Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
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Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
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Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
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Course Description Advanced Composite Beam Topics May 18, 2015 With an understanding of the basics of composite beam design now in hand, hand, this this lesson lesson will will delve delve into into more more advanc advanced ed topic topicss in comp composi osite te beam beam design design includ including ing the use of compos composite ite beam beam stiffn stiffness ess for drift drift control as well as the design of composite beam members as drag struts. A design example exploring potential limit states of composite drag strut member memberss such such as const constra raine ined d axis axis later lateral al‐torsio torsional nal buckli buckling ng will will be presented.
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Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Learning Objectives 1. Become familiar with the composite design concept of using composite beam stiffness for drift control. 2. Gain an understanding of the use of composite beam members as drag struts. 3. Become familiar with the limit states associated with composite drag strut members including constrained axis lateral ‐torsional buckling. 4. Gain an understanding of the design of drag struts through a presented design example.
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Design of Compos ite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite B eam Topics May 18, 2015 Presented by William P. Jacobs V, P.E., S.E. Principal Stanley D. Lindsey & Associates, Ltd. Atl anta, Geo rgi a
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Design of Compo site Floor Systems i n Steel Framed Buildings W. Samuel Easterli ng, PhD, PE Montague-Betts Professor of Structural Steel Design and Department Head Virgini a Tech Blacksburg, Virginia
William P. Jacobs , V, PE, SE Principal, Stanley D. Lindsey & Associates, Ltd. Atl anta, Geo rgi a
Thomas M. Mur ray, PhD, PE Emeritus Professor Virgini a Tech Blacksburg, Virginia
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Design of Composite Floor Systems in Steel F ramed Buildings Schedule Sam Easterling April 27 - Introduction to Composite Construction in Floor Systems May 4 - Fundamentals of Composite Beam Behavior and Design May 11 - Composite Girder Design and Member Serviceability Will Jacobs May 18 - Advanced Composite Beam Topics June 1 - Practical Implementation of Composite Floor Designs Tom Murray June 8 - Composite Floor Vibration – Part I: Basics of Floor Vibration Analysis June 22 - Composite Floor Vibration – Part II: Walking Vibrations June 29 - Composite Floor Vibration – Part III: Special Considerations
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Follow Up Reinforcement Over Girders
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Outline Session 4: Advanced Composite Beam Topics • Part 1: Drift Control • Part 2: Composite Collector Beams
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control AISC Design Example Building • www.aisc.org/designexamples • Part III – System Design Examples
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Drift Control AISC Design Example Building
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control AISC Design Example Building
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Drift Control AISC Design Example Building
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Frame – Strength Design
Drift Control
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Frame – Strength Design
Drift Control
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Frame – Strength Design
Drift Control
ROOF
Level 4
Level 3
h3
Level 2
• Target = H/400
Δ4
At Level 4: Overall Drift = 4 / h4
h4
δ4
Story Drift = 4 / (h4 h3 )
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Frame – Strength Design
Drift Control
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Frame – Drift Design (Noncomposite)
Drift Control
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Drift Control Was that Added Tonnage Necessary? • Standard Practice to Design as Steel‐Only for Lateral Loads • Conservative • Utilize What is Already There – For “Free”
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control What Stiffness to Use? • Schaffhausen and Wegmuller, “Multistory Rigid Frames with Composite Girders Under Gravity and Lateral Forces”, AISC Engineering Journal, 2nd Quarter, 1977, pp68‐77 (As Presented in AISC Steel Design After College) • G. Forcier, “A Parametric Study of Composite Frame Behavior”, M.S. Thesis, University of Minnesota, 1990 • AISC Commentary
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Drift Control STIFFNESS ZONES A
B
C
D
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control STIFFNESS ZONES A
B
C
D
Lateral Load Only
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Drift Control STIFFNESS ZONES A
B
C
D
Lateral + Gravity
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control STIFFNESS ZONES A
C
B
ZONE 3
ZONE 2
D
ZONE 1
L
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Drift Control STIFFNESS ZONES A
C
B
ZONE 3
ZONE 2
D
ZONE 1
L
Zone 1 = Negative Moment Region Stiffness = Bare Steel Beam Length = Less than L/2 where L is Beam Span
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control STIFFNESS ZONES A
C
B
ZONE 3
ZONE 2
D
ZONE 1
L
Zone 2 = Developed Positive Moment Region Stiffness = I of Composite Section with Full Beff Length = Greater than L/2 Minus Length of Zone 3
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Drift Control STIFFNESS ZONES 45°
Effective Width Zone 3 45°
2 e n o Z h t d i W e v i t c e f f E
CL Beam
Zone 3 Length
Zone 3 = Undeveloped Positive Moment Region Stiffness = I of Composite Section with Effective Width Equal to Column Flange Width (Conservative to Use I of Bare Steel) Reference: Schaffhausen and Wegmuller 2nd Quarter, EJ, 1977
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control STIFFNESS ZONES A
C
B
ZONE 3
ZONE 2
D
ZONE 1
Is it practical for design engineers to model typical buildings with multiple moments of inertia?
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Drift Control A
ZONE 3
B
ZONE 2
ZONE 1
ZONE 3 ZONE 2
C
ZONE 1
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control A
ZONE 3 ZONE 2
B
ZONE 1
ZONE 3 ZONE 2
C
ZONE 1
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Drift Control A
ZONE 3 ZONE 2
B
ZONE 1
ZONE 3 ZONE 2
C
ZONE 1
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control A
ZONE 3 ZONE 2
B
ZONE 1
ZONE 3 ZONE 2
C
ZONE 1
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Drift Control A
B
ZONE 1
C
ZONE 3 ZONE 2
• Isolate Beam Joint Model to Review Impact of Composite Beam on Rotational Stiffness • Conservatively Treating Zone 3 as Bare Steel Beam (For Now) 36
Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control
ZONE 1
ZONE 3 ZONE 2
L3 I steel
L1 I steel
L2 I c
Mo
θ
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Drift Control
ZONE 1
L1+L2+L3 I drift
ZONE 3 ZONE 2
L3 I steel
L1 I steel
L2
I c
Mo
θ
=
Mo
θ
This simple beam model can be used to calculate what constant moment of Inertia “Idrift” will provide same rotation angle as nonprismatic model.
