ten other beams & pinned frames Continental train platform, - - PowerPoint PPT Presentation

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ten other beams & pinned frames Continental train platform, - - PowerPoint PPT Presentation

Sep 19, 2022 257 likes •506 views

E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS S PRING 2019 lecture ten other beams & pinned frames Continental train platform, Grimshaw 1993 Pinned Frames 1 Elements of Architectural

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SLIDE 1

S2019abn 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 2019

ten

  • ther beams &

pinned frames

lecture

Continental train platform, Grimshaw 1993

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SLIDE 2

S2019abn Pinned Frames 2 Lecture 10 Elements of Architectural Structures ARCH 614

Continuous Beams

  • statically indeterminate
  • reduced moments than simple beam
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SLIDE 3

S2019abn Pinned Frames 3 Lecture 10 Elements of Architectural Structures ARCH 614

Continuous Beams

  • loading pattern affects

– moments & deflection

max

D

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SLIDE 4

S2019abn

max

D

Pinned Frames 4 Lecture 10 Elements of Architectural Structures ARCH 614

Continuous Beams

  • unload end span
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SLIDE 5

S2019abn Pinned Frames 5 Lecture 10 Elements of Architectural Structures ARCH 614

Continuous Beams

  • unload middle span

max

D

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SLIDE 6

S2019abn Pinned Frames 6 Lecture 10 Elements of Architectural Structures ARCH 614

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

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SLIDE 7

S2019abn Pinned Frames 7 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution (a)

  • no load

http:// nisee.berkeley.edu/godden

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SLIDE 8

S2019abn 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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SLIDE 9

S2019abn Pinned Frames 9 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution Method (c)

  • release joint 2

http:// nisee.berkeley.edu/godden

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SLIDE 10

S2019abn Pinned Frames 10 Lecture 10 Elements of Architectural Structures ARCH 614

Moment Distribution Method (d)

  • release joint 3

http:// nisee.berkeley.edu/godden

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SLIDE 11

S2019abn 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

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SLIDE 12

S2019abn Pinned Frames 12 Lecture 10 Elements of Architectural Structures ARCH 614

Analysis Methods

  • Approximate Methods

– location of inflection points

  • Force Method

– forces are unknowns

  • Displacement Method

– displacements are unknowns

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SLIDE 13

S2019abn Pinned Frames 13 Lecture 10 Elements of Architectural Structures ARCH 614

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

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SLIDE 14

S2019abn Pinned Frames 14 Lecture 10 Elements of Architectural Structures ARCH 614

Two Span Beams & Charts

  • equal spans & symmetrical loading
  • middle support as flat slope
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SLIDE 15

S2019abn Pinned Frames 15 Lecture 10 Elements of Architectural Structures ARCH 614

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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SLIDE 16

S2019abn Pinned Frames 16 Lecture 10 Elements of Architectural Structures ARCH 614

Rigid Frames

  • rigid frames have

no pins

  • frame is all one

body

  • typically statically

indeterminate

  • types

– portal – gable

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SLIDE 17

S2019abn Pinned Frames 17 Lecture 10 Elements of Architectural Structures ARCH 614

Rigid Frames with PINS

  • frame pieces with

connecting pins

  • not necessarily

symmetrical

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SLIDE 18

S2019abn Pinned Frames 18 Lecture 10 Elements of Architectural Structures ARCH 614

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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SLIDE 19

S2019abn Pinned Frames 19 Lecture 10 Elements of Architectural Structures ARCH 614

Arches

  • ancient
  • traditional shape to

span long distances

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SLIDE 20

S2019abn Pinned Frames 20 Lecture 10 Elements of Architectural Structures ARCH 614

Arches

  • primarily sees compression
  • a brick “likes an arch”
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SLIDE 21

S2019abn Pinned Frames 21 Lecture 10 Elements of Architectural Structures ARCH 614

Arches

  • behavior

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

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SLIDE 22

S2019abn Pinned Frames 22 Lecture 10 Elements of Architectural Structures ARCH 614

Three-Hinged Arch

  • statically determinant

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

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SLIDE 23

S2019abn 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

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SLIDE 24

S2019abn Pinned Frames 24 Lecture 10 Elements of Architectural Structures ARCH 614

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