K-12 Engineering Education Standards: - International Technology ...

ΣFy = 0
-F MT
sin θ –F NT
– F OT
sin θ = 0
-(-18.77)(.916) – 0 –F OT
(.916) = 0
-17.19/-.916 = F OT
18.77 N = F OT
(T)
ΣF X
= 0
-F MT
cos θ + F OT
cos θ + F TU
= 0
-(-18.77)(.41) + 18.77(.41) + F TU
= 0
-7.67 -7.67 = F TU
-15.35 N = F TU
(C)
Step 8.
Draw a free body diagram (Figure 8) around Joint O.
Figure 8.
ΣF y
= 0
-F NO
– F OT
cos θ + F OP
= 0
-(7.68) – 18.77(.41) + F OP
= 0
F OP
= -7.68 -7.68
F OP
= -15.35 N (T)
ΣFX = 0
F OT
sin θ + F OU
= 0
18.77(.916) + F OU
= 0
F OU
= -17.2 N (C)
Step 9.
Draw a free body diagram (Figure 9) around Joint U.
Figure 9. Joint U.
ΣF y
= 0
-11.45 –F OU
– F PU
sin θ = 0
-11.45 – (-17.2) – F PU
(.916) = 0
F PU
= -5.75/-.916 = 6.28 (T)
ΣF X
= 0
-F TU
+ F PU
cos θ + F UV
= 0
-(-15.34) + 6.28(.41) + F UV
= 0
F UV
= -17.9 N (C)
Since the bridge is symmetrical, the other side of the bridge
has the same forces acting upon its members. Below is a
table that reflects which members are equal on both sides of
the bridge. If the bridge is not symmetrical, the remaining
joints on the other side of the bridge will need free body
diagrams and equations of equilibrium to determine the
remaining members.
MT, SX = 18.77 N (C)
NO, QR = 7.68 N (T)
UV, VW = 17.9 N (C)
MN, RS = 7.68 N (T)
TU, WX = 15.35 N (C)
PV = 11.45 N (C )
NT, RX = 0
OU, WQ = 17.2 N (C)
OP, PQ = 15.35 (T)
OT, QX = 18.77 N (T)
PU, PW = 6.28 N (T)
Figure 10. Bridge with Compression and Tension
Summary
Bridges can be a very good tool for reinforcing
mathematical concepts with engineering and technology
students. The equations above are a template for any
teacher to use with his or her students when teaching
students about bridge building. This template can lead to
in-depth discussions about compression and tension and
give students an understanding of how bridges actually
work. Building and crushing bridges is fun for students,
but this activity can also be a means for them to implement
math and science skills through predictive analysis.
33 • Technology and Engineering Teacher • February 2011