Bridges 6 Computations
February 2, 2017 | Author: ebed_meleck | Category: N/A
Short Description
bridge design...
Description
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0
OUTPUT
BRIDGE DECK
The bridge deck is designed as composite concrete construction, where pre-cast concrete units used as permanent form works are combined with added in-situ concrete to resist flexure. The pre-cast unit is 75mm thick, and the in-situ concrete is 175mm thick, giving the deck a combined thickness of 250mm.
2.1 THE PRECAST CONCRETE UNITS The pre-cast concrete slab unit is cast in strips measuring 1.0m wide, and spanning from one beam girder to the other. They are designed to withstand their own weight, the dead load of the in-situ concrete part of the slab being supported by the pre-cast unit during construction, and a conservative imposed loading during construction works. Two types of pre-cast slab are available, TYPE A & TYPE B.
2.1.1 LOADING Precast Slab thickness
=
75 mm
In-situ concrete thickness
=
175 mm
=
1.80 KN/m2
1. Dead Load, Gk a.
Self Weight of Pre-cast unit
b.
Weight of In-situ Concrete
S
= =
4.20 KN/m2 6.00
KN/m2
2. Imposed Loading, Qk A nominal imposed loading is considered, purely for the movement of men and materials during the laying of reinforcement and casting of the insitu concrete Use an Imposed load, Qk
=
2.00
KN/m2
3. Design Loading, w Design udl = 1.6Qk +1.4Gk
=
11.60 KN/m2
2.1.2 THE PRECAST CONCRETE SLAB TYPE A
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member
Date___december '04
REF.
CALCULATIONS
2.0
OUTPUT
BRIDGE DECK
They are designed as simply supported, to span between girders. Therefore Span Length
=
2.40 Lm
Maximum Shear Force, V1
=
13.92 KN
Design Moment
=
8.352 KNm
DESIGN FOR BENDING Design as a rectangular - beam
\
=
8.352 KNm
Span Length
=
2,400 mm
Depth of slab/deck
=
75 mm
CALCULATION OF EFFECTIVE DEPTH, d beam depth, h
=
75 mm
width of beam web, bw
=
1000 mm
cover to reinforcement, d'
=
25.0 mm
reinforcement size, f
=
20.0 mm
stirrup diameter, t
=
6.0 mm
effective depth, d
=
=
1000
h - (d' + f/2 + t)
= effective width, b
75 mm
a.
Design Moment
34 mm bw 1,000 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
k
=
M/bd²fcu
therefore, k
1997
since k'
fcu
=
0.181
=
0.156
=
40 N/mm²
it implies that compression steel required. use z c.
=
0.775 d
TENSILE REINFORCEMENT fy
=
As '
=
410 N/mm² (k-k')fcu bd²/(0.87fy.(d-d')) Apply
= T 10
(As prov. =
As
=
(As prov. =
DESIGN FOR SHEAR
200
mm centres
393 mm²)
{k'fcubd²/(0.87fy.Z)} + As' Apply
@
355 mm²
= T 20
@
1,571 mm²)
1,122 mm² 200
mm centres
mm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
Date___december '04
REF.
CALCULATIONS i.
ii.
2.0
Design Shear Force ,V
BRIDGE DECK
Design Shear Stress, v
=
Design shear Force
=
V/bd
0.8(fcu)
Checks:
5.060
0.409 N/mm²
=
40 N/mm²
N/mm²
design okay with respect to shear
Obtaining the design concrete shear stress, vc (should be 3.00)
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc
(should not be < 1.00)
=
4.620
=
0.79(100As/(bvd))1/3(400/d)0.25/1.25
= iv.
=
13.920 KN
= fcu
iii.
OUTPUT
11.765 Use 400/d
=
1.949
=
11.76
N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
0.409 N/mm²
vc
=
1.949 N/mm²
vc + 0.4 =
2.349 N/mm²
i.e. 0.5vc +v < (vc + 0.4)
Asv/Sv = 0.4*bv/(0.87fyv)
and Asv/Sv reqd
=
Apply a
fyv
=
410 N/mm²
1.121
4 Leg stirrup T 10
and Asv/Sv provided =
@
250 mm centres
1.257
2.1.2 THE PRECAST CONCRETE SLAB TYPE B They are designed to be simply supported, to span at the girders and to also have an overhang of 700mm. Therefore Span Length
=
2.40 Lm
Cantilever Span
=
0.70 m
Maximum Shear Force, V1
=
22.04 KN
Design Span Moment
=
8.352 KNm
Design Cantilever Moment
=
2.842 KNm
DESIGN FOR BENDING (MAIN SPAN) Design as a rectangular - beam Design Moment
=
8.352 KNm
Span Length
=
2,400 mm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member
Date___december '04
REF.
CALCULATIONS
2.0
BRIDGE DECK
Depth of slab/deck
75 mm
CALCULATION OF EFFECTIVE DEPTH, d beam depth, h
=
75 mm
width of beam web, bw
=
1000 mm
mm
\
=
cover to reinforcement, d'
=
25.0 mm
75
a.
OUTPUT
reinforcement size, f
=
20.0 mm
stirrup diameter, t
=
6.0 mm
effective depth, d
=
=
mm
h - (d' + f/2 + t)
= effective width, b
1000
34 mm bw 1,000 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
k
=
M/bd²fcu
therefore, k
1997
since k'
fcu
=
0.181
=
0.156
=
40 N/mm²
it implies that compression steel required. use z c.
=
0.775 d
TENSILE REINFORCEMENT fy
=
As '
=
410 N/mm² (k-k')fcu bd²/(0.87fy.(d-d'))
=
Apply
T 10
(As prov. =
As
=
@
355 mm² 200
mm centres TOP
393 mm²)
{k'fcubd²/(0.87fy.Z)} + As'
=
Apply
T 20
(As prov. =
@
1,122 mm² 200
mm centres BOTTOM
1,571 mm²)
DESIGN FOR SHEAR (TYPE B SLAB) i.
Design shear Force Design Shear Force ,V
ii.
Design Shear Stress, v
= =
V/bd
= fcu
Checks:
0.8(fcu)
=
5.060
= N/mm²
22.040 KN 0.648 N/mm² 40 N/mm² design okay with respect to shear
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member
Date___december '04
REF.
CALCULATIONS iii.
2.0
BRIDGE DECK
Obtaining the design concrete shear stress, vc
(should be 3.00)
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc =
iv.
OUTPUT
=
4.620
=
(should not be < 1.00)
0.79(100As/(bvd))1/3(400/d)0.25/1.25
11.765 Use 400/d
=
=
1.949
11.76
N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
0.648 N/mm²
vc
=
1.949 N/mm²
vc + 0.4 =
2.349 N/mm²
i.e. 0.5vc +v < (vc + 0.4)
Asv/Sv = 0.4*bv/(0.87fyv)
and Asv/Sv reqd
=
Apply a
fyv
=
410 N/mm²
1.121
4 Leg stirrup T 10
and Asv/Sv provided =
@
250 mm centres
1.257
DESIGN FOR BENDING (CANTILEVERED PORTION) Design as a rectangular - beam
2.842 KNm
Span Length
=
700 mm
Depth of slab/deck
=
75 mm
CALCULATION OF EFFECTIVE DEPTH, d beam depth, h
=
75 mm
width of beam web, bw
=
1000 mm
mm
\
=
cover to reinforcement, d'
=
25.0 mm
75
a.
Design Moment
reinforcement size, f
=
20.0 mm
stirrup diameter, t
=
6.0 mm
effective depth, d
=
h - (d' + f/2 + t)
= effective width, b
=
1000
34 mm bw
mm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member
Date___december '04
REF.
CALCULATIONS
b.
2.0
BRIDGE DECK 1,000 mm
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
k
=
M/bd²fcu
therefore, k
1997
OUTPUT
since k'
fcu
=
0.061
=
0.156
=
40 N/mm²
it implies that compression steel not required.
ii.
z
d(0.5 + (0.25 - k/0.9)0.5)
=
use z c.
=
=
0.926 d
0.926 d
TENSILE REINFORCEMENT fy
=
As
=
410 N/mm² M/(0.87fy.Z)
=
253 mm²
Apply
T 12
(As prov. =
@
250
mm centres TOP
452 mm²)
2.2 DESIGN OF IN-SITU CONCRETE COMPONENT OF SLAB DECK 2.2.1 2.2.1
DECK GEOMETRY MEMBER SIZING
The pier are braced and restrained at both ends a.
width of deck
Effective Width , Le
=
carriageway width + walkway width
=
10,000mm
+
2 * 1,500
=
11.00m
b.
Total Depth of deck-slab
=
250 mm
c.
Depth of in-situ component of slab-deck
=
175 mm
d.
Depth of pre-cast concrete section
=
75 mm
2.2.2 STRUCTURAL SYSTEM OF DECK fig. 20.1; L.S. Blake (ed),
Cross - section of bridge structure is a multiple web system.
Civ. Engr's Ref
This system consists of a concrete deck/slab supported on, and integral
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0
OUTPUT
BRIDGE DECK
with longitudinal concrete beams (girders).
Book (4th ed)
2.2.3
SPACING OF GIRDERS
Section 17.20,
"Girder spacing ranges from 7 to 9 feet. A deck slab overhang of about 2ft
F.S.Merritt (ed)
6ins is economical".
Std H/bk for
The girders which are designed as rectangular sections (inorder to ease pre cast construction) have equal centre - centre of girder spacing as 2.40m,
Civ. Engrs.
and the edge - edge of girder as 2.20m, while the deck overhang is 700mm.
Fig 1: Sketch of the deck x-section
700
2 400
2.2.4
2 400
2 400
2 400
700
LOAD ANALYSIS
2.2.4.1
Dead loads, Gk (udl)
i.
Self weight of slab:
ii.
Weight of asphalt overlay:
24kN/m3 * 0.175m
TOTAL Gk
=
2 4.20 kN/m
=
2 1.15 kN/m
=
2 5.35 kN/m
=
2 6.153 kN/m
Clause 5.4
Design dead load
BS 5400:Part II: 1978
2.2.4.2 i.
Point Loads (dead) on cantilevered section: Pc
weight of walk ways/kerbs: 0.35m*0.70m*24KN/m3*1.15
ii.
=
6.76 KN
0.15m*1.50m*24KN/m*1.15
=
6.21 KN
TOTAL Pc
=
12.97 KN
Weight of concrete handrails
2 6.15 KN/m
12.97 KN
700
2 400
2 400
2 400
2 400
12.97 KN
700
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
Date___december '04
REF.
CALCULATIONS
2.0
OUTPUT
BRIDGE DECK
Fig 2: Slab/Deck dead loads
2.2.4.3 Table 33;
i.
Dead Load Moments
Negative Cantilever Moments (6.15KN/m2 *0.72*0.5)
=
10.59 KNm
udl per notional lane
=
30.00 KN/m
BS 5400:Part II:
width of carriageway
=
8.00 m
1978
number of notional lanes
=
3
(12.97KN * 0.70m)
Reynolds & Ste-
+
ed man : R.C Designer's H/bk
2.2.4.4 Clause 3.2.9.3
i.
HA Live Loads
width of notional lanes
8.00m/3
=
2.667 m
=
2 16.88 KN/m
ultimate udl due to HA - live loads
Table 1
=
BS 5400:Part II: 1978
=
ii.
30/2.67
=
2 11.3 KN/m *
Knife Edge Loads (KEL) ie
KEL
=
=
120/2.67
= =
1.5
120KN per notional lane 45 KN/m *
1.5
67.5 KN/m
To achieve the maximum effect,place KEL at * Free end of cantilevers, & * mid - span of interior spans 67.5 KN/m
700
2400
84.7 KN
2400
107.76KN 72.9
72.9
67.5 KN/m
67.5 KN/m
2400
2400
107.76KN 72.9
16.9 KN/m2
700
84.7 KN
Fig 3: Sketch of HA - Live Loads
2.2.5
DESIGN MOMENTS & SHEAR
The bridge deck and girders are required to support both static and moving loads. Each element of the bridge must therefore, be designed for the most severe conditions that can possibly be developed by a member.
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
Date___december '04
CALCULATIONS
2.0
OUTPUT
BRIDGE DECK
Live loads must be place where they will produce the most severe condition of loading. The critical positions for placing live loads will not be the same for every member. Influence lines are therefore used in determining the most severe condition for loading. Influence lines are primarily used to determine where to place live loads to cause the maximum effects.
