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Introduction to Stee Session 6: Plate Girder Des
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Introduction to Stee Session 6: Plate Girder Des
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Introduction to Stee Session 6: Plate Girder Des
Today’s live webinar will begin shortly. Please stand by. As a reminder, reminder, all lines lines have been muted. Please type any questions or comments through the Chat feature on the left portion of your screen. Today’s audio will be broadcast through the internet. Alternatively, Alternatively, to hear the audio through the phone, dial (800) 680-6953.
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Introduction to Stee Session 6: Plate Girder Des
Copyright Materials This presentation is protected b y US and International Copyright laws. Reproduction, dist distri ribu buti tion on,, disp display lay and and use use of the the pres presen enta tati tion on with withou outt writ writte ten n perm permis issi sion on of AISC AISC is proh prohib ibit ited ed..
© The American Institute of Steel Construction 2016 The The info inform rmat atio ion n pres presen entted here herein in is bas based on reco ecogniz gnized ed engi engine nee ering ring prin princ ciple iples s and and is for gen general eral info inform rmat atio ion n only only.. Whil While e it is beli believ eved ed to be acc accura urate, te, this his inf inform ormation tion shoul hould d not not be appl applie ied d to any any spec specif ific ic appl applic icat atio ion n with withou outt comp compet eten entt prof profes essi sion onal al exam examin inat atio ion n and and veri verifi fica cati tion on by a licen license sed d prof profes essi sion onal al engi engine neer er.. Anyo Anyone ne maki making ng use use of this this info inform rmat atio ion n assu assume mes s all all liab liabili ility ty arisin arising g from from such such use. use.
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Introduction to Stee Session 6: Plate Girder Des
Learning Objectives • Gain an an unders understand tanding ing of the the design design and and behavior behavior of of plate plate girders in steel bridges. • Gain an under understan standin ding g of prelimina preliminary ry sizing sizing of girders girders and and strength evaluation of composite girders. • Become Become familia familiarr with AASHTO AASHTO strengt strength h provisio provision n evaluatio evaluation n of member and system stability. • Become familiar with stability topics including including local local buckling, buckling, lateral torsional buckling and system buckling of narrow steel bridge systems.
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Session 6: Plate Girder Design and Stability
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Introduction to Stee Session 6: Plate Girder Des
Night School Course B1 Introduction to Steel Bridge Design • June 6 - Session ion 1: 1: Introduction to Bridge Engineering • June 13 13 - Sess ession 2: 2: Introduction and History of AASHTO LRFD Bridge Design Specifications • June 20 20 - Sess ession 3: 3: Steel Material Properties • Augu August st 8 - Sess Sessio ion n 4: Loads and Analysis • July 11 - Sess ession 5: 5: Steel Bridge Fabrication • July July 18 - Sessio Session n 6: Plate Girder Design and Stability • July 25 - Sess ession 7: 7: Effects of Curvature and Skew • Augu August st 1 - Sess Sessio ion n 8: Fatigue and Fracture Design
9
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Introduction to Stee Session 6: Plate Girder Des
Responsibilities of Designer • Design and behavior of the girders during placement of the concrete bridge deck (construction stage – steel girder generally carries the full construction load) • Design and behavior of the girders in the finished bridge (composite section). • The design requirements and corresponding limit states of the girders during these two stages are very different
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Introduction to Stee Session 6: Plate Girder Des
Material Properties of Steel • Structural steel is an extremely efficient material in terms of both strength and stiffness. • Comparing typical steel and concrete properties: Material
Strength
Stiffness (E)
Steel
Yield: 36~100 ksi
29000 ksi
Concrete
f’c = 3~7 ksi
3000~5000 ksi
• While concrete is primarily only relied upon in compression, steel is essentially equally strong in both tension and compression (from a material perspective). 13
