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E LEMENTS OF A RCHITECTURAL S TRUCTURES : Steel Beam Design F ORM, B EHAVIOR, AND D ESIGN ARCH 614 American Institute of Steel Construction D R. A NNE N ICHOLS Manual of Steel Construction S PRING 2019 ASD & LRFD lecture

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S2009abn Steel Beams 1 Lecture 16 Elements of Architectural Structures ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 614

  • DR. ANNE NICHOLS

SPRING 2019 lecture

sixteen

steel construction:

materials & beams

S2007abn Steel Beams 2 Lecture 16 Elements of Architectural Structures ARCH 614

Steel Beam Design

  • American Institute of Steel Construction

– Manual of Steel Construction – ASD & LRFD – combined in 2005

S2007abn Steel Beams 3 Lecture 16 Elements of Architectural Structures ARCH 614

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
  • - ASTM A913
  • some columns
  • Grade 65 and 70

S2007abn Steel Beams 4 Lecture 16 Elements of Architectural Structures ARCH 614

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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Steel Beams 5 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Structural Steel

  • standard rolled shapes (W, C, L, T)
  • open web joists
  • plate girders
  • decking

S2007abn Steel Beams 6 Lecture 16 Elements of Architectural Structures ARCH 614

Steel Construction

  • welding
  • bolts

http://courses.civil.ualberta.ca S2012abn

Unified Steel Design

  • 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

Steel Beams 7 Lecture 16 Elements of Architectural Structures ARCH 614

Ra ≤ Rn

S2012abn

Unified Steel Design

  • braced vs.

unbraced

Steel Beams 8 Lecture 16 Elements of Architectural Structures ARCH 614

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Steel Beams 9 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

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

n L L D D u

R R R R      

Steel Beams 10 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

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 

S2007abn Steel Beams 11 Lecture 16 Elements of Architectural Structures ARCH 614

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)

Steel Beams 12 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

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 13 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Steel Beams

  • lateral stability - bracing
  • local buckling – stiffen, or bigger Iy

Steel Beams 14 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Local Buckling

  • steel I beams
  • flange

– buckle in direction of smaller radius

  • f gyration
  • web

– force – “crippling”

Steel Beams 15 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Local Buckling

  • flange
  • web

Steel Beams 16 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Shear in Web

  • panels in plate girders or webs with large shear
  • buckling in compression direction
  • add stiffeners
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S2010abn

Shear in Web

  • plate girders and stiffeners

Steel Beams 17 Lecture 16 Elements of Architectural Structures ARCH 614 http:// nisee.berkeley.edu/godden S2010abn

Steel Beams

  • bearing

– provide adequate area – prevent local yield

  • f flange

and web

Steel Beams 18 Lecture 16 Elements of Architectural Structures ARCH 614 Steel Beams 18 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

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*

Z F M M R

y n b u i i

9 .      

Steel Beams 19 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Internal Moments - at yield

y y y

f bh f c I M 6

2

 

  • material hasn’t failed

 

y y

f bc f c b 3 2 6 2

2 2

 

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Steel Beams 20 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Internal Moments - ALL at yield

  • all parts reach yield
  • plastic hinge forms
  • ultimate moment
  • Atension = Acompression

y y p

M f bc M 2 3

2

 

E 1 y = 50ksi y = 0.001724   Steel Beams 21 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

n.a. of Section at Plastic Hinge

  • cannot guarantee at

centroid

  • fy·A1= fy·A2
  • moment found from

yield stress times moment area

i i a n y y p

d A f d A f M

. 1

  

Steel Beams 22 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Plastic Hinge Development

Steel Beams 23 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Plastic Hinge Examples

  • stability can be effected
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Steel Beams 24 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Plastic Section Modulus

  • shape factor, k

= 3/2 for a rectangle  1.1 for an I

  • plastic modulus, Z

y p

M M k 

y p

f M Z  S Z k 

S2007abn Steel Beams 25 Lecture 16 Elements of Architectural Structures ARCH 614

LRFD - Shear

Vu - maximum shear v - resistance factor for shear = 0.9 Vn - nominal shear Fyw - yield strength of the steel in the web Aw - area of the web = twd

) A F . ( . V V R

w yw n v u i i

6 1      

S2007abn Steel Beams 26 Lecture 16 Elements of Architectural Structures ARCH 614

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

n b u i i

M M R     

E F r . L

y y p

76 1 

S2012abn

Compact Sections

  • plastic moment can form before any

buckling

  • criteria

– – and

Steel Beams 28 Lecture 16 Elements of Architectural Structures ARCH 614

0.38 2

f f y

b E t F  3.76

c w y

h E t F 

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Steel Beams 28 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

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

C B A b

M M M M M C 3 4 2 5 . 2 5 . 12

max max

   

 

p b n

M C M  

moment based on lateral buckling

S2012abn

Beam Design Charts

Steel Beams 30 Lecture 16 Elements of Architectural Structures ARCH 614 Steel Beams 30 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

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

S2009abn Steel Beams 31 Lecture 16 Elements of Architectural Structures ARCH 614

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

 

b b

F f 

) M M (

n b u

 

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S2010abn

Beam Charts by Zx (pg. 250)

Steel Beams 33 Lecture 16 Elements of Architectural Structures ARCH 614 S2009abn Steel Beams 32 Lecture 16 Elements of Architectural Structures ARCH 614

Beam Design (revisited)

Unbraced roof trusses were blown down in 1999 at this project in Moscow, Idaho.

Photo: Ken Carper

4*. Include self weight for Mmax

– it’s dead load – and repeat 3 & 4 if necessary

  • 5. Consider lateral stability

S2007abn Steel Beams 33 Lecture 16 Elements of Architectural Structures ARCH 614

Beam Design (revisited)

  • 6. Evaluate shear - horizontal
  • r
  • W and rectangles
  • thin walled sections

web v

A V A V f  

2 3

max

Ib VQ fv 

max

 

v v

F f 

) (

n v u

V V  

Steel Beams 34 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

p p

F A P f   Beam Design (revisited)

  • 7. Provide adequate bearing

area at supports

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Steel Beams 35 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Beam Design (revisited)

  • 8. Evaluate torsion
  • circular cross section
  • rectangular

J T fv  

2 1ab

c T fv 

 

v v

F f 

Steel Beams 36 Lecture 16 Elements of Architectural Structures ARCH 614 S2007abn

Beam Design (revisited)

  • 9. Evaluate deflections – NO LOAD FACTORS

allowable actual

x y     ) (

max

S2007abn Steel Beams 37 Lecture 16 Elements of Architectural Structures ARCH 614

Load Tables & Equivalent Load

  • uniformly distributed loads
  • equivalent “w”

8

2 max

L w M

equivalent

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

S2009abn TOPIC 38 Elements of Architectural Structures ARCH 614

Steel Arches and Frames

  • solid sections
  • r open web

http:// nisee.berkeley.edu/godden

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TOPIC 39 Elements of Architectural Structures ARCH 614 S2009abn

Steel Shell and Cable Structures

TOPIC 40 Elements of Architectural Structures ARCH 614 S2009abn

Approximate Depths