Simple Truss-Basic Mecanical Engineering-Lecture Slides, Slides of Mechanical Engineering

Prof. Dasmaya Sidhu delivered this lecture at National Institute of Industrial Engineering for Basic Mechanical Engineering course. It includes: Simple, Truss, Tension, Compression, Wooden, Strut, Gusset, Loading, , Loads, Model, Action

Typology: Slides

2011/2012

Uploaded on 07/31/2012

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A Truss is a structure composed of slender members (two-force members) joined
together at their end points.
Members are either under tension or compression.
Joints are usually formed by bolting or welding the members to a common plate,
called a gusset plate, or simply passing a large bolt through each member.
Simple Truss
2
Joint-Welded
(Gusset Plate)
Member
(Wooden Strut)
Joint-Welded
(Gusset Plate)
Member
(Wooden Strut)
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A Truss is a structure composed of slender members (two-force members) joinedtogether at their end points. Members are either under tension or compression. Joints are usually formed by bolting or welding the members to a common plate,called a gusset plate, or simply passing a large bolt through each member.

Simple Truss

2

Joint-Welded

(Gusset Plate)

Member

(Wooden Strut)

Joint-Welded

(Gusset Plate)

Member

(Wooden Strut)

Loading of the Truss

The roof load is transmitted to the truss at the joints by means of a series

3

truss at the joints by means of a series of purlins.

Loads on a truss are applied at the joints

only

i.

Joints are pin-type connections (resist translation, not rotation).

ii.

Forces of action and reaction on a joint are equal and opposite.

iii.

Members in TENSION are being pulled

iv.

Members in COMPRESSION are being squeezed.

Simple Truss

5

iv.

Members in COMPRESSION are being squeezed.

v.

External forces act on the joints

Simple Planar Truss

When all members of a truss lie in a single plane, that truss is planar.

A plane truss is rigid if it does not change shape when subjected to a

general system of forces at it’s joints. The simplest stable or rigid form of a truss is a triangle, which is thebasic truss element

C

D

6

A

B

C

E

The basic truss ABC can be extended by adding

new members BD

and CD to the existing joints B and C and connecting them to form anew joint D.

Analysis of Trusses

Main goal of the Truss analysis is to determine the forces in the

members of a truss

8

• Typically used to find forces in all or several of the

members

• Each joint is a particle • Particle equilibrium in 2D:

F

F

The Method of Joints

9

• For each joint, we have 2 equations, therefore, we

can solve for 2 unknowns

• Must start process at a joint with only 2 unknown

forces

x

y

F

F

Apply equilibrium,

to solve for 2 unknown forces

+ sign: the force is tension (T)

sign: the force is compression (C)

0,

0

x

y

F

F

=

=

The Method of Joints

11

sign: the force is compression (C)

Find the next joint that has only 2 unknown forces andrepeat the process

  • Typically this is adjacent to the prior joint

Repeat with additional joints until all member forces areknown.

Remember to specify (T) or (C) for each force!

B

C

F

1

In this structure there are 5 joints each having afree body diagram as follows

The Method of Joints

12

A

B

C

D

E

F

2

F

3

A

y

D

y

D

x

FBD

∑∑∑∑ ∑∑∑∑ ∑∑∑∑

====

==== ====

0

M

0

F

0

F

y x

F

CD

F

EC

F

BC

F

1

C

Joint C

The Method of Joints

14

F

ED

F

CD

D

y

D

x

D

F

AE

F

3

F

BE

F

EC

F

ED

E

Joint E

Joint D

500 N

Determine the support reactions in the joints ofthe following truss and forces in each member ofthe truss

Example 6.

15

A

y

A

x

C

y

FBD

∑∑∑∑ ∑∑∑∑ ∑∑∑∑

====

=

=

====

0

M

0

F

0

F

x y

F

CA

C

y

Example 6.

17

N
F

sin

F
F

sin

F
F
F

CA

BC

CA

BC

CA

x

∑∑∑∑

N
C

cos

F
C
F

y

o

BC

y

y

∑∑∑∑

A

X

A

y

F

BA

F

CA

Example 6.

18

N
A
F
A
F

x

CA

x

x

∑∑∑∑

N
A
F
A
F

y

BA

y

y

∑∑∑∑

Problem 6.

A truss used to support a balcony is subjected to the loading as shown in figure. Approximate each joint as a pin and find out the force in each member of the truss State whether the members are in tension or in compression. P

1

= 600N

P

2

= 400N

20

A

B

C

P

1

P

2

C

x

C

Problem 6.

A truss used to support a balcony is subjected to the loading as shown in figure. Approximate each joint as a pin and find out the force in each member of the truss State whether the members are in tension or in compression. P

1

= 600N

P

2

= 400N

21

D

E

E

x

E

y

C

y

FBD

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