three equilibrium and planar trusses Equilibrium 1 Elements of - - PowerPoint PPT Presentation

▶
three
SMART_READER_LITE
LIVE PREVIEW

three equilibrium and planar trusses Equilibrium 1 Elements of - - PowerPoint PPT Presentation

Nov 08, 2022 290 likes •655 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 three equilibrium and planar trusses Equilibrium 1 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

slide-1
SLIDE 1

S2019abn 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

slide-2
SLIDE 2

S2019abn Equilibrium 2 Lecture 3 Elements of Architectural Structures ARCH 614

Equilibrium

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

X X

=

slide-3
SLIDE 3

S2019abn Equilibrium 3 Lecture 3 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

slide-4
SLIDE 4

S2019abn Equilibrium 4 Lecture 3 Elements of Architectural Structures ARCH 614

Equilibrium on a Point

  • collinear force system

– ex: cables

  

x x

F R   

y y

F R 

line in

F

slide-5
SLIDE 5

S2019abn Equilibrium 5 Lecture 3 Elements of Architectural Structures ARCH 614

Equilibrium on a Point

  • concurrent force system

– ex: cables

  

x x

F R   

y y

F R

slide-6
SLIDE 6

S2019abn Equilibrium 6 Lecture 3 Elements of Architectural Structures ARCH 614

Free Body Diagram

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

point including

– external forces – weights – force reactions – internal forces

slide-7
SLIDE 7

S2019abn Equilibrium 7 Lecture 3 Elements of Architectural Structures ARCH 614

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

slide-8
SLIDE 8

S2019abn Equilibrium 8 Lecture 3 Elements of Architectural Structures ARCH 614

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
slide-9
SLIDE 9

S2019abn Equilibrium 9 Lecture 3 Elements of Architectural Structures ARCH 614

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

slide-10
SLIDE 10

S2019abn Equilibrium 10 Lecture 3 Elements of Architectural Structures ARCH 614

Force Reactions

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

– known direction – related to motion prevented

no vertical motion no translation

slide-11
SLIDE 11

S2019abn Equilibrium 11 Lecture 3 Elements of Architectural Structures ARCH 614

Friction

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

– opposite to slide direction – static > kinetic

N μ F 

slide-12
SLIDE 12

S2019abn Equilibrium 12 Lecture 3 Elements of Architectural Structures ARCH 614

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

slide-13
SLIDE 13

S2019abn Equilibrium 13 Lecture 3 Elements of Architectural Structures ARCH 614

Cable-Stayed Structures

  • diagonal cables support horizontal

spans

  • typically symmetrical
  • Patcenter,

Rogers 1986

www.columbia.edu

slide-14
SLIDE 14

S2019abn Equilibrium 14 Lecture 3 Elements of Architectural Structures ARCH 614

Patcenter, Rogers 1986

  • column free space
  • roof suspended
  • solid steel ties
  • steel frame supports masts
slide-15
SLIDE 15

S2019abn Equilibrium 15 Lecture 3 Elements of Architectural Structures ARCH 614

Patcenter, Rogers 1986

  • dashes – cables pulling
slide-16
SLIDE 16

S2019abn Equilibrium 16 Lecture 3 Elements of Architectural Structures ARCH 614

Truss Structures

  • ancient (?) wood

– Romans 500 B.C.

  • Renaissance revival
  • 1800’s analysis
  • efficient
slide-17
SLIDE 17

S2019abn Equilibrium 17 Lecture 3 Elements of Architectural Structures ARCH 614

Truss Structures

– analogous to cables and struts

slide-18
SLIDE 18

S2019abn Equilibrium 18 Lecture 3 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

slide-19
SLIDE 19

S2019abn Equilibrium 19 Lecture 3 Elements of Architectural Structures ARCH 614

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

slide-20
SLIDE 20

S2019abn Equilibrium 20 Lecture 3 Elements of Architectural Structures ARCH 614

Truss Structures

  • compression and tension
slide-21
SLIDE 21

S2019abn Equilibrium 21 Lecture 3 Elements of Architectural Structures ARCH 614

Truss Structures

  • statically determinate
  • indeterminate
  • unstable
slide-22
SLIDE 22

S2019abn Equilibrium 22 Lecture 3 Elements of Architectural Structures ARCH 614

Trusses

  • common designs
slide-23
SLIDE 23

S2019abn Equilibrium 23 Lecture 3 Elements of Architectural Structures ARCH 614

Trusses

  • common designs
slide-24
SLIDE 24

S2019abn Equilibrium 24 Lecture 3 Elements of Architectural Structures ARCH 614

Trusses

  • uses

– roofs & canopies – long spans – lateral bracing

slide-25
SLIDE 25

S2019abn Equilibrium 25 Lecture 3 Elements of Architectural Structures ARCH 614

Truss Connections

  • “pins”

http:// nisee.berkeley.edu/godden

slide-26
SLIDE 26

S2019abn Equilibrium 26 Lecture 3 Elements of Architectural Structures ARCH 614

Sainsbury Center, Foster 1978

slide-27
SLIDE 27

S2019abn Equilibrium 27 Lecture 3 Elements of Architectural Structures ARCH 614

Sainsbury Center, Foster 1978

slide-28
SLIDE 28

S2019abn Equilibrium 28 Lecture 3 Elements of Architectural Structures ARCH 614

Truss Analysis

  • visualize compression and tension from

deformed shape

http:// nisee.berkeley.edu/godden

slide-29
SLIDE 29

S2019abn Equilibrium 29 Lecture 3 Elements of Architectural Structures ARCH 614

Truss Analysis

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

– of bodies – internal equilibrium

slide-30
SLIDE 30

S2019abn Equilibrium 30 Lecture 3 Elements of Architectural Structures ARCH 614

A B C P F E D P

Method of Joints

  • isolate each joint
  • enforce

equilibrium in Fx and Fy

  • can find all forces
  • long
  • easy to mess up
slide-31
SLIDE 31

S2019abn Equilibrium 31 Lecture 3 Elements of Architectural Structures ARCH 614

Joint Cases

  • two bodies connected

equal equal and 0

slide-32
SLIDE 32

S2019abn Equilibrium 32 Lecture 3 Elements of Architectural Structures ARCH 614

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

slide-33
SLIDE 33

S2019abn Equilibrium 33 Lecture 3 Elements of Architectural Structures ARCH 614

Joint Cases

  • crossed

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

equal

slide-34
SLIDE 34

S2019abn Equilibrium 34 Lecture 3 Elements of Architectural Structures ARCH 614

Tools – Visual Analysis (Educational)

  • in open access labs and VOAL and

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

slide-35
SLIDE 35

S2019abn 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

Tools – Visual Analysis (Educational)

slide-36
SLIDE 36

S2019abn Equilibrium 36 Lecture 3 Elements of Architectural Structures ARCH 614

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