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The building slab is subjected to four parallel column loadings. Determine the equivalent resultant force and specify its location (x, y) on the slab. Take { F }_{ 1 } = 8 kN and { F }_{ 2 } = 9 kN.

Step-by-step

Equivalent Resultant Force. Sum the forces along z axis by referring to
Fig. a

+\uparrow  { ({ F }_{ R }) }_{ z }  =  \sum { F}_{ z } ;            –{ F }_{ R } = -8 – 6 – 12 – 9                    { F }_{ R } = 35 kN

Location of the Resultant Force. Sum the moments about the x and y axes by
referring to Fig. a,

{ ({ M }_{ R }) }_{ x } =    \sum { M}_{ x } ;                -35 y = -12(8) – 6(20) – 9(20)

y = 11.31 m = 11.3 m

{ ({ M }_{ R }) }_{ y } =    \sum { M}_{ y } ;                35 x = 12(6) + 8(22) + 6(26)

x = 11.54 m = 11.5 m

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