## Question:

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