bearing Pressure" for the soil.

Reasoning: Soil behavior is incredibly complex and non-linear. The safety factors used in soil mechanics are massive (often 3.0 or more) compared to those used for manufactured materials like steel or concrete. Therefore, the structural engineer takes the unfactored service loads (Dead + Live) and divides by the allowable bearing pressure to find the required footing area. Once the area is found, they switch back to LRFD factored loads to design the actual concrete thickness and steel reinforcement within that footing.

A simply supported beam carries a dead load ($D$) of $15 \text{ kN/m}$ and a live load ($L$) of $20 \text{ kN/m}$. Calculate the ultimate design load ($U$) per NSCP 2015.

A roof structure is subjected to a dead load ($D$) of $2 \text{ kPa}$, a roof live load ($L_r$) of $1 \text{ kPa}$, and a wind uplift load ($W$) of $-3 \text{ kPa}$ (negative indicates uplift). Calculate the critical net uplift design load.

A structural frame column supports an axial dead load ($D$) of $500 \text{ kN}$, a live load ($L$) of $300 \text{ kN}$, and an earthquake load effect ($E$) of $\pm 400 \text{ kN}$. Calculate the maximum compressive design load.

Consider a typical commercial floor plan with columns spaced $6 \text{ m}$ apart in the $x$-direction and $8 \text{ m}$ apart in the $y$-direction. The floor supports a total uniform load (dead + live) of $5 \text{ kPa} \text{ (kN/m}^2)$. Calculate the tributary area and the total axial load for a typical interior column.

Using the same commercial floor plan (columns spaced $6 \text{ m}$ in $x$-direction, $8 \text{ m}$ in $y$-direction, $5 \text{ kPa}$ uniform load). Calculate the tributary area and load for a typical edge column located along the perimeter parallel to the $y$-axis. The slab ends flush with the center of the edge column.

Using the same layout ($6 \text{ m}$ in $x$, $8 \text{ m}$ in $y$, $5 \text{ kPa}$ load), consider the interior beams spanning the $6 \text{ m}$ direction (they connect the columns along the x-axis). Calculate the tributary width and the resulting uniform line load ($\text{kN/m}$) acting on this beam.