pinned frames Pinned Frames 2 Elements of Architectural...

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S2009abnPinned Frames 1

Lecture 10

Elements of Architectural Structures

ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES:

FORM, BEHAVIOR, AND DESIGN

ARCH 614

DR. ANNE NICHOLS

SPRING 2014

ten

other beams &

pinned frames

lecture

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Lecture 10


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Continuous Beams

• statically indeterminate

• reduced moments than simple beam

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Continuous Beams

• loading pattern affects

– moments & deflection

max

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Continuous Beams

max

• unload end span

2

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Continuous Beams

• unload middle span

max

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Moment Redistribution

• continuous slabs & beams with uniform

loading

– joints similar to fixed ends, but can rotate

• change in moment to center =

– Mmax for simply supported beam 8

2wL


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Moment Distribution (a)

• no load

http:// nisee.berkeley.edu/godden


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Moment Distribution (b)

• add load


3


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Moment Distribution Method (c)

• release joint 2



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Moment Distribution Method (d)

• release joint 3



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Moment Distribution Method (e)

• exposure of final shape after cycles over

initial shape


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Analysis Methods

• Approximate Methods

– location of inflection points

• Force Method

– forces are unknowns

• Displacement Method

– displacements are unknowns

4

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Theorem of Three Moments

• moments at three adjacent supports

(2 spans)

• distributed load and same I:

• concentrated loads and same I:

44

23

22

3

112321211

LwLwLMLLMLM

2321211 2 LMLLMLM

3

22

2

22

3

11

2

11 nnLPnnLP

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Two Span Beams & Charts

• equal spans & symmetrical loading

• middle support as flat slope

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Pinned Frames

• structures with at least one 3 force body

• connected with pins

• reactions are equal and opposite

– non-rigid – rigid

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Rigid Frames

• rigid frames have no pins

• frame is all one body

• typically statically indeterminate

• types

– portal

– gable

5

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Rigid Frames with PINS

• frame pieces with

connecting pins

• not necessarily

symmetrical

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Internal Pin Connections

• statically determinant

– 3 equations per body

– 2 reactions per pin + support forces

A

B

C

D

G

E F

Ax

Ay D


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Arches

• ancient

• traditional shape to

span long distances

Packhorse Bridge, UK

Roman AquaductsRainbow Bridge National Monument


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Arches

• primarily sees compression

• a brick “likes an arch”

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Arches

• behavior

– thrust related

to height to width

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Three-Hinged Arch

• statically determinant

– 2 bodies, 6 equilibrium equations

– 4 support, 2 pin reactions (= 6)


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Beams with Internal Pins

• statically determinant when

– 3 equilibrium equations per link =>

– total of support & pin reactions

(properly constrained)

• zero moment at pins

F1 F2 F1 F2

not independent

R1x

R1y

MR1

R3

(internal) pin R2yR2y

R2xR2x

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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

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