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E LEMENTS OF A RCHITECTURAL S TRUCTURES : Equilibrium F ORM, B EHAVIOR, AND D ESIGN ARCH 614 balanced D R. A NNE N ICHOLS steady S PRING 2019 resultant of forces on a particle is 0 lecture three X equilibrium = and planar trusses

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S2009abn Equilibrium 1 Lecture 3 Elements of Architectural Structures ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 614

  • DR. ANNE NICHOLS

SPRING 2019 lecture

three

equilibrium and planar trusses

Equilibrium 2 Lecture 5 Elements of Architectural Structures ARCH 614 S2006abn

Equilibrium

  • balanced
  • steady
  • resultant of forces on a particle is 0

X X

=

S2004abn Equilibrium 6 Elements of Architectural Structures ARCH 614

Equilibrium on a Point

  • analytically
  • Newton convinces us it will stay at rest

 

x x

F R  

y y

F R

http://www.physics.umd.edu Equilibrium 7 Elements of Architectural Structures ARCH 614 S2004abn

Equilibrium on a Point

  • collinear force system

– ex: cables

 

x x

F R  

y y

F R 

line in

F

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SLIDE 2

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Equilibrium 8 Elements of Architectural Structures ARCH 614 S2004abn

Equilibrium on a Point

  • concurrent force system

– ex: cables

  

x x

F R  

y y

F R

Equilibrium 10 Elements of Architectural Structures ARCH 614 S2004abn

Free Body Diagram

  • FBD (sketch)
  • tool to see all forces on a body or a

point including

– external forces – weights – force reactions – internal forces

Equilibrium 11 Elements of Architectural Structures ARCH 614 S2004abn

Free Body Diagram

  • determine point
  • FREE it from:

– ground – supports & connections

  • draw all external forces

acting ON the body

– reactions – (supporting forces) – applied forces – gravity

= m· g

Equilibrium 12 Elements of Architectural Structures ARCH 614 S2004abn

Free Body Diagram

  • sketch FBD with relevant geometry
  • resolve each force into components

– known & unknown angles – name them – known & unknown forces – name them

  • are any forces related to other forces?
  • for the unknowns
  • write only as many equilibrium

equations as needed

  • solve up to 2 equations
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Equilibrium 10 Lecture 5 Elements of Architectural Structures ARCH 614 S2006abn

Free Body Diagram

  • solve equations

– most times 1 unknown easily solved – plug into other equation(s)

  • common to have unknowns of

– force magnitudes – force angles

Equilibrium 19 Elements of Architectural Structures ARCH 614 S2004abn

Force Reactions

  • result of applying force
  • unknown size
  • connection or support type

– known direction – related to motion prevented

no vertical motion no translation

Equilibrium 11 Lecture 3 Elements of Architectural Structures ARCH 614 S2009abn

Friction

  • resistance to movement
  • contact surfaces determine 
  • proportion of normal force ()

– opposite to slide direction – static > kinetic

N μ F 

Equilibrium 28 Elements of Architectural Structures ARCH 614 S2004abn

Cable Reactions

  • equilibrium:

– more reactions (4) than equations – but, we have slope relationships – X component the same everywhere

A C 45 kN 4 m 2 m B 6 m 45 kN

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S2005abn Equilibrium 35 Lecture 5 Elements of Architectural Structures ARCH 614

Cable-Stayed Structures

  • diagonal cables support horizontal

spans

  • typically symmetrical
  • Patcenter,

Rogers 1986

www.columbia.edu Equilibrium 36 Lecture 5 Elements of Architectural Structures ARCH 614 S2005abn

Patcenter, Rogers 1986

  • column free space
  • roof suspended
  • solid steel ties
  • steel frame supports masts

Equilibrium 37 Lecture 5 Elements of Architectural Structures ARCH 614 S2005abn

Patcenter, Rogers 1986

  • dashes – cables pulling

Trusses Intro10 Elements of Architectural Structures ARCH 614 S2004abn

Truss Structures

  • ancient (?) wood

– Romans 500 B.C.

