Transcript
Page 1: Truss – Assumptions

Truss Truss –– Assumptions Assumptions There are four main assumptions made in the analysis of truss

Truss members are connected together at their ends only.

Truss are connected together by frictionless pins.

The truss structure is loaded only at the joints.

The weights of the members may be neglected.

1

2

3

4

Page 2: Truss – Assumptions

Simple TrussSimple Truss

The basic building block of a truss is a triangle. Large truss are constructed by attaching several triangles together A new triangle can be added truss by adding two members and a joint. A truss constructed in this fashion is known as a simple truss.

Page 3: Truss – Assumptions

Method of Joints Method of Joints --TrussTrussThe truss is made up of single bars, which are either in compression, tension or no-load. Themeans of solving force inside of the truss use equilibrium equations at a joint. This method is known as the method of joints.

Page 4: Truss – Assumptions

Method of Joints Method of Joints --TrussTrussThe method of joints uses the summation of forces at a joint to solve the force in themembers. It does not use the moment equilibrium equation to solve the problem. In a two dimensional set of equations,

In three dimensions,

x y0 0 F F= =∑ ∑

z 0 F =∑

Page 5: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Determine the loads in each of the members by using the method of joints.

Page 6: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Draw the free-body diagram. The summation of forces and moment about B result in

( ) ( ) ( )

x Ax B

y Ay Ay

A B

B

Ax

0

0 10 kips 10 kips 20 kips

0 5 ft 10 kips 10 ft 10 kips 20 ft60 kips

60 kips

F R R

F R R

M RRR

= = +

= = − − ⇒ =

= = − −

⇒ =⇒ = −

∑∑∑

Page 7: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Look at Joint B

x BC B BC BC

y BA BA

0 60 kips 60 kips

0 0 kips

F T R T T

F T T

= = + = + ⇒ = −

= = ⇒ =∑∑

Page 8: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Look at Joint D and find the angle

1 o

x DC DA

y DA DA

DC

5 ft.tan 14.0420 ft.

0 cos

0 sin 10 kips 41.231 kips

40 kips

F T T

F T T

T

α

α

α

− = =

= = − −

= = − ⇒ =

= −

∑∑

Page 9: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Look at Joint C and find the angle

( ) ( ) ( ) ( )

1 o

y CA CA

x CD CA CB

o

5 ft.tan 26.56510 ft.

0 sin 10 kips 22.361 kips

0 cos

40 kips 22.361 kips cos 26.565 60 kips

0

F T T

F T T T

β

β

β

− = =

= = − ⇒ =

= = − −

= − − − −

=

Page 10: Truss – Assumptions

Example ProblemExample Problem

Determine the forces in members FH, DH,EG and BE in the truss using the method of sections.

Page 11: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Draw the free-body diagram. The summation of forces and moment about H result in

( ) ( ) ( ) ( ) ( )

x Hx

Hx

y Hy I

H I

I

Hy

0 3 kips 3 kips 3 kips 3 kips12 kips

0

0 15 ft 3 kips 10 ft 3 kips 20 ft 3 kips 30 ft 3 kips 40 ft20 kips

20 kips

F RR

F R R

M RRR

= = + + + +

⇒ = −

= = +

= = − − − −

⇒ =⇒ = −

∑∑

Page 12: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Do a cut between BD and CE

Page 13: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Take moment about A

( )( ) ( )

1 0

0A CE

CE

10 fttan 53.137.5 ft

0 cos 53.13 20 ft 3 kips 10 ft

2.5 kips

M T

T

α − = =

= = +

⇒ = −∑

Page 14: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Do a cut between HD and GE

Page 15: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Take the moment about I

Take the moment about D

( ) ( ) ( )I HD

HD

0 20 kips 15 ft 15 ft 3 kips 10 ft18 kips

M TT

= = − −

⇒ =∑

( ) ( ) ( ) ( )D GE

GE

0 12 kips 20 ft 20 kips 15 ft 3 kips 10 ft 15 ft6 kips

M TT

= = − + + +

⇒ = −∑

Page 16: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Do a cut between HD and HI

Page 17: Truss – Assumptions

Truss Truss –– Example ProblemExample Problem

Take the sum of forces in y direction

( )

( )

1 0

0y HF HD

HF 0

10 fttan 53.137.5 ft

0 sin 53.13 20 kips

20 kips 18 kips 2.5 kipssin 53.13

F T T

T

α − = =

= = + −

−⇒ = =


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