An influence line for a particular response such as reactions, shear force, bending moment axial force is defined as a diagram in which the ordinate at any point equals the value of that response attributable to a unit load acting at that point on the structure. Influence lines provide a systematic procedure for determining how the force ( or moment or shear force) in a given part of a structure varies as the applied load moves about the structure.
2.2.5.1
Influence Lines for udl
This is used for plotting the influence lines for uniformly distributed loads such as those due to dead loads, and for the udl portion of HA - live loads. Influence lines for the bending moments at Support B (penultimate support) will be first to be plotted.
2.2.5.1.1 Geometric Properties i.
Stiffness Coefficients. Assume a parabolic profile for the deck.
hc
A
Chapter 5.7,
rBhc
B
rChc
C
rA
=
rE
=
0
rB
=
rD
=
1.3
rC
=
1.5
D
Design of r.c.bdg; Aswani, et al.
Fig. 5.25
with the above r values, the stiffness coefficients obtained from standard
rChc
E
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member
Date___december '04
REF.
CALCULATIONS
2.0
kBA
=
kBC
=
OUTPUT
BRIDGE DECK
charts for concrete bridges are:
Design of r.c.bdg; Aswani, et al.
ii.
10.50
=
KDE
16.00
=
KDC
Carry - over factors
Fig. 5.24
Using the same r values, the carry-over factors are obtained by interpolation as
Design of r.c.bdg;
shown below:
Aswani, et al.
CAB
=
-0.905
CBC
=
-0.760
CCD
=
-0.071
CBA
=
-0.415
CCB
=
-0.710
CDC
=
-0.076
CDE
=
-0.415
CED
=
-0.905
However, since the end spans are discontinuous, the stiffness values are modified inorder to make the applicable to the members. The stiffness coefficient at the discontinuous end of the beam AB,which is discontinuous at end A is k
=
(1 - CABCBA)KBA
CAB &CBA arecarryover factors of ends A & B of member AB, while KBA is the
k'BA
iii.
=
[ 1 - (-0.905 * - 0.415)] * 10.50
=
6.56 =
k'DE
Distribution factors We now compute the distribution factors using the stiffness coefficient:
DBA
=
kBA
=
6.56 / {6.56 + 16.00}
=
0.291
=
DDE
=
DDE
SkB
DBC
=
DCB
=
1 - DBA KcB
=
=
0.709
16.00 / {16.00 + 16.00} =
=
DDC
0.5
Skc
DCD
=
1 - DCB
=
0.500
=
DDC
2.2.5.1.2 Final Support Moments due to udl.
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member
Date___december '04
REF.
CALCULATIONS i.
2.0
OUTPUT
MAB, MBA, MBC, ...
BRIDGE DECK =
Final moments at the support
MAB, MBA, MBC, ...
=
Fixed end moments
CAB, CBA, CBC, ...
=
Carry - over factors
DAB, DBA, DBC, ...
=
Distribution factors
Notations
M1
=
MBA - CABMBA
M2
=
MBC - CCBMCB
M3
=
MCD - CDCMDC
M4
=
MDE - CEDMED
V
=
CBCDBCDCD
=
-0.760 * 0.709 * 0.500
=
-0.269
U
=
CBCCCBDBCDCB
=
-0.760 * -0.710 * 0.709 * 0.500
=
0.191
W
=
CCBDCBDBA
=
-0.710 * 0.500 * 0.291
=
-0.103
ii.
Numerical values of fixed end moments a.
Fig. 5.35
Load in span AB
Design of r.c.bdg;
MAB
=
-0.060L²
Aswani, et al.
MBA
=
-0.138L²
b.
c.
d.
iii.
Load in span BC MBC
=
-0.101L²
MCB
=
-0.111L²
Load in span CD MCD
=
-0.111L²
MDC
=
-0.101L²
Load in span DE MCD
=
-0.138L²
MDC
=
-0.060L²
Final support moments
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
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Member
Bridge Deck
Date___december '04
REF.
CALCULATIONS a.
2.0
OUTPUT
BRIDGE DECK
First span loaded (Span AB) MB
=
(1 - DBA) - (2 - DBA)U
M1
1 - 2U =
(1 - 0.291) - (2 -0.291)0.191
M1
=
0.619M1
[1 - (2 * 0.191) ]
But
M1
MB
=
0.619 [-0.138 - (-0.905 * -0.060)]L²
=
-0.119L²
b.
=
MBA - CABMAB
Second span loaded (Span BC) MB
=
DBA(1 -U)MBC - WMCB 1 - 2U
=
0.291(1 - 0.191)MBC - - 0.103MCB [1 - (2 * 0.191) ]
=
0.381MBC + 0.167MCB
Inserting the values for MBC & MCB,
MB
c.
=
(0.381 * -0.101)L² + (0.167 * -0.111)L²
=
-0.057L²
Third span loaded (Span CD) MB
=
- UDDEMDC + WMCD
=
(-0.191 * 0.291)MDC + (-0.103)MCD
1 - 2U =
[1 - (2 * 0.191) ]
-0.090MDC - 0.167MCD
Inserting the values for MDC & MCD,
MB
d.
=
(0.090 * -0.101)L² + (0.167 * -0.111)L²
=
-0.028L²
Fourth span loaded (Span DE) MB
=
UDDE 1-U
=
0.090M4
M4
=
0.191 * 0.291 [1 - (2 * 0.191) ]
M4
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0
M4
MB
=
0.090 [-0.138 - (-0.905 * -0.060)]L²
=
-0.017L²
d.
MDE - CEDMDC
Value of MB when all spans are loaded =
BRIDGE DECK
But
=
OUTPUT
( -0.119 - 0.057 - 0.028 - 0.017)L²
But L
=
2.40m
MB
=
-0.114 * 2.40²
e
=
-0.114L²
=
-0.657KNm
Bending Moment at various sections due to the application of unit load. after calculating the bending moment at support B, the bending moment at various sections is now computed due to the application of unit load. This is as tabulate below:
Section
Calculations
0.0
BM ordinates (KNm) 0.000
0.1
{(9/25) * (2.40²/8)} - 0.0657
0.194
0.2
{(16/25) * (2.40²/8)} - 0.1314
0.329
0.3
{(21/25) * (2.40²/8)} - 0.1971
0.408
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
Date___december '04
REF.
CALCULATIONS 0.4
2.0
OUTPUT
BRIDGE DECK
{(24/25) * (2.40²/8)} - 0.2628
0.428
{(25/25) * (2.40²/8)} - 0.3285
0.392
0.6
{(24/25) * (2.40²/8)} - 0.3942
0.297
0.7
{(21/25) * (2.40²/8)} - 0.4599
0.145
0.8
{(16/25) * (2.40²/8)} - 0.5256
-0.065
0.9
{(9/25) * (2.40²/8)} - 0.5913
-0.332
1.0
MB = -0.657
-0.657
1.1
{(9/25) * (2.40²/8)} - 0.6570
-0.398
1.2
{(16/25) * (2.40²/8)} - 0.6570
-0.196
1.3
{(21/25) * (2.40²/8)} - 0.6570
-0.052
1.4
{(24/25) * (2.40²/8)} - 0.6570
0.034
1.5
{(25/25) * (2.40²/8)} - 0.6570
0.063
1.6
{(24/25) * (2.40²/8)} - 0.6570
0.034
1.7
{(21/25) * (2.40²/8)} - 0.6570
-0.052
1.8
{(16/25) * (2.40²/8)} - 0.6570
-0.196
1.9
{(9/25) * (2.40²/8)} - 0.6570
-0.398
0.5
2.0
0.000 BM Influence Line Diagram For udl
0.600 0.400 0.200 0.000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
-0.200 -0.400
-0.600 -0.800
2.5.2 HA - live loads udl moments. from sections 2.2.4 of this report, the ultimate udl due to HA loading
=
16.875 KN/m2
Using this influence ordinate table above, we now compute the various moments
19
20
21
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0
as below;
a.
\
b.
BRIDGE DECK
Support moments influence line ordinate
=
-0.657 KNm
design HA udl live load
=
16.875 KN/m2
=
-11.09 KNm
HA udl support moments
Span moments
maximum span moment occurs at 0.4L (1st span) and at 3.6L (4th span)
\
influence line ordinate
=
0.428 KNm
design HA udl live load
=
16.875 KN/m2
=
7.22 KNm
HA udl span moments
2.3.4 Dead load udl moments. from section 2.2.4 of this report, the udl due to dead loading is
=
6.15 KN/m
Using this influence ordinate table above, we now compute the various moments as below; a.
\
Support moments influence line ordinate
=
-0.657 KNm
design dead load udl
=
6.1525 KN/m2
dead load udl support moments
= =
b.
-4.04 KNm
Span moments
maximum span moment occurs at 0.4L (1st span) and at 2.6L (3rd span)
\
influence line ordinate
=
0.428 KNm
design dead load udl
=
6.1525 KN/m2
dead load udl span moments
= =
2.4
2.63 KNm
Influence Lines for Point Loads
OUTPUT
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0
OUTPUT
BRIDGE DECK
The point loads are due primarily to either HA live loads or the HB live loads.
The beam girder is designed to be continuous over three spans, and has a constant moment of inertia over all the spans. We can therfore, plot the influence lines using standard influence line tables for a three span continuous beam.
The following assumptions are made in the analysis of the continuous bridge girders before using the standard influence tables: *
The girder is simply supported at the supports and monolithic with the supports.
*
Rocker or roller bearings are provided at all supports.
Find below the influence line tables and charts at sections 0.1L to 1.5L We prepared the influence charts only upto 1.5L as the loading is symmetrical over the three spans.
