Lecture on Truss Structure

DEN102Stress Analysis

Truss Structures

Dr P.H. Wen

[email protected]

1.0. Truss Element

F

F

T

F

Imaginary cut

Internal force T

T – F = 0

1.1. Simple plane trusses

• Two dimensional structures

• Two dimensional structures (more examples)

• Three dimensional structure

x

y

z

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

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

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

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

450 450

2m 2m

200kNa b

ced

(5) (6)

450 450

2m 2m

200kN

a b

ce

d

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

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

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

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

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

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

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

Lecture on Truss Structure

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