point equilibrium and planar trusses four

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lecture

four

point equilibrium

and planar trusses

http:// nisee.berkeley.edu/godden

A

RCHITECTURAL

S

TRUCTURES

:

F

ORM,

B

EHAVIOR, AND

D

ESIGN

A

RCH 331

HÜDAVERDİ TOZAN

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Equilibrium

• balanced

• steady

• resultant of forces on a particle is 0

X

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Equilibrium on a Point

• analytically

• Newton convinces us it will stay at rest

0 





_x

x

F

R

0 





_y

y

F

R

http://www.physics.umd.edu

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Equilibrium on a Point

• collinear force system

– ex: cables

0 





_x

x

F

R

_y





F

_y



0

0 



F

in



line

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Equilibrium on a Point

• concurrent force system

– ex: cables

0 





_x

x

F

R

0 





_y

y

F

R

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Free Body Diagram

• FBD (sketch)

• tool to see all forces on a body or a

point including

– external forces

– weights

– force reactions

– internal forces

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Free Body Diagram

• determine point

• FREE it from:

– ground

– supports & connections

• draw all external forces

acting ON the body

– reactions

(supporting forces)

– applied forces

– gravity

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Free Body Diagram

• sketch FBD with relevant geometry

• resolve each force into components

– known & unknown angles –

name

them

– known & unknown forces –

name

them

• are any forces related to other forces?

• for the unknowns

• write only as many equilibrium

equations as needed

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Free Body Diagram

• solve equations

– most times 1 unknown easily solved

– plug into other equation(s)

• common to have unknowns of

– force magnitudes

– force angles

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Truss Structures

• ancient (?) wood

– Romans 500 B.C.

• Renaissance revival

• 1800’s analysis

• efficient

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Truss Structures

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Truss Structures

• comprised of straight members

• geometry with triangles is stable

• loads applied only at pin joints

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Truss Structures

• 2 force members

– forces in line, equal and opposite

– compression

– tension

• 3 members connected

by 3 joints

• 2 more members need

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Truss Structures

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Truss Structures

• statically determinate

• indeterminate

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Trusses

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Trusses

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Trusses

• uses

– roofs & canopies

– long spans

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Truss Connections

• “pins”

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Truss Analysis

• visualize compression and tension from

deformed shape

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Truss Analysis

• Method of Joints

• Graphical Methods

• Method of Sections

• all rely on equilibrium

– of bodies

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A

_B

C

P

F

E

D

P

Method of Joints

• isolate each joint

• enforce

equilibrium in

F

_x

and F

_y

• can find all forces

• long

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Joint Cases

• two bodies connected

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Joint Cases

• three bodies with two in line

A

B

C

A

B

C

or

or even

C

B

A

D

0 x

0

0 x

x

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Joint Cases

• crossed

A

B

C

B

A

P

D

P

C

B

A

D

E

C

B

A

D

E

equal

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Tools – Multiframe

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• frame window

– define truss members

• or pre-defined truss

– select points, assign supports

– select members,

assign section &

assign pin ends

• load window

– select points,

add point load

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• to run analysis choose

– Analyze menu

• Linear

• plot

– choose options

• results

– choose

options

Tools – Multiframe