Math for Truss Calculation

1
Forging new generations of engineers
2
Math for Truss Calculation
3
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
4
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

5
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.
  

6
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.

7
Trusses
Before we can solve for the forces, we must break
FBC into its x and y components
FBCX FBC cos (45) FBCY FBC sin (45)
8
Trusses

??FX 0 500N FBCcos(45) 0 FBCcos(45)
500N cos(45) cos(45) FBC 707.1 N
(C) ??FY 0 FBCsin(45) FAB
0 707.1sin(45) FAB 0 FAB
707.1sin(45) FAB 500 N (T)
The following is the free-body diagram of joint
B. The force FBC has been replaced with its x
and y components
9
Trusses

??FX 0 500N FBCcos(45) 0 FBCcos(45)
500N cos(45) cos(45) FBC 707.1 N
(C) ??FY 0 FBCsin(45) FAB
0 707.1sin(45) FAB 0 FAB
707.1sin(45) FAB 500 N (T)
The (T) indicates tension and the (C) indicates
compression. Both solutions were positive
therefore our initially assumptions were correct.
(If the solution had been a negative number,
then we would simply reverse our assumption from
tension to compression or vice versa)
10
Trusses

??FX 0 FAC FBC cos (45) 0 FAC 707.1
cos (45) 0 FAC 707.1 cos(45) FAC 500 N
(T) ??FY 0 CY FBC sin(45) 0 CY
707.1 sin(45) 0 CY 500 N
The following is the free-body diagram of joint
C. The force FBC has been replaced with its x
and y components
11
Trusses

??FX 0 FAC - Ax 0 500 N - Ax 0 AX
500 N ??FY 0 FAB - AY 0 500 N - AY 0
AY 500 N
The following is the free-body diagram of joint A
12
Trusses
Solved!!!