Influence Line ordinates for BM at Support B (MB). Influence Ordinate BMD @ 1st Internal Support 0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L
0.0 -0.0258 -0.0502 -0.0718 -0.0874 -0.1000 -0.0994 -0.0928 -0.0742 -0.0408 0.0
0.0 -0.0619 -0.1205 -0.1723 -0.2098 -0.2400 -0.2386 -0.2227 -0.1781 -0.0979 0.0
0.1 0.1 0.0 1 -0.1 -0.1 -0.2 -0.2
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF. 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Load Position
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L
Date___december '04
CALCULATIONS
2.0
-0.0341 -0.0612 -0.0738 -0.0764 -0.0740 -0.0614 -0.0474 -0.0306 -0.0150 0.0 0.0063 0.0126 0.0189 0.0206 0.0200 0.0170 0.0135 0.0090 0.0045 0.0 -0.0014 -0.0028 -0.0042 -0.0056 -0.0070 -0.0056 -0.0042 -0.0028 -0.0014 0.0
-0.0818 -0.1469 -0.1771 -0.1834 -0.1776 -0.1474 -0.1138 -0.0734 -0.0360 0.0 0.0151 0.0302 0.0454 0.0494 0.0480 0.0408 0.0324 0.0216 0.0108 0.0 -0.0034 -0.0067 -0.0101 -0.0134 -0.0168 -0.0134 -0.0101 -0.0067 -0.0034 0.0
-0.3 -0.3
Influence Influence line line ordinates coefficient
0.0 0.0072 0.0138 0.0192 0.0234 0.0270 0.0270 0.0252 0.0198 0.0108 0.0
0.0 0.0173 0.0331 0.0461 0.0562 0.0648 0.0648 0.0605 0.0475 0.0259 0.0
OUTPUT
BRIDGE DECK
-0.2
Influence Line ordinates for BM at Support C (Mc). Influence Ordinate BMD @ 2nd Internal Support 0.1
0.1
0.0 1 -0.1
-0.1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
-0.1
2.0
1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
-0.0167 -0.0340 -0.0520 -0.0668 -0.0800 -0.0830 -0.0802 -0.0658 -0.0366 0.0 -0.0255 -0.0510 -0.0765 -0.0830 -0.0800 -0.0668 -0.0522 -0.0348 -0.0174 0.0 0.0052 0.0104 0.0156 0.0208 0.0260 0.0208 0.0156 0.0104 0.0052 0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L
0.0 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.0
-0.0401 -0.0816 -0.1248 -0.1603 -0.1920 -0.1992 -0.1925 -0.1579 -0.0878 0.0 -0.0612 -0.1224 -0.1836 -0.1992 -0.1920 -0.1603 -0.1253 -0.0835 -0.0418 0.0 0.0125 0.0250 0.0374 0.0499 0.0624 0.0499 0.0374 0.0250 0.0125 0.0
-0.2
BRIDGE DECK
-0.2
-0.3
MB coeff. µ + MB 0.0 -0.0026 -0.0050 -0.0072 -0.0087 -0.0100 -0.0099 -0.0093 -0.0074 -0.0041 0.0
Date___december '04
0.0 0.0874 0.0750 0.0628 0.0513 0.0400 0.0301 0.0207 0.0126 0.0059 0.0
Influence line ordinates
0.0 0.2098 0.1800 0.1508 0.1230 0.0960 0.0721 0.0497 0.0302 0.0142 0.0
Influence Line ordinates for BM at the section 0.1L (0.240m from support A)
Influence Ordinate BMD @ 0.1L 0.3
0.2
0.2
0.1
OUTPUT
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS
2.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L
0.0 0.08 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.0
-0.0034 -0.0061 -0.0074 -0.0076 -0.0074 -0.0061 -0.0047 -0.0031 -0.0015 0.0 0.0006 0.0013 0.0019 0.0021 0.0020 0.0017 0.0014 0.0009 0.0005 0.0 -0.0001 -0.0003 -0.0004 -0.0006 -0.0007 -0.0006 -0.0004 -0.0003 -0.0001 0.0
-0.0034 -0.0061 -0.0074 -0.0076 -0.0074 -0.0061 -0.0047 -0.0031 -0.0015 0.0 0.0006 0.0013 0.0019 0.0021 0.0020 0.0017 0.0014 0.0009 0.0005 0.0 -0.0001 -0.0003 -0.0004 -0.0006 -0.0007 -0.0006 -0.0004 -0.0003 -0.0001 0.0
MB coeff. µ + MB 0.0 -0.0052 -0.0100 -0.0144 -0.0175 -0.0200 -0.0199 -0.0186 -0.0148 -0.0082 0.0
0.0 0.0748 0.1500 0.1256 0.1025 0.0800 0.0601 0.0414 0.0252 0.0118 0.0
OUTPUT
BRIDGE DECK
-0.0082 -0.0147 -0.0177 -0.0183 -0.0178 -0.0147 -0.0114 -0.0073 -0.0036 0.0 0.0015 0.0030 0.0045 0.0049 0.0048 0.0041 0.0032 0.0022 0.0011 0.0 -0.0003 -0.0007 -0.0010 -0.0013 -0.0017 -0.0013 -0.0010 -0.0007 -0.0003 0.0
Influence line ordinates
0.0 0.1796 0.3599 0.3015 0.2460 0.1920 0.1443 0.0995 0.0604 0.0284 0.0
0.1
0.0 1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
-0.1
Influence Line ordinates for BM at the section 0.2L (0.480m from support A)
Influence Ordinate BMD @ 0.2L 0.4 0.4 0.3 0.3 0.2 0.2
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS
2.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
0.0 0.07 0.14 0.21 0.18 0.15 0.12 0.09 0.06 0.03
-0.0068 -0.0122 -0.0148 -0.0153 -0.0148 -0.0123 -0.0095 -0.0061 -0.0030 0.0 0.0013 0.0025 0.0038 0.0041 0.0040 0.0034 0.0027 0.0018 0.0009 0.0 -0.0003 -0.0006 -0.0008 -0.0011 -0.0014 -0.0011 -0.0008 -0.0006 -0.0003 0.0
-0.0068 -0.0122 -0.0148 -0.0153 -0.0148 -0.0123 -0.0095 -0.0061 -0.0030 0.0 0.0013 0.0025 0.0038 0.0041 0.0040 0.0034 0.0027 0.0018 0.0009 0.0 -0.0003 -0.0006 -0.0008 -0.0011 -0.0014 -0.0011 -0.0008 -0.0006 -0.0003 0.0
MB coeff. µ + MB 0.0 -0.0077 -0.0151 -0.0215 -0.0262 -0.0300 -0.0298 -0.0278 -0.0223 -0.0122
0.0 0.0623 0.1249 0.1885 0.1538 0.1200 0.0902 0.0622 0.0377 0.0178
OUTPUT
BRIDGE DECK
-0.0164 -0.0294 -0.0354 -0.0367 -0.0355 -0.0295 -0.0228 -0.0147 -0.0072 0.0 0.0030 0.0060 0.0091 0.0099 0.0096 0.0082 0.0065 0.0043 0.0022 0.0 -0.0007 -0.0013 -0.0020 -0.0027 -0.0034 -0.0027 -0.0020 -0.0013 -0.0007 0.0
Influence line ordinates
0.0 0.1494 0.2999 0.4523 0.3691 0.2880 0.2164 0.1492 0.0906 0.0426
0.1 0.1 0.0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
-0.1 -0.1
Influence Line ordinates for BM at the section 0.3L (0.720m from support A)
Influence Ordinate BMD @ 0.3L 0.5
0.4
0.3
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS 0.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
0.0 0.06 0.12 0.18 0.24 0.20 0.16 0.12 0.08 0.04
2.0
0.0 -0.0102 -0.0184 -0.0221 -0.0229 -0.0222 -0.0184 -0.0142 -0.0092 -0.0045 0.0 0.0019 0.0038 0.0057 0.0062 0.0060 0.0051 0.0041 0.0027 0.0014 0.0 -0.0004 -0.0008 -0.0013 -0.0017 -0.0021 -0.0017 -0.0013 -0.0008 -0.0004 0.0
0.0 -0.0102 -0.0184 -0.0221 -0.0229 -0.0222 -0.0184 -0.0142 -0.0092 -0.0045 0.0 0.0019 0.0038 0.0057 0.0062 0.0060 0.0051 0.0041 0.0027 0.0014 0.0 -0.0004 -0.0008 -0.0013 -0.0017 -0.0021 -0.0017 -0.0013 -0.0008 -0.0004 0.0
MB coeff. µ + MB 0.0 -0.0103 -0.0201 -0.0287 -0.0350 -0.0400 -0.0398 -0.0371 -0.0297 -0.0163
0.0 0.0497 0.0999 0.1513 0.2050 0.1600 0.1202 0.0829 0.0503 0.0237
OUTPUT
BRIDGE DECK
0.0 -0.0246 -0.0441 -0.0531 -0.0550 -0.0533 -0.0442 -0.0341 -0.0220 -0.0108 0.0 0.0045 0.0091 0.0136 0.0148 0.0144 0.0122 0.0097 0.0065 0.0032 0.0 -0.0010 -0.0020 -0.0030 -0.0040 -0.0050 -0.0040 -0.0030 -0.0020 -0.0010 0.0
Influence line ordinates
0.0 0.1192 0.2398 0.3631 0.4921 0.3840 0.2886 0.1989 0.1208 0.0568
0.2
0.1
0.0 1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
-0.1
Influence Line ordinates for BM at the section 0.4L (0.960m from support A)
Influence Ordinate BMD @ 0.4L 0.6
0.5
0.4
0.3
0.2
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS 0.2 0.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
0.0 0.05 0.10 0.15 0.20 0.25 0.20 0.15 0.10 0.05
2.0
0.0 -0.0136 -0.0245 -0.0295 -0.0306 -0.0296 -0.0246 -0.0190 -0.0122 -0.0060 0.0 0.0025 0.0050 0.0076 0.0082 0.0080 0.0068 0.0054 0.0036 0.0018 0.0 -0.0006 -0.0011 -0.0017 -0.0022 -0.0028 -0.0022 -0.0017 -0.0011 -0.0006 0.0
0.0 -0.0136 -0.0245 -0.0295 -0.0306 -0.0296 -0.0246 -0.0190 -0.0122 -0.0060 0.0 0.0025 0.0050 0.0076 0.0082 0.0080 0.0068 0.0054 0.0036 0.0018 0.0 -0.0006 -0.0011 -0.0017 -0.0022 -0.0028 -0.0022 -0.0017 -0.0011 -0.0006 0.0
MB coeff. µ + MB 0.0 -0.0129 -0.0251 -0.0359 -0.0437 -0.0500 -0.0497 -0.0464 -0.0371 -0.0204
0.0 0.0371 0.0749 0.1141 0.1563 0.2000 0.1503 0.1036 0.0629 0.0296
OUTPUT
BRIDGE DECK
0.0 -0.0327 -0.0588 -0.0708 -0.0733 -0.0710 -0.0589 -0.0455 -0.0294 -0.0144 0.0 0.0060 0.0121 0.0181 0.0198 0.0192 0.0163 0.0130 0.0086 0.0043 0.0 -0.0013 -0.0027 -0.0040 -0.0054 -0.0067 -0.0054 -0.0040 -0.0027 -0.0013 0.0
Influence line ordinates
0.0 0.0890 0.1798 0.2738 0.3751 0.4800 0.3607 0.2486 0.1510 0.0710
0.1
0.0 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
-0.1
-0.2
Influence Line ordinates for BM at the section 0.5L (1.200m from support A)
Influence Ordinate BMD @ 0.5L 0.6 0.5 0.4 0.3 0.2
33
35
37
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS 0.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
0.0 0.04 0.08 0.12 0.16 0.20 0.24 0.18 0.12 0.06
2.0
0.0 -0.0171 -0.0306 -0.0369 -0.0382 -0.0370 -0.0307 -0.0237 -0.0153 -0.0075 0.0 0.0032 0.0063 0.0095 0.0103 0.0100 0.0085 0.0068 0.0045 0.0023 0.0 -0.0007 -0.0014 -0.0021 -0.0028 -0.0035 -0.0028 -0.0021 -0.0014 -0.0007 0.0
0.0 -0.0171 -0.0306 -0.0369 -0.0382 -0.0370 -0.0307 -0.0237 -0.0153 -0.0075 0.0 0.0032 0.0063 0.0095 0.0103 0.0100 0.0085 0.0068 0.0045 0.0023 0.0 -0.0007 -0.0014 -0.0021 -0.0028 -0.0035 -0.0028 -0.0021 -0.0014 -0.0007 0.0
MB coeff. µ + MB 0.0 -0.0155 -0.0301 -0.0431 -0.0524 -0.0600 -0.0596 -0.0557 -0.0445 -0.0245
0.0 0.0245 0.0499 0.0769 0.1076 0.1400 0.1804 0.1243 0.0755 0.0355
OUTPUT
0.2
BRIDGE DECK
0.0 -0.0409 -0.0734 -0.0886 -0.0917 -0.0888 -0.0737 -0.0569 -0.0367 -0.0180 0.0 0.0076 0.0151 0.0227 0.0247 0.0240 0.0204 0.0162 0.0108 0.0054 0.0 -0.0017 -0.0034 -0.0050 -0.0067 -0.0084 -0.0067 -0.0050 -0.0034 -0.0017 0.0
Influence line ordinates
0.0 0.0588 0.1197 0.1846 0.2581 0.3360 0.4329 0.2984 0.1812 0.0852
0.1 0.0
1
4
7
10 13 16 19 22 25 28 31 34 37 40
-0.1 -0.2
Influence Line ordinates for BM at the section 0.6L (1.440m from support A)
Influence Ordinate BMD @ 0.6L 0.5 0.4 0.3 0.2
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS 0.2 0.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
0.0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.14 0.07
2.0
0.0 -0.0205 -0.0367 -0.0443 -0.0458 -0.0444 -0.0368 -0.0284 -0.0184 -0.0090 0.0 0.0038 0.0076 0.0113 0.0124 0.0120 0.0102 0.0081 0.0054 0.0027 0.0 -0.0008 -0.0017 -0.0025 -0.0034 -0.0042 -0.0034 -0.0025 -0.0017 -0.0008 0.0
0.0 -0.0205 -0.0367 -0.0443 -0.0458 -0.0444 -0.0368 -0.0284 -0.0184 -0.0090 0.0 0.0038 0.0076 0.0113 0.0124 0.0120 0.0102 0.0081 0.0054 0.0027 0.0 -0.0008 -0.0017 -0.0025 -0.0034 -0.0042 -0.0034 -0.0025 -0.0017 -0.0008 0.0
MB coeff. µ + MB 0.0 -0.0181 -0.0351 -0.0503 -0.0612 -0.0700 -0.0696 -0.0650 -0.0519 -0.0286
0.0 0.0119 0.0249 0.0397 0.0588 0.0800 0.1104 0.1450 0.0881 0.0414
OUTPUT
BRIDGE DECK
0.0 -0.0491 -0.0881 -0.1063 -0.1100 -0.1066 -0.0884 -0.0683 -0.0441 -0.0216 0.0 0.0091 0.0181 0.0272 0.0297 0.0288 0.0245 0.0194 0.0130 0.0065 0.0 -0.0020 -0.0040 -0.0060 -0.0081 -0.0101 -0.0081 -0.0060 -0.0040 -0.0020 0.0
Influence line ordinates
0.0 0.0287 0.0597 0.0954 0.1412 0.1920 0.2650 0.3481 0.2113 0.0995
0.1 0.0
1
4
7
10 13 16 19 22 25 28 31 34 37 40
-0.1 -0.2
Influence Line ordinates for BM at the section 0.7L (1.680m from support A)
Influence Ordinate BMD @ 0.7L 0.4
0.3
0.2
0.1
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS 0.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.08 0.0
2.0
0.0 -0.0239 -0.0428 -0.0517 -0.0535 -0.0518 -0.0430 -0.0332 -0.0214 -0.0105 0.0 0.0044 0.0088 0.0132 0.0144 0.0140 0.0119 0.0095 0.0063 0.0032 0.0 -0.0010 -0.0020 -0.0029 -0.0039 -0.0049 -0.0039 -0.0029 -0.0020 -0.0010 0.0
0.0 -0.0239 -0.0428 -0.0517 -0.0535 -0.0518 -0.0430 -0.0332 -0.0214 -0.0105 0.0 0.0044 0.0088 0.0132 0.0144 0.0140 0.0119 0.0095 0.0063 0.0032 0.0 -0.0010 -0.0020 -0.0029 -0.0039 -0.0049 -0.0039 -0.0029 -0.0020 -0.0010 0.0
MB coeff. µ + MB -0.0206 -0.0402 -0.0574 -0.0699 -0.0800 -0.0795 -0.0742 -0.0594 -0.0326 0.0
-0.0006 -0.0002 0.0026 0.0101 0.0200 0.0405 0.0658 0.1006 0.0474 0.0
OUTPUT
BRIDGE DECK
0.0 -0.0573 -0.1028 -0.1240 -0.1284 -0.1243 -0.1032 -0.0796 -0.0514 -0.0252 0.0 0.0106 0.0212 0.0318 0.0346 0.0336 0.0286 0.0227 0.0151 0.0076 0.0 -0.0024 -0.0047 -0.0071 -0.0094 -0.0118 -0.0094 -0.0071 -0.0047 -0.0024 0.0
Influence line ordinates
-0.0015 -0.0004 0.0061 0.0242 0.0480 0.0972 0.1578 0.2415 0.1137 0.0
0.1
0.0 1
4
7
10 13 16 19 22 25 28 31 34 37 40
-0.1
-0.2
Influence Line ordinates for BM at the section 0.8L (1.920m from support A)
Influence Ordinate BMD @ 0.8L 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS
2.0
0.0
0.0
0.0
µ
Load Position
coeff.