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
ZONE 1
Drift Control
ZONE 3 ZONE 2
L3 I steel
L1 I steel
L2 I c
Mo
θ 1 θ 2
θ
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ZONE 1
Drift Control
ZONE 3 ZONE 2
L3 I steel
L1 I steel
L2 I c
Mo
θ 1 θ 2
θ
3 2 L2 M 0 L32 M 0 L3 M 0 L3 2 1 EI steel L2 L3 2 L2 6 L2 L2 L3 2 L2 L3 3 EI steel I steel M 0 L32 M 0 L3 M 0 L3 I L L 2 2 3 c 1 1 1/ 2 2 3 M 0 L2 L3 I steel M 0 L3 M 0 L3 1 2 I c L2 2 6 L2 L3 3
M 0 L1
1
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Lower Bound Parametric Study: • Conservatively Assume Zone 1 = L/2
ZONE 1
L1 I steel
ZONE 3 ZONE 2
L3 I steel
L2 I c
• Conservatively Assume Zone 3 = Isteel • β = L2 / L3 from 1 to 5 • α = Ic / Isteel from 1 to 3
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Drift Control Lower Bound Parametric Study: • Conservatively Assume Zone 1 = L/2
ZONE 1
L1 I steel
ZONE 3 ZONE 2
L3 I steel
L2 I c
• Conservatively Assume Zone 3 = Isteel • β = L2 / L3 from 1 to 5 • α = Ic / Isteel from 1 to 3 I drift LB
0.001 I steel 4.34 2 15 2 3 2 2 21.5 2 50 960
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control
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Drift Control Parametric Study: • Conservatively Assume Zone 1 = L/2
ZONE 1
L1 I steel
ZONE 3 ZONE 2
L3 I c’
L2 I c
• Assume Zone 3: Inertia Ic’ based on maximum of α=1.5 and (1+ α)/2 • β = L2 / L3 from 1 to 5 • α = Ic / Isteel from 1 to 3 I drift
0.001 I steel 17.1 2 70.6 2 16.7 2 2 76.8 2 15.4 1180
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control
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Drift Control Upper Bound Study: • Assume L3 Fully Developed = Ic
ZONE 1
L1 I steel
ZONE 3 ZONE 2
L3 I c
L2 I c
• Can Solve Directly
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
ZONE 1
ZONE 2
L1 I steel
L2=L1 I c
Drift Control Each Side = L1
I drift
=
Mo
Mo
θ
θ
M L 1 0 1 2 3 EIc
M0 L1
1
3EI steel
1
M0 L1 1 1 2 3 E(Ic I steel )
M0 L1
3 EIdrift
2
M0 L1
3EI drift
1
1 M L 0 1 1 2 6 EI drift
1/
1/
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ZONE 1
ZONE 2
L1 I steel
L2=L1 I c
Drift Control Each Side = L1
I drift
=
Mo
Mo
θ
θ
M0 L1
3 E(Ic I steel ) 1 3( Ic I steel ) I drift upper
M0 L1
6EI drift
1 6I drift
0.5I steel 0.5I c 48
Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control What Stiffness to Use? • Schaffhausen and Wegmuller, “Multistory Rigid Frames with Composite Girders Under Gravity and Lateral Forces”, AISC Engineering Journal, 2nd Quarter, 1977, pp68‐77 (As Presented in AISC Steel Design After College) • G. Forcier, “A Parametric Study of Composite Frame Behavior”, M.S. Thesis, University of Minnesota, 1990 • AISC Commentary
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Drift Control Leon and Forcier • More advanced parametric study on low‐rise frames controlled by stiffness • Begin with similar model (half ‐span positive and half ‐span negative bending). • Split beams into 10 segments and iterated to assign either positive or negative bending stiffness onto each segment
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Leon and Forcier I drift
0.6 I steel 0.4I LB
where : I drift I steel I LB
Equivalent Moment of Inertia for Drift Calcs Bare Steel Moment of Inertia Lower Bound Moment of Inertia Per AISC Eq. C-I3-1 (As Tabulated in Manual Table 3-20)
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Drift Control What Stiffness to Use? • Schaffhausen and Wegmuller, “Multistory Rigid Frames with Composite Girders Under Gravity and Lateral Forces”, AISC Engineering Journal, 2nd Quarter, 1977, pp68‐77 (As Presented in AISC Steel Design After College) • G. Forcier, “A Parametric Study of Composite Frame Behavior”, M.S. Thesis, University of Minnesota, 1990 • AISC Commentary
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control AISC Commentary Section I3.2
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Drift Control AISC Commentary Section I3.2
I drift
I steel
I eff 2
where : I drift I steel I eff
Average Moment of Inertia for Drift Calcs Bare Steel Moment of Inertia Effective Moment of Inertia Per AISC Eq. C-I3-4
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Example Problem
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Drift Control Example Problem • Isteel of W21x50 = 984 in4 • ILB = ? • Ieff = ?
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control 3 in. deck with 3 in. concrete topping f c 4 ksi beff Qn
57 in. 21.5 kips/anchor
30 total anchors
ILB determined from Comm. Eq. C‐I3‐1:
Qn 2 2 I steel As YENA d3 2d3 d1 Y ENA F y ….OR from Manual Table 3‐20
I LB
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Drift Control Qn 15anchors 21.5 kips/anchor 323kips C Qn a 0.85 f 'c beff
323 kips 0.85 4 ksi 57 in.
