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Lecture 15

Architectural Structures

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ARCHITECTURAL STRUCTURES:

FORM, BEHAVIOR, AND DESIGN

ARCH 331

DR. ANNE NICHOLS

SUMMER 2013

lecture

fifteen

steel construction: materials & beams

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Steel Beam Design

• American Institute of Steel Construction

– Manual of Steel Construction

– ASD & LRFD

– combined in 13th ed.

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Steel Materials

• smelt iron ore

• add alloying elements

• heat treatments

• iron, carbon

• microstructure

AISC

A36 steel, JOM 1998

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Steel Materials

• cast into billets

• hot rolled

• cold formed

• residual stress

• corrosion-resistant

“weathering” steels

• stainless Cold Formed

Hot Rolled

AISC

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Steel Materials

• 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 Properties

• high strength to weight ratio

• elastic limit – yield (Fy)

• inelastic – plastic

• ultimate strength (Fu)

• ductile

• strength sensitive

to temperature

• can corrode

• fatigue

Winnepeg DOT

strain hardening

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Structural Steel

• standard rolled shapes (W, C, L, T)

• open web joists

• plate girders

• decking

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Steel Construction

• welding

• bolts

http://courses.civil.ualberta.ca

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Steel Construction

• fire proofing

– cementicious spray

– encasement in gypsum

– intumescent – expands

with heat

– sprinkler system

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Unified Steel Design

• ASD

– bending (braced) = 1.67

– bending (unbraced*) = 1.67

– shear = 1.67

– shear (bolts & welds) = 2.00

– shear (welds) = 2.00

* flanges in compression can buckle

n

a

RR

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Unified Steel Design

• braced vs.

unbraced

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LRFD

• loads on structures are

– not constant

– can be more influential on failure

– happen more or less often

– UNCERTAINTY

- resistance factor

- load factor for (D)ead & (L)ive load

nLLDDu RRRR

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LRFD Steel Beam Design

• limit state is yielding all across section

• outside elastic range

• load factors & resistance factors

E

1

fy = 50ksi

y = 0.001724

f

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LRFD Load Combinations

• 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)

ASCE-7

(2010)

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Beam Design Criteria (revisited) • strength design

– bending stresses predominate

– shear stresses occur

• serviceability – limit deflection

– stability

• superpositioning – use of beam charts

– elastic range only!

– “add” moment diagrams

– “add” deflection CURVES (not maximums)

+

=

+

=

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Steel Beams

• lateral stability - bracing

• local buckling – stiffen, or bigger Iy

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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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Shear in Web

• plate girders and stiffeners

http:// nisee.berkeley.edu/godden

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Steel Beams

• bearing

– provide

adequate

area

– prevent

local yield

of flange

and web

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LRFD - 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*

ZF.MMR ynbuii 90

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Internal Moments - at yield

• material hasn’t failed

yyy fbh

fc

IM

6

2

yy fbc

f)c(b

3

2

6

2 22

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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

yyp MfbcM2

32

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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

iia.n

yyp dAfdAfM 1

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Plastic Hinge Development

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Plastic Hinge Examples

• stability can be effected

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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

f

MZ

SZk

y

p

M

Mk

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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

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LRFD – Shear (compact shapes)

)AF.(.VVR wywnvuii 6001

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LRFD - Flexure Design

• limit states for beam failure

1. yielding

2. lateral-torsional buckling*

3. flange local buckling

4. web local buckling

• minimum Mn governs

E

Fr.L

y

yp 761

nbuii MMR

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• plastic moment can form before any

buckling

• criteria

–

– and

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Compact Sections

yw

c

F

E.

t

h763

yf

f

F

E.

t

b380

2

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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

moment based on

lateral buckling

CBAmax

maxb

MMMM.

M.C

34252

512

pbn MCM

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Beam Design Charts

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Charts & Deflections

• beam charts

– solid line is most economical

– dashed indicates there is another more

economical section

– self weight is NOT included in Mn

• deflections

– no factors are applied to the loads

– often governs the design

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Design Procedure (revisited)

1. Know unbraced length, material,

design method (, )

2. Draw V & M, finding Mmax

3. Calculate Zreq’d

4. Choose (economical) section from

section or beam capacity charts

(Ma ≤ Mn/)

)MM( nbu

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Beam Charts by Sx (Appendix A)

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Beam Charts by Zx

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Beam Design (revisited)

4*. Include self weight for Mmax

– it’s dead load

– and repeat 3 & 4

if necessary

5. Consider lateral stability

Unbraced roof trusses

were blown down in

1999 at this project in

Moscow, Idaho.

Photo: Ken Carper

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Beam Design (revisited)

6. Evaluate shear stresses - horizontal

• or

• rectangles and W’s

• general

w eb

vA

V

A

Vf

2

3max

Ib

V Qf v max

(Va ≤ Vn/)

Vn = 0.6 FywAw

)VV( nvu

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Beam Design (revisited)

7. Provide adequate bearing

area at supports

(Pa ≤ Pn/)

(Pu ≤ Pn)

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Beam Design (revisited)

8. Evaluate torsion

• circular cross section

• rectangular

J

Tf v

2

1abc

Tf v

vv Ff

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Beam Design (revisited)

9. Evaluate deflections – NO LOAD FACTORS

allowableactualmax )x(y

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Load Tables & Equivalent Load

• uniformly distributed loads

• equivalent “w” 8

2

max

LwM

eq u iva l en t

load for live load deflection limit

in RED, total in BLACK

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Sloped Beams

• stairs & roofs

• projected live load

• dead load over length

• perpendicular load to beam:

• equivalent distributed load:

cos

ww .adj

cosww

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Steel Arches and Frames

• solid sections

or open web

http:// nisee.berkeley.edu/godden

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Steel Shell and Cable Structures

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Approximate Depths