Transcript NWFP University of Engineering and Technology Peshawar
N.W.F.P. University of Engineering and Technology Peshawar Lecture 12: Composite Beams
By: Prof Dr. Akhtar Naeem Khan [email protected]
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Composite Beam
Floor construction in buildings and bridges often consists of a reinforced concrete slab supported on steel beams CE-409: Lecture 12 Prof. Dr Akhtar Naeem Khan 2
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.
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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).
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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.
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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.
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Analysis and Design methods of Composite beams
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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 12 Prof. Dr Akhtar Naeem Khan 8
Composite Beam
Effective Flange Width: AASHTO CE-409: Lecture 12 Prof. Dr Akhtar Naeem Khan 9
Composite Beam
Effective Flange Width: AASHTO For Interior Girder Effective Flange Width lesser of:
Be
L
4 ,
or Be
Bo
For Exterior Girder Effective Flange Width lesser of:
Be
L
( Distance from Beam Center to Edge of Slab) 8
Be
1 2
Bo
( Distance from Beam Center to Edge of Slab) CE-409: Lecture 12 Prof. Dr Akhtar Naeem Khan 10
Composite Beam
Effective Flange Width: AASHTO The effective flange width of slab to be smaller of One-forth of beam span Center to center distance of girders Twelve times the thickness of slab For girders having a flange on one side only: One-twelve of span One-half the distance center to center of next girder Six times thickness of slab CE-409: Lecture 12 Prof. Dr Akhtar Naeem Khan 11
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- half the Center to center distance of beams For edge beams the distance to the edge of slab CE-409: Lecture 12 Prof. Dr Akhtar Naeem Khan 12
Design of Composite Beam
AISC allows two methods of design Method 1 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.
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.
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Design of Composite Beam
ASIC/ASD Allowable stress 0.66Fy ………method 1 0.76Fy ………method 2 AISC/LRFD b = 0.9 for method 1 and method 2 Dead-load & Live- load factors are used CE-409: Lecture 12 Prof. Dr Akhtar Naeem Khan 14
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 12 Prof. Dr Akhtar Naeem Khan 15
Design of Shear Connectors
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Design of Shear Connectors
Shear Strength of a single shear connector is given by:
Qn
0 .
5
Asc fc
'
Ec
Asc Fu b
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
N
Vnh
Max moment to zero moment on each side of Mmax
Qn
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Design of Composite Beams
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Design of Composite Beams
Deflection Considerations If the dead loads are taken up by the steel beam, then the Dead Load Deflection is:
DL
5
w L
4 384
Es 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:
LL
5
w L L
4 384
Es Icomp
Total L
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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 concrete 0.45fc’.
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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 12 Prof. Dr Akhtar Naeem Khan 21
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 12 Prof. Dr Akhtar Naeem Khan 22
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
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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 ’ CE-409: Lecture 12 Prof. Dr Akhtar Naeem Khan 24
Thanks
Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 ASD
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Design Example 1 LRFD
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Design Example 1 LRFD
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Design Example 1 LRFD
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Design Example 1 LRFD
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Design Example 1 LRFD
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Design Example 1 LRFD
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Thanks
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