1. Composite Beams (cont’d)

4. Floor beam
Girder S L

5. b tc h

6. Effective concrete-steel T-Beam
The composite beam can be designed as an effective T-Beam, where width of the slab on either side is limited to:
1/8 of the beam span
½ distance to centerline of adjacent beam
The distance to the end of the slab

7. Shoring Temporary shores (supports) during construction are optional.
If temporary shores are NOT used, the steel section must have adequate strength to support all loads prior to concrete attaining 75% of f’c

8. Shear Strength
Design shear strength and allowable shear strength of composite beams are based on just the steel section!

9. Flexural Strength
Positive Flexural strength fbMn (or Mn/Wb) are determined as follows:
fb = (LRFD) and/or Wb = 1.67 (ASD)
Mn depends on h/tw as follows:
If determine Mn for yield from plastic stress distribution on composite section (flange yield)
Else, determine Mn from yielding from superposition of elastic stresses, considering shoring

10. b
0.85 f’c tc a h sy

11. Negative moment
The design Negative moment can be based on the steel section alone.
Could be based on plastic stress distribution through composite section provided
Steel beam is adequately braced compact section
Shear connectors in the negative moment area
Slab reinforcement parallel to steel is properly developed

12. Shear Connectors
Concrete Slab
Ribbed steel deck
Steel section

13. Effective width b tc Yc hr tw d tf bf

14. Composite beam with formed steel deck
Nominal rib height is limited to 3 inches.
Width of rib or haunch must be at least 2 inch. For calculations, never more than minimum clear width
Must be connected with shear connectors ¾” or less in diameter. Can be welded through deck or to steel cross-section.
Connectors must not extend more than 1.5” above the top of the deck.
Must be at least ½” cover

15. Composite beam with formed steel deck (cont)
Slab thickness must be at least 2”
Deck must be anchored to all supporting members at max spacing of 18”.
Stud connectors, or a combination of stud connectors and arc spot (puddle) welds may be used
If ribs are perpendicular to steel, concrete below the steel deck must be neglected for calculation section properties and concrete area

16. Composite beam with formed steel deck (cont)
For deck ribs parallel to steel beam, concrete below top of steel deck may be included in determining composite section properties and area of concrete.
Deck ribs over beams may be split and separated to form concrete haunch.
When depth of deck is 1.5” or greater, average width of supported haunch or rib must be at least 2” for the first stud plus four stud diameters for each additional stud.

19. Shear Connectors Shear force is transferred by the connectors
The total horizontal shear force, V’, between max positive moment and zero moment is the smallest of
Concrete crushing: V’ = 0.85 f’c Ac
Steel yielding: V’ = As sy
Connectors fail: V’ = ∑Qn

20. Shear Connectors
For negative moments, concrete cannot withstand tension. Rebar yields
Tensile yielding: V’ = Ar syr
Shear connectors: V’ = ∑ Qn

21. Number of shear connectors
Number of shear connectors = V’/Qn
Strength of one shear connector
Asc = x-sectional area of 1 connector,
Rg and Rp on next pages
su = tensile strength of connector

22. Rg Rg = 1 for Rg = 0.85 for Rg = 0.7 for
One stud welded in steel deck rib with deck perpendicular to steel shape;
Any number of studs welded in a row through steel deck with deck parallel to steel shape and ratio of rib width to depth ≥ 1.5
Rg = 0.85 for
Two studs welded through steel deck rib with deck perpendicular;
One stud welded through deck parallel to steel and rib width to depth < 1.5
Rg = 0.7 for
Three or more studs welded in the deck rib, perpendicular to steel

23. Rp Rp = 1.0 for Rp = 0.75 for Rp = 0.6 for
Studs welded directly to steel shape (not through steel deck) and having a haunch detail with not more than 50% of the top flange covered by deck or sheet steel closures.
Rp = 0.75 for
Studs welded in composite slab, deck perpendicular to steel, emid-ht ≥ 2 inch
Studs welded through deck, deck parallel to steel
Rp = 0.6 for
Studs welded in composite slab, deck perpendicular to steel and emid-ht < 2 inch
emid-ht = distance from edge of stud shank to steel deck web measured at mid height of deck rib in the load bearing direction of the stud (direction of maximum moment)

