THE METHOD OF JOINTS All joints are in equilibrium since the
truss is in equilibrium. The method of joints is applied using
equilibrium equations at each joint of the truss. 30 F B C A F BA F
BC F 60 B
Slide 3
To do this, the free-body diagram of the joints has to be dawn
keeping the geometry of the truss in mind. Always start with a
joint that has at least on known and at most two unknowns. Since
all forces passes the joint, then M B is automatically zero. Fx = 0
and Fy = 0 need to be solved to determine the unknowns. Assume the
direction of the force acting on the joint. If the results produced
positive scalar, then your assumption is correct, otherwise the
force is acting in the opposite direction if the results were
negative.
Slide 4
Procedure for Analysis Draw free-body diagram of the joint Stat
with the joint that has at least one known and at most two unknowns
External reactions at truss supports must be known Assume direction
of unknowns Apply equilibrium equations ( Fx = 0 and Fy = 0) Solve
for unknowns and verify their assumed directions Continue the
analysis for each joint. Always choose joints with at most two
unknowns and at least one known A force member found from one joint
can be used at the other end of the member for analysis of forces
acting on that member
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Zero-Force Members Zero-force members are used to: Increase
stability of the truss during construction Provide support if
applied loading is changed As a general rule: 1. Zero-force members
are formed when only two member form a truss joint and no external
load or support reaction is applied to that joint
Slide 15
A B C D E F F AF F AB Joint A x F DE F DC x y Joint D Fx = 0 ;
F AB = 0 Fy = 0 ; F AF = 0 Fy = 0 ; F DC sin = 0 F DC = 0 Fx = 0 ;
F DE = 0
Slide 16
2. If three members form a truss joint for which two of the
members are co-linear, the third member is a zero-force member
provided that no external force or support reaction is applied to
the joint. A C D E
Slide 17
x y F DA F DE F DC Fx = 0 ; F DA = 0 Fy = 0 ; F DC = F DE x y F
CA F CD F CB Fx = 0 ; F CA sin = 0 F CA = 0 Fy = 0 ; F CB = F CD
Joint C
