Example A heavy rectangular trapdoor ABCD with sides of length AB CI -2 m and BC

Question

Example A heavy rectangular trapdoor ABCD with sides of length AB CI -2 m and BC-DA-4 m weighs 1.5 kN and is hinged at A and at B to a vertical wall. The trapdoor is held in a horizontal position by a rope joining the corner D (diagonally opposite to B) to a point E on the wall 4 m directly above B If the hinge at B does not support an axial load, while the hinge atA does, find the reactions at the hinges and the tension in the rope for a static system MA2101 - 2017/2018 Systems of Forces 6 Solution Let B be the origin and use edges as axes as in diagram. The points A, B, C, D, E and the centre of mass G have coordinates A: (2,0,0), B: (0.0.0), C:(0.4.0). D (2,4,0), E: (0,0,4), G (1,2,0) The position of E relative to D is of magnitude V4+16+ 16-6. Hence the unit vector in the direction of ED is

Explanation / Answer

This is a statics problem on forces in space.

The formulae highlighted in blue come from the "Conditions of Equilibrium" or C.o.E which states that i) the sum of all external forces is zero and ii) sum of all moments is zero

So as the sum of all forces is zero, we get

A + B + W + T = 0;

If we break it down , we get

Sum of forces in x-direction is zero, i.e., ?Fx = 0 which gives us,

A1 – (1/3)T = 0 {sum of the x components of all the forces}

Sum of forces in y-direction is zero, i.e., ?Fy = 0 which gives us,

A2 + B2 – (2/3)T = 0    {sum of the y components of all the forces}

Sum of forces in z-direction is zero, i.e., ?Fz = 0 which gives us,

A3 + B3 + (2/3)T – 3/2 = 0    {sum of the z components of all the forces}

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