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A RCHITECTURAL S TRUCTURES : Steel Beam Design F ORM, B EHAVIOR, AND D ESIGN ARCH 331 American Institute of Steel Construction D R. A NNE N ICHOLS Manual of Steel Construction S PRING 2018 ASD & LRFD lecture eighteen combined

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SLIDE 1

1

F2009abn

eighteen

steel construction:

materials & beams

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 331

  • DR. ANNE NICHOLS

SPRING 2018

Steel Beams 1 Lecture 18 Architectural Structures ARCH 331

lecture

F2008abn Steel Beams 2 Lecture 18 Foundations Structures ARCH 331

Steel Beam Design

  • American Institute of Steel Construction

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

Steel Beams 3 Lecture 18 Foundations Structures ARCH 331 F2008abn

Steel Materials

  • smelt iron ore
  • add alloying elements
  • heat treatments
  • iron, carbon
  • microstructure

AISC

A36 steel, JOM 1998

Steel Beams 4 Lecture 18 Foundations Structures ARCH 331 F2008abn

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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SLIDE 2

2

Steel Beams 5 Lecture 18 Foundations Structures ARCH 331 F2008abn

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 Lecture 18 Foundations Structures ARCH 331 F2008abn

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

Steel Beams 7 Lecture 18 Foundations Structures ARCH 331 F2008abn

Structural Steel

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

F2008abn Steel Beams 8 Lecture 18 Foundations Structures ARCH 331

Steel Construction

  • welding
  • bolts

http://courses.civil.ualberta.ca

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SLIDE 3

3

Steel Beams 9 Lecture 18 Foundations Structures ARCH 331 F2008abn

Steel Construction

  • fire proofing

– cementicious spray – encasement in gypsum – intumescent – expands with heat – sprinkler system

F2008abn Steel Beams 10 Lecture 18 Foundations Structures ARCH 331

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

Ra ≤ Rn

F2008abn Steel Beams 11 Lecture 18 Foundations Structures ARCH 331

Unified Steel Design

  • braced vs.

unbraced

Steel Beams 12 Lecture 18 Foundations Structures ARCH 331 F2008abn

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      

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SLIDE 4

4

Steel Beams 13 Lecture 18 Foundations Structures ARCH 331 F2008abn

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 

F2008abn Steel Beams 14 Lecture 18 Foundations Structures ARCH 331

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)

Steel Beams 15 Lecture 18 Foundations Structures ARCH 331 F2008abn

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)

+ = + =

Steel Beams 16 Lecture 18 Foundations Structures ARCH 331 F2008abn

Steel Beams

  • lateral stability - bracing
  • local buckling – stiffen, or bigger Iy
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SLIDE 5

5

Steel Beams 17 Lecture 18 Foundations Structures ARCH 331 F2008abn

Local Buckling

  • steel I beams
  • flange

– buckle in direction of smaller radius

  • f gyration
  • web

– force – “crippling”

Steel Beams 18 Lecture 18 Foundations Structures ARCH 331 F2008abn

Local Buckling

  • flange
  • web

Steel Beams 19 Lecture 18 Foundations Structures ARCH 331 F2008abn

Shear in Web

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

F2008abn Steel Beams 20 Lecture 18 Foundations Structures ARCH 331

Shear in Web

  • plate girders and stiffeners

http:// nisee.berkeley.edu/godden

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SLIDE 6

6

Steel Beams 21 Lecture 18 Foundations Structures ARCH 331 F2008abn

Steel Beams

  • bearing

– provide adequate area – prevent local yield

  • f flange

and web

Steel Beams 22 Lecture 18 Foundations Structures ARCH 331 F2008abn

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 23 Lecture 18 Foundations Structures ARCH 331 F2008abn

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

 

Steel Beams 24 Lecture 18 Foundations Structures ARCH 331 F2008abn

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  

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SLIDE 7

7

Steel Beams 25 Lecture 18 Foundations Structures ARCH 331 F2008abn

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 26 Lecture 18 Foundations Structures ARCH 331 F2008abn