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efficient cross sections will often consist of relatively slender plate
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Introduction to Stee Session 6: Plate Girder Des
What is Buckling? • Buckling is a compression driven phenomenon in which the element experiences a loss of stiffness. • In most situations, the loss of stiffness is a gradual effect; however, in cases such as a bracing failure, buckling can be a sudden catastrophic failure. • As the buckling load is approached small changes in the applied loading can result in large deformations. 15
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Introduction to Stee Session 6: Plate Girder Des
Stability Limit States • Buckling Modes: • Local (plate) Buckling • Flanges (flange local buckling) • Web (web bend buckling)
• Member buckling • Lateral-Torsional Buckling, Geometry, unbraced length, support conditions
• Global/System Buckling • Buckling of Multiple Girders Acting as A Unit/System 17
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buckling vs. global buckling can have very different impacts on the behavior
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Introduction to Stee Session 6: Plate Girder Des
Plate Buckling Elastic plate buckling stress:
12 1 k = plate buckling coefficient E = modulus of elasticity of plate material (ksi)
= Poisson’s ratio = 0.3 b = plate width (in) t = plate thickness (in) 19
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Introduction to Stee Session 6: Plate Girder Des
Plate Buckling Local buckling in steel beam/girder applications can exist in several different limit states: • Flange Local Buckling • Web Local Buckling • Web Shear Buckling • Web Crippling or other effects around concentrated forces
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Compact Slenderness limit:
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Introduction to Stee Session 6: Plate Girder Des
Web Local Buckling Web Slenderness Compact and Noncompact Limits (AASHTO Appendix A6.2.1):
rw = 137 for Gr. 50 Most webs are designed with close to rw 23
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D
tw
Dc
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Introduction to Stee Session 6: Plate Girder Des
Web Bend Buckling (Unstiffened Webs) Web Bend Buckling: AASHTO 6.10.1.9 (for Slender web members): D
Dc
tw
Webs without Longitudinal Stiffeners – Nominal web bend buckling resistance:
D = web depth, D c = depth of web in compression. ( = 0.3)
Note – compare to previous plate buckling expression
25
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Introduction to Stee Session 6: Plate Girder Des
Lateral Torsional Buckling • Bending produces both tensile and compressive stresses • Doubly-symmetric shape • Neutral axis at mid-depth • Maximum tensile and compressive stresses equal
• Singly-symmetric shape • Neutral axis closer to larger flange • Maximum bending stress at smaller flange
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Introduction to Stee Session 6: Plate Girder Des
Torsional Resistance • 2 types of torsional resistance • Saint-Venant torsional stiffness (sometimes referred to as the uniform resistance). Related to GJ • Warping torsional stiffness (sometimes called the non-uniform torsional resistance)
• Shape-dependent • Restraint-dependent
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Introduction to Stee Session 6: Plate Girder Des
LTB – Doubly Symmetric Shape • Timoshenko’s equation for elastic critical buckling moment Mcr (k-in):
• L b = unbraced length (in) = spacing between crossframes • E = modulus of elasticity (ksi) • G = shear modulus (ksi) • J = torsional constant (in 4) • Cw= warping constant (in 6) • Iy = weak-axis moment of inertia (in 4) 31
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Introduction to Stee Session 6: Plate Girder Des
AASHTO LTB • AASHTO Appendix A6 equation for effective radius of gyration r t (in), used in previous slide:
• Where:
12 1 13
• bfc = width of compression flange (in) • tfc = thickness of compression flange (in) • Dc = depth of web in compression (in) • tw = thickness of web (in)
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
AASHTO Section 6.10.8.2.3 • AASHTO equation for lateral torsional buckling:
• The AASHTO main body equation is intended for slender web sections – which is why the web load shedding factor Rb is included. • Many engineers use this equation even for compact and non-compact sections.
