Composite Beams and Columns

siennatearfulUrban and Civil

Nov 25, 2013 (3 years and 10 months ago)

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Composite Beams and Columns

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 zero


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


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

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 in
2
/in


Reinforcement ratio must be at least 0.004

Available Compressive Strength


For axial load encased column, limit case of flexural
buckling


f
c

= 0.75 and
W
c

= 2.00




P
0

= nominal elastic compressive strength without length effects
(kips)


A
s

= area of steel section (in
2
)


A
sr

= area of continuous reinforcing bars (in
2
)


A
c

= area of concrete (in
2
)


s
y

= yield strength of steel section (ksi)


s
yr

= yield strength of reinforcement (ksi)


f’
c

= concrete compressive strength (ksi)


Elastic buckling strength





EI
eff
= effective rigidity of composite section (kip
-
in
2
)


K = effective length factor


L = laterally unbraced length of the member (in)

Effective rigidity




E
s

= modulus of steel (ksi)


E
c

= modulus of concrete (ksi)


I
s

= moment of inertia steel section (in
4
)


I
sr

= moment of inertia reinforcement (in
4
)


I
c

= moment of inertia concrete (in
4
)

Nominal compressive strength


If P
e

≥ 0.44 P
0





Else (P
e

< 0.44 P
0
)


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

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.

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

Equivalent shear force


V’ = required shear force


When external force is applied to the steel
section



When external force is applied to the concrete
encasement

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

Shear Connectors

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

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

Shear strength of a connector




A
sc

= cross
-
sectional area of stud (in2)


E
c

= modulus of concrete (ksi)


s
u

= tensile strength of connector (ksi)

Girder

Floor beam

L

S

Effective width

b

Y
c

t
w

t
f

b
f

t
c

h
r

d

Shear Connectors

Concrete Slab

Ribbed steel deck

Steel section