Plastic Hinge Development

Steel Beams 27 Lecture 18 Foundations Structures ARCH 331 F2008abn

Plastic Hinge Examples

  • stability can be effected

Steel Beams 28 Lecture 18 Foundations Structures ARCH 331 F2008abn

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 

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SLIDE 8

8

F2008abn Steel Beams 29 Lecture 18 Foundations Structures ARCH 331

LRFD – Shear (compact shapes)

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)

F2008abn Steel Beams 30 Lecture 18 Foundations Structures ARCH 331

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     

F2008abn

3.76

c w y

h E t F  0.38 2

f f y

b E t F 

Steel Beams 31 Lecture 18 Foundations Structures ARCH 331

Compact Sections

  • plastic moment can form before any

buckling

  • criteria

– – and

F2008abn Steel Beams 32 Lecture 18 Foundations Structures ARCH 331

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 max max b

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

 

p b n

M C M  

moment based on lateral buckling

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SLIDE 9

9

Su2011abn

Beam Design Charts

Steel Beams 33 Lecture 15 Foundations Structures ARCH 331 Steel Beams 34 Lecture 18 Foundations Structures ARCH 331 F2008abn

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

Su2011abn

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

Steel Beams 35 Lecture 15 Foundations Structures ARCH 331

) M M (

n b u

 

(Ma ≤ Mn/)

F2008abn Steel Beams 36 Lecture 18 Foundations Structures ARCH 331

Beam Charts by Sx (Appendix)

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SLIDE 10

10

F2011abn

Beam Charts by Zx (Appendix)

Steel Beams 37 Lecture 18 Foundations Structures ARCH 331 Su2011abn

Beam Design (revisited)

4*. Include self weight for Mmax

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

  • 5. Consider lateral stability

Steel Beams 37 Lecture 15 Foundations Structures ARCH 331

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

Photo: Ken Carper

Su2011abn

Beam Design (revisited)

  • 6. Evaluate shear - horizontal
  • r
  • rectangles and W’s
  • general

Steel Beams 38 Lecture 15 Foundations Structures ARCH 331

web max v

A V A V f  

2 3 Ib VQ f

max v

) V V (

n v u

 

(V

a ≤ Vn/)

Vn = 0.6 FywAw

F2008abn Steel Beams 39 Lecture 18 Foundations Structures ARCH 331

Beam Design (revisited)

  • 7. Provide adequate bearing

area at supports

(Pa ≤ Pn/) (Pu ≤ Pn)

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SLIDE 11

11

Steel Beams 40 Lecture 18 Foundations Structures ARCH 331 F2008abn

Beam Design (revisited)

  • 8. Evaluate torsion
  • circular cross section
  • rectangular

J T fv  

2 1ab

c T fv 

 

v v

F f 

Steel Beams 41 Lecture 18 Foundations Structures ARCH 331 F2008abn

Beam Design (revisited)

  • 9. Evaluate deflections – NO LOAD FACTORS

allowable actual

x y     ) (

max

F2008abn Steel Beams 42 Lecture 18 Architectural Structures ARCH 331

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

F2008abn Steel Beams 43 Lecture 18 Foundations Structures ARCH 331

Sloped Beams

  • stairs & roofs
  • projected live load
  • dead load over length
  • perpendicular load to beam:
  • equivalent distributed load:



 cos w w  

 cos w . adj w 

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SLIDE 12

12

F2008abn Steel Beams 44 Lecture 18 Foundations Structures ARCH 331

Steel Arches and Frames

  • solid sections
  • r open web

http:// nisee.berkeley.edu/godden Steel Beams 45 Lecture 18 Foundations Structures ARCH 331 F2008abn

Steel Shell and Cable Structures

Steel Beams 46 Lecture 18 Foundations Structures ARCH 331 F2008abn

Approximate Depths