N.W.F.P. University of Engineering and Technology Peshawar 1 By: Prof Dr. Akhtar Naeem Khan Lecture 12: Composite Beams

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 2 Composite Beam Floor construction in buildings and bridges often consists of a reinforced concrete slab supported on steel beams

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 3 Composite Beam Earlier it was assumed that beams act independently of the floor slab, because the natural bond cannot be depended upon to develop the shear VQ/I on interface between slab and beam. If the beam is completely encased in concrete or a mechanical bond established by means of shear connectors, the two will act as a unit.

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 4 Composite Beam Supported and Unsupported Construction During construction, steel beams are placed on the supports with cranes. The concrete- deck formwork is then constructed on top of these beams and the concrete deck is poured. During the deck placement, the steel beams may or may not have beam shoring along their length (supported or unsupported).

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 5 Composite Beam Supported and Unsupported Construction If the beams are shored (supported) until the concrete of the deck cures, the resulting composite beam will be effective for the entire dead load of both the beam and slab, as well as live loads. If the beams are unshored (unsupported) during construction, then the steel beam by itself must support its own dead load, and the composite beam section will only be effective for the dead load of the deck and live loads.

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 6 Composite Beam Supported and Unsupported Construction Normally, the cost of shoring is not practical when compared with the small increase in material costs required for unsupported construction. Unless the method of construction is definitely known, assume that unsupported construction methods were used.

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 7 Analysis and Design methods of Composite beams

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 8 Composite Beam Equivalent Flange Width A composite floor is assumed to act as a series of T beams. The beams are analyzes by transforming the effective x-sectional area of concrete slab into an equivalent area of steel by the use of modular ratio. n= Es/Ec where Ec=57,000/  f’c n= 500 /  f’c

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 9 Composite Beam Effective Flange Width: AASHTO

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 10 Composite Beam Effective Flange Width: AASHTO For Interior Girder Effective Flange Width lesser of: For Exterior Girder Effective Flange Width lesser of:

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 11 Composite Beam Effective Flange Width: AASHTO The effective flange width of slab to be smaller of One-forth of beam span One-forth of beam span Center to center distance of girders Center to center distance of girders Twelve times the thickness of slab Twelve times the thickness of slab For girders having a flange on one side only: One-twelve of span One-twelve of span One-half the distance center to center of next girder One-half the distance center to center of next girder Six times thickness of slab Six times thickness of slab

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 12 Composite Beam Effective Flange Width: AISC/ASD & AISC/LRFD The effective flange width of slab on each side of beam center line must not exceed: One-eighth of beam span One-eighth of beam span One- half the Center to center distance of beams One- half the Center to center distance of beams For edge beams the distance to the edge of slab For edge beams the distance to the edge of slab

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 13 Design of Composite Beam AISC allows two methods of design Method 1 Method 2 The steel section alone may be proportioned to resist the positive moment due to all loads. If this method is used, shoring is not required. The beam may be sized assuming the steel sections to carry all loads applied prior to hardening of concrete and composite section to carry all dead and live loads acting after the concrete has hardened. If shoring is used, all loads are assumed to be resisted by composite section.

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 14 Design of Composite Beam Allowable stress 0.66Fy ………method Fy ………method 2  b = 0.9 for method 1 and method 2  b = 0.9 for method 1 and method 2 Dead-load & Live- load factors are used Dead-load & Live- load factors are used ASIC/ASD AISC/LRFD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 15 Design of Shear Connectors The horizontal shear at the slab beam junction must be resisted by using shear studs to ensure composite action Bond between concrete slab and steel beam can not be relied upon Therefore mechanical shear connectors are required at the slab/ beam interface

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 16 Design of Shear Connectors

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 17 Design of Shear Connectors Shear Strength of a single shear connector is given by: Qn = Nominal Strength of one stud Asc = Sectional area of stud in sq. in. fc’ = Compressive strength of concrete Ec = Modulus of elasticity of concrete Number of connectors required is given by: Which are to be provided between pt of Max moment to zero moment on each side of Mmax

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 18 Design of Composite Beams

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 19 Design of Composite Beams If the dead loads are taken up by the steel beam, then the Dead Load Deflection is: The Live load deflections are assumed to be resisted by composite action and moment of inertia of composite section is used for the purpose: The Live load deflections are assumed to be resisted by composite action and moment of inertia of composite section is used for the purpose: Deflection Considerations

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 20 Design of Composite Beam ASIC/ASD Estimate As based on ultimate moment with FOS=2.2 Allowable stress in steel section 0.66Fy. Allowable stress in steel section 0.66Fy. Allowable stress in concrete 0.45fc’. Allowable stress in concrete 0.45fc’.

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 21 Design of Composite Beam ASIC/ASD Section properties for in unshored construction are computed by elastic theory. Bending stress in beam is the sum of (1)Dead-load moment (that the steel beam alone resists) (2)Live-load moment (that the composite beam resists). Allowable stress is 0.9Fy

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 22 Design of Composite Beam ASIC/LRFD A good estimate of required As of steel section based on ultimate moment is given by

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 23 Design of Composite Beam ASIC/LRFD Positive moment For plastic stress distribution on composite section hc/tw  640/  Fy …………………..  b=0.85 For hc/tw > 640/  Fy…………………..  b=0.90 Negative moment Mn is based on steel section alone …….  b=0.90 For plastic stress distribution…………….  b=0.85

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 24 Design of Composite Beam ASIC/LRFD Steel section for unshored construction must be designed to support all loads applied before the concrete attains 75% of specified fc’

Thanks

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 26 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 27 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 28 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 29 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 30 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 31 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 32 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 33 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 34 Design Example 1 ASD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 35 Design Example 1 LRFD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 36 Design Example 1 LRFD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 37 Design Example 1 LRFD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 38 Design Example 1 LRFD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 39 Design Example 1 LRFD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 40 Design Example 1 LRFD

CE-409: Lecture 12Prof. Dr Akhtar Naeem Khan 41 Thanks