F2018abnSteel Construction 1
Lecture 21
Applied Architectural Structures
ARCH 631
twenty one
steel construction
and design
lecture
APPLIED ARCHITECTURAL STRUCTURES:
STRUCTURAL ANALYSIS AND SYSTEMS
ARCH 631
DR. ANNE NICHOLS
FALL 2018
http://nisee.berkeley.edu/godden
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Applied Architectural Structures
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Steel
• cast iron – wrought iron - steel
• cables
• columns
• beams
• trusses
• frames
http://nisee.berkeley.edu/godden
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Steel Construction
• standard rolled shapes
• open web joists
• plate girders
• decking
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Steel Construction
• welding
• bolts
AISC Education
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Steel Construction
• fire proofing
– cementitious spray
– encasement in gypsum
– intumescent – expands
with heat
– sprinkler system
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Steel Materials
• high strength to
weight ratio
• ductile
• beam size
often limited by
deflection
• column size
limited by
slenderness
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Steel Beams
• types
– manufactured shapes
castellated
http://nisee.berkeley.edu/godden
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Steel Beams
• types
– wide flange
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Steel Beams
• types
– open web joists
(manufactured
trusses)
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Steel Beams
• types (more)
– plate girder
– decking
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Steel Beams
http://nisee.berkeley.edu/godden
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Steel Beams
• lateral stability - bracing
• local buckling - stiffen
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Local Buckling
• steel I beams
• flange
– buckle in
direction of
smaller radius
of gyration
• web
– force
– “crippling”
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Local Buckling
• flange
• web
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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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Steel Beams
• end conditions
• a) away from
connection - full
section effective
• b) high shear –
only web
effective
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Steel Beams
• end conditions
• c) bolt holes –
less material
• d) local web
buckling
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Steel Beams
• bearing
– provide
adequate
area
– prevent
local yield
of flange
and web
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Steel Beams
• connections
– welds
– bolts
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Steel Design – Open Web Joists
• SJI: www.steeljoist.com
• Vulcraft: www.vulcraft.com
– K Series (Standard)
• 8-30” deep, spans 8-50 ft
– LH Series (Long span)
• 18-48” deep, spans 25-96 ft
– DLH (Deep Long Spans)
• 52-72” deep, spans 89-144 ft
– SLH (Long spans with high strength steel)
• pitched top chord
• 80-120” deep, spans 111-240 ft
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Steel Design – Open Web Joists ASD
load for live load
deflection limit in RED
total in BLACK
F2018abn
load for live load deflection
limit (L/360) in RED
total in BLACK
Steel Design – Open Web Joists
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Steel Beam Design
• American Institute of Steel Construction
– 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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Steel Beam Design
• AISC: 14th ed.
– combined ASD & LRFD
in one volume in 2005
F2018abn
• 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
na
RR
Ω
Unified Steel Design
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Unified Steel Design
• braced vs.
unbraced
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E
1
fy = 50ksi
001724.0y
f
LRFD Steel Beam Design
• limit state is yielding all across section
• outside elastic range
• load factors & resistance factors
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Load Types
• D = dead load
• L = live load
• Lr = live roof load
• W = wind load
• S = snow load
• E = earthquake load
• R = rainwater load or ice water load
• T = effect of material & temperature
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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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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*
0.9i i u b n yR M M F Z
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Pure Flexure
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2
6y y y
I bhM f f
c
2 2(2 ) 2
6 3y y
b c bcf f
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Internal Moments - at yield
• material hasn’t failed
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2 32p y yM bc f M
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Internal Moments - ALL at yield
• all parts reach yield
• plastic hinge forms
• ultimate moment
• Atension = Acompression
E
1
y = 50ksi
y = 0.001724
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1.
p y y i in a
M f A d f A d
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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
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Plastic Hinge Development
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Plastic Hinge Examples
• stability can be effected
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p
y
Mk
M
ZkS
p
y
MZ
f
• shape factor, k
= 3/2 for a rectangle
1.1 for an I
• plastic modulus, Z
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Plastic Section Modulus
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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
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LRFD – Shear (compact shapes)
1.0(0.6 )i i u v n yw wR V V F A
F2018abn
i i u b nR M M
1.76y
p y
FL r
E
• limit states for beam failure
1. yielding
2. lateral-torsional buckling*
3. flange local buckling
4. web local buckling
• minimum Mn governs
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Flexure Design
F2018abn
• plastic moment can form before any
buckling
• criteria
–
– and
0.382
f
f y
b E
t F
3.76c
w y
h E
t F
Compact Sections
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F2018abn
Cb = modification factor
Mmax - |max moment|, unbraced segment
MA - |moment|, 1/4 point
MB = |moment|, center point
MC = |moment|, 3/4 point
n b pM C M
max
max
12.5
2.5 2 4 3b
A B C
MC
M M M M
Lateral Torsional Buckling
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moment based on
lateral buckling
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Beam Design Charts
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Deflection Limits
• based on service condition
• no “impairment” to serviceability
• avoid ponding
• L/360 due to live load for beams &
girders supporting plaster (service)
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Steel Arches and Frames
• solid sections
or open web
http://nisee.berkeley.edu/godden
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Steel Shell and Cable Structures
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Approximate Depths
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• limit states for failure
1. yielding
2. buckling
Fe – elastic buckling stress (Euler)
0.90c n cr gP F A
na
PP
u c nP P
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Unified Column Design
4.71 2.25yc
y e
FL Eor
r F F
4.71 2.25yc
y e
FL Eor
r F F
F2018abn
• Pn = FcrAg
– for
– for
– where
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Unified Column Design
4.71 0.658
y
e
F
Fccr y
y
L EF F
r F
4.71 0.877ccr e
y
L EF F
r F
2
2e
c
EF
Lr
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Procedure for Analysis
1. calculate KL/r• biggest of KL/r with respect to x axes and y axis
2. find Fcr from appropriate equation• tables are available
3. compute Pn = FcrAg
• or find fc = Pa/A or Pu/A
4. is Pa Pn/ or Pu Pn?• yes: ok
• no: insufficient capacity and no good
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1. guess a size (pick a section)
2. calculate KL/r• biggest of KL/r with respect to x axes and y axis
3. find Fcr from appropriate equations• or find a table
4. compute Pn = FcrAg
• or find fc = Pa/A or Pu/A
Procedure for Design
F2018abn
5. is Pa Pn/ or Pu Pn?• yes: ok
• no: pick a bigger section and go back to step 2.
6. check design efficiency
• percentage of stress =
• if between 90-100%: good
• if < 90%: pick a smaller section and
go back to step 2.
100%r
c
P
P
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Procedure for Design (cont’d)
F2018abn
• moment magnification (P-)
Cm – modification factor for end conditions
= 0.6 – 0.4(M1/M2) or
0.85 restrained, 1.00 unrestrained
Lc1 – effective length in plane of bending
Pe1 – Euler buckling strength
- 1.00 (LRFD), 1.60(ASD)
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Beam-Column Design
m1
u e1
CB
1 ( P / P )
1r ntM B M
2
1 2
1
e
c
EIP
L
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Beam-Column Design
• LRFD (Unified) Steel
– for
– for
Pr is required, Pc is capacity
Mrx is required, Mcx is capacity
Mry is required, Mcy is capacity
80.2 : 1.0
9
ryrxr r
c c cx cy
MMP P
P P M M
0.2 : 1.02
ryrxr r
c c cx cy
MMP P
P P M M
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