35
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Moment Gradient Effect (AASHTO) • AASHTO LRFD moment modification factor • C b = 1.75 – 1.05f 1/f 2 + 0.3(f 1/f 2)2 ≤ 2.3, where • f 2 = largest compressive bending stress at one end of unbraced length (ksi); taken as 0 if stress is zero / tensile at both ends • f 0 = compressive bending stress at opposite end of unbraced length (ksi); negative if in tension • f mid = compressive bending stress at middle of unbraced length (ksi) • f 1 = f 0 if variation of moment is concave between brace points • f 1
= 2f mid – f 2 ≥ f 0 otherwise (i.e., linear extrapolation) 37
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Moment Gradient Effect (AISC)
2.5 12.5 3 4 3 MB
M A X
X Lb
X – Brace
MC
Mmax can occur anywhere along the unbraced length Absolute value of moments are used in equation. 39
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Introduction to Stee Session 6: Plate Girder Des
Review of Composite Girder Fundamentals
41
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Introduction to Stee Session 6: Plate Girder Des
Composite Girder Strength CALCULATIONS FOR FLEXURAL MEMBERS
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Introduction to Stee Session 6: Plate Girder Des
Composite Girder Strength (positive bending) The composite girder strength is based upon an ultimate strength model that utilizes the following basic assumptions: • Concrete above the plastic neutral axis is at 0.85f ′c in compression and concrete below the neutral axis does not contribute • Steel above the neutral axis is at Fy in compression • Steel below the neutral axis is at Fy in tension 45
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Effective Flange Width, b e be
be
Exterior Girder
ts
Interior Girder
S
S
bedge
AASHTO Section 4.6.2.6
47
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
General Location of PNA The general location of the PNA can be found by comparing three idealized resultants found from equilibrium: Compressive Resultants = Tensile Resultants be
C* = 0.85f ′ cbe ts ts
Py = AsFy
Fy 49
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y
PNA in Steel web if P y web >C*
y web
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Doublysymmetric
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Introduction to Stee Session 6: Plate Girder Des
Example 1 – PNA in Concrete Deck Consider the doubly-symmetric steel (F y=50 ksi) girder (As = 48 in2) with a concrete deck with f’ c=4ksi. Find Mp of the composite girder. 8 in.
C* = 0.85f ′c be ts C* = 0.85(4 ksi) x(96”) x (8”) =2610 k
96 in. 12″x1″
Py = AsFy = 48 in2 x 50 ksi = 2400 k
Web: 48″x0.5″
C* =2610 k > 2400 k = P y
12″x1″
PNA is in Concrete Deck
51
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Cc = 0.85f ′ cbe a = 2400 k
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Introduction to Stee Session 6: Plate Girder Des
Example 2 – PNA in Steel Section Consider the doubly-symmetric steel (F y=50 ksi) girder (A s = 48 in2) with a concrete deck with f’ c=4ksi. Find Mp of the composite girder. Girder Spacing = 72 in. 8 in.
C* = 0.85f ′ cbe ts C* = 0.85(4 ksi) x(72”) x (8”) =1960 k
72 in. 12″x1″
Web: 48″x0.5″
Py = AsFy = 48 in2 x 50 ksi = 2400 k Py web = AwebFy = 24 in2 x 50 ksi = 1200 k Py=2400 k > 1960 k = C*
12″x1″
C* = 1960 k > 1200 k = P y web
PNA is in Steel Flange 53
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Cc =C*= 0.85f ′ cbe ts = 1960 k
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Example 2 (Continued) In Example 1, because the entire steel girder was in tension – we knew where the force resultant of the stresses in the steel section was positioned. In this problem, there are several force resultants. 8 in.
72 in.
Cc =C* TTF
24” + 1”
Fy
CTF
TWeb TBF Fy 55
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steel section can be used.
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Example 2 (Continued) 8 in.
Py = 2400 k 72 in.
