Composite Beams (cont d) Deflection of the beam The

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Composite Beams (contd)
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Floor beam
Girder
S
L
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b
tc
h
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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

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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 fc

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Shear Strength

• Design shear strength and allowable shear
  strength of composite beams are based on just the
  steel section!

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Flexural Strength

• Positive Flexural strength fbMn (or Mn/Wb) are
  determined as follows
• fb 0.90 (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

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b
0.85 fc
tc
a
h
sy
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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

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Shear Connectors
Concrete Slab
Ribbed steel deck
Steel section
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Effective width
b
tc
Yc
hr
tw
d
tf
bf
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Composite beamwith 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

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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

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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.

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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 fc Ac
• Steel yielding V As sy
• Connectors fail V ?Qn

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Shear Connectors

• For negative moments, concrete cannot withstand
  tension. Rebar yields
• Tensile yielding V Ar syr
• Shear connectors V ? Qn

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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

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Rg

• Rg 1 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 lt 1.5
• Rg 0.7 for
• Three or more studs welded in the deck rib,
  perpendicular to steel

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Rp

• Rp 1.0 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 lt 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)

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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

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Compressive Strength

• Concrete crushing Cc 0.85 fc 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

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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 lt Cc lt Ct
• Case 3 PNA is in the concrete slab. Cc Ct
• Note in Case 3, concrete below PNA is neglected!

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Case 1
0.85fc
a
Cc
Eff slab
hr
e
PNA
d
sy
d/2
tf
sy
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Case 2
0.85fc
a
Cc
Eff slab
hr
PNA
sy
e
d
d/2
tf
sy
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Case 3
0.85fc
a
Cc
Eff slab
hr
PNA
e
d
d/2
tf
sy
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Example

• Composite framing in typical multi-story building
• 3.25 lightweight concrete, 2 steel deck.
• Concrete r 115 lb/ft2 fc 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.

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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

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Example (p3)

• Have to pick a beam. Must handle 1.30.5 wt of
  beam.
• Using A992 (50 ksi) steel. Assume 22 lb/ft
  starting estimate
• W 1.30.5 0.022 kip/ft 0.672 kip/ft
• Factored load 1.40.672 0.941
• Factored moment 0.941 L2/8 0.941302/8
  105.8 kip-ft

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Plastic section modulus
Fortunately, a W14x22 has a Z33.2 in3, I199
in4, and w22
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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.

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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 0.0008(A-150) 0.0008(300-150)0.12
• So our live load is 0.5(1-0.12) 0.44 kip/ft

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Factored load

• Greater of
• 1.2(0.50.250.022) 1.6(0.44) 1.63 kip/ft
• 1.4(0.50.250.22) 1.081 kip/ft
• Factored moment is thus
• Mn 1.63 302/8 183.4 kip-ft

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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 fc Ac 0.85 x 3 x 90 x 3.25 745.9
  kips
• Ct As sy 6.49 x 50 324.5 kips

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Depth of concrete stress block
Since Cc gt Ct, PNA is in the concrete slab. The
distance between the compression and tension
forces, e, on the W14x22 e 0.5d 5.25 0.5a
0.5 x 13.7 5.25 0.51.414 11.393 in
We are expecting 183.4, so this passes