1. Advanced Flexure Design COMPOSITE BEAM THEORY SLIDES
Teaching Modules for
Steel Instruction
Advanced Flexure Design
COMPOSITE BEAM THEORY SLIDES
Developed by Scott Civjan
University of Massachusetts, Amherst
Composite Beam Theory

2. Composite Beams
Composite action accounts for the steel beam and floor slab working together to resist bending moments.
Advantages over non-composite design:
Increased strength
Increased stiffness
For given load conditions can achieve:
Less steel required
Reduced steel depth
Composite Beam Theory

3. Composite Behavior c T T c c NA NA Concrete Composite T NA Steel
Non-Composite
Slip at Interface
Two Neutral Axes
Mn= Mnconcrete+Mnsteel
I = Iconcrete + Isteel
Fully Composite
Assumed no slip at Interface
One Neutral Axes
Mn >> Mnconcrete+Mnsteel
I >> Iconcrete+Isteel
Shear at interface transferred by shear connectors.
Composite Beam Theory 3

4. Slabs Composite Metal Deck Slabs – most commonly used today.
Advantages:
Stay in place form.
Slab shoring typically not required.
Metal deck serves as positive reinforcement.
Metal deck serves as construction platform.
Flat Soffit Slabs – typically, older construction.
Composite Beam Theory

5. Effective Width of Slab
beff = effective width of the slab
Function of: Span length
Distance to nearest beam
Distance to edge of slab
beff
beff s3
edge s1 s2
edge
Composite Beam Theory

6. Flat Soffit Slabs
beff
ts, slab thickness
Composite Beam Theory

7. A A Metal Deck Slab - Ribs Parallel to Beam Span beff hr tc
hr = height of deck
tc = thickness of concrete above the deck
Composite Beam Theory 7 7

8. A A Metal Deck Slab - Ribs Perpendicular to Beam Span beff hr tc
Composite Beam Theory

9. REFERENCES: COMPOSITE BEAMS Steel Deck Institute web pages
Nelson Headed Studs web pages
Steel Deck Manufacturer Catalogs
These can be found on-line
Composite Beam Theory

10. Typical Framing Column Girder Beam Slab/Deck Span PLAN
Composite Beam Theory

11. INSERT PHOTOS: AISC Four Story Office Building Photo Slide Shows
Metal Decking Slides
Shear Studs Slides
Composite Beam Theory

12. Flexural Strength
Composite Beam Theory

13. Flexural Strength Positive Moment
The strength is determined as the plastic stress distribution on the composite section.
Negative Moment
It typically is assumed that the concrete carries no tensile forces and reinforcement is minimal, therefore strength is identical to a bare steel section.
Composite Beam Theory

14. Flexural Strength Positive Moment
Fully Composite: The strength of either the floor slab in compression or the steel beam in tension is transferred at the interface.
Partially Composite: The force transfer between the slab and beam is limited by the connectors.
Composite Beam Theory

15. Flexural Strength Positive Moment
Lateral Torsional Buckling is prevented by the slab (continuous bracing).
Local Flange Buckling is minimized by the slab.
In general, strength is controlled by Mp.
Composite Beam Theory

16. Handout on Calculations:
INSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS
Handout on Calculations:
FullyCompositeCalcs.PDF
Composite Beam Theory

17. Flexural Strength
The bare steel section must support the temporary construction loads (before the concrete has set), or the steel beam must be shored until the composite section is effective.
Composite Beam Theory

18. Shear Transfer Between Slab and Beam
Typically, provided by headed shear studs.
Shear flow, n, is calculated along the interface between slab and beam.
Minimal slip allows redistribution of forces among shear studs. Therefore, studs are uniformly distributed along the beam.
The total shear flow, n, must be provided on each side of Mmax.
Composite Beam Theory

19. Shear Transfer Between Slab and Beam
Compression Force
Tension Force
Composite Beam Theory 19 19

20. Shear Transfer Between Slab and Beam
Compression Force
Tension Force
Composite Beam Theory 20 20

21. Shear Transfer Between Slab and Beam
n = shear flow
Composite Beam Theory 21 21

22. Shear Transfer Between Slab and Beam
= shear flow to be transferred by shear studs
V = Shear at the location considered
Q = first moment of inertia of area above the interface
Itr = moment of inertia of the transformed cross section
Composite Beam Theory