24” + 1”
y = 0.37 in. Cc =C*= 0.85f ′ cbe ts = 1960 k 2Fy 2CTF= 2Fybf y 2CTF= 440k
Py =2400
Fy Mp = 2400 k (24” + 1” – 0.37”/2) + 1960(8”/2 + (0.37”/2) Mp = 67,760 k-in = 5645 k-ft. 57
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Introduction to Stee Session 6: Plate Girder Des
Strength of Shear Stud Consider ¾ in diameter shear studs with Fu=60 ksi:
0.5
f c (ksi) ′
Qn (kips)
3.0
20.9
3.5
23.5
4.0
26.0
59
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is based upon an ultimate
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Shear Stud Design • The number of shear studs that are required is based upon the compressive resultant in the concrete deck. • Therefore, the shear that needs to be developed is the smaller of either: 1) Py = AsFy 2) C* = 0.85f ′ cbets
ts
be
C* = 0.85f ′ cbe ts
Py = AsFy
Fy 61
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Revisit Example 1
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Cc = 0.85f ′ cbe a = 2400 k
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Introduction to Stee Session 6: Plate Girder Des
Revisit Example 1 For this example, assume the beam is simply supported. ¾” dia. Shear studs are used with F u=60 k: Qn = 26 k/stud M W X
X
Consider half the beam: Cc = 2400 k
Qn
Py = 2400 k M=0
MCL = 5865 k′
# Studs/half beam = 2400k/26k/stud = 92 studs (184 total studs) Follow AASHTO Guidelines on stud spacing and also check for fatigue 63
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action in the negative moment region, this
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Introduction to Stee Session 6: Plate Girder Des
Composite Strength in Negative Flexure Although shear studs are not “required” in the negative moment region, it is usually a good idea to provide some connectors to better control cracking in the concrete deck.
65
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Introduction to Stee Session 6: Plate Girder Des
Preliminary Sizing • A major difference between building and bridge design is the predominant use of rolled sections versus built-up sections. • Buildings predominantly make use of rolled sections and beam selection is facilitated by strength design tables/charts. • Bridges predominantly make use of built up sections that require the designer to initiate the design with preliminary sizes and iterate based upon the strength requirements in the finished bridge and the demand during construction. 67
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• Table 2.5.2.6.3-1 in AASHTO provides some
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Introduction to Stee Session 6: Plate Girder Des
Deck Forming Systems • Many steel bridges are constructed using stayin-place (SIP) forming systems. • These forms provide a working surface relatively quickly for the construction personnel and as the name implies, the forms stay on the bridge permanently. • The forms are supported on a cold-formed angle that allows the contractor to account for variations in the flange thickness along the girder length and differential camber across the bridge width. 69
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haunch
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Introduction to Stee Session 6: Plate Girder Des
Stay-in-Place Forms
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considering dead and live loading (HL93 Truck
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Preliminary Sizing – Step 1 be
ts
a ycon
d/2
Based upon the design moment, Mu, in kip-ft
Py = AsFy
Fy
Cc = Py
12 2 2
The slab thickness, t s, will typically be 8-10 in. depending on girder spacing. Pick “d” based upon L/d ratios and guess a=0.75t s. 73
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The web thickness is often selected based upon a target
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Introduction to Stee Session 6: Plate Girder Des
Preliminary Sizing – Step 2 (continued) • As guidelines in flange proportioning, AASHTO allows a minimum ratio of the compression flange width to girder depth of 1/6 (Section 6.10.2.2). This is actually a very slender girder. A better target value will be b f /d = 0.25. • Other criteria for flange sizing is the compact flange provisions. =bf /2tf < 9.15 = p (for grade 50 steel). Going slightly above 9.15 will typically not have a significant impact on the behavior; however Section 6.10.2.2 has an upper limit of 12 to control distortion during welding. • If the flange is non-compact, flange local buckling needs to be evaluated.
75
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Assuming the neutral axis is still in the slab and selecting
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Introduction to Stee Session 6: Plate Girder Des
Preliminary Sizing – Step 4 • If “areq’d” from Step 3 is less than t s, the neutral axis is in the deck. If the value is significantly different than the value from step 1, recalculate the area of steel required in step 1 and iterate through the steps until “a” stabilizes. This will usually only take 1-2 iterations. • If “areq’d” is greater than t s, the neutral axis is in the steel girder. • Calculate the moment strength and adjust the girder proportions appropriately.