1.67in. d1 tslab a / 2 6.00in. 1.67 in./2 5.17 in. d3 d / 2 20.8 in./2 10.4in.
Fig. C ‐I3.3
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control
Y ENA
I LB
Qn As d3 F y 2d3 d 1 Qn As F y 323kips 14.7 in.2 10.4 in. 50 ksi 2 10.4 in. 5.17 in. 15.2 in. 323 kips 2 14.7 in. 50 ksi Qn 2 2 I steel As YENA d3 2d3 d1 Y ENA F y 2 323 kips 2 984 in.4 14.7 in. 15.2 in. 10.4 in. 2 10.4 in. 5.17 in. 15.2 in. 50 ksi 2073 in.4
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Drift Control Example Problem • Isteel of W21x50 = 984 in4 • ILB = 2073 in4 • Ieff = ?
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Ieff determined from Comm. Eq. C‐I3‐4: I equiv
I steel
Q
n
/Cf
I
tr
I steel
• Ieff = ? x Iequiv • Latest research indicates no reduction required • See AISC Design Example I‐2 for complete “by‐hand” example of Ieff determination • Most common method of calculation is…
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Drift Control Ieff determined from Comm. Eq. C‐I3‐4: I equiv
I steel
Q
n
/Cf
I
tr
I steel
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Example Problem • Isteel of W21x50 = 984 in4 • ILB = 2073 in4 • Ieff = 2440 in4
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Drift Control Compare Drift Calculation Methods • Beam Rotation Model • Leon and Forcier • AISC Commentary
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Compare Drift Calculation Methods • Beam Rotation Model
ZONE 1
• Isteel = 984 in4
L1 I nc
• α = Ic / Isteel
ZONE 3 ZONE 2
L3 I nc
L2 I c
• β = L2 / L3
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Drift Control Compare Drift Calculation Methods • Edge Beam
45°
Effective Width Zone 3
h t d i W e v i t 2 c e e n f f o E Z
CL Beam
Zone 3 Length
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Compare Drift Calculation Methods • Parameters L 30 ft = 360 in. L3
beff eos 57 in. 12 in. 45 in.
L2
( L / 2) L3 360 in. 2 45 in. 135 in. L2 L3 3.0 1.0 5.0 o.k.
I c I steel
2440 in.4 984 in.4
2.48
1.0 3.0
o.k.
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Drift Control Compare Drift Calculation Methods • Beam Rotation Model (Lower ‐Bound) I drift LB I drift LB I steel
0.001 I steel 4.34 2 15 2 3 2 2 21.5 2 50 960 2 2 2 2 0.001 4.34 2.48 3.0 15 3.0 2.48 3 2.48 3.0
21.5 3.0 I drift LB I steel
2
50 3.0 960
1.17
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Compare Drift Calculation Methods • Beam Rotation Model
0.001 I steel 17.1 2 70.6 2 16.7 2 2 76.8 2 15.4 1180
I drift I drift I steel
2 2 2 2 0.001 17.1 2.48 3.0 70.6 3.0 2.48 16.7 2.48 3.0
76.8 3.0 I drift I steel
2
15.4 3.0 1180
1.50
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Drift Control Compare Drift Calculation Methods • Beam Rotation Model – Lower Bound (Idrift‐LB / Isteel = 1.17) • Beam Rotation Model (Idrift‐LB / Isteel = 1.50) • Leon and Forcier I drift
0.6I steel 0.4I LB
I drift
I 0.6 0.4 LB I steel 2073 in.4 0.6 0.4 4 984 in. 1.44
I steel
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Compare Drift Calculation Methods • Beam Rotation Model – Lower Bound (Idrift‐LB / Isteel = 1.17) • Beam Rotation Model (Idrift‐LB / Isteel = 1.50) • Leon and Forcier (Idrift / Isteel = 1.44)
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Drift Control Compare Drift Calculation Methods • Beam Rotation Model – Lower Bound (Idrift‐LB / Isteel = 1.17) • Beam Rotation Model (Idrift‐LB / Isteel = 1.50) • Leon and Forcier (Idrift / Isteel = 1.44) • AISC Commentary
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Compare Drift Calculation Methods • Beam Rotation Model – Lower Bound (Idrift‐LB / Isteel = 1.17) • Beam Rotation Model (Idrift‐LB / Isteel = 1.50) • Leon and Forcier (Idrift / Isteel = 1.44) • AISC Commentary I drift I drift I steel
I steel
I eff 2
I 0.5 0.5 eff I steel 2440 in.4 0.5 0.5 1.74 4 984 in. 73
Drift Control Compare Drift Calculation Methods • Beam Rotation Model – Lower Bound (Idrift‐LB / Isteel = 1.17) • Beam Rotation Model (Idrift‐LB / Isteel = 1.50) • Leon and Forcier (Idrift / Isteel = 1.44) • AISC Commentary (Idrift / Isteel = 1.74) • Which one would you use???
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Updated Frame Results
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Drift Control Updated Frame Results
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Drift Control Updated Frame Results
• Overall Drift Reduced by Approx. 20% in this Example • Utilizing Slab Resulted in W21x50 having the equivalent stiffness of a W21x68 (with Commentary Method)
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Drift Control Topic Summary • Can Increase Bare Beam Stiffness by 20%‐60% for Drift Control by Looking at Composite Action in Positive Moment Regions • Depending on Frame Configuration this Can Result in Drift Reductions in Range of 10% to 30% • Utilize What is Already There – For “Free” • Using A Smeared Moment of Inertia Approach is Simple to Apply • Negative Moment Region Reinforcement??? 78
Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Outline Session 4: Advanced Composite Beam Topics • Part 1: Drift Control • Part 2: Composite Collector Beams
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Collector Beams Composite Collector Beams – The Basics
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Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Composite Collector Beams – The Basics
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Collector Beams Composite Collector Beams – The Basics
B
L 82
Copyright © 2015 American Institute of Steel Construction
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Composite Collector Beams Beams – – The Basics
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Collector Beams Composite Collector Beams Beams – – The Basics
V=wL/2
V=wL/2
w(plf ) 84
Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Composite Collector Beams Beams – – The Basics
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Collector Beams Composite Collector Beams Beams – – The Basics
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Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Composite Collector Beams Beams – – Resources • AISC Specification and Commentary
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Collector Beams Composite Collector Beams Beams – – Resources •
Sabell Sabe lli, i, R., Sabol, T.A., and Easterling, S.W. (2011), NEHRP Seismic Design of Composite Steel Steel Deck Deck and and Concrete Concrete ‐Filled Diaphragms – A Guide Guide for for Practicing Practicing Engineers,, NIST GCR 11‐917‐10, NEHRP Seismic Design Technical Brief Engineers Brief No. No. 5, NIST, Gaithersburg, MD.
