ELEMENTS OF A STRUCTURES FORM, B …faculty.arch.tamu.edu/media/cms_page_media/4211/notes10...1...

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S2009abnPinned Frames 1Lecture 10

Elements of Architectural StructuresARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES:

FORM, BEHAVIOR, AND DESIGN

ARCH 614

DR. ANNE NICHOLS

SPRING 2015

ten

other beams &

pinned frames

lecture

Pinned Frames 2

Lecture 10

Elements of Architectural Structures

ARCH 614

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Continuous Beams

• statically indeterminate

• reduced moments than simple beam

Pinned Frames 3

Lecture 10


ARCH 614

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Continuous Beams

• loading pattern affects

– moments & deflection

max∆

Pinned Frames 4

Lecture 10


ARCH 614

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Continuous Beams

max∆

• unload end span

2

Pinned Frames 5

Lecture 10


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Continuous Beams

• unload middle span

max∆

Pinned Frames 6Lecture 10


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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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Lecture 10


ARCH 614

Moment Distribution (a)

• no load

http:// nisee.berkeley.edu/godden


Lecture 10


ARCH 614

Moment Distribution (b)

• add load


3


Lecture 10


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Moment Distribution Method (c)

• release joint 2



Lecture 10


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Moment Distribution Method (d)

• release joint 3



Lecture 10


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Moment Distribution Method (e)

• exposure of final shape after cycles over initial shape


Pinned Frames 12

Lecture 10


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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


Lecture 10


ARCH 614

Arches

• ancient

• traditional shape tospan long distances

Packhorse Bridge, UK

Roman AquaductsRainbow Bridge National Monument


Lecture 10


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Arches

• primarily sees compression

• a brick “likes an arch”

6



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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)

S2007abnPinned Frames 23Lecture 10


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 F1F2

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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