23. Partially Composite Beam
Consider when fully composite strength is greater than required. This may occur when:
The shape is based on construction loads.
The shape is based on architectural constraints.
The lightest shape has excess strength.
Composite Beam Theory

24. Handout on Calculations:
INSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS
Handout on Calculations:
PartiallyCompositeCalcs.PDF
Composite Beam Theory

25. Serviceability For composite section deflections:
Transform section into equivalent steel section.
Compute center of gravity of transformed section.
Compute Itr of transformed section.
Composite Beam Theory

26. Serviceability beff beff/n tc tc hr hr Composite Beam Transformed Beam
Note:
modular ratio, n = Es/Ec
Composite Beam
Transformed Beam
Composite Beam Theory 26 26

27. Shear Strength
It typically is assumed that the slab carries no shear forces, therefore composite strength is identical to that of a bare steel section.
Composite Beam Theory

28. AISC Manual -14th Edition
Teaching Modules for
Steel Instruction
Advanced Beam Design
COMPOSITE BEAM
AISC Manual -14th Edition
Developed by Scott Civjan
University of Massachusetts, Amherst

29. Composite Beam - AISC Manual 14th Ed
Chapter I: Composite Member Design
Composite Beam - AISC Manual 14th Ed

30. Composite Beam - AISC Manual 14th Ed
Slab effective width, be
To each side of the beam, be is limited by:
one-eighth beam span
one-half distance to adjacent beam
distance to edge of slab
Lowest value controls.
Composite Beam - AISC Manual 14th Ed

31. Composite Beam - AISC Manual 14th Ed
Metal Deck Slab
≥0.5”
tc ≥ 2”
≥1.5”
hr ≤ 3”
wr ≥ 2”
steel beam
wr = average deck width
hr = height of deck
tc = thickness of concrete above the deck
Composite Beam - AISC Manual 14th Ed 31 31

32. Composite Beam - AISC Manual 14th Ed
Fully Composite Beam:
Bending Strength
Composite Beam - AISC Manual 14th Ed

33. Composite Beam - AISC Manual 14th Ed
fb = 0.90 (Wb = 1.67)
Bending Strength
Composite Beam - AISC Manual 14th Ed

34. Composite Beam - AISC Manual 14th Ed
Bending Strength
POSITIVE MOMENT
For h/tw
The strength is determined as the plastic stress distribution of the composite section. 
(*Note: All current ASTM A6 W, S and HP shapes satisfy this limit.)
NEGATIVE MOMENT
It is typically assumed that the concrete carries no tensile forces and reinforcement is minimal, therefore strength is identical to a bare steel section.
Composite Beam - AISC Manual 14th Ed

35. Composite Beam - AISC Manual 14th Ed
INSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS
Handout on Calculations:
FullyCompositeCalcs.PDF
Composite Beam - AISC Manual 14th Ed

36. Composite Beam - AISC Manual 14th Ed
Bending Strength
Fully Composite Strength can be determined by using Table 3-19.
Y2 - Calculated per handout
Y1 = 0 if PNA in the slab,
Calculated per handout if PNA in the beam flange or web.
Composite Beam - AISC Manual 14th Ed

37. Composite Beam - AISC Manual 14th Ed
Table 3-19 Nomenclature
(Pg. 3-14) 1
TFL 2
4 Eq. spaces 3 tf 4
BFL 5
Beam Flange Enlarged Detail be
a/2
Location of effective concrete flange force (SQn) a
Ycon Y2
TFL(pt.1) 1 5
BFL(pt.5) 6 7
Y1 = Distance from top of steel flange to any of the seven tabulated PNA locations
Composite Beam - AISC Manual 14th Ed

38. Composite Beam - AISC Manual 14th Ed
Bending Strength
To reach fully composite strength,
shear studs must transfer SQn for Y1 = 0 (maximum value) listed in Table 3-19.
This is equivalent to value C* in calculations (handout).
Composite Beam - AISC Manual 14th Ed