•
SDI (2004), Diaphragm Design Manual , Third Edition (SDI DDMO3), Steel Deck Institute, Fox Grove, IL.
•
Burm Bu rmei eist ster er,, S. and Jacobs, W.P. (2008), “Under Foot: Horizontal Floor Diaphragm Load Effects on Composite Beam Designs,” Modern Steel Steel Construction Construction,, AISC, December.
•
Pras Pr asa ad, B.K., Thompson, D.S., Sabelli, R. (2009), NCSEA Guide to the Design of Diaphragms, Chords and and Collectors, Collectors, ICC, Country Club Hills, IL
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Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Composite Collector Beams – A Closer Look W16x40 L=22’ ‐6” Mu =225 kip‐ ft (1 st Order)
Pu = 200 kips 6” NW Slab (3”, 20Ga. Deck + 3” Concrete) Spanning 10’ ‐0” w/ 1 stud/ft
89
Collector Beams Composite Collector Beams – A Closer Look
90
Copyright © 2015 American Institute of Steel Construction
45
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Composite Collector Beams – A Closer Look
91
Collector Beams Composite Collector Beams – A Closer Look
92
Copyright © 2015 American Institute of Steel Construction
46
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Some Questions • What is the Effect of the Eccentricity of the Diaphragm to the Connection/Beam Centerline? • What Axial Capacity Should Be Used? • What About Second Order Effects? • How to Take Advantage of Composite Flexural Capacity? • Shear Anchors?
93
Collector Beams Eccentricity • I’ve got a P • I’ve got an e
P e
• Sooo….M???
94
Copyright © 2015 American Institute of Steel Construction
47
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
• W36 – 20 ft. Long • 100 kips Applied at 24 in. eccentricity
95
Collector Beams Eccentricity
• W36 – 20 ft. Long • 100 kips Applied at 24 in. eccentricity
96
Copyright © 2015 American Institute of Steel Construction
48
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
• Moment = Pe / 2 = 1,200 in‐kips
97
Collector Beams Eccentricity
• Moment = Pe / 2 = 1,200 in‐kips • Reactions = Shear = Pe / L = 10 kips
98
Copyright © 2015 American Institute of Steel Construction
49
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
• What if Applied Shear is Distributed at 3 Points? • Same Total “P” – Same e
99
Collector Beams Eccentricity
• What if Applied Shear is Distributed at 3 Points? • Same Total “P” – Same e
100
Copyright © 2015 American Institute of Steel Construction
50
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
• Max Internal Moment Cut in Half (600 in.‐kips)
101
Collector Beams Eccentricity
• Max Internal Moment Cut in Half (600 in.‐kips) • Shear / Reactions the Same
102
Copyright © 2015 American Institute of Steel Construction
51
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
• Split it again – now at 7 discrete locations • Same Total “P” – Same e
103
Collector Beams Eccentricity
• Split it again – now at 7 discrete locations • Same Total “P” – Same e
104
Copyright © 2015 American Institute of Steel Construction
52
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
• Max internal moment cut in half again – now 300 in.‐kips • This trend will continue ad infinitum
105
Collector Beams Eccentricity
• Max internal moment cut in half again – now 300 in.‐kips • External reactions and shear always hold constant
106
Copyright © 2015 American Institute of Steel Construction
53
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
A
B
d A : vL R B L 0 2
R B vd/2
V beam d 2L 107
Collector Beams Eccentricity
A
B
d A : vL R B L 0 2
R B vd/2
V beam d 2L
200 k ips 16 in. 2 22.5 ft 12 in./ft
5.92 kips 108
Copyright © 2015 American Institute of Steel Construction
54
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Eccentricity
A
f1
vL vx
f 2
vd 2
d M A vx f 2 x f1 0 m 1 0 2 d vd vx x 0 m1 0 2 2 solve for m 1 m 1 0
• If diaphragm shears are assumed to be applied in a continuous distributed fashion – beam moment = 0.
109
Collector Beams Some Questions • What is the Effect of the Eccentricity of the Diaphragm to the Connection/Beam Centerline? • What Axial Capacity Should Be Used? • What About Second Order Effects? • How to Take Advantage of Composite Flexural Capacity? • Shear Anchors?
110
Copyright © 2015 American Institute of Steel Construction
55
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity What Controls? (a) Flexural Buckling About Strong Axis (b) Flexural Buckling About Weak Axis (c) Torsional Buckling (d) Other?
111
Collector Beams Axial Capacity Major (Strong) Axis Buckling – KL = Full Length of Beam Between Supports • AISC Spec. Chapter E • For this Member which is Slender (Slender Web) it is Most Expedient to Use Tables in Part 6 of Steel Manual
112
Copyright © 2015 American Institute of Steel Construction
56
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Major (Strong) Axis Buckling – KL = Full Length of Beam Between Supports KL x , EQUI V
KL y r x r y
22.5 ft 4.22
5.33 ft Enter Table 6-1
113
Collector Beams Axial Capacity
p
2.26 103 114
Copyright © 2015 American Institute of Steel Construction
57
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Major (Strong) Axis Buckling – KL = Full Length of Beam Between Supports p
2.26 10 3 Table 6-1, LRFD
c Pn x
1 p
c Pnx Pu
442 kips (compare to 448.8 kips "exact") o.k.
