ten other beams & pinned frames Pinned Frames 2 Elements of - - PowerPoint PPT Presentation

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S2009abn Pinned Frames 1 Lecture 10 Elements of Architectural Structures ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 614

• DR. ANNE NICHOLS

SPRING 2018

ten

• ther beams &

pinned frames

lecture

Pinned Frames 2 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Continuous Beams

• statically indeterminate
• reduced moments than simple beam

Pinned Frames 3 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Continuous Beams

• loading pattern affects

– moments & deflection

max



Pinned Frames 4 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Continuous Beams

max



• unload end span

2

Pinned Frames 5 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Continuous Beams

• unload middle span

max



Pinned Frames 6 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

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

2

wL

S2007abn Pinned Frames 7 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution (a)

• no load

http:// nisee.berkeley.edu/godden S2007abn Pinned Frames 8 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution (b)

• add load

http:// nisee.berkeley.edu/godden

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S2007abn Pinned Frames 9 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution Method (c)

• release joint 2

http:// nisee.berkeley.edu/godden S2007abn Pinned Frames 10 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution Method (d)

• release joint 3

http:// nisee.berkeley.edu/godden S2007abn Pinned Frames 11 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution Method (e)

• exposure of final shape after cycles over

initial shape

http:// nisee.berkeley.edu/godden Pinned Frames 12 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Analysis Methods

• Approximate Methods

– location of inflection points

• Force Method

– forces are unknowns

• Displacement Method

– displacements are unknowns

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Pinned Frames 13 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Theorem of Three Moments

• moments at three adjacent supports

(2 spans)

• distributed load and same I:
• concentrated loads and same I:

 

4 4 2

3 2 2 3 1 1 2 3 2 1 2 1 1

L w L w L M L L M L M      

 

   

2 3 2 1 2 1 1

2 L M L L M L M

   

 

   

3 2 2 2 2 2 3 1 1 2 1 1

n n L P n n L P

Pinned Frames 14 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Two Span Beams & Charts

• equal spans & symmetrical loading
• middle support as flat slope

Pinned Frames 15 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Pinned Frames

• structures with at least one 3 force body
• connected with pins
• reactions are equal and opposite

– non-rigid – rigid

Pinned Frames 16 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Rigid Frames

• rigid frames have

no pins

• frame is all one

body

• typically statically

indeterminate

• types

– portal – gable

5

Pinned Frames 17 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Rigid Frames with PINS

• frame pieces with

connecting pins

• not necessarily

symmetrical

Pinned Frames 18 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

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

S2007abn Pinned Frames 19 Lecture 10 Elements of Architectural Structures ARCH 614

Arches

• ancient
• traditional shape to

span long distances

Packhorse Bridge, UK Roman Aquaducts Rainbow Bridge National Monument S2007abn Pinned Frames 20 Lecture 10 Elements of Architectural Structures ARCH 614

Arches

• primarily sees compression
• a brick “likes an arch”

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S2007abn Pinned Frames 21 Lecture 10 Elements of Architectural Structures ARCH 614

Arches

• behavior

– thrust related to height to width – funicular: to load

Pinned Frames 22 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

Three-Hinged Arch

• statically determinant

– 2 bodies, 6 equilibrium equations – 4 support, 2 pin reactions (= 6)

S2007abn Pinned Frames 23 Lecture 10 Elements of Architectural Structures ARCH 614

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 R2y R2y R2x R2x

Pinned Frames 24 Lecture 10 Elements of Architectural Structures ARCH 614 S2007abn

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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