39. Composite Beam - AISC Manual 14th Ed
Shear Stud Strength
Composite Beam - AISC Manual 14th Ed

40. Composite Beam - AISC Manual 14th Ed
Strength of each stud, Qn
Equation I8-1
limits value to crushing of concrete around the shear stud.
limits value to strength of individual shear studs.
Note that this indicates that push-out of a stud through a rib could be minimized by increasing Fu of the stud, which is not realistic. The equations assume standard materials.
Composite Beam - AISC Manual 14th Ed

41. Composite Beam - AISC Manual 14th Ed
Asa = cross sectional area of shear stud
Ec = modulus of elasticity of concrete
Fu = shear stud minimum tensile strength
(typically 65ksi)
Rg accounts for number of studs welded in each deck rib and wr/hr.
Values are 1.0, 0.85 or 0.7.
Rp accounts for deck rib orientation with respect to the beam, stud engagement in the concrete above the rib, and weak or strong stud location.
Values are 0.75 or 0.6.
Composite Beam - AISC Manual 14th Ed

42. Strength, Qn, for one shear stud Table 3-21
Composite Beam - AISC Manual 14th Ed

43. Limitations on shear stud placement
for shear studs placed in metal decking:
Center-Center Spacing: > 4 times diameter
≤ 8 times slab thickness
≤ 36 inches
Shear Stud Diameter: ≤ 3/4”
≤ 2.5 times flange thickness unless over web
Composite Beam - AISC Manual 14th Ed

44. Composite Beam - AISC Manual 14th Ed
Composite strength requires that shear studs transfer SQn to each side of the maximum moment in the span.
If SQn strength of the shear studs is inadequate to provide fully composite action, the beam is partially composite.
Composite Beam - AISC Manual 14th Ed

45. Composite Beam - AISC Manual 14th Ed
Partially Composite Beam:
Bending Strength
Fb = 0.90 (Wb = 1.67)
Composite Beam - AISC Manual 14th Ed

46. Composite Beam - AISC Manual 14th Ed
INSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS
Handout on Calculations:
PartiallyCompositeCalcs.PDF
Composite Beam - AISC Manual 14th Ed

47. Composite Beam - AISC Manual 14th Ed
Partially Composite Strength can be determined by using
Table 3-19.
Y2 - Calculated per handout
Y1 - Calculated per handout
Composite Beam - AISC Manual 14th Ed

48. Composite Beam - AISC Manual 14th Ed
Partially Composite Action is limited by the total strength of shear studs.
SQn listed in Table 3-19.
This is equivalent to value C* in calculations (handout).
Composite Beam - AISC Manual 14th Ed

49. Composite Beam - AISC Manual 14th Ed
Composite Beam: Shear Strength
Composite Beam - AISC Manual 14th Ed

50. Composite Beam - AISC Manual 14th Ed
SHEAR STRENGTH
It typically is assumed that the slab carries no shear forces. Therefore, strength is identical to a bare steel section.
Composite Beam - AISC Manual 14th Ed

51. Composite Beam - AISC Manual 14th Ed
Deflection Calculations
Composite Beam - AISC Manual 14th Ed

52. Deflection Calculations
Fully Composite
Itr = transformed section moment of inertia
Lower bound values of Itr are found in Table 3-20.
Values assume concrete area equal to SQn/Fy rather than actual area.
Composite Beam - AISC Manual 14th Ed

53. Deflection Calculations
Partially Composite
Equation C-I3-4
Ieff = effective moment of inertia
Is = moment of inertia of steel section only
Itr = fully composite moment of inertia
ΣQnr= partially composite shear transfer
Cf = fully composite shear transfer
Composite Beam - AISC Manual 14th Ed

54. Deflection Calculations
Partially Composite
Equation C-I3-5
Seff = effective elastic section modulus
Ss = elastic section modulus of steel section only
Str = fully composite elastic section modulus
ΣQnr= partially composite shear transfer
Cf = fully composite shear transfer
Composite Beam - AISC Manual 14th Ed

55. Deflection Calculations
Partially Composite
Table 3-20 can be used for
lower bound values of Ieff.
Composite Beam - AISC Manual 14th Ed