115
Collector Beams Axial Capacity Minor (Weak) Axis Buckling – Conservative to Assume Full Unbraced Length for Weak Axis Buckling • Generally Bare Deck Is Adequate to Provide Lateral Brace (Particularly with Ribs Perpendicular to the Beam) • Composite Slab Will Definitely Act as a Brace
116
Copyright © 2015 American Institute of Steel Construction
58
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Minor (Weak) Axis Buckling – Conservative to Assume Full Unbraced Length for Weak Axis Buckling
KL y
22.5 ft Enter Table 6-1
117
Collector Beams
p
11.1 103 118
Copyright © 2015 American Institute of Steel Construction
59
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Minor (Weak) Axis Buckling – Conservative to Assume Full Unbraced Length for Weak Axis Buckling p
11.1 103 Table 6-1, LRFD
c Pn y
1 p
c Pny Pu
90.1kips (compare to 90.1 kips "exact") n.g.
119
Collector Beams Axial Capacity Torsional Buckling • Generally Does Not Control Over Weak Axis Buckling for Standard Rolled Shapes • Specification Section E4
120
Copyright © 2015 American Institute of Steel Construction
60
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity 2 EC w 1 GJ 2 K z L I x I y
Fe
Spec. Eq. E4 - 4
2 29, 0 00 k si 1, 730 in . 1 1, 2 00 2 1.0 22.5 ft 12 in./ft 2 8. 7 k si
k si 0.794 in.4
518 in.
4
1 28.9 in.4
Though W eb is Slender it can be shown for this case that Q a 1.0 F y F e
5 0 k si 2 8. 7 k si
1.74 2.25
use Spec. Eq. E3 - 2
F y
Fcr
0.658
F E
F y
1.74
0.658
50
ksi 24.1 ksi
c Pn 0.9 Fcr Ag 0.9 24.1 ksi 11.8 in.2 256 kips
Torsional Buckling Strength = 256 kips 121
Collector Beams Axial Capacity Torsional Buckling • Generally Does Not Control Over Weak Axis Buckling for Standard Rolled Shapes • Specification Section E4
122
Copyright © 2015 American Institute of Steel Construction
61
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Constrained Axis Flexural Torsional Buckling
123
Collector Beams Axial Capacity Constrained Axis Flexural Torsional Buckling •
Timoshenko, S.P. and Gere J.M. (1961), Theory of Elastic Stability , McGraw‐Hill, New York NY.
•
AISC Design Guide 25 (2011) ‐ p36
•
AISC Seismic Design Manual (2012) – pp 8‐5:8‐7
•
Liu, D., Davis, B., Arber, L. and Sabelli, r. (2013), “Torsional and Constrained ‐Axis Flexural‐Torsional Buckling Tables for Steel W‐Shapes in Compression,” Engineering Journal , AISC, Fourth Quarter
124
Copyright © 2015 American Institute of Steel Construction
62
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Constrained Axis Flexural Torsional Buckling •
Not Currently Covered in Steel Construction Manual
125
Collector Beams Axial Capacity Constrained Axis Flexural Torsional Buckling •
Not Currently Covered in Steel Construction Manual…but coming soon.
126
Copyright © 2015 American Institute of Steel Construction
63
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Constrained Axis Flexural Torsional Buckling •
Not Currently Covered in Steel Construction Manual…but coming soon.
•
Helwig, T.A., and Yura, J.A. (1999), “Torsional Bracing of Columns,” Journal of Structural Engineering, ASCE, Vol. 125, No. 5, pp. 547‐ 555.
127
Collector Beams Axial Capacity Constrained Axis Flexural Torsional Buckling
2 E Cw I y a 2 1 Fe 0.9 GJ 2 2 K z L I x I y a Ag • After Seismic Manual Eq. 8‐2 • Includes 0.9 Stiffness Reduction Factor
128
Copyright © 2015 American Institute of Steel Construction
64
AISC Night School May 18, 2015
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
Collector Beams
129
Collector Beams
130
Copyright © 2015 American Institute of Steel Construction
65
AISC Night School May 18, 2015
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
Collector Beams
131
Collector Beams
132
Copyright © 2015 American Institute of Steel Construction
66
AISC Night School May 18, 2015
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
Collector Beams
133
Collector Beams
Reference: Helwig and Yura, “Torsional Bracing of Columns”, J. Struct. Eng., May, 1999
134
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67
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams
Reference: Helwig and Yura, “Torsional Bracing of Columns”, J. Struct. Eng., May, 1999
135
Collector Beams
Fe
2 E C w I y d / 2 2 1 0.9 GJ 2 2 K z L I x I y d / 2 Ag 2 29, 000 ksi 1, 730 in. 28.9 in.4 16 in. / 2 2 11, 200 0.9 2 1.0 22.5 ft 12 in./ft 1 2 518 in.4 28.9 i n.4 16 in. / 2 11.8 in. 15.9 ksi
ksi 0.794 in.4
136
Copyright © 2015 American Institute of Steel Construction
68
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams
Though Web is Slender it can be shown for this case that Qa 1.0 F y F e Fcr
50 ksi 15.9 ksi
3.15 2.25
use Spec. Eq. E3 - 3
0.877 F e 0.877 17.6 ksi 13.9 ksi
c Pn 0.9 Fcr Ag 0.9 13.9 ksi 11.8 in.2 148 kips c Pn Pu
n.g.