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-0.0273 -0.0490 -0.0590 -0.0611 -0.0592 -0.0491 -0.0379 -0.0245 -0.0120 0.0 0.0050 0.0101 0.0151 0.0165 0.0160 0.0136 0.0108 0.0072 0.0036 0.0 -0.0011 -0.0022 -0.0034 -0.0045 -0.0056 -0.0045 -0.0034 -0.0022 -0.0011 0.0
-0.0273 -0.0490 -0.0590 -0.0611 -0.0592 -0.0491 -0.0379 -0.0245 -0.0120 0.0 0.0050 0.0101 0.0151 0.0165 0.0160 0.0136 0.0108 0.0072 0.0036 0.0 -0.0011 -0.0022 -0.0034 -0.0045 -0.0056 -0.0045 -0.0034 -0.0022 -0.0011 0.0
MB coeff. µ + MB 0.0 -0.0232 -0.0452 -0.0646 -0.0787 -0.0900 -0.0895 -0.0835 -0.0668 -0.0367
0.0 -0.0132 -0.0252 -0.0346 -0.0387 -0.0400 -0.0295 -0.0135 0.0132 0.0533
OUTPUT
0.0500
BRIDGE DECK
-0.0655 -0.1175 -0.1417 -0.1467 -0.1421 -0.1179 -0.0910 -0.0588 -0.0288 0.0 0.0121 0.0242 0.0363 0.0396 0.0384 0.0326 0.0259 0.0173 0.0086 0.0 -0.0027 -0.0054 -0.0081 -0.0108 -0.0134 -0.0108 -0.0081 -0.0054 -0.0027 0.0
0.0000
-0.0500
4
7
10 13 16 19 22 25 28 31 34 37 40
-0.1000 -0.1500 -0.2000
Influence line ordinates
0.0 -0.0317 -0.0604 -0.0831 -0.0928 -0.0960 -0.0707 -0.0324 0.0317 0.1279
1
Influence Line ordinates for BM at the section 0.9L (2.160m from support A)
Influence Line Ordinate BMD @ 0.9L 0.2 0.1 0.1 0.0 1
4
7
10 13 16 19 22 25 28 31 34 37 40
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0307 -0.0551 -0.0664 -0.0688 -0.0666 -0.0553 -0.0427 -0.0275 -0.0135 0.0 0.0057 0.0113 0.0170 0.0185 0.0180 0.0153 0.0122 0.0081 0.0041 0.0 -0.0013 -0.0025 -0.0038 -0.0050 -0.0063 -0.0050 -0.0038 -0.0025 -0.0013 0.0
0.0 -0.0307 -0.0551 -0.0664 -0.0688 -0.0666 -0.0553 -0.0427 -0.0275 -0.0135 0.0 0.0057 0.0113 0.0170 0.0185 0.0180 0.0153 0.0122 0.0081 0.0041 0.0 -0.0013 -0.0025 -0.0038 -0.0050 -0.0063 -0.0050 -0.0038 -0.0025 -0.0013 0.0
MB coeff. MC coeff. 0.0 -0.0232 -0.0452 -0.0646 -0.0787 -0.0900 -0.0895 -0.0835 -0.0668 -0.0367
0.0 0.0007 0.0014 0.0019 0.0023 0.0027 0.0027 0.0025 0.0020 0.0011
1
4
7
OUTPUT
10 13 16 19 22 25 28 31 34 37 40
BRIDGE DECK
0.0 -0.0737 -0.1 -0.1322 -0.1594 -0.1 -0.1650 -0.1598 -0.2 -0.1326 -0.1024 -0.2 -0.0661 -0.0324 0.0 0.0136 0.0272 0.0408 0.0445 0.0432 0.0367 0.0292 0.0194 0.0097 0.0 -0.0030 -0.0060 -0.0091 -0.0121 -0.0151 -0.0121 -0.0091 -0.0060 -0.0030 0.0
µ + MB + MC
Influence line ordinates
0.0 -0.0225 -0.0438 -0.0627 -0.0763 -0.0873 -0.0868 -0.0810 -0.0648 -0.0356
0.0 -0.0540 -0.1051 -0.1505 -0.1832 -0.2095 -0.2082 -0.1944 -0.1555 -0.0855
Influence Line ordinates for BM at the section 1.1L (0.240m from support B) Influence Line Ordinate BMD @ 1.1L 0.2 0.2 0.1 0.1
0.0 1 -0.1
4
7 10 13 16 19 22 25 28 31 34 37 40
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS1 4 7 10 13 16 19 22 25 28 31 OUTPUT 34 37 40
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0307 -0.0551 -0.0664 -0.0688 -0.0666 -0.0553 -0.0427 -0.0275 -0.0135 0.0 0.0057 0.0113 0.0170 0.0185 0.0180 0.0153 0.0122 0.0081 0.0041 0.0 -0.0013 -0.0025 -0.0038 -0.0050 -0.0063 -0.0050 -0.0038 -0.0025 -0.0013 0.0
0.0 -0.0017 -0.0034 -0.0052 -0.0067 -0.0080 -0.0083 -0.0080 -0.0066 -0.0037 0.0 -0.0026 -0.0051 -0.0077 -0.0083 -0.0080 -0.0067 -0.0052 -0.0035 -0.0017 0.0 0.0005 0.0010 0.0016 0.0021 0.0026 0.0021 0.0016 0.0010 0.0005 0.0
MB coeff. MC coeff. 0.0 -0.0206 -0.0402 -0.0574 -0.0699 -0.0800 -0.0795 -0.0742 -0.0594 -0.0326
0.0 0.0014 0.0028 0.0038 0.0047 0.0054 0.0054 0.0050 0.0040 0.0022
BRIDGE DECK
0.0 0.0576 0.0215 -0.0016 -0.0154 -0.0246 -0.0236 -0.0207 -0.0141 -0.0072 0.0 0.0031 0.0062 0.0094 0.0102 0.0100 0.0086 0.0069 0.0046 0.0023 0.0 -0.0007 -0.0015 -0.0022 -0.0030 -0.0037 -0.0030 -0.0022 -0.0015 -0.0007 0.0
0.0 0.1383 0.0516 -0.0039 -0.0371 -0.0590 -0.0565 -0.0496 -0.0339 -0.0172 0.0 0.0075 0.0150 0.0225 0.0246 0.0240 0.0207 0.0166 0.0111 0.0055 0.0 -0.0018 -0.0036 -0.0053 -0.0071 -0.0089 -0.0071 -0.0053 -0.0036 -0.0018 0.0
µ + MB + MC
Influence line ordinates
0.0 -0.0192 -0.0374 -0.0536 -0.0652 -0.0746 -0.0741 -0.0692 -0.0554 -0.0305
0.0 -0.0461 -0.0898 -0.1286 -0.1566 -0.1790 -0.1779 -0.1661 -0.1330 -0.0732
-0.1
-0.1 -0.2 -0.2
-0.3
Influence Line ordinates for BM at the section 1.2L (0.480m from support B)
Influence Line Ordinate BMD @ 1.2L 0.3 0.3 0.2 0.2 0.1 0.1
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.08 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0273 -0.0490 -0.0590 -0.0611 -0.0592 -0.0491 -0.0379 -0.0245 -0.0120 0.0 0.0050 0.0101 0.0151 0.0165 0.0160 0.0136 0.0108 0.0072 0.0036 0.0 -0.0011 -0.0022 -0.0034 -0.0045 -0.0056 -0.0045 -0.0034 -0.0022 -0.0011 0.0
0.0 -0.0033 -0.0068 -0.0104 -0.0134 -0.0160 -0.0166 -0.0160 -0.0132 -0.0073 0.0 -0.0051 -0.0102 -0.0153 -0.0166 -0.0160 -0.0134 -0.0104 -0.0070 -0.0035 0.0 0.0010 0.0021 0.0031 0.0042 0.0052 0.0042 0.0031 0.0021 0.0010 0.0
MB coeff. MC coeff. 0.0 -0.0181 -0.0351 -0.0503 -0.0612 -0.0700 -0.0696 -0.0650 -0.0519 -0.0286
0.0 0.0022 0.0041 0.0058 0.0070 0.0081 0.0081 0.0076 0.0059 0.0032
OUTPUT
0.1
BRIDGE DECK
0.0 0.0494 0.1042 0.0706 0.0455 0.0248 0.0143 0.0060 0.0024 0.0007 0.0 -0.0001 -0.0001 -0.0002 -0.0001 0.0000 0.0002 0.0004 0.0002 0.0001 0.0 -0.0001 -0.0002 -0.0002 -0.0003 -0.0004 -0.0003 -0.0002 -0.0002 -0.0001 0.0
0.0 0.1185 0.2502 0.1693 0.1092 0.0595 0.0343 0.0145 0.0057 0.0016 0.0 -0.0001 -0.0003 -0.0004 -0.0003 0.0000 0.0006 0.0009 0.0006 0.0003 0.0 -0.0002 -0.0004 -0.0006 -0.0008 -0.0010 -0.0008 -0.0006 -0.0004 -0.0002 0.0
µ + MB + MC
Influence line ordinates
0.0 -0.0159 -0.0310 -0.0445 -0.0542 -0.0619 -0.0615 -0.0574 -0.0460 -0.0253
0.0 -0.0382 -0.0744 -0.1068 -0.1300 -0.1486 -0.1476 -0.1378 -0.1104 -0.0608
0.0
-0.1
1
4
7 10 13 16 19 22 25 28 31 34 37 40
-0.1 -0.2 -0.2 -0.3
0.4
0.3
0.2
0.1
Influence Line ordinates for BM at the section 1.3L (0.720m from support B) Influence Line Ordinate BMD @ 1.3L
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.07 0.14 0.21 0.18 0.15 0.12 0.09 0.06 0.03 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0239 -0.0428 -0.0517 -0.0535 -0.0518 -0.0430 -0.0332 -0.0214 -0.0105 0.0 0.0044 0.0088 0.0132 0.0144 0.0140 0.0119 0.0095 0.0063 0.0032 0.0 -0.0010 -0.0020 -0.0029 -0.0039 -0.0049 -0.0039 -0.0029 -0.0020 -0.0010 0.0
0.0 -0.0050 -0.0102 -0.0156 -0.0200 -0.0240 -0.0249 -0.0241 -0.0197 -0.0110 0.0 -0.0077 -0.0153 -0.0230 -0.0249 -0.0240 -0.0200 -0.0157 -0.0104 -0.0052 0.0 0.0016 0.0031 0.0047 0.0062 0.0078 0.0062 0.0047 0.0031 0.0016 0.0
MB coeff. MC coeff. 0.0 -0.0155 -0.0301 -0.0431 -0.0524 -0.0600 -0.0596 -0.0557 -0.0445 -0.0245
0.0 0.0029 0.0055 0.0077 0.0094 0.0108 0.0108 0.0101 0.0079 0.0043
OUTPUT
0.1
BRIDGE DECK
0.0 0.0411 0.0870 0.1427 0.1065 0.0742 0.0521 0.0328 0.0188 0.0085 0.0 -0.0032 -0.0065 -0.0097 -0.0105 -0.0100 -0.0081 -0.0062 -0.0041 -0.0021 0.0 0.0006 0.0012 0.0017 0.0023 0.0029 0.0023 0.0017 0.0012 0.0006 0.0
0.0 0.0987 0.2087 0.0 0.3426 0.2556 0.1781 -0.1 0.1251 0.0786 0.0452 -0.2 0.0204 0.0 -0.0078 -0.0156 -0.0233 -0.0252 -0.0240 -0.0195 -0.0149 -0.0099 -0.0050 0.0 0.0014 0.0028 0.0042 0.0056 0.0070 0.0056 0.0042 0.0028 0.0014 0.0
µ + MB + MC
Influence line ordinates
0.0 -0.0126 -0.0246 -0.0354 -0.0431 -0.0492 -0.0488 -0.0456 -0.0366 -0.0202
0.0 -0.0302 -0.0590 -0.0850 -0.1034 -0.1181 -0.1172 -0.1094 -0.0878 -0.0484
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
Influence Line ordinates for BM at the section 1.4L (0.960m from support B) 0.5
0.4
0.3
0.2
Influence Line Ordinate BMD @ 1.4L
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.06 0.12 0.18 0.24 0.20 0.16 0.12 0.08 0.04 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0205 -0.0367 -0.0443 -0.0458 -0.0444 -0.0368 -0.0284 -0.0184 -0.0090 0.0 0.0038 0.0076 0.0113 0.0124 0.0120 0.0102 0.0081 0.0054 0.0027 0.0 -0.0008 -0.0017 -0.0025 -0.0034 -0.0042 -0.0034 -0.0025 -0.0017 -0.0008 0.0
