In simplest practical language, Allowable stress Design (ASD) is about reducing the strength capability of the structure. say reduce 40 percent. Still confused, say you can lift 20kg but we reduce 40%, you only allowed to carry 20kg x 0.6 = 12kg. Why we do this? because there are many factors out there that you cannot control and anticipate. For example, the standard of material, the human error in calculating loadings, error of contractor and many more.
How about LRFD? LRFD is all about is all about load combination. In stead of reducing the capacity of the structural you maintain it but you increase the loading for 30%, 50%.
So we can argue which one is good. They all have their strength and specific function in specific circumstances. Just rember this, ASD give conservative result if the ratio of Live Load to Dead Load is less than 1 to 3. On the other hand, LRFD method give conservative design is the Live Load to Dead Load is more than 1 to 3.
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