f = 36 ksi & f = 58 ksi steel beams 1 s2009abn steel beams
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S2009abnSteel Beams 1
Lecture 16
Elements of Architectural Structures
ARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES:
FORM, BEHAVIOR, AND DESIGN
ARCH 614
DR. ANNE NICHOLS
SPRING 2014
lecture
sixteen
steel construction:
materials & beams
S2007abnSteel 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
Steel Beams 3
Lecture 16
Elements of Architectural Structures
ARCH 614
S2007abn
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
S2007abnSteel 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
2
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
S2007abnSteel 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
3
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
nLLDDu RRRR
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
S2007abnSteel Beams 11
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)
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)
+
=
+
=
4
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
of 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
5
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
of 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*
ZFMMR ynbuii 9.0
Steel Beams 19
Lecture 16
Elements of Architectural Structures
ARCH 614
S2007abn
Internal Moments - at yield
yyy fbh
fc
IM
6
2
• material hasn’t failed
yy f
bcf
cb
3
2
6
2 22
6
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
yyp MfbcM2
32
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
iian
yyp dAfdAfM.
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
7
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
Mk
y
p
f
MZ
SZk
S2007abnSteel 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
)AF.(.VVR wywnvuii 6001
S2007abnSteel 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
nbuii MMR
E
Fr.L
y
yp 761
S2012abn
Compact Sections
• plastic moment can form before any
buckling
• criteria
–
– and
Steel Beams 28
Lecture 16
Elements of Architectural Structures
ARCH 614
8
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
CBA
bMMMM
MC
3425.2
5.12
max
max
pbn MCM 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
S2009abnSteel 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
bb Ff
)MM( nbu
9
S2010abn
Beam Charts by Zx (pg. 250)
Steel Beams 33
Lecture 16
Elements of Architectural Structures
ARCH 614
S2009abnSteel 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
– and repeat 3 & 4
if necessary
5. Consider lateral stability
Steel Beams 33
Lecture 16
Elements of Architectural Structures
ARCH 614
S2007abn
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
Steel Beams 34
Lecture 16
Elements of Architectural Structures
ARCH 614
S2007abn
pp FA
Pf
Beam Design (revisited)
7. Provide adequate bearing
area at supports
10
Steel Beams 35
Lecture 16
Elements of Architectural Structures
ARCH 614
S2007abn
Beam Design (revisited)
8. Evaluate torsion
• circular cross section
• rectangular
J
Tfv
2
1abc
Tfv
vv Ff
Steel Beams 36
Lecture 16
Elements of Architectural Structures
ARCH 614
S2007abn
Beam Design (revisited)
9. Evaluate deflections – NO LOAD FACTORS
allowableactualxy )(max
S2007abnSteel Beams 37
Lecture 16
Elements of Architectural Structures
ARCH 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 Structures
ARCH 614
Steel Arches and Frames
• solid sections
or open web
http:// nisee.berkeley.edu/godden
11
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
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