| THEORY & FORMULAE |
A rigid body subjected to forces acting in a vertical plane will be equilibrium when the following two conditions are satisfied: i) vector summation of all forces must be zero, and ii) sum of all torques acting on the body must be zero. The weight of the body is assumed to act through its center of gravity.
Consider a uniform beam hinged at one end and carrying an object. A tie-rope is connected to the beam to keep it horizontal as shown. The equilibrium forces at work in the system can be described by the equations:
where
L1 = length of beam
L2 = horizontal distance to point of hanging object from wall
L3 = horizontal distance to rope-beam connection point from wall
L4 = vertical distance to rope-wall connection point from beam
Fo = weight of hanging object
Fb = weight of beam
Ft = tensile force acting in tie-rope
Frh = horizontal component of reactive force at hinge
Frv = vertical component of reactive force at hinge
Fr = reactive force at hinge
θ = angle of inclination of tie-rope to the horizontal, < 90°
φ = inclination angle of resultant force at hinge, >= -90°, <= 90°
◊ Use link
EXAMPLE Of Input/Output
to demo data entry expectations and results; you may edit & use it as starting point