four http:// nisee.berkeley.edu/godden point equilibrium and - - PowerPoint PPT Presentation

▶

Jun 08, 2023 370 likes •679 views

A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN A RCH 331 D R. A NNE N ICHOLS S PRING 2018 lecture four http:// nisee.berkeley.edu/godden point equilibrium and planar trusses Point Equilibrium 1 Architectural Structures S2018abn

SLIDE 1

S2018abn Point Equilibrium 1 Lecture 4 Architectural Structures ARCH 331

lecture

four

point equilibrium and planar trusses

http:// nisee.berkeley.edu/godden

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN ARCH 331

DR. ANNE NICHOLS

SPRING 2018

SLIDE 2

S2018abn Point Equilibrium 2 Lecture 4 Architectural Structures ARCH 331

Equilibrium

balanced
steady
resultant of forces on a particle is 0

X X

=

SLIDE 3

S2018abn Point Equilibrium 3 Lecture 4 Architectural Structures ARCH 331

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

S2018abn Point Equilibrium 4 Lecture 4 Architectural Structures ARCH 331

Equilibrium on a Point

collinear force system

– ex: cables

  

x x

F R   

y y

F R 



line in

F

SLIDE 5

S2018abn Point Equilibrium 5 Lecture 4 Architectural Structures ARCH 331

Equilibrium on a Point

concurrent force system

– ex: cables

  

x x

F R   

y y

F R

SLIDE 6

S2018abn Point Equilibrium 6 Lecture 4 Architectural Structures ARCH 331

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

S2018abn Point Equilibrium 7 Lecture 4 Architectural Structures ARCH 331

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

S2018abn Point Equilibrium 8 Lecture 4 Architectural Structures ARCH 331

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

S2018abn Point Equilibrium 9 Lecture 4 Architectural Structures ARCH 331

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

S2018abn Point Equilibrium 10 Lecture 4 Architectural Structures ARCH 331

Truss Structures

ancient (?) wood

– Romans 500 B.C.

Renaissance revival
1800’s analysis
efficient

SLIDE 11

S2018abn Point Equilibrium 11 Lecture 4 Architectural Structures ARCH 331

Truss Structures

– analogous to cables and struts

SLIDE 12

S2018abn Point Equilibrium 12 Lecture 4 Architectural Structures ARCH 331

Truss Structures

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

http:// nisee.berkeley.edu/godden

SLIDE 13

S2018abn Point Equilibrium 13 Lecture 4 Architectural Structures ARCH 331

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 14

S2018abn Point Equilibrium 14 Lecture 4 Architectural Structures ARCH 331

Truss Structures

compression and tension

SLIDE 15

S2018abn Point Equilibrium 15 Lecture 4 Architectural Structures ARCH 331

Truss Structures

statically determinate
indeterminate
unstable

SLIDE 16

S2018abn Point Equilibrium 16 Lecture 4 Architectural Structures ARCH 331

Trusses

common designs

SLIDE 17

S2018abn Point Equilibrium 17 Lecture 4 Architectural Structures ARCH 331

Trusses

common designs

SLIDE 18

S2018abn Point Equilibrium 18 Lecture 4 Architectural Structures ARCH 331

Trusses

uses

– roofs & canopies – long spans – lateral bracing

SLIDE 19

S2018abn Point Equilibrium 19 Lecture 4 Architectural Structures ARCH 331

Truss Connections

“pins”

http:// nisee.berkeley.edu/godden

SLIDE 20

S2018abn Point Equilibrium 20 Lecture 4 Architectural Structures ARCH 331

Sainsbury Center, Foster 1978

SLIDE 21

S2018abn Point Equilibrium 21 Lecture 4 Architectural Structures ARCH 331

Sainsbury Center, Foster 1978

SLIDE 22

S2018abn Point Equilibrium 22 Lecture 4 Architectural Structures ARCH 331

Truss Analysis

visualize compression and tension from

deformed shape

http:// nisee.berkeley.edu/godden

SLIDE 23

S2018abn Point Equilibrium 23 Lecture 4 Architectural Structures ARCH 331

Truss Analysis

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

– of bodies – internal equilibrium

SLIDE 24

S2018abn Point Equilibrium 24 Lecture 4 Architectural Structures ARCH 331

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 25

S2018abn Point Equilibrium 25 Lecture 4 Architectural Structures ARCH 331

Joint Cases

two bodies connected

equal equal and 0

SLIDE 26

S2018abn Point Equilibrium 26 Lecture 4 Architectural Structures ARCH 331

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 27

S2018abn Point Equilibrium 27 Lecture 4 Architectural Structures ARCH 331

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 28

S2018abn Point Equilibrium 28 Lecture 4 Architectural Structures ARCH 331

Tools – Multiframe

in open access labs and virtual OAL

SLIDE 29

S2018abn Point Equilibrium 29 Lecture 4 Architectural Structures ARCH 331

frame window

– define truss members

or pre-defined truss

– select points, assign supports – select members, assign section & assign pin ends

load window

– select points, add point load

Tools – Multiframe

SLIDE 30

S2018abn

to run analysis choose

– Analyze menu

Linear
plot

– choose options

results

– choose

ptions

Point Equilibrium 30 Lecture 4 Architectural Structures ARCH 331