ARCHITECTURAL S FORM, B DESIGN ARCH 331 DR...

1

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eighteen

steel construction:

materials & beams

ARCHITECTURAL STRUCTURES:

FORM, BEHAVIOR, AND DESIGN

ARCH 331

DR. ANNE NICHOLS

SPRING 2015

Steel Beams 1Lecture 18

Architectural StructuresARCH 331

lecture

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Lecture 18

Foundations Structures

ARCH 331

Steel Beam Design

• American Institute of Steel Construction

– Manual of Steel Construction

– ASD & LRFD

– combined in 2005

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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

2

Steel Beams 5

Lecture 18


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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

Steel Beams 6

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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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Foundations Structures ARCH 331

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



Unified Steel Design

• ASD

– bending (braced) Ω = 1.67

– bending (unbraced*) Ω = 1.67

– shear Ω = 1.5 or 1.67

– shear (bolts & welds) Ω = 2.00

– shear (welds) Ω = 2.00

* flanges in compression can buckle

Ra ≤Rn

Ω



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

φ - resistance factor

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

nLLDDu RRRR φγγ ≤+=

4



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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

εy = 0.001724

f

ε



LRFD Load Combinations

• 1.4(D + F)

• 1.2(D + F + T)+ 1.6(L + H)+ 0.5(Lr or S or R)

• 1.2D + 1.6(Lr or S or R) + (L or 0.8W)

• 1.2D + 1.6W + L + 0.5(Lr or S or R)

• 1.2D + 1.0E + L + 0.2S

• 0.9D + 1.6W + 1.6H

• 0.9D + 1.0E + 1.6H

ASCE-7

(2005)

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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

5

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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


Lecture 18


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Shear in Web

• plate girders and stiffeners

http:// nisee.berkeley.edu/godden

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Steel Beams

• bearing

– provide

adequatearea

– prevent

local yieldof flange

and web

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LRFD - Flexure

Mu - maximum moment

φb - 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=≤=Σ φγ

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Internal Moments - at yield

yyy fbh

fc

IM

6

2

==

• material hasn’t failed

( )yy f

bcf

cb

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

yyp MfbcM2

32 ==

E

1

σy = 50ksi

εy = 0.001724

σ

ε

7

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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

iian

yyp dAfdAfM.

1Σ==

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Plastic Hinge Development

Steel Beams 27

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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

M

Mk =

y

p

f

MZ =

SZk =

8



LRFD – Shear (compact shapes)

Vu - maximum shear

φv - resistance factor for shear = 1.0

Vn - nominal shear

Fyw - yield strength of the steel in the web

Aw - area of the web = twd

ΣγiRi = Vu ≤ φvVn = 1.0(0.6FywAw)



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

nbuii MMR φγ ≤=Σ

1.76

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3.76c

w y

h E

t F≤

0.382

f

f y

b E

t F≤

Steel Beams 31

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Compact Sections

• plastic moment can form before any buckling

• criteria

–

– and



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

CBAmax

maxb

MMMM.

M.C

34352

512

+++=

[ ] pbn MCM ≤= moment based on

lateral buckling

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Beam Design Charts


Foundations StructuresARCH 331

Steel Beams 34

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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 (Ω, φ)

2. Draw V & M, finding Mmax

3. Calculate Zreq’d

4. Choose (economical) section from

section or beam capacity charts



)MM( nbu φ≤(Ma ≤ Mn/Ω)

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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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6. Evaluate shear stresses - horizontal

• or

• rectangles and W’s

• general



web

maxvA

V

A

Vf ≈=−

2

3

Ib

VQf maxv =−

)VV( nvu φ≤(Va ≤ Vn/Ω)

Vn = 0.6 FywAw




7. Provide adequate bearing

area at supports (Pa ≤ Pn/Ω)

(Pu ≤ φPn)

11

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8. Evaluate torsion

• circular cross section

• rectangular

J

Tfv

ρ=

2

1abc

Tfv =

( )vv Ff ≤

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9. Evaluate deflections – NO LOAD FACTORS

allowableactualxy ∆≤∆=)(max


Lecture 18

Architectural Structures

ARCH 331

Load Tables & Equivalent Load

• uniformly distributed loads

• equivalent “w”8

2

max

LwM

equivalent=

load for live load deflection limit in RED, total in BLACK



Sloped Beams

• stairs & roofs

• projected live load

• dead load over length

• perpendicular load to beam:

• equivalent distributed load:

α

αcosww ⋅=⊥

αcos

w

.adjw =

12


Lecture 18


ARCH 331

Steel Arches and Frames

• solid sections or open web

http:// nisee.berkeley.edu/godden

Steel Beams 45

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Steel Shell and Cable Structures

Steel Beams 46

Lecture 18


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Approximate Depths

ARCHITECTURAL S FORM, B DESIGN ARCH 331 DR...

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