Get documents about "steel construction materials beams
Document Sample
FOUNDATIONS STRUCTURES:
FORM, BEHAVIOR, AND DESIGN Steel Beam Design
ARCH 331
DR. ANNE NICHOLS • American Institute of Steel Construction
SPRING 2010 – Manual of Steel Construction
– ASD & LRFD
lecture
eighteen – now combined in 13th ed.
(2005)
steel construction:
materials & beams
Steel Beams 1 Foundations Structures F2009abn
Lecture 18 ARCH 331 Steel Beams 2 Foundations Structures F2008abn
Lecture 18 ARCH 331
Steel Materials Steel Materials
• smelt iron ore • cast into billets
• add alloying elements • hot rolled
• heat treatments • cold formed
Hot Rolled
• iron, carbon • residual stress
• microstructure • corrosion-resistant
“weathering” steels
• stainless Cold Formed
AISC
AISC
A36 steel, JOM 1998
Steel Beams 3 Foundations Structures F2008abn Steel Beams 4 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
1
Steel Materials Steel Properties
• steel grades • high strength to weight ratio
– ASTM A36 – carbon • elastic limit – yield (Fy)
• plates, angles • inelastic – plastic
• Fy = 36 ksi & Fu = 58 ksi • ultimate strength (Fu)
– ASTM A572 – high strength low-alloy • ductile strain hardening
• some beams • strength sensitive
• Fy = 60 ksi & Fu = 75 ksi to temperature
– ASTM A992 – for building framing • can corrode
• most beams • fatigue
• Fy = 50 ksi & Fu = 65 ksi
Winnepeg DOT
Steel Beams 6 Foundations Structures F2008abn
Steel Beams 5 Foundations Structures F2008abn
Lecture 18 ARCH 331
Lecture 18 ARCH 331
Structural Steel Steel Construction
• standard rolled shapes (W, C, L, T) • welding
• open web joists • bolts
• plate girders
• decking
http://courses.civil.ualberta.ca
Steel Beams 7 Foundations Structures F2008abn Steel Beams 8 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
2
Steel Construction ASD Steel Design
• fire proofing • bending (braced) Fb = 0.66Fy
– cementicious spray • bending (unbraced*) Fb = 0.60Fy
– encasement in gypsum • shear Fv = 0.40Fy
– intumescent – expands
• shear (bolts) tabulated
with heat
– sprinkler system • shear (welds) Fv = 0.30Fweld
* flanges in compression can buckle
Steel Beams 9 Foundations Structures F2008abn Steel Beams 10 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
ASD Steel Design LRFD
• braced vs. • loads on structures are
unbraced – not constant
– can be more influential on failure
– happen more or less often
– UNCERTAINTY
Ru = γ D RD + γ L RL ≤ φRn
φ - resistance factor
γ - load factor for (D)ead & (L)ive load
Steel Beams 12 Foundations Structures F2008abn
Steel Beams 11 Foundations Structures F2008abn Lecture 18 ARCH 331
Lecture 18 ARCH 331
3
ASCE-7
LRFD Steel Beam Design LRFD Load Combinations (2005)
• limit state is yielding all across section • 1.4(D + F)
• outside elastic range • 1.2(D + F + T)+ 1.6(L + H)+
• load factors & resistance factors 0.5(Lr or S or R)
f • 1.2D + 1.6(Lr or S or R) + (L or 0.8W)
fy = 50ksi
• 1.2D + 1.6W + L + 0.5(Lr or S or R)
1
E
• 1.2D + 1.0E + L + 0.2S)
ε
εy = 0.001724
• 0.9D + 1.6W + 1.6H
• 0.9D + 1.0E + 1.6H
Steel Beams 14 Foundations Structures F2008abn
Steel Beams 13 Foundations Structures F2008abn Lecture 18 ARCH 331
Lecture 18 ARCH 331
Beam Design Criteria (revisited) Steel Beams
• strength design • lateral stability - bracing
– bending stresses predominate
– shear stresses occur
• local buckling – stiffen, or bigger Iy
• serviceability
– limit deflection +
– stability
• superpositioning
– use of beam charts
=
– elastic range only!
