ELEMENTS OF TRUCTURES FORM, B DESIGN...
Transcript of ELEMENTS OF TRUCTURES FORM, B DESIGN...
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S2009abnSteel Beams 1Lecture 16
Elements of Architectural StructuresARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES:
FORM, BEHAVIOR, AND DESIGN
ARCH 614
DR. ANNE NICHOLS
SPRING 2015
lecture
sixteen
steel construction:
materials & beams
S2007abnSteel Beams 2Lecture 16
Elements of Architectural StructuresARCH 614
Steel Beam Design
• American Institute of Steel Construction
– Manual of Steel Construction
– ASD & LRFD
– combined in 2005
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Lecture 16
Elements of Architectural Structures
ARCH 614
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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
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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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Lecture 16
Elements of Architectural Structures
ARCH 614
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Structural Steel
• standard rolled shapes (W, C, L, T)
• open web joists
• plate girders
• decking
S2007abnSteel Beams 6Lecture 16
Elements of Architectural StructuresARCH 614
Steel Construction
• welding
• bolts
http://courses.civil.ualberta.ca
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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
Steel Beams 7Lecture 16
Elements of Architectural StructuresARCH 614
Ra ≤Rn
Ω
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Unified Steel Design
• braced vs.
unbraced
Steel Beams 8Lecture 16
Elements of Architectural StructuresARCH 614
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Steel Beams 9
Lecture 16
Elements of Architectural Structures
ARCH 614
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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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Lecture 16
Elements of Architectural Structures
ARCH 614
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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
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Lecture 16
Elements of Architectural Structures
ARCH 614
LRFD Load CombinationsASCE-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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Elements of Architectural StructuresARCH 614
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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 13Lecture 16
Elements of Architectural StructuresARCH 614
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Steel Beams
• lateral stability - bracing
• local buckling – stiffen, or bigger Iy
Steel Beams 14Lecture 16
Elements of Architectural StructuresARCH 614
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Local Buckling
• steel I beams
• flange
– buckle in
direction of
smaller radius
of gyration
• web
– force
– “crippling”
Steel Beams 15Lecture 16
Elements of Architectural StructuresARCH 614
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Local Buckling
• flange
• web
Steel Beams 16Lecture 16
Elements of Architectural StructuresARCH 614
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Shear in Web
• panels in plate girders or webs with large shear
• buckling in compression direction
• add stiffeners
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Shear in Web
• plate girders and stiffeners
Steel Beams 17Lecture 16
Elements of Architectural StructuresARCH 614
http:// nisee.berkeley.edu/godden
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Steel Beams
• bearing
– provideadequatearea
– preventlocal yield
of flangeand web
Steel Beams 18Lecture 16
Elements of Architectural StructuresARCH 614
Steel Beams 18Lecture 16
Elements of Architectural StructuresARCH 614
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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 19Lecture 16
Elements of Architectural StructuresARCH 614
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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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Steel Beams 20Lecture 16
Elements of Architectural StructuresARCH 614
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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
Steel Beams 21Lecture 16
Elements of Architectural StructuresARCH 614
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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==
Steel Beams 22Lecture 16
Elements of Architectural StructuresARCH 614
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Plastic Hinge Development
Steel Beams 23Lecture 16
Elements of Architectural StructuresARCH 614
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Plastic Hinge Examples
• stability can be effected
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Steel Beams 24Lecture 16
Elements of Architectural StructuresARCH 614
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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 =
S2007abnSteel Beams 25Lecture 16
Elements of Architectural StructuresARCH 614
LRFD - Shear
Vu - maximum shear
φv - resistance factor for shear = 0.9
Vn - nominal shear
Fyw - yield strength of the steel in the web
Aw - area of the web = twd
)AF.(.VVR wywnvuii 6001=≤=Σ φγ
S2007abnSteel Beams 26Lecture 16
Elements of Architectural StructuresARCH 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
nbuii MMR φγ ≤=Σ
E
Fr.L
y
yp 761=
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Compact Sections
• plastic moment can form before any
buckling
• criteria
–
– and
Steel Beams 28Lecture 16
Elements of Architectural StructuresARCH 614
0.382
f
f y
b E
t F≤
3.76c
w y
h E
t F≤
8
Steel Beams 28Lecture 16
Elements of Architectural StructuresARCH 614
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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
CBA
bMMMM
MC
3425.2
5.12
max
max
+++=
[ ] pbn MCM ≤= moment based onlateral buckling
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Beam Design Charts
Steel Beams 30Lecture 16
Elements of Architectural StructuresARCH 614
Steel Beams 30Lecture 16
Elements of Architectural StructuresARCH 614
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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
S2009abnSteel Beams 31Lecture 16
Elements of Architectural StructuresARCH 614
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
( )bb Ff ≤
)MM( nbu φ≤
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Beam Charts by Zx (pg. 250)
Steel Beams 33Lecture 16
Elements of Architectural StructuresARCH 614
S2009abnSteel Beams 32Lecture 16
Elements of Architectural StructuresARCH 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
– and repeat 3 & 4 if necessary
5. Consider lateral stability
Steel Beams 33Lecture 16
Elements of Architectural StructuresARCH 614
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Beam Design (revisited)
6. Evaluate shear stresses - horizontal
• or
• W and rectangles
• thin walled sections
web
vA
V
A
Vf ≈=−
2
3max
Ib
VQfv =−max
( )vv Ff ≤ )( nvu VV φ≤
Steel Beams 34Lecture 16
Elements of Architectural StructuresARCH 614
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pp FA
Pf ≤=
Beam Design (revisited)
7. Provide adequate bearingarea at supports
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Steel Beams 35Lecture 16
Elements of Architectural StructuresARCH 614
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Beam Design (revisited)
8. Evaluate torsion
• circular cross section
• rectangular
J
Tfv
ρ=
2
1abc
Tfv =
( )vv Ff ≤
Steel Beams 36Lecture 16
Elements of Architectural StructuresARCH 614
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Beam Design (revisited)
9. Evaluate deflections – NO LOAD FACTORS
allowableactualxy ∆≤∆=)(max
S2007abnSteel Beams 37Lecture 16
Elements of Architectural StructuresARCH 614
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
S2009abnTOPIC 38 Elements of Architectural StructuresARCH 614
Steel Arches and Frames
• solid sections
or open web
http:// nisee.berkeley.edu/godden
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TOPIC 39 Elements of Architectural Structures
ARCH 614
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Steel Shell and Cable Structures
TOPIC 40 Elements of Architectural Structures
ARCH 614
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Approximate Depths