  • Renaissance revival
  • 1800’s analysis
  • efficient
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Trusses Intro11 Elements of Architectural Structures ARCH 614 S2004abn

Truss Structures

– analogous to cables and struts

S2004abn Trusses Intro12 Elements of Architectural Structures ARCH 614

Truss Structures

  • comprised of straight members
  • geometry with triangles is stable
  • loads applied only at pin joints

http:// nisee.berkeley.edu/godden Trusses Intro13 Elements of Architectural Structures ARCH 614 S2004abn

Truss Structures

  • 2 force members

– forces in line, equal and opposite – compression – tension

  • 3 members connected

by 3 joints

  • 2 more members need

1 more joint

3 2   n b

Trusses Intro14 Elements of Architectural Structures ARCH 614 S2004abn

Truss Structures

  • compression and tension
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6

Trusses Intro15 Elements of Architectural Structures ARCH 614 S2004abn

Truss Structures

  • statically determinate
  • indeterminate
  • unstable

Trusses Intro16 Elements of Architectural Structures ARCH 614 S2004abn

Trusses

  • common designs

Trusses Intro17 Elements of Architectural Structures ARCH 614 S2004abn

Trusses

  • common designs

Trusses Intro18 Elements of Architectural Structures ARCH 614 S2004abn

Trusses

  • uses

– roofs & canopies – long spans – lateral bracing

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SLIDE 7

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S2004abn Trusses Intro19 Elements of Architectural Structures ARCH 614

Truss Connections

  • “pins”

http:// nisee.berkeley.edu/godden Trusses Intro20 Elements of Architectural Structures ARCH 614 S2004abn

Sainsbury Center, Foster 1978

Trusses Intro21 Elements of Architectural Structures ARCH 614 S2004abn

Sainsbury Center, Foster 1978

S2005abn Trusses Intro 22 Lecture 6 Elements of Architectural Structures ARCH 614

Truss Analysis

  • visualize compression and tension from

deformed shape

http:// nisee.berkeley.edu/godden

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SLIDE 8

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Trusses Intro22 Elements of Architectural Structures ARCH 614 S2004abn

Truss Analysis

  • Method of Joints
  • Graphical Methods
  • Method of Sections
  • all rely on equilibrium

– of bodies – internal equilibrium

Trusses Intro23 Elements of Architectural Structures ARCH 614 S2004abn

Method of Joints

  • isolate each joint
  • enforce

equilibrium in Fx and Fy

  • can find all forces
  • long
  • easy to mess up

A B C P F E D P

Trusses Intro 25 Lecture 6 Elements of Architectural Structures ARCH 614 S2005abn

Joint Cases

  • two bodies connected

equal equal and 0

Trusses Intro 26 Lecture 6 Elements of Architectural Structures ARCH 614 S2005abn

Joint Cases

  • three bodies with two in line

A B C A B C

  • r
  • r even

C B A D D D

x x x

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Trusses Intro 27 Lecture 6 Elements of Architectural Structures ARCH 614 S2005abn

Joint Cases

  • crossed

A B C C B A P D D P C B A D E C B A D E equal

F2018abn

Tools – Visual Analysis (Educational)

  • in open access labs and VOAL and

https://www.iesweb.com/edu/index.htm

Equilibrium 34 Lecture 3 Elements of Architectural Structures ARCH 614 F2018abn

Tools – Visual Analysis (Educational)

Equilibrium 35 Lecture 3 Elements of Architectural Structures ARCH 614

  • model view / structure tab

– grid and units – define truss members

  • or pre-defined truss (Create)

– select points, assign supports – select members, assign member shapes & assign releases

F2018abn

Tools – Visual Analysis (Educational)

  • loading tab

– select points, add point load – edit load case with no self weight

  • results view

– status bar – results filter – Fx, axis force

  • member graph

– choose options

  • report view - choose and drag options

Equilibrium 6 Lecture 3 Elements of Architectural Structures ARCH 614