77
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Preliminary Design Example (Step 1): Approximate Steel Area Assuming PNA in slab with a=0.75t s=6 in.:
12 12"/′18000′ 6" 2 2 50 72" 8" 2" 2 2 100 in Total A = 100 in – 72” x 0.56” = 60 in
2
2
f
2
Assume a singly-symmetric section with A bf =1.5Atf
1.5 60 : 24 , 36
79
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For top flange - targeting b f /d = 0.25, results in a width of: Special offer for students: Only $4.99/month. bf = 0.25*72″ = 18″. Try 18″ x 1.125 ″
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Preliminary Sizing (step 2) – section properties 18” x 1.125” 72”x9/16”
Atf = 20.25 in 2, Abf = 35.8 in2, Aweb = 40.5in2
35.873.94 20.251.13/2 40.537.12 96.6
ys-top
43.1
22” x 1.625”
″
Atot = 96.6 in2
81
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Preliminary Sizing – Step 4
= 15.7in /18 =0.87
Distance from top of girder to PNA,
2
Py = 96.6in2x50ksi = 4830k 120 in.
″
8″
″
f
″
Cc =C*= 0.85f ′ cbe ts = 3264 k
2” haunch
2″
″
2Fy
43.1”
2CTF= 2Fybf y 2CTF= 1566k
Modified stress diagram
Py =4830k Fy Mp = 4830 k (43.1 ″ – 0.87″/2) + 3264k (8”/2 + 2 ″+(0.87″/2)) Mp = 227,075 k-in = 18900 k-ft. > 18000 k-ft = M u OK 83
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Stability in Finished Bridge • We talked about the different stability limit states at the outset of this lecture; however our recent example did not consider any stability limit states. • With the exception of the negative moment region, stability in the finished bridge is often not a concern. • The reason for this is the location of both the PNA and the elastic neutral axis as well as the lateral/torsional restraint provided by the cured concrete deck. Local buckling in the positive moment region is not generally a problem. • We will therefore not focus on the stability behavior in the finished bridge. 85
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Stability During Construction • While stability in the finished bridge of our example was not an issue, we do need to consider the behavior during construction. • The critical stage for lateral torsional buckling will often be during placement of the concrete bridge deck. • Stability is generally provided by the cross frames or diaphragms that are positioned along the length. • The design moments will be the moments during deck placement. • The AASHTO specification has a load factor of 1.4 that is applied to dead load during construction.
87
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A = 20.25 in 2, Abf = 35.8 in2, Aweb = 40.5in
tf Special offer for students: Only $4.99/month.
Load Factor on Component
W = 2 k/ft
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Construction Stage Preliminary Sizing Example Atf = 20.25 in 2, Abf = 35.8 in2, Aweb = 40.5in2
121 72 0.56 40.5 43.1 37.12 43.1” 20.3 43.1 1.12/2 72” x 0.56” 1.62 35.8 72 1.12 2 43.1 89500 22” x 1.62” 8950043.1 2077 13 13 18 1.12 72 0.56 22 1.62 43.8 18” x 1.12”
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Introduction to Stee Session 6: Plate Girder Des
Construction Stage – Bracing Layout • Although the girder has a non-compact web, we will start assuming elastic behavior and use the equation from the main body of AASHTO, which if you recall is for a slender web section.
• Design Construction Stress:
562512 32 2077
Note: 32 ksi<35 ksi = 0.7Fy – therefore elastic as assumed
91
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150′
150′
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Introduction to Stee Session 6: Plate Girder Des
Construction Stage – Bracing Layout • We can also check the elastic behavior using the expression for L r from AASHTO Eq. 6.10.8.2.3-5:
4.41 29000 35 399. 417. Elastic as assumed.
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r
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that rely on both the St. Venant and Warping torsion.
