A rectangular slab 5 log 75 m supports three columns which e

A rectangular slab 5 log 7.5 m, supports three columns which exert on the slab the forces shown in the figure. Determine the equilent force and couple at o Determine in the magnitude and print of application of the single force equivalent to the given system

Solution

Equivalent force = ( 5 + 3 + 4) kN = 12 kN

a couple is a pair of forces of same magnitude but oppositely directed and displaced by a moment

sice all forces are in same direction in the question so there can be moment at o but not couple

Now we try to find the torque using vectors

torque T = r x F

T= r1x (-5 k) + r2 x (-3k) + r3 x (-4k)

= ( 5 i ) x ( - 5 k) + ( 5 j) x ( - 3k) + (5 i + 7.5 j) x -4k

= (25 j - 15 i + 20 j - 30 i)

=-45 i + 45 j kNm