other beams & pinned frames eleven

(1)

eleven

other beams &

pinned frames

lecture

Continental train platform, Grimshaw 1993

A

RCHITECTURAL

S

TRUCTURES

:

F

ORM,

B

EHAVIOR, AND

D

ESIGN

A

RCH 331

HÜDAVERDİ TOZAN

(2)

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Pinned Frames 2 Architectural Structures

Pinned Frames

• structures with at least one 3 force body

• connected with pins

• reactions are equal and opposite

(3)

Rigid Frames

• rigid frames have

no pins

• frame is all one

body

• typically statically

indeterminate

• types

– portal

– gable

(4)

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Rigid Frames with PINS

• frame pieces with

connecting pins

• not necessarily

(5)

Internal Pin Connections

• statically determinant

– 3 equations per body

– 2 reactions per pin + support forces

A

B

C

D

G

E

_F

A

x

A

y

_D

(6)

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Arches

• ancient

• traditional shape to

span long distances

Packhorse Bridge, UK

Roman Aquaducts Rainbow Bridge National Monument

(7)

Arches

• primarily sees compression

• a brick “likes an arch”

(8)

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Arches

• behavior

– thrust related

(9)

Three-Hinged Arch

• statically determinant

– 2 bodies, 6 equilibrium equations

– 4 support, 2 pin reactions (= 6)

(10)

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F

₁

F

₂

F

₁

F

₂

not independent

Compound Beams

• statically determinant when

– 3 equilibrium equations per link =>

– total of support & pin reactions

(properly constrained)

• zero moment at pins

R

_1x

R

_1y

M

_R1

R

₃

(internal) pin

_R

2y

R

2y

R

_2x

R

2x

(11)

Procedure

• solve for all support forces you can

• draw a FBD of each member

– pins are integral with member

– pins with loads should belong to 3+ force

bodies

– pin forces are equal and opposite on

connecting bodies

– identify 2 force bodies vs. 3+ force bodies

– use all equilibrium equations

(12)

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Rigid Body Types

• two force bodies

– forces in line, equal and opposite

• three force bodies

– concurrent or parallel forces

two

A

F

2

B

F

1

a

three

F

2

A

F

1

B

C

F

3

d

1

d

2

F

2

A

F

1

B

C

F

3

a

(13)

Continuous Beams

• statically indeterminate

(14)

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Continuous Beams

• loading pattern affects

– moments & deflection

max

D

(15)

max

D

Continuous Beams

(16)

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Continuous Beams

• unload middle span

max

(17)

Analysis Methods

• Approximate Methods

– location of inflection points

• Force Method

– forces are unknowns

• Displacement Method

(18)

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