Procedure for Analysis CE 213

The following procedure provides a method for determining the joint
reactions for structures composed of pin-connected members.
Free-Body Diagrams
• Disassemble the structure and draw a free-body diagram of each
member. Also, it may be convenient to supplement a member
free-body diagram with a free-body diagram of the entire structure.
Some or all of the support reactions can then be determined using
this diagram.
• Recall that reactive forces common to two members act with
equal magnitudes but opposite directions on the respective freebody
diagrams of the members.
• All two-force members should be identified. These members,
regardless of their shape, have no external loads on them, and
therefore their free-body diagrams are represented with equal
but opposite collinear forces acting on their ends.
• In many cases it is possible to tell by inspection the proper
arrowhead sense of direction of an unknown force or couple
moment; however, if this seems difficult, the directional sense canbe assumed.


Equations of Equilibrium
• Count the total number of unknowns to make sure that an
equivalent number of equilibrium equations can be written for
solution. Except for two-force members, recall that in general
three equilibrium equations can be written for each member.
• Many times, the solution for the unknowns will be straightforward
if the moment equation is applied about a point (O)
that lies at the intersection of the lines of action of as many
unknown forces as possible.
• When applying the force equations and
orient the x and y axes along lines that will provide the simplest
reduction of the forces into their x and y components.
• If the solution of the equilibrium equations yields a negative
magnitude for an unknown force or couple moment, it indicates
that its arrowhead sense of direction is opposite to that which was
assumed on the free-body diagram.
©Fx = 0 ©Fy = 0,
©MO = 0