architectural s form, b design arch 331 dr...
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1
F2009abn
fifteen
steel construction:
materials & beams
ARCHITECTURAL STRUCTURES:
FORM, BEHAVIOR, AND DESIGN
ARCH 331
DR. ANNE NICHOLS
SUMMER 2014
Steel Beams 1
Lecture 15
Architectural Structures
ARCH 331
lecture
F2011abn
Steel Beam Design
• American Institute of Steel Construction
– Manual of Steel Construction
– ASD & LRFD
– combined in 13th ed.
Steel Beams 2Lecture 15
Foundations StructuresARCH 331
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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Steel Beams 5
Lecture 18
Foundations Structures
ARCH 331
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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
Lecture 18
Foundations Structures
ARCH 331
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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
Steel Beams 7
Lecture 18
Foundations Structures
ARCH 331
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Structural Steel
• standard rolled shapes (W, C, L, T)
• open web joists
• plate girders
• decking
F2008abnSteel Beams 8
Lecture 18
Foundations Structures
ARCH 331
Steel Construction
• welding
• bolts
http://courses.civil.ualberta.ca
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Steel Beams 9
Lecture 18
Foundations Structures
ARCH 331
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Steel Construction
• fire proofing
– cementicious spray
– encasement in gypsum
– intumescent – expands
with heat
– sprinkler system
F2008abnSteel Beams 10Lecture 18
Foundations Structures ARCH 331
Unified Steel Design
• ASD
– bending (braced) Ω = 1.67
– bending (unbraced*) Ω = 1.67
– shear Ω = 1.67
– shear (bolts & welds) Ω = 2.00
– shear (welds) Ω = 2.00
* flanges in compression can buckle
Ra ≤Rn
Ω
F2008abnSteel Beams 11Lecture 18
Foundations Structures ARCH 331
Unified Steel Design
• braced vs. unbraced
Steel Beams 12Lecture 18
Foundations Structures ARCH 331
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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 ≤+=
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Steel Beams 13
Lecture 18
Foundations Structures
ARCH 331
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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
F2011abn
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)Steel Beams 14Lecture 15
Foundations StructuresARCH 331
ASCE-7
(2010)
Steel Beams 15Lecture 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 16Lecture 18
Foundations Structures ARCH 331
F2008abn
Steel Beams
• lateral stability - bracing
• local buckling – stiffen, or bigger Iy
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Steel Beams 17Lecture 18
Foundations Structures ARCH 331
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Local Buckling
• steel I beams
• flange
– buckle in
direction of
smaller radius
of gyration
• web
– force
– “crippling”
Steel Beams 18Lecture 18
Foundations Structures ARCH 331
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Local Buckling
• flange
• web
Steel Beams 19Lecture 18
Foundations Structures ARCH 331
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Shear in Web
• panels in plate girders or webs with large shear
• buckling in compression direction
• add stiffeners
F2008abnSteel Beams 20Lecture 18
Foundations Structures ARCH 331
Shear in Web
• plate girders and stiffeners
http:// nisee.berkeley.edu/godden
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Steel Beams 21Lecture 18
Foundations Structures ARCH 331
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Steel Beams
• bearing
– provideadequatearea
– preventlocal yield
of flangeand web
Steel Beams 22Lecture 18
Foundations Structures ARCH 331
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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
Steel Beams 23Lecture 18
Foundations Structures ARCH 331
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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
==
Steel Beams 24Lecture 18
Foundations Structures ARCH 331
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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
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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
iian
yyp dAfdAfM.
1Σ==
Steel Beams 26
Lecture 18
Foundations Structures
ARCH 331
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Plastic Hinge Development
Steel Beams 27
Lecture 18
Foundations Structures
ARCH 331
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Plastic Hinge Examples
• stability can be effected
Steel Beams 28
Lecture 18
Foundations Structures
ARCH 331
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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 =
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F2008abnSteel Beams 29
Lecture 18
Foundations Structures
ARCH 331
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)
F2008abnSteel 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
nbuii MMR φγ ≤=Σ
1.76
F2008abnSteel Beams 31
Lecture 18
Foundations Structures
ARCH 331
Compact Sections
• plastic moment can form before any
buckling
• criteria
–
– and
F2008abnSteel 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
CBAmax
maxb
MMMM.
M.C
34352
512
+++=
[ ] pbn MCM ≤= moment based on
lateral buckling
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Beam Design Charts
Steel Beams 33Lecture 15
Foundations StructuresARCH 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 (Ω, φ)
2. Draw V & M, finding Mmax
3. Calculate Sreq’d
or Z
4. Choose (economical) section from section or beam capacity charts
Steel Beams 35Lecture 15
Foundations StructuresARCH 331
)MM( nbu φ≤(Ma ≤ Mn/Ω)
Steel Beams 36
Lecture 18
Foundations Structures
ARCH 331
F2008abn
Beam Charts by Sx (Appendix A)
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F2011abn
Beam Charts by Zx
Steel Beams 37
Lecture 18
Foundations Structures
ARCH 331
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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
Steel Beams 37Lecture 15
Foundations StructuresARCH 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 stresses - horizontal
• or
• rectangles and W’s
• general
Steel Beams 38Lecture 15
Foundations StructuresARCH 331
web
maxvA
V
A
Vf ≈=−
2
3
Ib
VQf maxv =−
)VV( nvu φ≤(Va ≤ Vn/Ω)
Vn = 0.6 FywAw
F2008abnSteel Beams 39
Lecture 18
Foundations Structures
ARCH 331
Beam Design (revisited)
7. Provide adequate bearing
area at supports (Pa ≤ Pn/Ω)
(Pu ≤ φPn)
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Steel Beams 40
Lecture 18
Foundations Structures
ARCH 331
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Beam Design (revisited)
8. Evaluate torsion
• circular cross section
• rectangular
J
Tfv
ρ=
2
1abc
Tfv =
( )vv Ff ≤
Steel Beams 41
Lecture 18
Foundations Structures
ARCH 331
F2008abn
Beam Design (revisited)
9. Evaluate deflections – NO LOAD FACTORS
allowableactualxy ∆≤∆=)(max
F2008abnSteel Beams 42Lecture 18
Foundations 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
F2008abnSteel 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:
α
αcosww ⋅=⊥
αcos
w
.adjw =
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F2008abnSteel Beams 44
Lecture 18
Foundations Structures
ARCH 331
Steel Arches and Frames
• solid sections or open web
http:// nisee.berkeley.edu/godden
Steel Beams 45
Lecture 18
Foundations Structures
ARCH 331
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Steel Shell and Cable Structures
Steel Beams 46
Lecture 18
Foundations Structures
ARCH 331
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Approximate Depths