– “add” moment diagrams
– “add” deflection CURVES
(not maximums)
Steel Beams 16 Foundations Structures F2008abn
Steel Beams 15 Foundations Structures F2008abn Lecture 18 ARCH 331
Lecture 18 ARCH 331
4
Local Buckling Local Buckling
• steel I beams • web
• flange • flange
– buckle in
direction of
smaller radius
of gyration
• web
– force
– “crippling”
Steel Beams 17 Foundations Structures F2008abn Steel Beams 18 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
Shear in Web Shear in Web
• panels in plate girders or webs with large shear • plate girders and stiffeners
• buckling in compression direction
• add stiffeners
http:// nisee.berkeley.edu/godden
Steel Beams 19 Foundations Structures F2008abn Steel Beams 20 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
5
Steel Beams LRFD - Flexure
• bearing
– provide Σγ i Ri = M u ≤ φb M n = 0.9 Fy Z
adequate
area Mu - maximum moment
– prevent φb - resistance factor for bending = 0.9
local yield Mn - nominal moment (ultimate capacity)
of flange
Fy - yield strength of the steel
and web
Z - plastic section modulus*
Steel Beams 22 Foundations Structures F2008abn
Steel Beams 21 Foundations Structures F2008abn Lecture 18 ARCH 331
Lecture 18 ARCH 331
Internal Moments - at yield Internal Moments - ALL at yield
• material hasn’t failed • all parts reach yield
• plastic hinge forms
I bh 2 • ultimate moment
M y = fy = fy • Atension = Acompression
c 6
b (2 c )
2
2 bc 2 σ
= fy = fy Mp = bc f y = 3 M y
2 σy = 50ksi
6 3 2 1
E
ε
εy = 0.001724
Steel Beams 23 Foundations Structures F2008abn Steel Beams 24 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
6
n.a. of Section at Plastic Hinge Plastic Hinge Development
• cannot guarantee at
centroid
• fy·A1= fy·A2
• moment found from
yield stress times
moment area
M p = f y A1 d = f y Σ Ai d i
n .a
Steel Beams 25 Foundations Structures F2008abn Steel Beams 26 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
Plastic Hinge Examples Plastic Section Modulus
• stability can be effected • shape factor, k
M
k= p
My
= 3/2 for a rectangle
≈ 1.1 for an I k=Z
S
M
Z =
p
• plastic modulus, Z
fy
Steel Beams 27 Foundations Structures F2008abn Steel Beams 28 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
7
LRFD - Shear LRFD - Flexure Design
• limit states for beam failure
300 × ry
Σγ i Ri = Vu ≤ φvVn = 0.9(0.6 Fyw Aw ) 1. yielding Lp =
2. lateral-torsional buckling* Fy
Vu - maximum shear 3. flange local buckling
φv - resistance factor for shear = 0.9 4. web local buckling
Vn - nominal shear • minimum Mn governs
Fyw - yield strength of the steel in the web
Aw - area of the web = twd Σγ i Ri = M u ≤ φb M n
Steel Beams 29 Foundations Structures F2008abn Steel Beams 30 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
Compact Sections Lateral Torsional Buckling
• plastic moment can form before any M n = Cb [ moment buckling ] ≤ M p
lateral
based on
buckling
• criteria 12.5M max
Cb =
bf 65 2.5M max + 2M A + 4 M B + 3M C
– ≤ Cb = modification factor
2t f Fy
Mmax - |max moment|, unbraced segment
hc 640 MA - |moment|, 1/4 point
– and ≤ MB = |moment|, center point
tw Fy
MC = |moment|, 3/4 point
Steel Beams 31 Foundations Structures F2008abn Steel Beams 32 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
8
Beam Design Charts 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
Steel Beams 33 Foundations Structures F2008abn Steel Beams 34 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
Design Procedure (revisited) Beam Charts by Sx (Appendix A)
1. Know Fall for the material or
FU for LRFD
2. Draw V & M, finding Mmax
3. Calculate Sreq’d ( f b ≤ Fb )
or Z (M ≤φ M u b n )
4. Choose (economical) section from
section or beam capacity charts
Steel Beams 35 Foundations Structures F2008abn Steel Beams 36 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
9
Beam Design (revisited) Beam Design (revisited)
4*. Include self weight for Mmax 6. Evaluate shear stresses - horizontal
– and repeat 3 & 4 • ( f v ≤ Fv ) or (Vu ≤ φvVn )
if necessary
3V V
• rectangles and W’s f v − max = ≈
2 A Aweb
5. Consider lateral stability
Unbraced roof trusses
VQ
were blown down in
1999 at this project in
• general f v −max =
Moscow, Idaho.
Ib
Photo: Ken Carper
Steel Beams 37 Foundations Structures F2008abn Steel Beams 38 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
Beam Design (revisited) Beam Design (revisited)
7. Provide adequate bearing 8. Evaluate torsion
P
area at supports f p = ≤ Fp ( f v ≤ Fv )
A
• circular cross section
Tρ
fv =
J
• rectangular
T
fv =
c1ab 2
Steel Beams 39 Foundations Structures F2008abn Steel Beams 40 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
10
Beam Design (revisited) Load Tables & Equivalent Load
9. Evaluate deflections – NO LOAD FACTORS • uniformly distributed loads
wequivalent L2
• equivalent “w” M max =
8
load for live load deflection limit
in RED, total in BLACK
y max ( x ) = Δ actual ≤ Δ allowable
Steel Beams 41 Foundations Structures F2008abn Steel Beams 42 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
Sloped Beams Steel Arches and Frames
• stairs & roofs • solid sections
• projected live load or open web
• dead load over length α
• perpendicular load to beam:
w⊥ = w ⋅ cos α
http:// nisee.berkeley.edu/godden
Steel Beams 43 Foundations Structures F2008abn Steel Beams 44 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
11
Steel Shell and Cable Structures Approximate Depths
Steel Beams 45 Foundations Structures F2008abn Steel Beams 46 Foundations Structures F2008abn
Lecture 18 ARCH 331 Lecture 18 ARCH 331
12
Related docs
