6.3.1. LRFD

Load factors are applied to the service loads, and a member is selected that will have enough strength to resist the factored loads.

In LRFD (Load and Resistance Factor Design), engineers apply load factors to service loads, scaling them up to account for uncertainties. This ensures that the selected structural member can safely support these higher loads. Essentially, instead of using the regular loads that structures will experience, we multiply these service loads by certain factors to ensure the structure's safety under worst-case scenarios.

Think of this like planning a picnic. If you know that on a sunny day only a few people will join, you might pack just enough food. But to be safe, you consider that it might rain and more people might show up. So, you pack extra food, accounting for the unforeseen circumstances—just like how engineers pack in a safety factor for loads.

In addition, the theoretical strength of the member is reduced by the application of a resistance factor.

In LRFD, we also modify the strength of the member itself by introducing a resistance factor. This factor reduces the theoretical strength to account for material defects, design imperfections, or construction variability. The key formula here states that the sum of all factored loads (which are made larger by load factors) must not exceed the factored strength of the structural element (which is lower due to resistance factors).

Imagine you have a jar that can hold 10 pounds of cookies. However, some cookies are crumbled, and the jar might not function perfectly all the time, so instead of planning for 10 pounds, you consider the jar's limitations and plan for 8 pounds of cookies instead. This is akin to applying a resistance factor—adjusting your expectations based on practical realities.

The factored loads are the loads that bring the structure or member to its limit. In terms of safety, this limit state can be fracture, yielding, or buckling, and the factored resistance is the useful strength of the member, reduced from the theoretical value by the resistance factor.

Limit states refer to conditions beyond which a structure or member fails to perform its intended function, such as breaking, bending beyond recovery, or buckling. To ensure safety, engineers must design structures with factored loads that represent these extreme conditions, while ensuring that the materials used have adequate strength—factored resistance—to handle such loads.

Consider a bridge designed to hold a certain number of cars. If you assume that each car weighs less than that number but load on the bridge increases due to more cars than expected, you reach a 'limit state.' The bridge must be built to handle this scenario to avoid failure, similar to how safety margins are required in engineering.

The criterion that must be satisfied in the selection of a member is Factored LoadFactored Strength.

This key principle of LRFD emphasizes that, during design, the summed factored loads applied to a member must be less than or equal to the member’s factored strength. This ensures that the structure can safely carry expected loads under all reasonable conditions.

It is like budgeting for an event—you must ensure your expenses (factored loads) do not exceed your total budget (factored strength). If you overspend, you risk running out of money, just as a structure could risk failure if loads exceed its capacity.

--