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sixteen steel construction: materials & beams Steel Beams 1 - - PowerPoint PPT Presentation

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E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS S PRING 2019 lecture sixteen steel construction: materials & beams Steel Beams 1 Elements of Architectural Structures S2019abn Lecture

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SLIDE 1

S2019abn 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

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SLIDE 2

S2019abn 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

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SLIDE 3

S2019abn 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
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SLIDE 4

S2019abn 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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SLIDE 5

S2019abn Steel Beams 5 Lecture 16 Elements of Architectural Structures ARCH 614

Structural Steel

  • standard rolled shapes (W, C, L, T)
  • open web joists
  • plate girders
  • decking
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SLIDE 6

S2019abn Steel Beams 6 Lecture 16 Elements of Architectural Structures ARCH 614

Steel Construction

  • welding
  • bolts

http://courses.civil.ualberta.ca

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SLIDE 7

S2019abn Steel Beams 7 Lecture 16

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

Elements of Architectural Structures ARCH 614

Ω R R

n a 

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SLIDE 8

S2019abn Steel Beams 8 Lecture 16 Elements of Architectural Structures ARCH 614

Unified Steel Design

  • braced vs.

unbraced

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SLIDE 9

S2019abn Steel Beams 9 Lecture 16 Elements of Architectural Structures ARCH 614

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 10

S2019abn Steel Beams 10 Lecture 16 Elements of Architectural Structures ARCH 614

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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SLIDE 11

S2019abn 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)
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SLIDE 12

S2019abn Steel Beams 12 Lecture 16 Elements of Architectural Structures ARCH 614

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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SLIDE 13

S2019abn Steel Beams 13 Lecture 16 Elements of Architectural Structures ARCH 614

Steel Beams

  • lateral stability - bracing
  • local buckling – stiffen, or bigger Iy
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SLIDE 14

S2019abn Steel Beams 14 Lecture 16 Elements of Architectural Structures ARCH 614

Local Buckling

  • steel I beams
  • flange

– buckle in direction of smaller radius

  • f gyration
  • web

– force – “crippling”

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SLIDE 15

S2019abn Steel Beams 15 Lecture 16 Elements of Architectural Structures ARCH 614

Local Buckling

  • flange
  • web
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SLIDE 16

S2019abn Steel Beams 16 Lecture 16 Elements of Architectural Structures ARCH 614

Shear in Web

  • panels in plate girders or webs with large shear
  • buckling in compression direction
  • add stiffeners
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SLIDE 17

S2019abn

Shear in Web

  • plate girders and stiffeners

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

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SLIDE 18

S2019abn Steel Beams 18 Lecture 16 Elements of Architectural Structures ARCH 614

Steel Beams

  • bearing

– provide adequate area – prevent local yield

  • f flange

and web

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SLIDE 19

S2019abn Steel Beams 19 Lecture 16 Elements of Architectural Structures ARCH 614

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      

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SLIDE 20

S2019abn Steel Beams 20 Lecture 16 Elements of Architectural Structures ARCH 614

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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SLIDE 21

S2019abn Steel Beams 21 Lecture 16 Elements of Architectural Structures ARCH 614

Internal Moments - ALL at yield

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

E 1 y = 50ksi y = 0.001724  

y y p

M f bc M 2 3

2

 

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SLIDE 22

S2019abn Steel Beams 22 Lecture 16 Elements of Architectural Structures ARCH 614

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

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SLIDE 23

S2019abn Steel Beams 23 Lecture 16 Elements of Architectural Structures ARCH 614

Plastic Hinge Development

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SLIDE 24

S2019abn Steel Beams 24 Lecture 16 Elements of Architectural Structures ARCH 614

Plastic Hinge Examples

  • stability can be effected
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SLIDE 25

S2019abn Steel Beams 25 Lecture 16 Elements of Architectural Structures ARCH 614

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 26

S2019abn Steel Beams 26 Lecture 16 Elements of Architectural Structures ARCH 614

LRFD - Shear

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)

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SLIDE 27

S2019abn Steel Beams 27 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

E F r . L

y y p

76 1 

n b u i i

M M R     

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SLIDE 28

S2019abn Steel Beams 28 Lecture 16 Elements of Architectural Structures ARCH 614

Compact Sections

  • plastic moment can form before any

buckling

  • criteria

– – and

y f f

F E . t b 38 2 

y w c

F E . t h 76 3 

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SLIDE 29

S2019abn Steel Beams 29 Lecture 16 Elements of Architectural Structures ARCH 614

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

 

p b n

M C M  

C B A max max b

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

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SLIDE 30

S2019abn Steel Beams 30 Lecture 16 Elements of Architectural Structures ARCH 614

Beam Design Charts

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SLIDE 31

S2019abn Steel Beams 31 Lecture 16 Elements of Architectural Structures ARCH 614

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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SLIDE 32

S2019abn Steel Beams 32 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

(Ma ≤ Mn/)

) M M (

n b u

 

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SLIDE 33

S2019abn

Beam Charts by Zx (pg. 250)

Steel Beams 33 Lecture 16 Elements of Architectural Structures ARCH 614

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SLIDE 34

S2019abn Steel Beams 34 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
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SLIDE 35

S2019abn Steel Beams 35 Lecture 16 Elements of Architectural Structures ARCH 614

Beam Design (revisited)

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

web v

A V A V f  

2 3

max

Ib VQ fv 

max

 

  / V V

n a

) (

n v u

V V  

Vn = 0.6 FywAw

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SLIDE 36

S2019abn Steel Beams 36 Lecture 16 Elements of Architectural Structures ARCH 614

Beam Design (revisited)

  • 7. Provide adequate bearing

area at supports

(Pa ≤ Pn/) (Pu ≤ Pn)

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SLIDE 37

S2019abn Steel Beams 37 Lecture 16 Elements of Architectural Structures ARCH 614

Beam Design (revisited)

  • 8. Evaluate torsion
  • circular cross section
  • rectangular

J T fv  

2 1ab

c T fv 

 

v v

F f 

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SLIDE 38

S2019abn Steel Beams 38 Lecture 16 Elements of Architectural Structures ARCH 614

Beam Design (revisited)

  • 9. Evaluate deflections – NO LOAD FACTORS

allowable actual max

) x ( y    

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SLIDE 39

S2019abn

  • uniformly distributed loads
  • equivalent “w”

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

Steel Beams 39 Lecture 16 Elements of Architectural Structures ARCH 614

Load Tables & Equivalent Load 8

2 max

L w M

equivalent

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SLIDE 40

S2019abn Steel Beams 40 Lecture 16 Elements of Architectural Structures ARCH 614

Steel Arches and Frames

  • solid sections
  • r open web

http:// nisee.berkeley.edu/godden

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SLIDE 41

S2019abn Steel Beams 41 Lecture 16 Elements of Architectural Structures ARCH 614

Steel Shell and Cable Structures

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SLIDE 42

S2019abn Steel Beams 42 Lecture 16 Elements of Architectural Structures ARCH 614

Approximate Depths