twenty one lecture

F2018abnSteel Construction 1

Lecture 21

Applied Architectural Structures

ARCH 631

twenty one

steel construction

and design

lecture

APPLIED ARCHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS

ARCH 631

DR. ANNE NICHOLS

FALL 2018

http://nisee.berkeley.edu/godden


Lecture 21


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Steel

• cast iron – wrought iron - steel

• cables

• columns

• beams

• trusses

• frames



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Steel Construction

• standard rolled shapes

• open web joists

• plate girders

• decking


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Steel Construction

• welding

• bolts

AISC Education


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Steel Construction

• fire proofing

– cementitious 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


Lecture 21


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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



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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


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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

http://www.steeljoist.com/

http://www.vulcraft.com/


Lecture 21


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Steel Design – Open Web Joists ASD

load for live load

deflection limit in RED

total in BLACK

F2018abn

load for live load deflection

limit (L/360) in RED

total in BLACK

Steel Design – Open Web Joists

Steel Construction 22

Lecture 21


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Lecture 21


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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-- ASTM A913• some columns

• Grade 65 and 70


Lecture 21


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Steel Beam Design

• AISC: 14th ed.

– combined ASD & LRFD

in one volume in 2005

F2018abn

• 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

na

RR

Ω

Unified Steel Design


Lecture 21


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Lecture 21


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Unified Steel Design

• braced vs.

unbraced


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E

1

fy = 50ksi

001724.0y

f

LRFD Steel Beam Design

• limit state is yielding all across section

• outside elastic range

• load factors & resistance factors


Lecture 21


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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


Lecture 21


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LRFD Load Combinations 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)

F2018abn

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*

0.9i i u b n yR M M F Z


Lecture 21


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Pure Flexure

F2018abn

2

6y y y

I bhM f f

c

2 2(2 ) 2

6 3y y

b c bcf f


Lecture 21


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Internal Moments - at yield

• material hasn’t failed

F2018abn

2 32p y yM bc f M


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Internal Moments - ALL at yield

• all parts reach yield

• plastic hinge forms

• ultimate moment

• Atension = Acompression

E

1

y = 50ksi

y = 0.001724

F2018abn

1.

p y y i in a

M f A d f A d


Lecture 21


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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


Lecture 21


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Plastic Hinge Development


Lecture 21


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Plastic Hinge Examples

• stability can be effected

F2018abn

p

y

Mk

M

ZkS

p

y

MZ

f

• shape factor, k

= 3/2 for a rectangle

1.1 for an I

• plastic modulus, Z


Lecture 21


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Plastic Section Modulus

F2018abn

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


Lecture 21


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LRFD – Shear (compact shapes)

1.0(0.6 )i i u v n yw wR V V F A

F2018abn

i i u b nR M M

1.76y

p y

FL r

E

• limit states for beam failure

1. yielding

2. lateral-torsional buckling*

3. flange local buckling

4. web local buckling

• minimum Mn governs


Lecture 21


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Flexure Design

F2018abn

• plastic moment can form before any

buckling

• criteria

–

– and

0.382

f

f y

b E

t F

3.76c

w y

h E

t F

Compact Sections


Lecture 21


ARCH 631


Lecture 21


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Beam Design Charts


Lecture 21


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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)


Lecture 21


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Steel Arches and Frames

• solid sections

or open web



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Steel Shell and Cable Structures


Lecture 21


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Approximate Depths

F2018abn

• limit states for failure

1. yielding

2. buckling

Fe – elastic buckling stress (Euler)

0.90c n cr gP F A

na

PP

u c nP P


Lecture 21


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Unified Column Design

4.71 2.25yc

y e

FL Eor

r F F

4.71 2.25yc

y e

FL Eor

r F F

F2018abn

• Pn = FcrAg

– for

– for

– where


Lecture 21


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Unified Column Design

4.71 0.658

y

e

F

Fccr y

y

L EF F

r F

4.71 0.877ccr e

y

L EF F

r F

2

2e

c

EF

Lr


Lecture 21


ARCH 631

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


Lecture 21


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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

F2018abn

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.

100%r

c

P

P


Lecture 21


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Procedure for Design (cont’d)


Lecture 21


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Column Tables

F2018abn

• moment magnification (P-)

Cm – modification factor for end conditions

= 0.6 – 0.4(M1/M2) or

0.85 restrained, 1.00 unrestrained

Lc1 – effective length in plane of bending

Pe1 – Euler buckling strength

- 1.00 (LRFD), 1.60(ASD)


Lecture 21


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Beam-Column Design

m1

u e1

CB

1 ( P / P )

1r ntM B M

2

1 2

1

e

c

EIP

L


Lecture 21


ARCH 631

Beam-Column Design

• LRFD (Unified) Steel

– for

– for

Pr is required, Pc is capacity

Mrx is required, Mcx is capacity

Mry is required, Mcy is capacity

80.2 : 1.0

9

ryrxr r

c c cx cy

MMP P

P P M M

0.2 : 1.02

ryrxr r

c c cx cy

MMP P

P P M M


Lecture 21


ARCH 631

Construction Supervision

• proper grade material

– high strength bolts

• quality welds

• proper bolted

conditions (ex. sc)

• fabrication and erection

of steel frame

connection details

www.architecture.uwaterloo.ca

twenty one lecture

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