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How do I use the system over strength factor Ω0. Is it used as a multiplier on the load side or the strength side of the equation?

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The system over strength factor Ω0 is used as a multiplier on the load side of the equation.
For example, in a braced-frame system, it is applied as a multiplier on the axial load in the brace. The resulting  amplified force is used to compare to each applicable limit state.
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