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1. B.Tech Admission in India
By:
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2. Composite Beams and Columns
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3. General Provisions
• When determining load effects in members and
connections of a structure with composite
members consider effective sections at the time
each increment of load is applied.
• Properties of the concrete and reinforcing steel
are per ACI 318
• Available strength of members is from either
plastic stress distribution or strain compatibility
• Tensile strength of concrete is assumed to be
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4. Plastic Stress Distribution
• Available strength assumes steel has hit yield
stress in either tension or compression, and
the concrete in compression is at 085 f’c
– This method is typically used for regular sections
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5. Strain compatibility method
• Linear strain distribution across the section is
assumed.
• Maximum concrete compressive strain of
0.003 is used
• We use this method in Structures:
Compressive
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6. Encased composite columns
• Cross-sectional area of steel must be at least
1% of total cross-section
• Concrete encasement must be reinforced with
continuous longitudinal bars and lateral
ties/spirals
– Transverse reinforcement ≥ 0.009 in2/in
• Reinforcement ratio must be at least 0.004
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7. Available Compressive Strength
• For axial load encased column, limit case of flexural
buckling
– fc = 0.75 and Wc = 2.00
=As sy
'
– P0 = nominal elastic compressive strength without length effects
(kips)
– As = area of steel section (in2)
– Asr = area of continuous reinforcing bars (in2)
– Ac = area of concrete (in2)
– sy = yield strength of steel section (ksi)
– syr = yield strength of reinforcement (ksi)
– f’c = concrete compressive strength (ksi)
P0
+Asr ssr+0.85Ac
fc
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8. Elastic buckling strength
Pe =
p2EIeff
(KL)2
• EIeff = effective rigidity of composite section (kip-in2)
• K = effective length factor
• L = laterally unbraced length of the member (in)
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9. Effective rigidity
• Es = modulus of steel (ksi)
• Ec = modulus of concrete (ksi)
• Is = moment of inertia steel section (in4)
• Isr = moment of inertia reinforcement (in4)
• Ic = moment of inertia concrete (in4)
EIeff=Es
Is+0.5Es
Isr+C1
Ec
Ic
C1
=0.1+2
As
Ac
+As
æ
ç
è
ö
ø
÷ £0.3
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10. Nominal compressive strength
• If Pe ≥ 0.44 P0
é ç æ
÷
ö
è
ë
Pn=P0 0.658
• Else (Pe < 0.44 P0)
P0
Pe
ø
ê
ù
ú
û
=0.877Pe
Pn
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11. Shear Connectors
• It is necessary to ensure that load is
transferred from the concrete to the steel
• Shear connectors accomplish this
• Resist the shear force between the slab and
beam
• Prevent separation of the slab from the beam
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12. Shear Connectors
• Stud connectors are the most common in U.S.
– Short round steel bar, welded to the beam at one
end, with a head at the other end.
– Diameter from 1⁄2 in. to 1 in. and lengths from 2 to 8
in.
– The ratio of the length to diameter ≥ 4.
– Most commonly used sizes are 3⁄4 in. or 7/8 in. dia.
• Head diameter is 1⁄2 in. larger than stud and the
head thickness is 3/8 in. or 1⁄2 in.
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13. Shear studs
• ASTM-A108, AISI Grades C1010, C1015, C1017 or
C1020 cold-drawn steel with a minimum tensile
strength of 60 ksi and a minimum elongation of 20%
– specified in the AWS Structural Welding Code D1.1-75.
• To prevent premature failure of studs because of
tearing of base metal, the size of a stud not located
over the beam web is limited to 2 1⁄2 times the flange
thickness.
• The strength of stud connectors increases with stud
length up to a length of about four diameters and
remains approximately constant for greater lengths
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14. Equivalent shear force
• V’ = required shear force
• When external force is applied to the steel
section
æ
è
V'=V1-
ö
ø
Assy
P0
ç
÷
• When external force is applied to the concrete
encasem e nt
æ
è
V'=V
Assy
P0
ç
ö
÷
ø
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15. Distribution
• Shear connectors that can hold the required
V’ must be distributed along the length for at
least 2.5 times the depth of the encased
column above and below the applied load
• Maximum spacing is 16”
• Connectors must be on at least 2 faces,
symmetrically
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16. Shear Connectors
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17. Additional issues
• At least four longitudinal bars must be used.
• Transverse reinforcement must be spaced at
the lesser of
– 16 longitudinal bar diameters
– 48 tie bar diameters
– Half of the least dimension of the composite
section
• At least 1.5 inches of clear cover is required
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18. Built-up Composite columns
• If the steel section is built from two or more
encased steel shapes, the shapes must be
interconnected
– Lacing
– Tie plates
– Batten plates
– Etc
• To prevent buckling of individual shapes
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19. Shear strength of a connector
=0.5Asc fc
• Asc = cross-sectional area of stud (in2)
• Ec = modulus of concrete (ksi)
• su = tensile strength of connector (ksi)
Qn
'Ec
£Ascsu
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20. Girder
Floor beam
L
S
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21. Effective width
b
Yc
tw
tf
bf
tc
hr
d
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22. Shear Connectors Concrete Slab Ribbed steel deck
Steel section
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