Composite Beam Simply Supported Design

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DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM
Location : Primary Beam
Section Type : Welded Section
Span L = 15700 mm
L
ey
= 15700 mm
Average Space b
o
= 8000 mm
Original strength = 345 N/mm
2
Design strength = 345.000 FPC Available
325 Welded Section
ρ
y
= 315
N/mm
2
Effective Width, B
e
= 3925 Primary Beam
D
s
=
175 D
p
= 57
Section Depth = 1700
D = Flange Width = 400
1700 Flange Thickness = 20
Web Thickness = 18
D
s
, Overall Depth of slab = 175
D
p
, Depth of deck profile = 57
Cube Strength of concrete, f
cu
= 30
Area of "I" Beam, A = 45880
Compressive and Tensile Capacities of Concrete and Steel
The Tensile Capacity of the steel
R
s
= A ρ
y
= 14452.2 kN
The Compressive Capacity of the concrete slab over its effective width
R
c
= 0.45f
cu
B
e
(D
s
-D
p
)
= 6252.53 kN
The axial Capacity of the web The axial Capacity of the Flange
R
w
= R
s
- 2R
f
R
f
= Btρ
y
= 9412.2 kN = 2520
D
s
-D
p
= 118
Check for fully Composite
Moment capacity 03 =
= 12182.12 kNm
Web compression depth= 258.63 mm
38tε = 639.10 mm
Stress Diagram for Fully Composite Beam
(PNA lies in web of steel beam)
Check for Shear Connection
R
s
= 14452.2 kN
R
c
= 6252.53 kN
Smaller of R
C
and R
S
is 6252.53 kN
Nominal Shank Diameter = 19 mm
Welded Height = 95 mm
Concrete Grade = 30 N/mm
2
Design Capacity, Q = 80 kN Normal Concrete
No of shear connector per trough = 2
Average trough width, b
r
= 200 mm
Overall Depth of the stud = 95 mm
Reduction factor for deck profile, k = 1 Primary Beam
Resistance of a shear connector = 80 kN
Trough Spacing = 200 mm
No of connectors for fully composite = 78.2 (For half span of beam)
No of connectors can accommodate = 78.5 (For half span of beam)
No of connectors can accommodate
No of connectors for fully composite
= 1.00
Degree of shear connection =
1
V
C P S
c s
R
dR D D D
R M
4 2
2
÷
(
¸
(

¸
+ +
+
Tension
Rc, Compression
Compression
PNA
Tension
Rc, Compression
Compression
PNA
p
a
N
N
0 . 1 1 6 . 0 s
(
(
¸
(


¸

÷
(
(
¸
(


¸

=
p p
r
D
h
D
b
k
Check for Partial Composite PARTIAL COMPOSITE NOT APPLICABLE
Resistance of overall web depth, R
w
= R
s
- R
f
= 9412.20 kN
Now Compression of Concrete, R
q
= 6280 kN
Moment Capacity 04 =
= 12207.03 kNm
d/t= 92.22 < Moment Capacity 06 Not Applicable
Moment Capacity 06 =
= 10048.67 kNm NA
Stress Diagram for Partially Composite Beam
PNA in Web
Check for Shear
Applied Shear force = 2254 kN
Shear Resistance, 0.5x P
v
=
= 2891.7 kN OK
2
p
a
N
N
( )
( )
4 2 2
2
T
R
R R
D D
R
R
D R
D
R
f
q s
P S
c
q
S q S
÷
÷
(
¸
(

¸
÷
÷ +
( )
( )( )
4
2
2 2
0
2
d
R
R R R R R R
D D
R
R
D
D
R M
V
q V q V q
P S
C
q
S q S
÷ ÷ ÷ +
÷
(
¸
(

¸
÷
÷ + +
Compression
Tension
R
q
, Compression
PNA
R
q
, Compression
Tension
PNA
( )
yw
Dtp 6 . 0 5 . 0
v
q
R
R
÷ 1
76c
Check for Deflection (Unpropped Construction)
Length = 15.7 m
During Construction
Dead Loads 8 m
Floor (Concrete Slab) = 33.60 kN/m
Steel Beam Weight = 3.37 kN/m
Live Loads 8 m
Construction Loads = 1.5 kN/m
2
= 12 kN/m
During Composite Stage
Dead Loads
Total Dead Load = 7.2 kN/m
2
= 57.6 kN/m
Live Loads
Total Imposed Load = 20.0 kN/m
2
= 160.0 kN/m
Serviceability Deflection (During the Construction Stage)
Construction stage Deflection, δ =
= 10.41 mm With Construction Live Load
Serviceability Deflection (During the Composite Stage)
Modular Ratio, Long term, α
l
= 18 Normal Concrete
Modular Ratio, Short term, α
s
= 6
ρ
l
= 1
Modular Ratio, Steel to Concrete, α
e
= 18
I
g
=
= mm
4
Actual Deflection, δ =
Composite Stage = 25.02 mm Full Composite Deflection
Total Deflection = 35.43 mm
Allowable Deflection = 43.61 mm Deflection Satisfied
33564743016
EI
WL
384
5
4
( ) ( )
( ) | |
p s e e
p s p s e
e
p s e
x
D D B A
D D D D D AB D D B
I
÷ +
+ + ÷
+
÷
+
o o 4
) (
12
2 3
g
EI
WL
384
5
4
Check for Service Stresss
= 1673.76 <A Section is Uncracked
Bending Stress in steel section (During the Construction Stage)
M = 1508.89 kNm
Bending Stress, f
bf
= 70.66 N/mm
2
Bending Stress in steel section (During the Composite Stage)
(Depth of neutral axis below top of the
concrete flange)
Thus, Y
g
=
= 677.90 mm
M = 6704.528 kNm
Bending Stress in Concrete, f
bc
= 7.52 N/mm
2
< Satisfied
Bending Stress in Steel, f
bs
= 239.12 N/mm
2
Total Stress in steel = 309.78 N/mm
2
Satisfied
6
( )
e p
e p s
D D
B D D
o 2
) (
2
+
÷
( )
( )
e p
e p s
D D
B D D
A
o 2
2
+
÷
>
( ) ( )
| | ) ( 2
2
2
p s e e
p s e s e
D D B A
D D B D D A
÷ +
÷ + +
o
o
cu
f 5 . 0
Web Classification - Composite Stage
r = -0.71
Table 01
Flange/Web Classification - Construction Stage
Flange Classification Welded Section
ε = 0.934
Flange Class 1- Plastic
Table 02
Web Classification Welded Section
ε = 0.934
Web Class 2- Compact
Class 1, Plastic
Class 2, Compact
Class 3, Semi Compact
74.7
93.4
112.1
92.2
Class 1, Plastic
Class 2, Compact
Class 3, Semi Compact
9.55
26.16
29.90
37.37
92.2
208.0
247.0
Class 01 Compact
Class 02 Compact
-51.4
Class 03 Semi Compact, When r <
0
-65.9
Class 03 Semi Compact, When r
0.66
-250.6
Class 03 Semi Compact, When
0.66 > r 0
9
10
t
d
r + 1
64c
r + 1
76c
c |
.
|