0.0 -0.0067 -0.0136 -0.0208 -0.0267 -0.0320 -0.0332 -0.0321 -0.0263 -0.0146 0.0 -0.0102 -0.0204 -0.0306 -0.0332 -0.0320 -0.0267 -0.0209 -0.0139 -0.0070 0.0 0.0021 0.0042 0.0062 0.0083 0.0104 0.0083 0.0062 0.0042 0.0021 0.0
MB coeff. MC coeff. 0.0 -0.0129 -0.0251 -0.0359 -0.0437 -0.0500 -0.0497 -0.0464 -0.0371 -0.0204
0.0 0.0036 0.0069 0.0096 0.0117 0.0135 0.0135 0.0126 0.0099 0.0054
OUTPUT
BRIDGE DECK
0.0 0.0329 0.0697 0.1149 0.1674 0.1236 0.0900 0.0595 0.0353 0.0164 0.0 -0.0064 -0.0128 -0.0193 -0.0208 -0.0200 -0.0165 -0.0128 -0.0085 -0.0043 0.0 0.0012 0.0025 0.0037 0.0050 0.0062 0.0050 0.0037 0.0025 0.0012 0.0
0.0 0.0789 0.1672 0.2758 0.4019 0.2966 0.2159 0.1428 0.0848 0.0393 0.0 -0.0154 -0.0308 -0.0462 -0.0500 -0.0480 -0.0396 -0.0307 -0.0204 -0.0102 0.0 0.0030 0.0060 0.0089 0.0119 0.0149 0.0119 0.0089 0.0060 0.0030 0.0
µ + MB + MC
Influence line ordinates
0.0 -0.0093 -0.0182 -0.0263 -0.0320 -0.0365 -0.0362 -0.0338 -0.0272 -0.0150
0.0 -0.0223 -0.0437 -0.0631 -0.0768 -0.0876 -0.0869 -0.0811 -0.0653 -0.0360
0.1
0.0 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
-0.1
-0.2
Influence Line ordinates for BM at the section 1.5L (1.200m from support B) 0.5
0.4
0.3
0.2
Influence Line Ordinate BMD @ 1.5L
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.05 0.10 0.15 0.20 0.25 0.20 0.15 0.10 0.05 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0171 -0.0306 -0.0369 -0.0382 -0.0370 -0.0307 -0.0237 -0.0153 -0.0075 0.0 0.0032 0.0063 0.0095 0.0103 0.0100 0.0085 0.0068 0.0045 0.0023 0.0 -0.0007 -0.0014 -0.0021 -0.0028 -0.0035 -0.0028 -0.0021 -0.0014 -0.0007 0.0
0.0 -0.0084 -0.0170 -0.0260 -0.0334 -0.0400 -0.0415 -0.0401 -0.0329 -0.0183 0.0 -0.0128 -0.0255 -0.0383 -0.0415 -0.0400 -0.0334 -0.0261 -0.0174 -0.0087 0.0 0.0026 0.0052 0.0078 0.0104 0.0130 0.0104 0.0078 0.0052 0.0026 0.0
MB coeff. MC coeff. 0.0 -0.0103 -0.0201 -0.0287 -0.0350 -0.0400 -0.0398 -0.0371 -0.0297 -0.0163
0.0 0.0043 0.0083 0.0115 0.0140 0.0162 0.0162 0.0151 0.0119 0.0065
OUTPUT
BRIDGE DECK
0.0 0.0246 0.0524 0.0871 0.1284 0.1730 0.1278 0.0862 0.0518 0.0242 0.0 -0.0096 -0.0192 -0.0288 -0.0312 -0.0300 -0.0249 -0.0194 -0.0129 -0.0065 0.0 0.0019 0.0038 0.0057 0.0076 0.0095 0.0076 0.0057 0.0038 0.0019 0.0
0.0 0.0590 0.1258 0.2090 0.3082 0.4152 0.3067 0.2069 0.1243 0.0581 0.0 -0.0230 -0.0461 -0.0691 -0.0749 -0.0720 -0.0598 -0.0464 -0.0310 -0.0155 0.0 0.0046 0.0091 0.0137 0.0182 0.0228 0.0182 0.0137 0.0091 0.0046 0.0
µ + MB + MC
Influence line ordinates
0.0 -0.0060 -0.0118 -0.0172 -0.0209 -0.0238 -0.0236 -0.0220 -0.0178 -0.0098
0.0 -0.0144 -0.0283 -0.0413 -0.0502 -0.0571 -0.0565 -0.0528 -0.0427 -0.0236
0.1
0.0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
-0.1
-0.2
Influence Line ordinates for BM at the section 1.6L (1.440m from support B) 0.5
0.4
0.3
0.2
Influence Line Ordinate BMD @ 1.6L
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.04 0.08 0.12 0.16 0.20 0.24 0.18 0.12 0.06 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0136 -0.0245 -0.0295 -0.0306 -0.0296 -0.0246 -0.0190 -0.0122 -0.0060 0.0 0.0025 0.0050 0.0076 0.0082 0.0080 0.0068 0.0054 0.0036 0.0018 0.0 -0.0006 -0.0011 -0.0017 -0.0022 -0.0028 -0.0022 -0.0017 -0.0011 -0.0006 0.0
0.0 -0.0100 -0.0204 -0.0312 -0.0401 -0.0480 -0.0498 -0.0481 -0.0395 -0.0220 0.0 -0.0153 -0.0306 -0.0459 -0.0498 -0.0480 -0.0401 -0.0313 -0.0209 -0.0104 0.0 0.0031 0.0062 0.0094 0.0125 0.0156 0.0125 0.0094 0.0062 0.0031 0.0
MB coeff. MC coeff. 0.0 -0.0077 -0.0151 -0.0215 -0.0262 -0.0300 -0.0298 -0.0278 -0.0223 -0.0122
0.0 0.0050 0.0097 0.0134 0.0164 0.0189 0.0189 0.0176 0.0139 0.0076
OUTPUT
BRIDGE DECK
0.0 0.0163 0.0351 0.0593 0.0894 0.1224 0.1656 0.1129 0.0683 0.0320 0.0 -0.0128 -0.0256 -0.0383 -0.0416 -0.0400 -0.0333 -0.0259 -0.0173 -0.0086 0.0 0.0026 0.0051 0.0077 0.0102 0.0128 0.0102 0.0077 0.0051 0.0026 0.0
0.0 0.0392 0.0843 0.1423 0.2145 0.2938 0.3975 0.2710 0.1639 0.0769 0.0 -0.0307 -0.0613 -0.0920 -0.0997 -0.0960 -0.0799 -0.0622 -0.0415 -0.0207 0.0 0.0061 0.0123 0.0184 0.0246 0.0307 0.0246 0.0184 0.0123 0.0061 0.0
µ + MB + MC
Influence line ordinates
0.0 -0.0027 -0.0054 -0.0081 -0.0098 -0.0111 -0.0109 -0.0102 -0.0084 -0.0047
0.0 -0.0065 -0.0130 -0.0194 -0.0236 -0.0266 -0.0262 -0.0245 -0.0202 -0.0112
0.1
0.0 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
-0.1
-0.2
Influence Line ordinates for BM at the section 1.7L (1.680m from support B) 0.4
0.3
0.2
0.1
Influence Line Ordinate BMD @ 1.7L
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.14 0.07 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0102 -0.0184 -0.0221 -0.0229 -0.0222 -0.0184 -0.0142 -0.0092 -0.0045 0.0 0.0019 0.0038 0.0057 0.0062 0.0060 0.0051 0.0041 0.0027 0.0014 0.0 -0.0004 -0.0008 -0.0013 -0.0017 -0.0021 -0.0017 -0.0013 -0.0008 -0.0004 0.0
0.0 -0.0117 -0.0238 -0.0364 -0.0468 -0.0560 -0.0581 -0.0561 -0.0461 -0.0256 0.0 -0.0179 -0.0357 -0.0536 -0.0581 -0.0560 -0.0468 -0.0365 -0.0244 -0.0122 0.0 0.0036 0.0073 0.0109 0.0146 0.0182 0.0146 0.0109 0.0073 0.0036 0.0
MB coeff. MC coeff. 0.0 -0.0052 -0.0100 -0.0144 -0.0175 -0.0200 -0.0199 -0.0186 -0.0148 -0.0082
0.0 0.0058 0.0110 0.0154 0.0187 0.0216 0.0216 0.0202 0.0158 0.0086
OUTPUT
BRIDGE DECK
0.0 0.0081 0.0178 0.0315 0.0503 0.0718 0.1035 0.1396 0.0848 0.0399 0.0 -0.0160 -0.0319 -0.0479 -0.0519 -0.0500 -0.0417 -0.0325 -0.0217 -0.0108 0.0 0.0032 0.0064 0.0097 0.0129 0.0161 0.0129 0.0097 0.0064 0.0032 0.0
0.0 0.0194 0.0428 0.0755 0.1208 0.1723 0.2484 0.3351 0.2034 0.0957 0.0 -0.0383 -0.0766 -0.1149 -0.1246 -0.1200 -0.1000 -0.0780 -0.0520 -0.0260 0.0 0.0077 0.0155 0.0232 0.0309 0.0386 0.0309 0.0232 0.0155 0.0077 0.0
µ + MB + MC
Influence line ordinates
0.0 0.0006 0.0010 0.0010 0.0012 0.0016 0.0017 0.0016 0.0010 0.0005
0.0 0.0014 0.0024 0.0024 0.0030 0.0038 0.0041 0.0038 0.0024 0.0012
0.0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
-0.1
-0.2
Influence Line ordinates for BM at the section 1.8L (1.920m from support B) 0.3
Influence Line Ordinate BMD @ 1.8L
0.3
0.2
0.2
0.1
0.1
`
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
CALCULATIONS 0.1
1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.08 0.0
Load Position
µ
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L
Date___december '04
0.0
0.0
coeff. 0.0
2.0
0.0 -0.0068 -0.0122 -0.0148 -0.0153 -0.0148 -0.0123 -0.0095 -0.0061 -0.0030 0.0 0.0013 0.0025 0.0038 0.0041 0.0040 0.0034 0.0027 0.0018 0.0009 0.0 -0.0003 -0.0006 -0.0008 -0.0011 -0.0014 -0.0011 -0.0008 -0.0006 -0.0003 0.0
0.0 -0.0134 -0.0272 -0.0416 -0.0534 -0.0640 -0.0664 -0.0642 -0.0526 -0.0293 0.0 -0.0204 -0.0408 -0.0612 -0.0664 -0.0640 -0.0534 -0.0418 -0.0278 -0.0139 0.0 0.0042 0.0083 0.0125 0.0166 0.0208 0.0166 0.0125 0.0083 0.0042 0.0
MB coeff. MC coeff. 0.0 -0.0026 -0.0050 -0.0072 -0.0087 -0.0100 -0.0099 -0.0093 -0.0074 -0.0041
0.0 0.0065 0.0124 0.0173 0.0211 0.0243 0.0243 0.0227 0.0178 0.0097
OUTPUT
BRIDGE DECK
0.0 -0.0002 0.0006 0.0036 0.0113 0.0212 0.0413 0.0664 0.1012 0.0477 0.0 -0.0191 -0.0383 -0.0574 -0.0623 -0.0600 -0.0500 -0.0391 -0.0260 -0.0130 0.0 0.0039 0.0078 0.0116 0.0155 0.0194 0.0155 0.0116 0.0078 0.0039 0.0
0.0 -0.0004 0.0013 0.0087 0.0271 0.0509 0.0992 0.1593 0.2430 0.1145 0.0 -0.0459 -0.0919 -0.1378 -0.1495 -0.1440 -0.1201 -0.0937 -0.0625 -0.0312 0.0 0.0093 0.0186 0.0279 0.0372 0.0466 0.0372 0.0279 0.0186 0.0093 0.0
µ + MB + MC
Influence line ordinates
0.0 0.0039 0.0074 0.0101 0.0123 0.0143 0.0144 0.0134 0.0104 0.0056
0.0 0.0094 0.0178 0.0242 0.0296 0.0343 0.0345 0.0322 0.0250 0.0135
0.0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
-0.1
-0.1
-0.2
-0.2
Influence Line ordinates for BM at the section 1.9L (2.160m from support B) Influence Line Ordinate BMD @ 1.9L
0.2
0.1
0.1
0.0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF. 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L 3.1L 3.2L 3.3L 3.4L 3.5L 3.6L 3.7L 3.8L 3.9L 4.0L
Date___december '04