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Construction Stage – Bracing Layout • With Lb=450 in., r t=4.41 in., J=43.8 in 4, Sxc=2077 in3, h=73.4 in. (distance between flange centroids), Appendix A6 Equation A6.3.3-8:
29000 1.0 43.8 450 450 10.078 207773.4 4.41 30.5 32 4.41 No Good – Stay with Lb=30 ft.
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System Buckling of Narrow
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Introduction to Stee Session 6: Plate Girder Des
History of System Buckling Mode • Marcy Pedestrian Bridge – consisted of a single box girder with no top lateral truss. Girder had closely spaced internal K-frames (behaves very similar to a twin I-girder system) Marcy tub girder behaved as twin I-girders
97
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Global Buckling of Narrow Steel Units (con.)
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Girder Bottom
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Introduction to Stee Session 6: Plate Girder Des
Global Buckling of Narrow Steel Units • For a twin-girder system: L b vs. Lg • Bracing spacing controls individual girder lateraltorsional buckling
• Bracing size and spacing doesn’t control system buckling
99
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useful Useful Not AASHTO Currently limits Cancel anytime. moment to 50% of capacity predicted by this equation nd
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Introduction to Stee Session 6: Plate Girder Des
Global Buckling of Narrow Steel Units y
75.8x1.0
x
x 31.9x0.738
y s
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Considering all of the gird
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6.10.3.4.2-1
ss the width of the unit within the
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Introduction to Stee Session 6: Plate Girder Des
Lecture 6 Recap • Buckling limit states involve a loss of stiffness of a cross sectional element, an overall member, or an entire structural system. • Local buckling modes include Local Flange Buckling, Local Web Buckling (Web Bend Buckling), and potentially effects around concentrated forces such as Web Crippling. • Global Member Buckling for beams consists of Lateral Torsional Buckling. • System Buckling modes where a few girders may buckle as a unit can occur in relatively narrow bridges. • In many situations with global buckling, the structure provides significant warning of problems (lack of fit, etc.) 103
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Lecture 6 Recap (continued)
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NSBA Night School July 18, 2016
Introduction to Stee Session 6: Plate Girder Des
Lecture 6 Recap (Continued) • In preliminary sizing, efficient proportions of the cross section can be obtained based upon a number of basic guidelines: ‒
Typical span/depth ratios
Assumptions on PNA location for composite girder
‒ ‒
Web slenderness between 120~137 (Gr. 50 steel)
‒
Compression Flange/Depth ratio of approximately 0.25
• The spacing between cross frames and diaphragms is often controlled by lateral torsional buckling during casting of the construction deck.
105
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Nsba Night School Course b1 Session 6
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Night School 10 Session 7
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NSBA Night School July 18, 2016
NIGHT SCHOOL 8 SESSION 4.pdf
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Introduction to Stee Session 6: Plate Girder Des
Individual Webinar Registrants CEU/PDH Certificates Within 2 business days… • You will receive an email on how to report attendance from:
[email protected]. • Be on the lookout: Check your spam filter! Check your junk folder! • Completely fill out online form. Don’t forget to check the boxes next to each attendee’s name!
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Individual Webinar Registrants Master your semester with Scribd Read Free Foron 30this Days Sign up to vote title CEU/PDH Certificates & The New York Times Useful Not useful Within 2 business days… Special offer for students: Only $4.99/month.
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Nsba Night School Course b1 Session 6
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Nsba Night School Course b1 Session 6
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Night School 10 Session 7
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NSBA Night School July 18, 2016
NIGHT SCHOOL 8 SESSION 4.pdf
ns13session8handout2p
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Introduction to Stee Session 6: Plate Girder Des
8-Session Registrants CEU/PDH Certificates One certificate will be issued at the conclusion of all 8 sessions.
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8-Session Master your semester with Scribd Registrants Read Free Foron 30this Days Sign up to vote title Quizzes & The New York Times Useful Not useful anytime. Access to the quiz: Information for accessing the quiz will be Cancel emailed to you by It will contain a link to access the quiz. EMAIL COMES FROM
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