This video shows how to the resultant force on a structure. This equation is then minimised using two techniques - differentiation and software (Wolfram Alpha).
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Recap of Resultant Vectors in 2D
(2-32) Resultant Force Example #1
(2-46) Resultant Force Example #2
(2-53) Resultant Force Example #3
Recap of Moments
(3-15) Moment Example #1
(3-11&12) Moment Example #2
Recap of Couples and Equivalent Systems
Resultant of Couples Example
Equivalent System Example
Recap of FBD, Supports, Equilibrium Equations
Why FBD?