decking plate girders 1 Lecture 21 ARCH 631 standard...

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APPLIED ARCHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631

DR. ANNE NICHOLS

SPRING 2018

twenty one

steel construction

and designSteel Construction 1

Lecture 21

Applied Architectural Structures

ARCH 631

lecture

http://nisee.berkeley.edu/godden

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Steel

• cast iron – wrought iron - steel

• cables

• columns

• beams

• trusses

• frames

Steel Construction 2

Lecture 21

Architectural Structures III

ARCH 631



Lecture 20


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Steel Construction

• standard rolled shapes

• open web joists

• plate girders

• decking

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Steel Construction

• welding

• bolts


Lecture 21


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AISC Education

2


Lecture 20


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Steel Construction

• fire proofing

– cementicious spray

– encasement in gypsum

– intumescent – expands

with heat

– sprinkler system


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Steel Materials

• high strength to

weight ratio

• ductile

• beam size

often limited by

deflection

• column size

limited by

slenderness

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Steel Beams

• types

– manufactured shapes

castellated



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Steel Beams

• types

– wide flange

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Steel Beams

• types

– open web joists

(manufactured

trusses)


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Steel Beams

• types (more)

– plate girder

– decking

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Steel Beams


Lecture 21


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Steel Beams

• lateral stability - bracing

• local buckling - stiffen

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Local Buckling

• steel I beams

• flange

– buckle in

direction of

smaller radius

of gyration

• web

– force

– “crippling”


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Local Buckling

• flange

• web


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Shear in Web

• panels in plate girders or webs with large shear

• buckling in compression direction

• add stiffeners


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Steel Beams

• end conditions

• a) away from

connection - full

section effective

• b) high shear –

only web

effective

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Steel Beams

• end conditions

• c) bolt holes –

less material

• d) local web

buckling


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Steel Beams

• bearing

– provide

adequate

area

– prevent

local yield

of flange

and web


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Steel Beams

• connections

– welds

– bolts


Lecture 20


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Steel Design – Open Web Joists

• SJI: www.steeljoist.com

• Vulcraft: www.vulcraft.com

– K Series (Standard)

• 8-30” deep, spans 8-50 ft

– LH Series (Long span)

• 18-48” deep, spans 25-96 ft

– DLH (Deep Long Spans)

• 52-72” deep, spans 89-144 ft

– SLH (Long spans with high strength steel)

• pitched top chord

• 80-120” deep, spans 111-240 ft

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load for live load

deflection limit in RED

total in BLACK

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load for live load deflection

limit (L/360) in RED

total in BLACK



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Lecture 20


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Steel Beam Design

• American Institute of Steel Construction

– steel grades

• ASTM A36 – carbon

– plates, angles

– Fy = 36 ksi & Fu = 58 ksi

• ASTM A572 – high strength low-alloy

– some beams

– Fy = 60 ksi & Fu = 75 ksi

• ASTM A992 – for building framing

– most beams

– Fy = 50 ksi & Fu = 65 ksi

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Steel Beam Design

• AISC: 14th ed.

– combined ASD & LRFD

in one volume in 2005


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• ASD

– bending (braced) = 1.67

– bending (unbraced*) = 1.67

– shear = 1.5 or 1.67

– shear (bolts & welds) = 2.00

– shear (welds) = 2.00

* flanges in compression can buckle

Ra ≤Rn

Unified Steel Design


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Unified Steel Design

• braced vs.

unbraced


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LRFD Steel Beam Design

• limit state is yielding all across section

• outside elastic range

• load factors & resistance factors


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E

1

fy = 50ksi

001724.0y

f


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Load Types

• D = dead load

• L = live load

• Lr = live roof load

• W = wind load

• S = snow load

• E = earthquake load

• R = rainwater load or ice water load

• T = effect of material & temperature

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LRFD Load Combinations


Lecture 21


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ASCE-7

(2010)

• 1.4D

• 1.2D + 1.6L + 0.5(Lr or S or R)

• 1.2D + 1.6(Lr or S or R) + (L or 0.5W)

• 1.2D + 1.0W + L + 0.5(Lr or S or R)

• 1.2D + 1.0E + L + 0.2S

• 0.9D + 1.0W

• 0.9D + 1.0E• F has same factor as D in 1-5 and 7

• H adds with 1.6 and resists with 0.9 (permanent)


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Pure Flexure

Mu - maximum moment

b - resistance factor for bending = 0.9

Mn - nominal moment (ultimate capacity)

Fy - yield strength of the steel

Z - plastic section modulus*

ZFMMR ynbuii 9.0


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Internal Moments - at yield

yyy fbh

fc

IM

6

2

• material hasn’t failed

y

2

y

2

f3

bc2f

6

c2b


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Internal Moments - ALL at yield

