# Chapter 3 Trusses - موقع المهندس حماده شعبان 3 final2 (2).pdfb + r 2 j statically indeterminate degree of indeterminacy = b + r – 2 j ،ٹپي ٽڃ٫پ ٽ ٲأ سٷڒ ٠ ى ڍض)ڄڍ ڒوئ حڂڍض( حڋڇ٪ جڍ كذج

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• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

Chapter 3

Trusses

.

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

Trusses

(members) *

(joints) (forces) (joints)

(member) (tension) (compression).

(compression) (tension) *

(members) (joint method) (member)

(section method)

*

.

(joint) (tension) (member) *

(compression) (joint).

.

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

Analysis of Trusses

considering:

b = number of members.

r = number of reactions.

j = number of joints.

:tabilityS

:tructure will be unstable in the following casesS

1) b + r < 2 j

2) b + r 2 j (but all reactions are parallel)

3) b + r 2 j (but all reactions are concurrent)

: of stability) providedeterminacy (D

b + r = 2 j statically determinate

b + r > 2 j statically indeterminate

degree of indeterminacy = b + r 2 j

( )

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

members (zero) truss *

(. )

(only 2 members) (joint) *

(.A, D) ((zero member

(only 3 members) (joint) *

(. C, D) ((zero member ((member

zero members

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

.((members

.((support reactions 1

(. )

(only 2 members) (joint) 2

. 3

(joints) 3 ,2 4

2 - members)) .

.((members ( 4) 5

(tension) ((member 6

(compression) .

. 7

joint method

.

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

((members

. ( truss)

.((support reactions 1

( )

2

members) .)

( ) 3

4

.

((members - 2 5

.

((members 6

.

( section method) ( joint method) 7

. ((members

ethodmection s

, ,

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

a)

statically indeterminate to the 4th degree

b)

statically determinate.

c)

statically indeterminate to the first degree

d)

the left panel is a collapsible component

(6)

parallel are reactions all satisfied

d

be not can F

< r b

j

r

b

r b

j

r

b

r b

j

r

b

r b

j

r

b

x 0

11

6

2

9

9 2 19

9

4

15

8 2 16

8

3

13

10 2 24

10

4

20

unstable

3-2 classify each of the following trusses as statically determinate, statically indeterminate, or unstable.

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

a)

stable, statically determinate.

b)

stable, statically indeterminate to 1.

c)

stable, statically indeterminate to 1.

d)

(r + b) 2 j = 1

stable, statically indeterminate to 1.

6

10

3

12)(

6

9

4

12)(

6

9

4

2)(

8

13

3

j

b

r

jbr

j

b

r

jbr

j

b

r

jbr

j

b

r

3-3 classify each of the following trusses as statically determinate, statically

indeterminate, or unstable. If indeterminate, state its degree.

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

Gy

Gx FGF = 20 kN

FAG = 15 kN Ax

FAB = 10 kN

20 kN

18 kN

7.5kN

FEF

FBC = FCD

15 kN

FCD

FED = 8.33 kN

5 kN

FCD = 6.67 kN

5 kN

10 kN 6.67 kN

FBF

G

A C

F

B

D

FBE = 4.17 kN

FAf = 18 kN 15 kN FAF = 18 kN

;

members *

( C) ( T)

.

. ( , ) *

joint F:

3-8 Determine the force in each member of the roof truss. State if the members

are in tension or compression. Assume all members are pin connected.

56.3o

56.3o

http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

• July 2011

SMS

Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Stre