Mechanics & Materials I
FAMU-FSU College of Engineering
Department of Mechanical Engineering
Chapter 5
Chapter 5
Structural Analysis
Structural Analysis
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Structural Analysis: Trusses, Method of Joints, Method of Sections, Frames and Machines, Exercises of Structural Analysis
– The member are joined together by smooth pins. • concurrent joining members. – Two force members. Page 5. Trusses.
Typology: Exercises
2022/2023
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Mechanics & Materials I
FAMU-FSU College of Engineering
Department of Mechanical Engineering
Chapter 5^ Chapter 5
Structural Analysis^ Structural Analysis
Trusses
- Slender members– Joined at end points
TrussesTrusses
- Assumptions for design
- All loadings are applied at the joints.
- neglect weights of the members
- The member are joined together by smooth
- neglect weights of the members
- All loadings are applied at the joints.
pins.
concurrent
joining members
- Two force members
TrussesTrusses
- Example -
: Free-body diagram
A
B
C
F
A
B
C
F
A
y
A
x
B
y
F
BC
F
BC
F
AB
F
AB
F
AC
F
AC
F
AC
F
BC
F
C
A^ A
y
A
x
F
AC
F
AB
B B
y
F
BC
F
AB
Method of JointsMethod of Joints
- Draw the free-body diagram of the truss.– Find the external reactions (if necessary).– (Try to) Start with a joint having at least one
known force and at most two unknown forces(why 2?).
- Draw the joints free-body diagram and find the
unknown forces.
- Continue to analyze each of the other joints.
ExampleExample
1: Method of Joints1: Method of Joints
Problem:
Use the method ofjoints to find the forcein each member of thetruss at the shownfigure.
Solution Cont.,..Solution Cont.,..
FBD of pin D
0
1000
=
−
=
↑
=
→
AD
CD
T
F
T
F
Solution cont.Solution cont.
FBD of pin C
lb
2500
cos )
(^1118) (
2000
T
lb
1118
cos
T
lb
1000
T
that
knowing
8
4
4
cos
8
4
8
sin
0
sin
2000
0
cos
AC BC
cd
2
2
2
2
−
−
−
==
=
−
−
=
=
=
=
= − − − = ↑ +
= − − = → +
∑
∑
θ
θ
θ θ
θ
θ
CD
AC
AC CB
CD
ADACCDAC^ T
where
T
T
F
T
T
F
SelfSelf
Practice !!Practice !!
Problem:
The truss shown in the figuresupports one side of a bridge,; anidentical truss supports the otherside. Floor beams carry vehicleloads to the truss joints. A 2000 kgcar is stopped on the bridge.Calculate the forces in eachmember of the truss using themethod of joints.
Answers:
n)
Compressio (
N
Tension) (
N
Tension) (
N
n)
Compressio (
N
BD
CD
BC
CE
AC
DE
AB T
T
T
T
T
T
T
ZeroZero
Force MembersForce Members
- The
zero
force
members
are
used
to
increase the
stability
of the truss during
construction and to provide support if theapplied loading is changed.
- There are two geometries that lead to zero
force
members
learn
to
look
for
and
identify them readily!
Example: Two MembersExample: Two Members
Member
BC
and
CD
are two
non-collinear members, theyshare joint
C.
There are no external forces orreactions applied to joint
C
Hence, members
BC
and
CD
are zero force members.
Proof:
and 0
sin
cos
∑
∑
BC
CD
o
CD
o
CD
BC
T
T
T
F
T
T
F
After Eliminating theZero Force Members After Eliminating theZero Force Members
Initial Truss Initial Truss
Example: 3 MembersExample: 3 Members
Joint B holds three members , and thereis no external loads or reactions at thejoint.
Members
AB
and
BC
are collinear,
while member
BD
makes an angle with
the two collinear members.Hence,member
BD
is zero force
member.
Proof:
Question
is
AD
a zero force member?
∑
∑
=
−
↑
= + − = → +
0
0
BD
y
BC
AB
x
T
F
T
T
F
Practice !!Practice !!