\
|
÷13
41
r
>
r 2 1
114
+
c
>
( )
( )
2
3
2 1
1 114
r
r
+
+ c
T
b
c 28
c 32
c 40
t
d
c 80
c 100
c 120
Table 03
Design Summary
APPLICABLE
PARTIAL COMPOSITE NOT APPLICABLE
OK
Deflection Satisfied
Satisfied
Satisfied
Web Classification during
construction
Web Class 2- Compact
Web Classification during
composite
Refer Table 01
Flange Classification during
construction
Flange Class 1- Plastic
Bending Stress in Concrete
during composite
7.52
N/mm
2
Total Stress in Steel during
composite
309.78
N/mm
2
Section Behaviour
70.66
N/mm
2
Section is Uncracked
Bending Stress in steel during
construction
Shear Resistance 2891.70 kN
Deflection 35.43 mm
Fully Composite Moment
Partially Composite Moment 12207.03 kNm
12182.12 kNm
10
1
2
3
4
5
6
7
8
9
mm
mm
mm
mm
mm
mm
N/mm
2
mm
2
kN
0 . 1 1 6 . 0 s
(
(
¸
(


¸

÷
(
(
¸
(


¸

=
p p
r
D
h
D
b
k
Moment Capacity 06 Not Applicable
2
3
( )
( )( )
4
2
2 2
0
2
d
R
R R R R R R
D D
R
R
D
D
R M
V
q V q V q
P S
C
q
S q S
÷ ÷ ÷ +
÷
(
¸
(

¸
÷
÷ + +
v
q
R
R
÷ 1
76c
r + 1
64c
r + 1
76c
c |
.
|

\
|
÷13
41
r
r 2 1
114
+
c
4
( ) ( )
( ) | |
p s e e
p s p s e
e
p s e
x
D D B A
D D D D D AB D D B
I
÷ +
+ + ÷
+
÷
+
o o 4
) (
12
2 3
( )
( )
2
3
2 1
1 114
r
r
+
+ c
(Depth of neutral axis below top of the
Satisfied
Satisfied
7
8
5
PARTIAL COMPOSITE NOT APPLICABLE
( )
(
¸
(

¸

÷ ÷ +
p s
c
s
s s
D D
R
R D
D R
2 2
( )
( )
4 2 2
2
T
R
R R
D D
R
D
R
f
c s
p s
c s
÷
÷
|
|
.
|


\
| +
+
V
C P S
c s
R
dR D D D
R M
4 2
2
÷
(
¸
(

¸
+ +
+
Tension

Rc, Compression

Compression

PNA
R
c
, Compression

Tension

PNA
R
S
, Compression

Tension, R
S
PNA
4 2 2
2
d
R
R
D D
R
R
D
D
R M
v
q
P S
c
q
S C S
÷
(
¸
(

¸

|
.
|

\
| ÷
÷ + +
( )
( )
4 2 2
2
T
R
R R
D D
R
R
D R
D
R
f
q s
P S
c
q
S q S
÷
÷
(
¸
(

¸
÷
÷ +
0 . 1 1 85 . 0 s
(
(
¸
(


¸

÷
(
(
¸
(


¸

=
p p
r
D
h
D
b
k
8 . 0 1 6 . 0 s
(
(
¸
(


¸

÷
(
(
¸
(


¸

=
p p
r
D
h
D
b
k
6 . 0 1 5 . 0 s
(
(
¸
(


¸

÷
(
(
¸
(


¸

=
p p
r
D
h
D
b
k
0 . 1 1 6 . 0 s
(
(
¸
(


¸

÷
(
(
¸
(


¸

=
p p
r
D
h
D
b
k
Compression

Tension

R
q
, Compression

PNA
R
q
, Compression

Tension

PNA

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