The take-home problems require a good understanding of
homework due on 10/24/22 and the problems solved in the
classes.
1. A stone beam is in structurally static equilibrium due to a
hanging stone pillar that is attached to the beam but does
not touch the ground, and the entire structure rests on a
pillar that is on an extensive- curved stone.
Beam mass $m_b$= 15000 Kg; Each of the pillars' mass
$m_p$=5000 Kg (same mass pillars); Pillar 1 is at a 2 m
distance from the center of gravity (c.o.g) point of the beam
as shown in the below figure.
Stone Beam
Hanging
pillar
Pillar
on the
ground
1.1. Draw accurate freebody diagrams separately for the
forces acting on the beam and pillars. (Points 30).
1.2. How far away is the hanging pillar attached from the
center of gravity (c.o.g) point of the beam? (Points 30).
1.3. Calculate all the forces acting on the beam and both
pillars. (Points 30).
2. A solid stone ball of mass 2000 kg of radius 0.75 meters is
placed one meter away to the right side of the c.o.g point on
the beam. (Beam mass and the mass of the pillar touching
the ground are the same as in problem 1. The hanging pillar
is placed at the distance you get from the previous
calculations; answer to 1.2. The hanging pillar mass is
unknown at this time.)
Hanging
pillar
Pillar
on the
ground
Stone Beam
2.1. Draw accurate freebody diagrams for the forces acting
on the beam, two pillars, and the ball. (Points 40).
2.2. What is the mass of the hanging pillar that keeps the
structure in the equilibrium state? (Points 40).
2.3. Calculate all the forces acting on the beam, pillars, and
ball. (Points 40).