137
Collector Beams
138
Copyright © 2015 American Institute of Steel Construction
69
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams
•
Torsional Buckling = 256 kips (matches)
139
Collector Beams
•
Torsional Buckling = 256 kips (matches)
•
CAFTB = 149 kips (vs. 148 kips…) 140
Copyright © 2015 American Institute of Steel Construction
70
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Approximate Alternate 8tw
c Pn c Fy b f t f 8t w2 2 0.9 50 ksi 7.0 in. 0.505 in. 8 0.305 in. 193 kips
• AISC Design Example III‐84/85
141
Collector Beams Axial Capacity • Flexural Buckling About Major Axis = 442 kips • Flexural Buckling About Minor Axis = 90.0 kips • Torsional Buckling = 256 kips • Constrained Axis Flexural Torsional Buckling = 148 kips
142
Copyright © 2015 American Institute of Steel Construction
71
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity • Flexural Buckling About Major Axis = 442 kips • Flexural Buckling About Minor Axis = 90.0 kips • Torsional Buckling = 256 kips • Constrained Axis Flexural Torsional Buckling = 148 kips
143
Collector Beams
144
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72
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams
145
Collector Beams Required Stiffness for Continuous Torsional Bracing
• Utilize Equation (14) from Helwig and Yura, 1999 as a Basis • Re‐Arrange Terms / Substitute in a = d/2 • Modify for Continuous Instead of Discrete Bracing • Utilize Spec. Appendix 6 to Account for Web Distortion • Utilize Tau to Account for Stiffness Reductions
146
Copyright © 2015 American Institute of Steel Construction
73
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Required Stiffness for Continuous Torsional Bracing
T
Tb
T
1.5
sec
Spec.Eq. A-6-10
1 T sec Pr rs
2
Pny* d 2 2
2
3.3 Et w 3
Eq.1
a EI y d 2
Spec.Eq. A-6-13
12 ho
147
Collector Beams Required Stiffness for Continuous Torsional Bracing Tb T sec Pr rs
2 *
Pny
Required Brace Stiffness (kips-in./rad per unit length) Overall Brace System Stiffness (kips-in./rad per unit length) Web Distortional Stiffness (kips-in./rad per unit length) Required Strength in Axial Compression (kips) rx
2
ry 2 d
0.877 a Pey
2
2
(kips) - Strength Associated with Stiffness Contribution (kips)
2
EI y
Pey
a
2.724 Pr
2
L y
- Weak Axis Buckling Strength over Full Column Length (kips)
QPy ln Pr / QPy
1.0 Q Net Red ucti on P y As F y (kips)
when Pr / Py
0.39
when Pr / Py
0.39
Facto r fro m Spec. Section E7 evalu ated at Pr
148
Copyright © 2015 American Institute of Steel Construction
74
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Required Stiffness for Continuous Torsional Bracing Pr 200 k ips Pr
P y
(Given)
200 kips
11.8 in. 50 ksi 2
2
6.63 in. 1.57
rs 2
Pey
0.34
in.
2
16
2 29, 000 ksi 28.9 in.4 2
*
in. / 2
1.0 2
110
in.2
114 kips
22.5 ft 12 in./ft 0.877 1.0 114 kips 99.5
Pny
a
kips
149
Collector Beams Required Stiffness for Continuous Torsional Bracing 2 99.5 kips 16 in. 2 200 kips 110 in. 2 1.5 T 2 4 1.0 29, 000 ksi 28.9 in. 16 in.
2
0.81 kips-in./rad/in. length sec
Tb
3.3 29, 000 ksi 0.305 in. 12 16 in. 0.505 in. 0.81 1 0.81 14.6
3
14.6 kips-in./rad/in. length
0.86 kips-in./rad/in. length
150
Copyright © 2015 American Institute of Steel Construction
75
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Required Stiffness for Continuous Torsional Bracing • Required Stiffness is 0.86 kips‐in/rad per inch of beam • Check Provided Using Just the Deck in Single Curvature • Provided Stiffness = 2EI/L • Moment of Inertia of 3 in. 20 Ga. Deck = 0.920 in4/ft
2 29, 000 provi ded
0.920 in.2 / ksi 12 in./ft 10 ft 12 in./ft
ft
37.0 kips-in/rad
• Stiffness of Just Deck is Sufficient to Increase Available Strength 151
Collector Beams Required Stiffness for Continuous Torsional Bracing • What about concrete stiffness? • Can calculate per ANSI/SDI C‐2011 • Tabulated in SDI’s Floor Deck Design Manual
Ref: Sputo, T. (2014), Floor Deck Design Manual , 1st Ed., Steel Deck Institute, Glenshaw, PA. 152
Copyright © 2015 American Institute of Steel Construction
76
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Required Stiffness for Continuous Torsional Bracing • What about concrete stiffness? • Can calculate per ANSI/SDI C‐2011 • Tabulated in SDI’s Floor Deck Design Manual
2 29, 000 provid ed
13.34 in.2 / ksi 12 in./ft 10 ft 12 in./ft
ft
537
kips-in/rad
153
Collector Beams
154
Copyright © 2015 American Institute of Steel Construction
77
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Required Stiffness for Continuous Torsional Bracing • Utilizing Stiffness Provided for this Example Yields:
37 kips-in/rad c Pn 3 29 k ip s
provi ded
(deck only)
537 kips-in/rad (composite slab) c Pn 3 49 k ip s
provi ded
155
Collector Beams Required Stiffness for Continuous Torsional Bracing to Prevent Constrained Axis Torsional Buckling Length (ft) 10 15 20 25 30 35 40 45 50
Cw <= (in^6) 100.0 1000.0 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%
100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%
3000.0
10000.0
30000.0
50000.0
100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%
100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%
100.0% 100.0% 100.0% 99. 7% 97. 2% 95. 1% 93. 6% 92. 0% 90. 7%
100.0% 100.0% 99. 2% 93. 9% 89. 4% 85. 8% 82. 9% 80. 7% 79. 0%
100000.0 300000.0 100.0% 100.0% 94.2% 87.6% 81.9% 77.3% 73.7% 70.8% 68.5%
