Question (1): The shown two-dimensional rigid plate (40m40m) is subjected to eig

Question

Question (1): The shown two-dimensional rigid plate (40m40m) is subjected to eight external translational forces. The coordinate of the point of application of each force is given as follows: A(r,y) = A(5m, 35m); B(5m, 5m); C(35m, 5m); D(35m, 35m); E(15m, 30m); F(10m, 15m); G(25m, 10m); H(30m, 25m) (a) Determine the magnitude, direction and point of application of an external translational force that if it is applied to the system, then the system will be in equilibrium conditions (Hint: you may use equilibrium equations to solve this part of the question) .1 (a) 40 KN 5 KN 40m 5 KN 4-0m

Explanation / Answer

The resultant of force E,F,G,H is 0 since E cancels out G and G cancels out F.

Also, the resultant of the forces A,B,C,D in the vertical direction is 0 since A+D cancels out B+C

so there is a net force in the +x direction.

the magnitude of the net force = Ax+Bx+Cx+Dx (where subscript x denotes the x component of the force)

=(-10-20+30+40)*cos(45)

=40cos(45)

=28.28 kN

hence we need to apply a force of 28.28N in the negative x-direction)

Assuming that the sheet rotates about ists center,

total torque acting on it = torque due to E,F,G and H (since A,B,D,C pass thorugh the center)

so, Torque = 15*(30-20)+ 5*(20-10) + 15*(25-20) + 5*(25-20)

=300 k kNm

so let the force be applied at pos xi + yj

so,

300 = -28.28*(y-20)

or y=9.391 m

so it is applied at y=9.319 m in the negative x direction with a force of 28.28 N

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