University of Babylon
College of Engineering
Department of Environmental Engineering
Engineering Analysis I (ENAN 103)
Truss (Method of Joints) II
Undergraduate Level, 1st Stage
Mr. Waleed Ali Tameemi
College of Engineering/ Babylon University
M.Sc. Civil Engineering/ the University of Kansas/ USA
2016-2017
Example 1
Determine the external reactions as well as the internal force of each member of
the following truss.
500N
D
4m
A
4m
B
4m
C
Solution
Draw free-body diagram for the truss.
∅ = tan
4
= 45°
4
500N
D
For the wholeRAtruss:
x A
4m
RAy
4m
B
2
4m
C
RCy
∑
=0
→ (+
.)
=0
∑
=0
at point A
. .
(+
.)
× 8 − 500 × 4 = 0
= 500 ×
∑
4
= 250
8
=0
+
↑ (+
↑
.)
− 500 = 0
+ 250 − 500 = 0
= 250
↑
3
500N
D
Joint A
A
4m
4m
4m
B
250 N
250 N
Joint A
FAB
250 N
∑
=0
−
=
∑
.)
× sin 45 = 0
250
= 353.5
sin 45
=0
−
↑ (+
→ (+
C
(
)
.)
× cos 45 = 0
= 353.5 × cos 45 = 250
(
)
4
Joint C
FCB
Joint C
250 N
∑
=0
−
=
∑
.)
× sin 45 = 0
250
= 353.5
sin 45
=0
−
↑ (+
→ (+
(
)
.)
× cos 45 = 0
= 353.5 × cos 45 = 250
(
)
5
Joint D
500 N
FDB
Joint D
∑
=0
× sin 45 +
↑ (+
.)
× sin 45 +
− 500 = 0
353.5 × sin 45 + 353.5 × sin 45 +
250 + 250 +
− 500 = 0
− 500 = 0
=0
∑
=0
× cos 45 −
→ (+
.)
× cos 45 = 0
250 − 250 = 0 (Equilibrium Check)
You may use Joint B for checking purposes!
6