100.0% 100.0% 95.1% 85.8% 76.9% 69.2% 63.0% 58.1% 54.4%
1130000.0 100.0% 100.0% 92.6% 82.3% 72.6% 64.3% 57.7% 52.5% 48.7%
• Table Indicates % Pure Torsional Buckling Strength Achieved with Provided Stiffness of 37 kip‐in/in (20 Ga. 3in. Deck / 10ft / 1 way) • Our W16x40 has a Cw of 1,730 in6 156
Copyright © 2015 American Institute of Steel Construction
78
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Required Stiffness for Continuous Torsional Bracing to Prevent Constrained Axis Torsional Buckling Length (ft) 10 15 20 25 30 35 40 45 50
Cw <= (in^6) 100.0 1000.0 100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 100. 0% 100. 0% 100. 0%
100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 100. 0% 100. 0% 100. 0%
3000.0
10000.0
30000.0
50000.0
100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 100. 0% 100. 0% 100. 0%
100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 100. 0% 100. 0% 100. 0%
100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 100. 0% 100. 0% 100. 0%
100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 100. 0% 100. 0% 100. 0%
100000.0 300000.0 100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 100. 0% 100. 0% 100. 0%
100.0% 100.0% 100.0% 100.0% 100. 0% 100. 0% 99. 7% 98. 3% 97. 1%
1130000.0 100.0% 100.0% 100.0% 100.0% 99. 2% 96. 6% 94. 4% 92. 7% 91. 4%
• Table Indicates % Pure Torsional Buckling Strength Achieved with Provided Stiffness of 477 kip‐in/in (3.25 in. LW Conc. on 3 in. 20 Ga. Deck / 10ft / 1 way) 157
Collector Beams Required Strength for Continuous Torsional Bracing to Prevent Constrained Axis Torsional Buckling M rb
=
T
Eq.2 500 d 0.86 kips-in/rad 1000 lb/kip 500 16 in.
0.11 lb-in / inch spacing between connectors
158
Copyright © 2015 American Institute of Steel Construction
79
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Required Strength for Continuous Torsional Bracing to Prevent Constrained Axis Torsional Buckling M rb
=
T
Eq.2 500 d 537 kips-in/rad 1000 lb/kip
67
500 16 in. lb-in / inch of spacing between connectors
= 67 lb-in / inch 24 in.
1, 611 lb-in
159
Collector Beams Required Strength for Continuous Torsional Bracing to Prevent Constrained Axis Torsional Buckling T C
C
T
T
M RB b f 3
1,611 lb in
7 in. 3 in.
77 lbs negligible
160
Copyright © 2015 American Institute of Steel Construction
80
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Axial Capacity Summary • Flexural Buckling About Major Axis = 442 kips • Flexural Buckling About Minor Axis = 90.0 kips • Torsional Buckling = 256 kips • Constrained Axis Flexural Torsional Buckling = 148 kips • Constrained Axis Flexural Torsional Buckling w/ Continuous Torsional Bracing = 349 kips
161
Collector Beams Some Questions • What is the Effect of the Eccentricity of the Diaphragm to the Connection/Beam Centerline? • What Axial Capacity Should Be Used? • What About Second Order Effects? • How to Take Advantage of Composite Flexural Capacity? • Shear Anchors?
162
Copyright © 2015 American Institute of Steel Construction
81
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Second Order Effects • Axial Force in Collector will Magnify Gravity Moments • Account for with Direct Analysis (Chapter C)…OR • The Old Fashioned Way (Effective Length Method – Appendix 7 with Approximate Second‐Order Analysis)
163
Collector Beams Second Order Effects – Effective Length • K=1.0, Full Stiffness • Appendix 8 – Approximate Second Order Analysis • All of the moment on a drag strut is typically “non translational” Mnt moment (unless part of a moment frame). • Composite Stiffness?
164
Copyright © 2015 American Institute of Steel Construction
82
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Second Order Effects – Effective Length B1M nt
M r B1
C m
(A-8-1) (A-8-3 LRFD)
1 Pu Pe1
1.0 typ. for collectors
C m
Pe1
B2 M lt
2 EI x*
EI x
*
(A-8-5 About Major Axis)
( K1 L x ) 2
EIx
for Equiv. Length Method
165
Collector Beams Second Order Effects – Effective Length
Pe1
B1
M r
2 29, 000 ksi 518 in.4
1.0 22.5 ft 12 in./ft 1.0 1 200 kips 2034 kips
2
2034 kips
1.11
B1M nt 1.11 225 kip-ft 250 kip-ft
166
Copyright © 2015 American Institute of Steel Construction
83
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Second Order Effects – Direct Analysis • K=1.0 • Use Reduced Stiffness (τb) • Could Still Use Appendix 8 – Approximate Second Order Analysis (B1 / B2) • In Practice Typically Use “Rigorous” Second‐Order Analysis when using the Direct Analysis Method • Member Slenderness Magnification (P‐δ) is typically addressed by splitting analysis member into several segments. This produces amplifications analogous to B1. 167
Collector Beams Second Order Effects – Direct Analysis APPLIED LOADS
FIRST ORDER: Mu = 225 kip‐ft
SECOND ORDER: Mu = 259 kip‐ft Effective “B1” = 259/225 = 1.15 168
Copyright © 2015 American Institute of Steel Construction
84
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Second Order Effects – Direct Analysis APPLIED LOADS
FIRST ORDER: Mu = 225 kip‐ft
SECOND ORDER (NO Tau): Mu = 251 kip‐ft Effective “B1” = 251/225 = 1.11 (MATCHES HAND CALC) 169
Collector Beams Some Questions • What is the Effect of the Eccentricity of the Diaphragm to the Connection/Beam Centerline? • What Axial Capacity Should Be Used? • What About Second Order Effects? • How to Take Advantage of Composite Flexural Capacity? • Shear Anchors?
