trusses & columnsfaculty.arch.tamu.edu/media/cms_page_media/4350/lect5.pdfColumns & Trusses 23 F2016abn Lecture 5 Applied Architectural Structures ARCH 631 Truss Configurations •special

F2016abnColumns & Trusses 1

Lecture 5

Applied Architectural Structures

ARCH 631

five

trusses

& columns

lecture

www.nyc-architecture.com

APPLIED ACHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631

DR. ANNE NICHOLS

FALL 2016

F2016abnCables & Arches 2

Lecture 6


ARCH 631

Calibrated Peer Review / Turnitin


Lecture 5


ARCH 631

Trusses

• ancient (?) wood

• 1800’s analysis

• efficient

• long spans


Lecture 5


ARCH 631

Trusses

• comprised of straight members

• geometry with triangles is stable

• loads applied only at joints

http://nisee.berkeley.edu/godden

F2016abn

• 2 force members

– compression

– tension

• 3 members connected by 3 joints

• 2 more members need

1 more joint

Columns & Trusses 5

Lecture 5


ARCH 631

Trusses

32 nb)32( jn


Lecture 5


ARCH 631

Truss Analysis

• visualize compression and tension from

deformed shape

http://nisee.berkeley.edu/godden


Lecture 5


ARCH 631

Truss Analysis

• Method of Joints

–

• Method of Sections–

–

• Graphical Methods

• all rely on equilibrium

– of bodies

– internal equilibrium

http:// nisee.berkeley.edu/godden

0 F

0 F

0 M


Lecture 5


ARCH 631

Truss Connections

• “pins”

– can’t resist rotation



Lecture 5


ARCH 631

Trusses

• require lateral bracing

• consider buckling

• indeterminate trusses

– extra members

– solvable with statics

• cables can’t hold compression

– displacement methods

• elastic elongation

– too few members, unstable



Lecture 5


ARCH 631

• pyramid

• tetrahedron

Space Trusses



Lecture 5


ARCH 631

Space Trusses

• connections • supports


Lecture 5


ARCH 631

Crystal Cathedral, Johnson 1980



Lecture 5


ARCH 631

Expo 70 Festival Plaza

• Tange & Kamiya 1970


Lecture 5


ARCH 631

Jacob K. Javits Convention Center

• I.M. Pei 1980


Lecture 5


ARCH 631

Jacob K. Javits Convention Center


Lecture 5


ARCH 631

Louvre Museum Addition, Pei 1989


Lecture 5


ARCH 631

Truss Design

• variables

– spans

– depths

– length of members

– spacing

– transverse beam

spacing

– pattern

– materials; size & strength efficiency

F2016abnColumns & Trusses 19Lecture 5

Applied Architectural StructuresARCH 631

Trusses

• common designs


Lecture 5


ARCH 631

Trusses

• common designs


Lecture 5


ARCH 631

Truss Configurations

• external factors

– roof form

– openings

• basic forms

– symmetrical loading

– maximum bending

– cables in tension only



Truss Configurations

• parallel chords

– verticals common

– longer members in tension

– often cross members - indeterminate

• funicular shapes

– efficient

– similar sizedforces

– some zero force


Lecture 5


ARCH 631

Truss Configurations• special shapes

– Vierendeel

– “frame”

• depth– depends on loads, span

– rules of thumb, charts

• structurally– tension members can

have holes!

– compression members can buckle

– 3D trusses stable


F2016abn

• in classrooms and open access labs

Columns & Trusses 24

Lecture 5


ARCH 631

Tools – Multiframe


Lecture 5


ARCH 631


• 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

F2016abn

• to run analysis choose

– Analyze menu

• Linear

• plot

– choose options

• results

– choose

options


Lecture 5


ARCH 631



Lecture 5


ARCH 631

Columns

• compression members

• column behavior is length dependant

– short: crush

– long: buckle (sudden) in slender direction

– end restraints

• bearing walls

– continuous in one direction

– can resist lateral forces


Lecture 5


ARCH 631

Columns

• column buckling crushing


Lecture 5


ARCH 631

Columns

• stability

– stable equilibrium

• P < Pcr

– neutral equilibrium

• P = Pcr

– unstable equilibrium

• P > Pcr

F2016abn

• related to deflected shape (P)

• shape of sine wave

• Euler’s Formula

• I minimum

• stiffness related to E, I, & L


Lecture 5


ARCH 631

Buckling Load

2min

2

L

EIPcritical

F2016abn

• short columns

• slenderness ratio = Le/r (L/d)

• radius of gyration =


Lecture 5


ARCH 631

Critical Stress

weak axis

aactual

critical FA

Pf

A

Ir

22

2

22

rL

E

LA

EAr

A

Pf

ee

criticalcritical

2

e

2

critical

rL

EAP

F2016abn

• when a column gets stubby, Fy will limit the

load

• real world has loads

with eccentricity

• buckling for steel

when Fe < 0.44Fy


Lecture 5


ARCH 631

Critical Stresses

yF

E.

r

KL714


Lecture 5


ARCH 631

Columns

• end conditions affect shape

• effective length factor, k



Bracing

• bracing affects shape of buckle

in one direction

• both directions should be checked!


Lecture 5


ARCH 631

Columns and Walls

• bearing & shear


Lecture 5


ARCH 631

Columns

• typical cross sections


Lecture 5


ARCH 631

Centric & Eccentric Loading

• centric

– allowable stress from strength or buckling

• eccentric

– combined stresses

F2016abn

– axial + bending

– design


Lecture 5

Foundations Structures

ARCH 331

Combined Stresses

I

Mc

A

Pf max

ePM

..max

SF

fFf crcr


Lecture 5


ARCH 631

Column Materials

• wood

• steel

– W sections can buckle about both axes

• concrete & masonry

– compression primarily in concrete

– reinforcement for bending

Trans

Documents

trusses & columnsfaculty.arch.tamu.edu/media/cms_page_media/4350/lect5.pdfColumns & Trusses 23 F2016abn Lecture 5 Applied Architectural Structures ARCH 631 Truss Configurations •special