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Wize University Statics Textbook (Master) > Structural Analysis - Trusses, Frames, Machines

Method of Joints

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APPROACH #1 : Method of Joints (MOJ) - NEED TO KNOW F's in ALL THE MEMBERS

The method of joints analyzes the one joint (connection point) at a time. This method is useful when wanting to solve for the forces in ALL THE MEMBERS OR the forces in members near the edge OR for trusses with few total members. If asked about forces in members near the middle of the truss, then this method could take a really long time.
General steps:
  1. Solve the external reaction forces / find SUPPORT REACTIONS.
  2. Identify all zero force members, remove and REDRAW.
  3. Begin at a joint with a maximum of 2 UNKNOWN forces & at least 1 KNOWN force. Assume all unknown members are in tension.
  4. Sum F's (x & y) to solve for unknown forces in members.
  5. TENSION vs COMPRESSION: Positive values typically mean tension, negative means compression – clearly state your convention. Or..... thinks of TENSION as PULLING (on or away) from the joint, and COMPRESSION as PUSHING (on or into) the joint.
  6. As you know the forces in more members, move across to other joints and continue solving. Remember that you can only solve for 2 unknowns at a time
Determine the force in each member. Indicate whether the member is in tension or compression.
FAC=0F_{AC}=0 (so redraw truss WITHOUT AC)
ΣMB=0=(300)(4)−3FA=0\Sigma M_B=0=(300)(4)-3F_A=0
FA=400lb ←F_A=400lb \ \leftarrow
ΣFy=By−300=0\Sigma{F}_y=B_y-300=0 By=300lb↑B_y=300lb \uparrow
ΣFx=−400+Bx=0\Sigma{F}_x=-400+B_x=0 Bx=400lb→B_x=400lb \rightarrow


ΣFy=35FDC−300=0→FDC=500lb=FBC\Sigma F_y=\frac{3}{5}F_{DC}-300=0\to F_{DC}=500lb=F_{BC}
ΣFx=45FDC+FAD=0→FAD=−400lb\Sigma F_x=\frac{4}{5}F_{DC}+F_{AD}=0\to F_{AD}=-400lb
ΣFy=FAB=0\Sigma {F}_y=F_{AB}=0
FAC=FAB=0F_{AC}=F_{AB}=0
FDC=FBC=500lb(T)F_{DC}=F_{BC}=500lb(T)
FAD=400lb(c)F_{AD}=400lb(c)
Determine the forces in all members of the truss. State whether each member is in tension or compression.




checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Determine the tension in members: AB, AH, BH, HC, BC and HG. Indicate whether the member is in tension or compression.

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Determine the forces in each member of the following truss.