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Math for Truss Calculation

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Math for Truss Calculation
                            Trusses
Trusses are structures made up of beams joined together at
their endpoints.
Solve for the force in each member of the truss in this example
to find whether the members are in tension or compression.
Start be replacing the supports with reaction forces:

         B           500                                500
                     N                                  N
   2m
                45°
         A                 C                 A
                                             X
                2m                                 A          CY
                            Trusses
This truss consists of:
     •2 unknown member forces and 1 unknown external force at joint B
     •2 unknown member forces and 2 unknown reaction forces at joint A
     •2 unknown member forces and 1 unknown reaction force at joint C

Draw the free-body diagrams for each pin:
                 500                                   500 N
                 N



 A                                     A
 X                                     X
        AY             CY                    AY             CY
                          Trusses
These three separate free-body diagrams assume that:
     •Member AB is in tension
     •Member BC is in compression
     •Member AC is in tension
If these assumptions are incorrect, then our solution will show
a negative quantity for force.
                                                  500 N
              500 N
                                         FAB FBC

                                          FAB        FBC

AX                                   AX         FAC FAC
                                           AY             CY
       AY           CY
                           Trusses
To really “see” that
•Member AB is in tension
•Member BC is in
compression
•Member AC is in tension
We must look at the
free-body diagrams of
the beams, which show
the effects of the pins
on the beams.
                       Trusses
Before we can solve for the forces, we must break FBC into its
x and y components:




               FBC
   FBCY                     FBCX = FBC * cos (45)
             45°            FBCY = FBC * sin (45)
            FBCX
                          Trusses
                                 ®S FX = 0 ;
                                 +
The following is the free-body         500N – FBCcos(45) = 0
diagram of joint B. The force
                                       FBCcos(45) = 500N
FBC has been replaced with
its x and y components:                  cos(45)   cos(45)
                                       FBC = 707.1 N (C)

            FBC sin(45)           S
                                 +­ FY = 0 ;
                                       FBCsin(45) – FAB = 0
FBC cos(45)            500 N           707.1*sin(45) – FAB = 0
                                       FAB = 707.1*sin(45)
               FAB
                                       FAB = 500 N (T)
                       Trusses
                              ®S FX = 0 ;
                              +
The (T) indicates tension
                                    500N – FBCcos(45) = 0
and the (C) indicates
compression. Both                   FBCcos(45) = 500N
solutions were positive               cos(45)   cos(45)
therefore our initially
                                    FBC = 707.1 N (C)
assumptions were correct.
(If the solution had been a    S
                              +­ FY = 0 ;
negative number, then we
would simply reverse our            FBCsin(45) – FAB = 0
assumption from tension to          707.1*sin(45) – FAB = 0
compression or vice versa)          FAB = 707.1*sin(45)
                                    FAB = 500 N (T)
                        Trusses
                             + SFX = 0 ;
                             ®
The following is the free-         – FAC+ FBC cos (45) = 0
body diagram of joint C.           – FAC+ 707.1 cos (45) = 0
The force FBC has been
replaced with its x and y          FAC = 707.1 cos(45)
components:                        FAC = 500 N (T)

        FBC
                              S
                             +­ FY = 0 ;
      45°                          CY – FBC *sin(45) = 0
      FAC                          CY – 707.1 *sin(45) = 0
                                   CY = 500 N
              CY
                        Trusses
                            + SF = 0 ;
                            ® X
The following is the free         FAC - Ax = 0
-body diagram of joint
                                  500 N - Ax = 0
A:
                                  AX = 500 N

         FAB                 S
                            +­ FY = 0 ;
                                  FAB - AY = 0
  AX           FAC                500 N - AY = 0
                                  AY = 500 N
          AY
                           Trusses
 Solved!!!



      B            500 N                                      500 N




                                        500 N (T)

                                                     70
                                                       7.
2m




                                                        1
                                                          N
                                                            (C
                                                              )
             45°
      A                    C   500 N                500 N (T)


             2m                        500 N                      500 N

				
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posted:7/14/2013
language:English
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