Operating conditions and basic assumptions

$$ The door is represented by a homogeneous plate of the

length l$,$ thickness h$,$ and width b$,$ which is made of material

with mass density $.$ When opened, it must be maintained

in its horizontal position OA by means of the cable ABCD,

which is attached to the heavy block of wight W connected

to the electric motor by the rope with tensile force F$.$ The

supporting beam OP is massless.

$$ The pulley with center P has the outer radius R and blocked

to rotate when the motor is turned off, and the entire

structure is in impending motion equilibrium condition.

$$ The static friction coefficient between the block W and the

floor is $,$ and between the cable and pulley is $.$

Goals of the project

$$ There is upper limit on the tensile force F$,$ which can be

developed by the motor when stopped. The material

density $$ of the door is fixed.

$$ Determine the minimal weight W of the block, which

guarantees the structural equilibrium assuming the

geometrical parameters fixed.

$$ Obtain bending moment, shear force, and compression

force profiles for the supporting beam OP and the door OA$.$

Introduce a separate Cartesian

frame for the supporting beam

as shown above.

Equations must be written in

general form for arbitrary

parameters.