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DEN102Stress Analysis

Truss Structures

Dr P.H. Wen

E118

p.h.wen@qmul.ac.uk

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1.0. Truss Element

F

F

T

F

Imaginary cut

Internal force T

T F = 0

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1.1. Simple plane trusses

Two dimensional structures

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Three dimensional structure

x

y

z

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1.3. Classification of truss structures

(a) Unstable structure (mechanism): if m+r2j(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=++ yc yai y R RF (1) 0=+ xa

i x RF

Rxab

d

a c

e

y

x

F

(3) 0)(=+

ac yci

A l RF M

(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

30 0 30 0

1m 1m

100kNb

ca

d

(1)

30 0 30 0

1m 1m

100kN

b

ca

d45 0

(2)

45 0 45 0

2m 2m

200kNa

b

ce d

(3) (4)

45 0 45 0

2m 2m

200kN

ab

c

ed

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450

450

2m 2m

200kNa b

ce

d

(5) (6)

450

450

2m 2m

200kN

a b

c

ed

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1.5. Characteristics of Truss System

Simplest framework that can be formedfrom a minimum number of trusses is atriangle;

Internal force is axial force, zero bodyforce, zero bending moment;

External forces are applied at joints; Internal force

Positive: tensile

Negative: compressive

B

T1 T3

T2

develop

1

2

34

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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

45 0

30 0

A

B

C

1

2

T1

T2 100kN

B x

y

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30 0 30 0

a a

100kN

A

B

CE

D

Example 3. Find axial forces in each truss.

1

524

3 6

-100 32000-100 30200

654321

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1.8. Final Remarks

If number of unknown forces at node > 2, reaction forces shouldbe determined firstly.

Example 5. Find the axial forces for all each trusses.

30 0 30 0

5m 5m

A

B

C

100kN

D

1

54

32

50500-100/

3100/

3

54321

Rxa = -100, R ya= -50/ 3, R yc=50/ 3

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Home work 1. Find the axial forces in each truss.

45 0 45 0

2m 2m

10kN

ab

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 3m

4 m

10 2-10-101010 2-20654321

-60-45750045045-20-452530-20-30500-40

1716151413121110987654321

(b)

R xa =0, R ya =40, R yb=60