CALCULATIONS 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0
0.0
0.0
2.0
0.0 -0.0034 -0.0061 -0.0074 -0.0076 -0.0074 -0.0061 -0.0047 -0.0031 -0.0015 0.0 0.0006 0.0013 0.0019 0.0021 0.0020 0.0017 0.0014 0.0009 0.0005 0.0 -0.0001 -0.0003 -0.0004 -0.0006 -0.0007 -0.0006 -0.0004 -0.0003 -0.0001 0.0
0.0 -0.0150 -0.0306 -0.0468 -0.0601 -0.0720 -0.0747 -0.0722 -0.0592 -0.0329 0.0 -0.0230 -0.0459 -0.0689 -0.0747 -0.0720 -0.0601 -0.0470 -0.0313 -0.0157 0.0 0.0047 0.0094 0.0140 0.0187 0.0234 0.0187 0.0140 0.0094 0.0047 0.0
BRIDGE DECK
0.0 -0.0084 -0.0167 -0.0242 -0.0278 -0.0294 -0.0208 -0.0069 0.0177 0.0556 0.0 -0.0223 -0.0446 -0.0670 -0.0726 -0.0700 -0.0584 -0.0456 -0.0304 -0.0152 0.0 0.0045 0.0091 0.0136 0.0182 0.0227 0.0182 0.0136 0.0091 0.0045 0.0
0.0 -0.0203 -0.0401 -0.0580 -0.0666 -0.0706 -0.0500 -0.0166 0.0425 0.1333 0.0 -0.0536 -0.1071 -0.1607 -0.1743 -0.1680 -0.1402 -0.1095 -0.0730 -0.0365 0.0 0.0109 0.0218 0.0327 0.0436 0.0545 0.0436 0.0327 0.0218 0.0109 0.0
-0.1
-0.1
-0.2
-0.2
Since the structure is symmetrical, influence lines are only drawn for load positions upto 2.0L (i.e. Support C)
2.5 Bending moments due to HA live loads (point loads) Sections 1.2 of this report
The point loads due to HA live loads is the HA Knife - Edge load (KEL). With reference to Clause 6.2.2 of BS 5400: Part II: 1978, 120KN of KEL is recommended per notional lane. Based on this, the ultimate KEL per deck span is computed as 67.32KN/m².
a. Support moments
OUTPUT
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS i. ii. iii. iv. v.
2.0
OUTPUT
BRIDGE DECK
when first span loaded; apply KEL at 0.5L: when second span loaded; apply KEL at 1.4L: when third span loaded; apply KEL at 2.4L: when fourth span loaded; apply KEL at 3.5L: when all four spans are loaded where P = design KEL = 67.5 KN/m Therefore M
= = = = =
-0.2400 -0.1834 0.0494 -0.0168 -0.3908
P P P P P
-26.379 KNm
=
b. Span moments i. ii. iii. iv. v.
when first span loaded; apply KEL at 0.4L: when second span loaded; apply KEL at 1.5L: when third span loaded; apply KEL at 2.5L: when fourth span loaded; apply KEL at 3.6L: when all four spans are loaded where P = design KEL = 67.5 KN/m Therefore M
= = = = = =
0.4921 0.4152 0.4152 0.4921 1.8146
P P P P P
122.159 KNm
2.6 Total Bending moments due to HA live loads + Dead loads a. Support moments Sections 3.2.1.3 3.2.1.4 & 3.2.2.1 of this report
moments due to HA point loads moments due to HA udl loads moments due to dead loads Design HA + Dead loads
= = = =
-26.38 -11.09 -4.04 -41.51
KNm KNm KNm KNm
= = = =
122.16 7.22 2.63 132.01
KNm KNm KNm KNm
HA + Gk support mmts = -44.38KN/m²
b. Span moments moments due to HA point loads moments due to HA udl loads moments due to dead loads Design HA + Dead loads
HA + Gk support mmts = 133.93KN/m²
2.7 HB Live loading 2.7.1
Wheel Loads
This is done using a 45 - unit HB loading. A 45 - unit HB vehicle has 4 axles, carrying 4 wheels each. weight of each axle = 10KN Total axle weight = 10KN /axle * 4Axles = For a 45 - unit HB loading, wheel load = 45 * 40KN = 1,800KN Total No. of wheels supported = 16No. Therefore, load exerted by each wheel = 1,800/16 = 112.50KN Alternative method of calculating Load exerted by each wheel: 2,500j Newtons = (where j = no of units of HB load )
40KN
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
2.0 =
Date___december '04
CALCULATIONS 2,500 * 45 / 1,000 = 112.5KN
OUTPUT
BRIDGE DECK 6,100
1,800
1,800
Fig 3: Dimensions of a HB vehicle 75
1,000
375
Table 9, R.C. H/Bk,
1,000
Reynolds & Stee-
DIRECTION OF TRAVEL
dman. (10th ed)
1,000
1,800
CAXLE
6,100
CAXLE
CAXLE
1,800
CAXLE
Fig 4 : A unit of HB - vehicle configuration
2.7.2
DISPERSION OF WHEEL LOADS
Sect. 1.17(11) Design of R.C. Bridges
F = Wheel load
F ax
d
REINFORCEMENT
ax = Contact length (varies: 0 - 380mm) by = width of tyre (varies: 75 - 450mm)
A by ax
B = by + 2d
B
wheel load dispersal = A * B
A = ax + 2d
The dispersal is carried out at an angle of 45o through the concrete. The dispersal is treated separately between the concrete and the surfacing. Load = 1.1N/mm²
a.
Load Dispersal Through Asphalt
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0 f
where,
=
OUTPUT
BRIDGE DECK
2,500j [ (2,500j/1.1)0.5 + h' ]²
2
1
f = pressure in N/mm² j = No. of units of HB loading = 45
h' = depth below surface at which load is acting
f b.
=
2,500 * 45 [ (2,500 * 45/1.1)0.5 + 0 ]²
= 1.1N/mm²
Load Dispersal Through Concrete
f
=
=
2,500j [ (2,500j/1.1)0.5 + 2h' ]² 2,500 * 45 [ (2,500 * 45/1.1)0.5 + (2 * 0.05) ]²
=
0.97
Use f = 1.1N/mm²
2.7.3
MOMENTS DUE TO HB LIVE LOADS
The tyres of a HB vehicle are spaced at 1,000mm as shown in the sketch above.
a.
Supports
The point loads are placed at critical positions to produce maximum effect. i.
when 1st span only is loaded The tyres of a HB vehicle are spaced at 1,000mm as shown in the sketch above. Load Position BM ordinate BM But P = 112.5KNm 0.5L -0.2400 P -27.00 KNm 0.9L -0.0979 P -11.01 KNm -38.01 KNm
ii.
when only 2nd span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 1.3L -0.1771 P -19.92375 KNm 1.7L -0.1138 P -12.8025 KNm -32.73 KNm
ii.
when only 3rd span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 2.4 0.0494 P 5.5575 KNm 2.8L 0.0216 P 2.43 KNm 7.99 KNm
ii.
But P = 112.5KNm
when only 4th span is loaded
But P = 112.5KNm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0 iii.
OUTPUT
BRIDGE DECK
The influence values are as tabulated below. Load Position BM ordinate BM 3.2L -0.0034 P -0.3825 KNm 3.6L -0.0134 P -1.5075 KNm -1.89 KNm
But P = 112.5KNm
When all four spans are loaded: Total moments due to HB load = -38.01KNm -32.73KNm + 7.99KNm -1.89KNm = -64.64 KNm
b. Span moment The point loads are placed at critical positions to produce maximum effect. i.
when 1st span only is loaded The tyres of a HB vehicle are spaced at 1,000mm as shown in the sketch above. Load Position BM ordinate BM But P = 112.5KNm 0.5L 0.2425 P 27.28 KNm 0.9L 0.1079 P 12.14 KNm 39.42 KNm
ii.
when only 2nd span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 1.3L 0.1920 P 21.6 KNm 1.7L 0.1351 P 15.19875 KNm 36.80 KNm
ii.
when only 3rd span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 2.4L 0.1916 P 21.555 KNm 2.8L 0.1430 P 16.0875 KNm 37.64 KNm
ii.
But P = 112.5KNm
when only 4th span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 3.2L 0.1715 P 19.29375 KNm 3.6L 0.1863 P 20.95875 KNm 40.25 KNm
iii.
But P = 112.5KNm
When all four spans are loaded:
But P = 112.5KNm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
2.0
OUTPUT
BRIDGE DECK
Total moments due to HB load = 154.11 KNm
2.7.4 Total Bending moments due to HB live loads + Dead loads a. Support moments Sections 3.2.1.4 & 3.3.3
moments due to HB point loads moments due to dead loads
= =
-64.64 KNm -4.04 KNm
of this report
DesignHB + Gk support mmts
Design HB + Dead loads
=
-68.68 KNm
= =
154.11 KNm 2.63 KNm
= 71.64KNm
b. Span moments moments due to HB point loads moments due to dead loads
design HB + Gk span mmts
Design HB + Dead loads
=
156.75 KNm
2.8 Design Moments The design moment is obtained by comparing the HA + Dead load moments with those of the HB + Dead load moments.
a.
Support Moments
HA + Dead Load Moments = HB + Dead Load Moments = Design moment is that due to HB + Dead load moment =
b.
Span Moments
HA + Dead Load Moments = HB + Dead Load Moments = Design moment is that due to HB + Dead load moment =
-26.379 KNm -68.685 KNm -68.685 KNm
122.159 KNm 156.747 KNm 156.747 KNm
DESIGN MOMENTS
2.9
Design support moments
=
68.685 KNm (Hogging)
Design span mmts
=
156.747 KNm (Sagging)
DESIGN FOR BENDING DESIGN OF SPAN
Design as a rectangular - beam Design Moment
=
156.747 KNm
= 304.29KNm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member
Date___december '04
REF.