• all parts reach yield

• plastic hinge forms

• ultimate moment

• Atension = Acompression

yyp MfbcM 232

E

1

y = 50ksi

y = 0.001724

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n.a. of Section at Plastic Hinge

• cannot guarantee at

centroid

• fy·A1= fy·A2• moment found from

yield stress times

moment area

1.

p y y i in a

M f A d f A d


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Plastic Hinge Development


Lecture 20


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Plastic Hinge Examples

• stability can be effected


Lecture 20


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Plastic Section Modulus

• shape factor, k

= 3/2 for a rectangle

1.1 for an I

• plastic modulus, Z

y

p

M

Mk

y

p

f

MZ

SZk

10


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Shear

Vu - maximum shear

v - resistance factor for shear = 1.0

Vn - nominal shear

Fyw - yield strength of the steel in the web

Aw - area of the web = twd

iRi = Vu ≤ vVn = 1.0(0.6FywAw)

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Flexure Design

• limit states for beam failure

1. yielding

2. lateral-torsional buckling*

3. flange local buckling

4. web local buckling

• minimum Mn governs


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1.76y

p y

FL r

E

i i u b nR M M

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Compact Sections

• plastic moment can form before any

buckling

• criteria

–

– and


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0.382

f

f y

b E

t F

3.76c

w y

h E

t F

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Cb = modification factor

Mmax - |max moment|, unbraced segment

MA - |moment|, 1/4 point

MB = |moment|, center point

MC = |moment|, 3/4 point

Lateral Torsional Buckling


Lecture 21


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pbn MCM moment based onlateral buckling

CBAmax

maxb

MMMM.

M.C

34352

512

11

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Beam Design Charts


Lecture 21


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Lecture 20


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Deflection Limits

• based on service condition

• no “impairment” to serviceability

• avoid ponding

• L/360 due to live load for beams &

girders supporting plaster (service)

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Steel Arches and Frames

• solid sections

or open web


Lecture 21


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Lecture 20


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Steel Shell and Cable Structures

12


Lecture 20


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Approximate Depths

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Unified Column Design

• limit states for failure

1. yielding

2. buckling

Fe – elastic buckling stress (Euler)


Lecture 21


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ncu PP gcrnc AFP. 900

ye

y

F.ForF

E.

r

KL440714

ye

y

F.ForF

E.

r

KL440714

na

PP

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Unified Column Design

• Pn = FcrAg– for

– for

– where


Lecture 21


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yF

E.

r

KL714 y

F

F

cr F.Fe

y

6580

ecr F.F 8770

22

rKL

EFe

yF

E.

r

KL714

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Procedure for Analysis

1. calculate KL/r• biggest of KL/r with respect to x axes and y axis

2. find Fcr from appropriate equation• tables are available

3. compute Pn = FcrAg• or find fc = Pa/A or Pu/A

4. is Pa Pn/ or Pu Pn?• yes: ok

• no: insufficient capacity and no good


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13

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1. guess a size (pick a section)

2. calculate KL/r• biggest of KL/r with respect to x axes and y axis

3. find Fcr from appropriate equations• or find a table

4. compute Pn = FcrAg• or find fc = Pa/A or Pu/A

Procedure for Design


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Procedure for Design (cont’d)

5. is Pa Pn/ or Pu Pn?• yes: ok

• no: pick a bigger section and go back to step 2.

6. check design efficiency

• percentage of stress =

• if between 90-100%: good

• if < 90%: pick a smaller section and

go back to step 2.


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%P

P

c

r 100

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Column Tables


Lecture 21


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Beam-Column Design

• moment magnification (P-)

Cm – modification factor for end conditions

= 0.6 – 0.4(M1/M2) or

0.85 restrained, 1.00 unrestrained

Pe1 – Euler buckling strength


Lecture 21


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factoredmaxu MBM 1 )PP(

CB

eu

m

1

11

22

1

rKl

EAPe

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Beam-Column Design

• LRFD (Unified) Steel

– for

– for

Pr is required, Pc is capacity

c - resistance factor for compression = 0.9

b - resistance factor for bending = 0.9


Lecture 21


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019

8.

M

M

M

M

P

P

nyb

uy

nxb

ux

nc

u

:.P

P

c

r 20

012

.M

M

M

M

P

P

nyb

uy

nxb

ux

nc

u

:.P

P

c

r 20


Lecture 20


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Construction Supervision

• proper grade material

– high strength bolts

• quality welds

• proper bolted

conditions (ex. sc)

• fabrication and erection

of steel frame

connection details

decking plate girders 1 Lecture 21 ARCH 631 standard...

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