24. Channels
Channels welded to steel beam may be used as shear connectors.
Welds must develop the shear resistance Qn
Effects of eccentricity must be considered
Where tf = flange thickness of channel connector
tw = web thickness of channel shear connector
Lc = length of channel shear connector

25. Compressive Strength
Concrete crushing: Cc = 0.85 f’c Ac
Steel yielding: Ct = As sy
Connectors fail: Cs = ∑Qn
Similar to shear values
The location of the plastic neutral axis affects the failure criteria

26. Location of Plastic Neutral Axis
Case 1: PNA is in the web of the steel. Occurs when concrete compressive force is less than web force, Cc ≤ Pyw
Case 2: PNA is in the thickness of the top flange. Pyw < Cc < Ct
Case 3: PNA is in the concrete slab. Cc ≥ Ct
Note: in Case 3, concrete below PNA is neglected!

27. Case 1
0.85f’c a Cc
Eff slab hr e
PNA d sy
d/2 tf sy

28. Case 2
0.85f’c a Cc
Eff slab hr
PNA sy e d
d/2 tf sy

29. Case 3
0.85f’c a Cc
Eff slab hr
PNA e d
d/2 tf sy

30. Example Composite framing in typical multi-story building
3.25” lightweight concrete, 2” steel deck.
Concrete: r = 115 lb/ft2; f’c = 3 ksi
Additional 30% dead load assumed for equipment during construction
Deck is supported on steel beams with stud connectors.
¾” diameter, 3.5” long
Unshored construction
Beams must support their own weight, weight of concrete before it hardens, deck weight and construction loads.
Check floor for vibration with damping ration of 5%.

31. Example (p2) Typical beam is 30 ft long.
Distance to adjacent beams is 10 ft.
Ribs are perpendicular to the beam
Uniform dead loads on beam are, 500 lb/ft + 30% for equipment loads
Superimposed loads are 250 lb/ft
Live loads (uniform) 500 lb/ft

32. Example (p3) Have to pick a beam. Must handle 1.3*0.5 + wt of beam.
Using A992 (50 ksi) steel. Assume 22 lb/ft starting estimate
W = 1.3* kip/ft = kip/ft
Factored load: 1.4*0.672 = 0.941
Factored moment: * L2/8 = 0.941*302/8 = kip-ft

33. Plastic section modulus
Fortunately, a W14x22 has a Z=33.2 in3, I=199 in4, and w=22

34. Deflection of the beam The deflection of the beam is given as
So camber the beam by 1.6” prior to pouring the concrete. Probably make it 1.5” in drawings.

35. Next step
We know that a W14x22 will handle the unshored loads. We need to consider live loads as well.
We can apply the load reduction factor considering our area (30’ x 10’ between beams and supports)
R = (A-150) = ( )=0.12
So our live load is 0.5*(1-0.12) = 0.44 kip/ft

36. Factored load Greater of Factored moment is thus
1.2( ) + 1.6(0.44) = 1.63 kip/ft
1.4( ) = kip/ft
Factored moment is thus
Mn = 1.63 * 302/8 = kip-ft

37. Concrete compressive force
Concrete flange with is lesser of
B = 10x12 = 120” or
B = 2 (30 x 12/8) = 90” **
Compressive force in concrete is smaller of
Cc = 0.85 f’c Ac = 0.85 x 3 x 90 x 3.25 = kips
Ct = As sy = 6.49 x 50 = kips **

38. Depth of concrete stress block
Since Cc > Ct, PNA is in the concrete slab.
The distance between the compression and tension forces, e, on the W14x22
e = 0.5d – 0.5a
= 0.5 x – 0.5*1.414 = in
We are expecting 183.4, so this passes