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If { F }_{ A } = 7 kN and { F }_{ B } = 5 kN , represent the force system acting on the corbels by a resultant force, and specify its location on the x–y plane.

Step-by-step

Equivalent Resultant Force: By equating the sum of the forces in Fig. a along the z
axis to the resultant force { F }_{ R }, Fig. b,

+\uparrow   { F }_{ R }\sum { F}_{ z } ; -{ F }_{ R } = -6- 5- 7- 8

{ F }_{ R }  = 26 kN

Point of Application: By equating the moment of the forces shown in Fig. a and { F }_{ R } ,
Fig. b, about the x and y axes,

{ ({ M }_{ R }) }_{ x } =  \sum { M}_{ x } ;          -26(y) = 6(650) + 5(750) – 7(600) – 8(700)

y = 82.7 mm

{ ({ M }_{ R }) }_{ y }  =  \sum { M}_{ y } ;          26(x) = 6(100) + 7(150) – 5(150) – 8(100)

x = 3.85 mm

 

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