170
Copyright © 2015 American Institute of Steel Construction
85
Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Interaction From Commentary to I7
171
Collector Beams Interaction When Pu / c Pn
I
Pu
c Pn STEEL _ O NLY
When Pu / c Pn
I
0.2 M u 8 9 b M n COMPOSITE
0.2
Pu
2 c Pn STEEL _ ONLY
M u
b M n COMPOSITE 172
Copyright © 2015 American Institute of Steel Construction
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Interaction • Controlling Noncomposite Axial Strength = 349 kips • Composite Moment Strength = 420 kip‐ft (40% Composite with 1 stud/ft) • Pu = 200 kips, Mu = 250 kip‐ft
200 I
kips / 349 kips 0.57 0.2
8 250 kip-ft 1.10 1.0 349 kips 9 420 kip-ft
200 kips
n.g.
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Collector Beams Some Questions • What is the Effect of the Eccentricity of the Diaphragm to the Connection/Beam Centerline? • What Axial Capacity Should Be Used? • What About Second Order Effects? • How to Take Advantage of Composite Flexural Capacity? • Shear Studs (aka Steel Headed Stud Anchors)?
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Shear Anchors Additional Anchors Beyond those Required For Flexural Strength are Often Unnecessary
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Collector Beams Shear Anchors
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Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Shear Anchors What Anchor Strength to Use?
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Collector Beams
Q n = 17.2 kips What about What about Phi? Phi?
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Copyright © 2015 American Institute of Steel of Steel Construction
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Design of Composite of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Shear Anchors Section I8.3a Provides Phi and Omega Factors that Can Be Used as a Lower Bound
ΦQn =
0.65(17.5 kips) =11.4 kips/stud 179
Collector Beams Shear Anchors Example Problem:
nstuds
Pr
cQn
200 200 kips ips 11.4 11.4 kips/a kips/anc nchor hor
18 anchors
• 18 req’d < 22 provided for flexural design design – – OK • Note that in general the slab shear capacity will govern vs. stud requirements (diaphragm capacity approx. 5.5 kips/ft so studs at 2’ o.c. will develop diaphragm)
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Collector Beams Misc. Notes •
Recommended to Provide Min. 50% Composite Action on Collector Beams Even if Unnecessary for Flexural Design
•
Per User Note in AISC 341 Section D2.8, 25% Reduction of Stud Strength Not Rq’d for Collector Elements Subject to Amplified Seismic Load
•
Overstrength Factor Rq’d in Seismic Load Combinations for Collector Beams EVEN IN SEISMIC DESIGN CATEGORY C Per ASCE 7‐10 Sec. 12.10.2
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Collector Beams Topic Summary •
Effect of Diaphragm to Connection Eccentricity May Generally Be Safely Ignored
•
For Composite Slabs it is Likely that Constrained Axis Lateral Torsional Buckling will Control Axial Strength and it is Possible to Address with Torsional Slab Restraint
•
Don’t Forget to Account for Moment Magnification
•
Interaction Effects take into Account Composite Flexural and Noncomposite Axial Strengths
•
Studs for Gravity Generally Acceptable for Lateral – Hold a Minimum Composite Action of 50% For Distribution
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Outline Session 4: Advanced Composite Beam Topics • Part 1: Drift Control • Part 2: Composite Collector Beams Thank you: • • • •
Mark Denavit, Stanley D. Lindsey & Associates, Ltd. Larry Griffis, Walter P Moore Todd Helwig, University of Texas Rafael Sabelli, Walter P Moore
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Design of Composite Floor Systems in Steel F ramed Buildings Schedule Sam Easterling April 27 - Introduction to Composite Construction in Floor Systems May 4 - Fundamentals of Composite Beam Behavior and Design May 11 - Composite Girder Design and Member Serviceability Will Jacobs May 18 - Advanced Composite Beam Topic June 1 - Practical Implementation of Composite Floor Designs Tom Murray June 8 - Composite Floor Vibration – Part I: Basics of Floor Vibration Analysis June 22 - Composite Floor Vibration – Part II: Walking Vibrations June 29 - Composite Floor Vibration – Part III: Special Considerations
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Session 5: Practical Implementation of Composite Floor Designs • Reinforcing Composite Beams • Guidelines for Openings and Slab Penetrations • Best Practices and Tips for Composite Designs
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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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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
Individual Webinar Registrants CEU/PDH Certificates Within 2 business days… • New reporting site (URL will be provided in the forthcoming email). • Username: Same as AISC website username. • Password: Same as AISC website password.
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8‐Session Registrants CEU/PDH Certificates One certificate will be issued at the conclusion of all 8 sessions.
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Design of Composite Floor Systems in Steel Framed Buildings Session 4: Advanced Composite Beam Topics
AISC Night School May 18, 2015
8‐Session Registrants Access to the quiz: Information for accessing the quiz will be emailed to you by Thursday. It will contain a link to access the quiz. EMAIL COMES FROM
[email protected] Quiz and Attendance records: Posted Tuesday mornings. www.aisc.org/nightschool ‐ click on Current Course Details. Reasons for quiz: •EEU – must take all quizzes and final to receive EEU •CEUs/PDHS – If you watch a recorded session you must take quiz for CEUs/PDHs. •REINFORCEMENT – Reinforce what you learned tonight. Get more out of the course. NOTE: If you attend the live presentation, you do not have to take the quizzes to receive CEUs/PDHs.
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8‐Session Registrants Access to the recording: Information for accessing the recording will be emailed to you by this Wednesday. The recording will be available for two weeks. For 8‐session registrants only. EMAIL COMES FROM
[email protected].
CEUs/PDHS – If you watch a recorded session you must take AND PASS the quiz for CEUs/PDHs.
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