Chap 4
Equilibrium of Rigid Bodies
� 𝐹𝐹𝑦𝑦 = 0
� 𝐹𝐹𝑥𝑥 = 0
� 𝑀𝑀0 = 0
Prof. Osama Ahmed Mohamed, Ph.D., P.E., M.ASCE
Review
• Components of force
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(𝜃𝜃)
𝜃𝜃
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(𝜃𝜃)
• Moment
F
d
R
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(𝜃𝜃)
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(𝜃𝜃)
𝜃𝜃
𝑀𝑀 = 𝐹𝐹𝐹𝐹
R
Definition:
2-force member is the one that is pinned at
both ends and there is no load on it between
the pinned ends.
I can write the three equations of
equilibrium which allow me to
calculate 3 unknowns
The number of unknown reactions is more
than three, therefore, the three equations of
equilibrium will not solve this problem.
One way to solve this
problem is to write the
tension forces in
cables AB and AD in
vector form
Write the two forces in vector
form so you can identify
which component produces
moment about point B.
⃗
𝑑𝑑
Recall: 𝐹𝐹⃗ = 𝐹𝐹
𝑑𝑑
Ropes, cables, wires,
and rods are under
tension.
Notice that a 2Force member
doesn’t need to
be straight.
𝜃𝜃 = 450
𝜃𝜃
𝜃𝜃
Consider a Free
Body Diagram
consisting of BC
only
𝜃𝜃 = 450
100 inches
𝜃𝜃 = 450
100
𝜃𝜃