CALCULATIONS
2.0
Depth of slab/deck
\
=
2,400 mm
=
175 mm
CALCULATION OF EFFECTIVE DEPTH, d beam depth, h
=
175 mm
width of beam web, bw
=
1000 mm
Flange depth, hf
=
175 mm
cover to reinforcement, d' reinforcement size, f
=
0.0 mm
=
16.0 mm
=
10.0 mm
stirrup diameter, t effective depth, d
=
=
1000
mm
h - (d' + f/2 + t)
= effective width, b
175 mm
a.
OUTPUT
BRIDGE DECK
Span Length
157 mm bw 1,000 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
k
=
M/bd²fcu
therefore, k
1997
since k'
fcu
=
0.159
=
0.156
=
40 N/mm²
it implies that compression steel not required. use z c.
=
0.775 d
TENSILE REINFORCEMENT fy
=
As '
=
410 N/mm² (k-k')fcu bd²/(0.87fy.(d-d')) Apply
= T 16
(As prov. =
As
=
{k'fcubd²/(0.87fy.Z)} + As'
= T 25
(As prov. =
Checks for minimum steel:
Mosley, Bungay
As min
= Apply
BS8110:PART1: 1997
a.
@
0.13Ac/100 T 12
(As prov. =
Table 3.10
mm centres TOP
3,596 mm² 125
mm centres BOTTOM
3,927 mm²)
Table A.7
3.4.2
300
670 mm²)
Apply
Hulse: r.c. design, 5th ed.
@
52 mm²
= @
250
227.50 mm² mm centres as distribution bars
452 mm²)
CHECKS FOR DEFLECTION
Basic span - effective depth ratio
=
20.00
To avoid damages to finishes, modified ratio
=
16.67
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
Date___december '04
REF.
CALCULATIONS b.
Table 3.11
2.0
BRIDGE DECK
Tensile reinforcement modification factor:
BS8110:PART1: 1997
OUTPUT
Note:
i.
M/bd²
ii.
service stress, fs
iii.
By interpolation, Modification Factor, MF =
MF should not
=
= 5fyAsreq./8Asprov.)*1/bb
=
0.55 + (477 - fs)/(120(0.9+(M/bd²)) Use MF
be greater than 2
c.
Modified span - effective depth ratio = MF * Basic span - effective ratio =
d.
Actual span - effective depth ratio
=
6.36
260.75 N/mm²
=
0.80
=
0.80 13.30
L/d
=
9.60
NB: Actual span-effective ratio based on the total slab depth of 250mm Since Modified L/d > Actual L/d,
Design okay w.r.t deflection.
DESIGN FOR SHEAR i.
ii.
Design shear Force Shear due to Precast Slab
=
22.04 KN
Shear due to insitu works
=
84.70 KN
Design Shear Force ,V
=
106.74 KN
Design Shear Stress, v
=
V/bd
= fcu
Checks: iii.
=
=
40 N/mm²
5.060 N/mm²
design okay with respect to shear
Obtaining the design concrete shear stress, vc (should be 3.00)
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc =
iv.
0.8(fcu)
0.680 N/mm²
(should not be < 1.00)
=
0.427
=
2.548 Use 400/d
0.79(100As/(bvd))1/3(400/d)0.25/1.25
=
=
1.00
0.476 N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
0.680 N/mm²
vc
=
0.476 N/mm²
vc + 0.4 =
i.e. 0.5vc +v < (vc + 0.4)
and Asv/Sv reqd
Asv/Sv = 0.4*bv/(0.87fyv) =
1.121
fyv
=
410 N/mm²
0.876 N/mm²
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Bridge Deck
Member REF.
Date___december '04
CALCULATIONS
2.0
Apply a
OUTPUT
BRIDGE DECK
4 Leg stirrup T 10
@
and Asv/Sv provided =
250 mm centres
1.257
CHECK FOR INTER-PHASE SHEAR There's need to compute the shear force at the inter phase between the precast and insitu concrete.
Shear connectors will be required to prevent slippage between the insitu concrete and the precast concrete sections to enable them act as a single composite unit. The slippage that occurs is a maximum at the supported end of the slabs, where the shear,V and the rate of change of moment dm/dx are a maximum. This slippage to zero at midspan where moments is at a maximum, and shear force, SF, V = 0 for a udl.
The shear connectors are the shear reinforcement for the maximum inter-phase shear force.
Since the inter-phase between the precast concrete and the in-situ concrete is located in the horizontal direction, it implies that the maximum interphase shear under consideration is in the vertical direction. Section 2.1.2 &
Shear due to Precast Slab
=
13.92 KN
of this report
Therefore, the design inter phase shear, V1
=
13.92 KN
CHECKS: V1 must not exceed the lesser of
clause 7.4.2.3 BS 5400:Part 4:1990
a.
k 1 .f cu .Ls
b.
v 1 .Ls + 0.7Ae.fy
where, k1 is a constant depending on the concrete bond,obtained from Table 31, BS 5400:Part 4 fcu is the characteristic cube strenght of concrete Ls is the length of theshear plane under consideration v1 is the ultimate longitudinal shear stress in the concrete for shear plane under consideration taken from Table 31, BS5400:Part 4 Ae is the area of fully anchored reinforcement per unit length crossing the shear plane under consideration fy is the characteristic strenght of the reinforcement.
Table 31
k1
=
0.15
Ae
=
314 mm²
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked Page No.
Member
Bridge Deck
REF.
Date___december '04
CALCULATIONS
BS 5400:Part 4:1990
fcu
and parts of
Ls
2.0 =
40 N/mm²
=
2.4 m
OUTPUT
BRIDGE DECK fy
=
410 N/mm²
v1
=
0.5 N/mm²
this report a.
k 1 .f cu .Ls
=
14.400
b.
v 1 .Ls + 0.7Ae.fy
=
90164.909
Since V1 is less than or
a.
k 1 .f cu .Ls
b.
v 1 .Ls + 0.7Ae.fy
the inter phase shear is okay.
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DesignHB + Gk support mmts = 71.64KNm
design HB + Gk span mmts = 304.29KNm
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Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member:
Diaphragm/Transverse Beam
REF.
CALCULATIONS
Date___december '04
Page No.
OUTPUT
3.0 DIAPHRAGM/TRANSVERSE BEAMS 3.1 INTRODUCTION For the purpose of this designs, diaphragm beams are used only at supports as end beams to the various spans. They act as stiffeners, distribute concentrated loads, reduce local deflections, act as chords for the lateral system, and secure the aerodynamic stability of the structure. During construction, they are cast in two parts; one part as thte pre cast pier cap and the second part is cast in-situ and integral with the pier cap beams. A sketch of the slab/ deck, showing the location of diaphragm beams is as shown below: 11.0m
Diaphragm Beams
17.80m
Slab area supported by diaph ragm beam 17.80m
Beam Girder
17.80m
0.70m 2.40m
2.40m
2.40m
2.40m 0.70m
1 Area of slab - deck supported by intermediate diaphragm beam: = 2 * (0.5 * 1.40 * 0.70 ) + { 8 * (0.5 * 2.4 * 1.2)} 2 12.50m =
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member:
Diaphragm/Transverse Beam
REF.
CALCULATIONS
3.2
Section 2.2 of this report
Gk Dead Loads, Self weight of beam
ii.
Dead loads from slab deck; 10.65KN/m2 12.50m2 * TOTAL Gk Qk Live Loads, HA udl Bridge span Equivalent udl load
=
24 * 0.45 * 1.00 * 11
= =
=
118.80KN
= =
133.13KN 251.93KN
17.50m 10.5KN/m2
And load per beam = 10.50 * 8.0 * 0.5 = 42.0KN/m where 8.0m = c/way width, and 0.5 used because there are 2No.diaphragm beams per span. Table 9 ; Reynolds & Steedman : R.C Designer's H/bk
ii
Clause 6.2.2 BS 5400: Part II
iii.
4.2KN/m2 2No. =
Foot path live load = 4.2KN/m2 * = Total udl Live Loads
=
5.6KN/m 47.6KN/m
HA KEL 120KN is recommended as KEL per notional lane. Total KEL = 360KN, since we have 3 notional lanes. There fore Total KEL per beam = Each beam has 4No spans. There fore Total KEL per span =
c.
Design dead load dead udl =
ii
iii.
iv.
=
180KN
180KN/4
=
45KN
= =
377.90KN 34.35KN/m
Design live loads(udl) = 1.50 * 47.60 TOTAL UDL
= =
71.40KN/m 105.75KN/m
Design concentrated live loads (KEL) = 1.50 * 45.0
=
67.50KN
= 1.50 * 251.93KN 377.90KN/11m
LOADING DIAGRAMS 67.50KN
216.01
d.
360KN * 0.5
LOAD COMBINATIONS i.
MOMENTS
105.75KN/m
67.50KN
297.73
67.50KN
297.73
Page No.
OUTPUT
LOAD ANALYSIS a. i.
b i.
Table 11; Reynolds & Steedman : R.C Designer's H/bk
Date___december '04
67.50KN
297.73
216.01
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member:
Diaphragm/Transverse Beam
REF.
CALCULATIONS I.
Cantilever mmts (Negative) 105.75 * 0.50 *0.702 Mcant =
Date___december '04
Page No.
OUTPUT =
25.91 KNm
ii.
Max Span mmts Take mmts about the middle od the 2nd internal slab: Mspan = - (105.75 * 4.3 * 0.5) + (216.01 * 3.6 ) + (297.73 * 1.2 ) - (67.50 * 2.4 ) = 1,069.55 KNm
ii.
Max Support mmts Take mmts about the 3rd internal support, Msupp = (105.75 * 5.5 * 0.5) + 67.50 * ( 1.2 + 3.6 ) ( 216.01 * 4.8 ) ( 297.73 * 2.4 ) = 2,366.21 KNm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member:
Diaphragm/Transverse Beam
REF.
CALCULATIONS
Page No.
Date___december '04
OUTPUT
DESIGN FOR BENDING & SHEAR 3.3.1
DESIGN FOR BENDING (MID - SPAN)
Design as a rectangular - beam
\
=
Span Length
=
1,069.550 KNm 2,400 mm
Depth of slab/deck
=
250 mm
beam depth, h
=
1250 mm
width of beam web, bw
=
400 mm
Flange depth, hf
=
250 mm
cover to reinforcement, d' reinforcement size, f
=
30.0 mm
=
16.0 mm
=
12.0 mm
stirrup diameter, t
effective depth, d
400 mm
h - (d' + f/2 + t)
= =
effective width, b
mm
CALCULATION OF EFFECTIVE DEPTH, d
1250
a.
Design Moment
1,200 mm
=
bw+(0.7L/5) 400 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
1997
k therefore, k
=
M/bd²fcu
since k' ii.
0.046
=
0.156
it implies that compression steel not required. d(0.5 + (0.25 - k/0.9)0.5) = =
z use z
c.
fcu
=
=
40 N/mm²
0.945 d
0.945 d
TENSILE REINFORCEMENT fy
=
As
=
410 N/mm² M/(0.87fy.Z)
=
Apply
2,643 mm² 6
T 25
(As prov. = Table A.7
Checks for minimum steel:
Mosley, Bungay
As min
=
Bottom
2,945 mm²)
0.13Ac/100
Apply
Hulse: r.c. design, 5th ed.
= 4
T 16
650.00 mm² Top
(A's prov.
3.3.2 a.
Table 3.10
=
BS8110:PART1: 1997
b.
804.25 mm² )
CHECKS FOR DEFLECTION
Basic span - effective depth ratio
=
20.00
To avoid damages to finishes, modified ratio
=
16.67
Tensile reinforcement modification factor:
Table 3.11
i.
M/bd²
=
BS8110:PART1:
ii.
service stress, fs = 5fyAsreq./8Asprov.)*1/bb By interpolation, Modification Factor, MF
=
=
=
1.22
=
1.22
=
2.00
1997
iii.
Note: MF should not be greater than 2
0.55 + (477 - fs)/(120(0.9+(M/bd²)) Use MF
c.
Modified span - effective depth ratio = MF * Basic span - effective ratio =
d.
Actual span - effective depth ratio Since Modified L/d > Actual L/d,
Design okay w.r.t deflection.
=
L/d
1.86 255.49 N/mm²
20.33
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member:
Diaphragm/Transverse Beam
REF.
CALCULATIONS DESIGN FOR SHEAR
3.3.3 i.
Design shear Force Design Shear Force ,V
ii.
Design Shear Stress, v
V/bd
iii.
iv.
298 KN
= fcu
0.8(fcu)
Checks:
OUTPUT
= =
=
Page No.
