Post on 18-Nov-2014
description
DEN102Stress Analysis
Truss Structures
Dr P.H. Wen
E118p.h.wen@qmul.ac.uk
Page 2
1.0. Truss Element
F
F
T
F
Imaginary cut
Internal force T
T – F = 0
Page 3
1.1. Simple plane trusses
• Two dimensional structures
Page 4
• Two dimensional structures (more examples)
Page 5
• Three dimensional structure
x
y
z
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1.2. Support and reactive forces
Simply support(1) XOY coordinate system
(2) Pin support
(3) Roller support
Pin support Roller support
o
y
xRxa
Rya Ryc
d
a
b
c
e
F
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1.3. Classification of truss structures
(a) Unstable structure (mechanism): if m+r<2j(b) Redundant structure: if m+r>2j(c) Statically determinate structures: if m+r=2j
m: number of truss; r: number of reactive force; j: number of joint
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1.4. Determine Reactive Forces
(2) 0=++∑ ycyaiy RRF
(1) 0=+∑ xai
x RF
Rxab
d
a c
e
y
x
F
(3) 0)( =×+∑ acyci
A lRFM
(1.4.1) Reactive Forces (1.4.3) Evaluation of Reactive forces
(1.4.2) Direction of reactive forces - Force along x-axis
- Force along y-axis
- Moment along anticlockwise about point A
Rya Ryc
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Example 1. Classify following truss structures and determine the reactive forces for these statically determinate structures
300 300
1m 1m
100kNb
ca
d
(1)
300 300
1m 1m
100kN
b
ca
d450
(2)
450 450
2m 2m
200kNa b
ced
(3) (4)
450 450
2m 2m
200kN
a b
ce
d
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450 450
2m 2m
200kNa b
ced
(5) (6)
450 450
2m 2m
200kN
a b
ce
d
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1.5. Characteristics of Truss System • Simplest framework that can be formed
from a minimum number of trusses is a triangle;
• Internal force is axial force, zero body force, zero bending moment;
• External forces are applied at joints;• Internal force
Positive: tensileNegative: compressive
B
T1 T3
T2
develop
1
2
3
4
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1.6. Method of Joint• Number of unknown forces at node ≤ 2
Example 2. Find the axial forces in each truss.
100kN
450
300
A
B
C
1
2
T1
T2 100kN
B x
y
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300 300
a a
100kN
A
B
CED
Example 3. Find axial forces in each truss.
1
524
3 6
-100√32000-100√30200
654321
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1.7. Method of section
Example 4. Find the axial forces in trusses AB, BE and DE.
300 300
a a
100kN
A
B
CED
100kN
B
CD
T1
T2
T3
E
CUT
1
6
54
3
2
• Number of unknown forces in section ≤ 3
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1.8. Final Remarks
• If number of unknown forces at node > 2, reaction forces should be determined firstly.
Example 5. Find the axial forces for all each trusses.
300 300
5m 5m
A
B
C
100kN
D
1
54
32
50500-100/√3100/√3
54321
Rxa= -100, Rya= -50/√3, Ryc=50/√3
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Example 6. Find the axial forces in each truss.
c
6m 6m
a
d
e
100kN
b
4m
15kN
1
4
3
2
5 67
60-10010010525-105-150
7654321
Rxa= -15, Rya=120, Rye=80
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Home work 1. Find the axial forces in each truss.
450 450
2m 2m
10kN
a b
c
ed
(a)
6
5
4
3
2
1a c d e b
f g h j k
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
20kN 60kN
20kN
3m 3m 3m 3m4m
10√2-10-101010√2-20
654321
-60-45750045045-20-452530-20-30500-40
1716151413121110987654321
(b)
Rxa=0, Rya=40, Ryb=60