ES-120 Trusses - Method of Joints
A truss is defined by these criteria:
  1. All members are straight.
  2. Members are connected at their extremities only (joints). No member is continuous through a joint.
  3. All joints are pinned (No moment).
  4. All members carry loads only in their direction (No transverse force).
  5. All loads are applied at joints.
A simple truss is shown to the left.
The method of joints is used to find forces in all members and to find all reactions.
A step by step procedure will be outlined for the structure shown.
1. FIND AS MANY REACTIONS AS POSSIBLE

The pinned connected at A has two reactions, Ax and Ay, and the roller at C has only a vertical reaction. Taking moments about A yields Fc, and SFx and SFx yield Ax and Ay respectively.

2. CHOOSE A JOINT
(preferably one with only two unknowns, since the moment equation is identically satisfied at each joint),
DRAW A FBD AND SOLVE FOR UNKNOWNS.

If we choose joint A, the following FBD results:

Note: The forces are along members. has been assumed to in compression. (A wrong assumption will cause a negative answer for a force.) and has been assumed to be in tension.

The forces may be solved for.

Lengths a and c are given in the original diagram.

Ax and Ay where found from the equations for the reactions, hence

Another joint is now selected and the procedure repeated.

Note: If AB was in tension as found at A it will also be in tension at point B.
The procedure is continued until all forces are found and generally, if more equations are available, should be checked to see if solutions "zero out".

The complete procedure is shown diagrammatically here...
REACTION/
MEMBER		 FORCE TENSION/
COMPRESSION
Ax  
Ay  
Cy  
AD  
AB  
DB  
BC  
DC  
 A tabular method for listing solutions as they are found is suggested for convenience of book-keeping.
Note: A considerable amount of time may be saved in the case of a geometrically symmetric truss, symmetrically loaded. Members and reactions on either side of the line of symmetry will have identical forces.
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