Date___december '04
0.620 N/mm²
=
40 N/mm²
5.060 N/mm²
design okay with respect to shear
Obtaining the design concrete shear stress, vc (should be 3.00)
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc 0.79(100As/(bvd))1/3(400/d)0.25/1.25 = =
(should not be < 1.00)
=
0.614
=
0.333 Use 400/d
=
0.537 N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
for this design
then Asv/Sv = bv(v - vc)/(0.87fyv)
v
=
0.620 N/mm²
vc
=
0.537 N/mm²
vc + 0.4 =
0.937 N/mm²
i.e. 0.5vc +v < (vc + 0.4)
Asv/Sv = 0.4*bv/(0.87fyv)
and Asv/Sv reqd
=
Apply a
fyv
=
410 N/mm²
0.449 2 Leg stirrup
T 10
@
and Asv/Sv provided =
300 mm centres 0.524
3.4.1 DESIGN FOR BENDING (SUPPORTS) Design as a rectangular - beam
\
Design Moment
=
Span Length
=
2,366.213 KNm 2,400 mm
Depth of slab/deck
=
250 mm
CALCULATION OF EFFECTIVE DEPTH, d beam depth, h
=
1250 mm
width of beam web, bw
=
400 mm
Flange depth, hf
=
250 mm
fire resistance
=
2.0 hrs
cover to reinforcement, d' reinforcement size, f
=
30.0 mm
=
16.0 mm
stirrup diameter, t
=
12.0 mm
effective depth, d
= =
400 mm
h - (d' + f/2 + t)
= effective width, b
1250 mm
a.
1,200 mm bw+(0.7L/5) 400 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
1997
k therefore, k
=
since k'
M/bd²fcu
fcu
=
0.103
=
0.156
=
it implies that compression steel not required. ii.
1.00
z use z
=
d(0.5 + (0.25 - k/0.9)0.5) =
0.869 d
=
0.869 d
40 N/mm²
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member:
Diaphragm/Transverse Beam
REF.
CALCULATIONS c.
OUTPUT
TENSILE REINFORCEMENT fy
=
As
=
410 N/mm² M/(0.87fy.Z)
=
Apply
6,364 mm² 8
T 32
(As prov. = Table A.7
Checks for minimum steel:
Mosley, Bungay
As min
=
TOP
6,434 mm²)
0.13Ac/100
Apply
Hulse: r.c. design, 5th ed.
= 4
T 16
650.00 mm² BOTTOM
(A's prov.
3.4.2 a.
Table 3.10
Page No.
Date___december '04
BS8110:PART1: 1997
b.
804.25 mm² )
CHECKS FOR DEFLECTION
Basic span - effective depth ratio
=
20.00
To avoid damages to finishes, modified ratio
=
16.67
Tensile reinforcement modification factor:
Table 3.11
i.
M/bd²
=
BS8110:PART1:
ii.
service stress, fs = 5fyAsreq./8Asprov.)*1/bb By interpolation, Modification Factor, MF
=
=
=
0.88
=
0.88
=
2.00
1997
iii.
Note: MF should not be greater than 2
0.55 + (477 - fs)/(120(0.9+(M/bd²)) Use MF
c.
Modified span - effective depth ratio = MF * Basic span - effective ratio =
d.
Actual span - effective depth ratio
=
L/d
4.11 281.63 N/mm²
14.58
Since Modified L/d > Actual L/d,
Design okay w.r.t deflection. 3.4.3 DESIGN FOR SHEAR i.
Design shear Force Design Shear Force ,V
ii.
Design Shear Stress, v
= =
V/bd fcu
Checks: iii.
iv.
0.8(fcu)
298 KN
=
=
0.620 N/mm²
=
40 N/mm²
5.060 N/mm²
design okay with respect to shear
Obtaining the design concrete shear stress, vc (should be 3.00)
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc 0.79(100As/(bvd))1/3(400/d)0.25/1.25 = =
(should not be < 1.00)
=
1.340
=
0.333 Use 400/d
=
1.00
0.697 N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
0.620 N/mm²
vc
=
0.697 N/mm²
vc + 0.4 =
i.e. 0.5vc +v < (vc + 0.4)
Asv/Sv = 0.4*bv/(0.87fyv)
and Asv/Sv reqd
=
Apply a
0.449 2 Leg stirrup
T 10 and Asv/Sv provided =
@
300 mm centres 0.524
fyv
=
410 N/mm²
1.097 N/mm²
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CALCULATIONS
OUTPUT
4.0 BEAM GIRDERS These are the main longitudinal load bearing members. They are designed as rectangular sections, to allow for ease in precast construction. Their arrangement and spacing is as shown in fig. 1 of this report. They are designed to be continuous over three spans
15 m
4.1
15 m
15 m
LOADS
4.1.1 Dead loads, Gk: This is a udl. a. slab weight b. Cantilever wt c. d. e.
= =
0.20 * (2.4 * 4) * 24 = 46.08KN/m 24 { 2 (0.2 * 0.7 ) + 2 *(0.5 * 0.7)} = 23.52KN/m Railings = 2 * (24 * 0.2 * 1.5 ) = 14.40KN/m 5No. * 0.40m * 1.0m * 24KN/m3 Self wt of beams = = 48.00KN/m 0.05m * 8.0m * 23KN/m3 wt of surfacing (50mm asphalt) = = 9.20KN/m Total Dead loads, Gk = 141.20KN/m
Dead load on each beam
=
141.20/5
=
28.24KN/m
4.1.2 CONCENTRATED LOADS,PD Dead loads from diaphragm beam = For each beam, PD = 468.96KN/5
4.1.3 i. Clause 6.2.2 BS 5400:Part II: 1978
a.
b
Table 11; Reynolds & Ste-
IMPOSED (LIVE) LOADING
HA Livel loads HA Knife edge load (KEL) 120KN is recommended as KEL per notional lane. No of notional lanes Total KEL = 120 * 3 Total KEL per beam per span
ii.Table 9; Reynolds & Steedman : R.C Designer's H/bk
468.96KN = 93.80KN
Foot path live load =
HA udl across bridge For bridge span
= = =
3 360KN 360KN/5
=
2
4.0KN/m = 4.0KN/m2 * 0.70m * 2No
=
17.80m
=
5.6KN/m
72.0KN
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CALCULATIONS
Total udl
OUTPUT
10.50KN/m2 = = 10.50 * 8.0/5 = 16.8KN/m 8.0 used above represents the c/way width. 16.8KN/m2 5.6KN/m + 22.40KN/m
Equivalent HA udl is ie load per beam
edman : R.C Designer's H/bk
= =
4.1.4 Load combinations: (HA live Loads + Dead Loads) I. Table 1 BS 5400:Part II: 1978
Loads factors:
a.
ii. Clause 5.1.2 BS 5400:Part II: 1978
Dead Live
= =
Gk Design dead loads, udl, = 28.24KN/m * 1.15
1.15 1.50
=
32.48KN/m ( per beam)
b.
PD Design concentrated dead loads per beam, = 93.80KN * 1.15 = 107.87KN
c.
Design live loads , udl, Qk 22.40KN/m * 1.50
= d.
Design concentrated live loads ( KEL) = 72KN * 1.50
=
=
33.60KN/m
108KN
2*107.87
66.08KN/m 107.87
740.07KN
108
2*107.87
2*740.07KN
108
2*107.87
108
2*740.07KN
2*107.87
2*740.07KN
Loading diagram : HA + Dead Load
4.2
DESIGN MOMENTS & SHEAR
The bridge deck and girders are required to support both static and moving loads. Each element of the bridge must therefore, be designed for the most severe conditions
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CALCULATIONS
OUTPUT
that can possibly be developed by a member. Live loads must be place where they will produce the most severe condition of loading. The critical positions for placing live loads will not be the same for every member. Influence lines are therefore used in determining the most severe condition for loading. Influence lines are primarily used to determine where to place live loads to cause the maximum effects. An influence line for a particular response such as reactions, shear force, bending moment axial force is defined as a diagram in which the ordinate at any point equals the value of that response attributable to a unit load acting at that point on the structure. Influence lines provide a systematic procedure for determining how the force ( or moment or shear force) in a given part of a structure varies as the applied load moves about the structure.
4.2.1
Influence Lines for udl
This is used for plotting the influence lines for uniformly distributed loads such as those due to dead loads, and for the udl portion of HA - live loads. Influence lines for the bending moments at Support B (penultimate support) will be first to be plotted.
4.2.1.1 i.
Geometric Properties
Stiffness Coefficients. Assume a parabolic profile for the girders.
A Chapter 5.7,
rBhc
B
rChc
C
rA
=
rE
=
0
rB
=
rD
=
1.3
D
rChc
Design of r.c.bdg; Aswani, et al.
rC = 1.5 with the above r values, the stiffness coefficients obtained from standard charts for concrete bridges are: kBA KDE = 10.50 =
Fig. 5.25 Design of r.c.bdg; Aswani, et al.
ii. Fig. 5.24 Design of r.c.bdg; Aswani, et al.
kBC KDC = 16.00 = Carry - over factors Using the same r values, the carry-over factors are obtained by interpolation as shown below: CAB = CBC = CCD = -0.905 -0.760 -0.071 CBA = CCB = CDC = -0.415 -0.710 -0.076 CDE = CED = -0.415 -0.905 However, since the end spans are discontinuous, the stiffness values are modified inorder to make the applicable to the members. The stiffness coefficient at the discontinuous end of the beam AB,which is discontinuous at end A is k = (1 - CABCBA)KBA
E
hc
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CALCULATIONS
OUTPUT
CAB &CBA arecarryover factors of ends A & B of member AB, while KBA is the k'BA iii.
=
[ 1 - (-0.905 * - 0.415)] * 10.50
=
6.56 =
k'DE
Distribution factors We now compute the distribution factors using the stiffness coefficient: DBA
=
DBC
=
kBA
=
6.56 / {6.56 + 16.00}
=
0.291
=
DDE
=
DDE
SkB DCB
=
DCD
=
1 - DBA KcB
=
=
0.709
16.00 / {16.00 + 16.00} =
=
DDC
0.5
Skc 1 - DCB
=
0.500
=
DDC
4.3.2 Final Support Moments due to udl. i.
Notations MAB, MBA, MBC, ...
=
Final moments at the support
MAB, MBA, MBC, ...
=
Fixed end moments
CAB, CBA, CBC, ...
=
Carry - over factors
DAB, DBA, DBC, ...
Distribution factors
M1
=
= MBA - CABMBA
M2
=
MBC - CCBMCB
M3
=
MCD - CDCMDC
V
M4 =
MDE - CEDMED = CBCDBCDCD = -0.760 * 0.709 * 0.500
=
U
=
CBCCCBDBCDCB
=
-0.760 * -0.710 * 0.709 * 0.500
=
0.191
W
=
CCBDCBDBA
=
-0.710 * 0.500 * 0.291
=
-0.103
ii.
Numerical values of fixed end moments a.
Fig. 5.35 Design of r.c.bdg; Aswani, et al.
b.
c.
Load in span AB MAB = -0.060L² MBA = -0.138L² Load in span BC MBC = -0.101L² MCB = -0.111L² Load in span CD MCD = -0.111L² MDC
d.
-0.101L²
Load in span DE MCD = -0.138L² MDC
iii.
=
=
-0.060L²
Final support moments
-0.269
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CALCULATIONS a.
First span loaded (Span AB) (1 - DBA) - (2 - DBA)U M1 MB = 1 - 2U (1 - 0.291) - (2 -0.291)0.191 = [1 - (2 * 0.191) ]
OUTPUT
M1
But
M1
MB
= =
b.
Second span loaded (Span BC) DBA(1 -U)MBC - WMCB MB = 1 - 2U 0.291(1 - 0.191)MBC - - 0.103MCB = [1 - (2 * 0.191) ] = 0.381MBC + 0.167MCB
=
=
0.619M1
MBA - CABMAB
0.619 [-0.138 - (-0.905 * -0.060)]L² -0.119L²
Inserting the values for MBC & MCB,
MB
= =
(0.381 * -0.101)L² + (0.167 * -0.111)L² -0.057L²
c.
Third span loaded (Span CD) - UDDEMDC + WMCD MB = 1 - 2U = -0.090MDC - 0.167MCD Inserting the values for MDC & MCD,
MB d.
But
=
(-0.191 * 0.291)MDC + (-0.103)MCD [1 - (2 * 0.191) ]
= (0.090 * -0.101)L² + (0.167 * -0.111)L² = -0.028L² Fourth span loaded (Span DE) UDDE M4 MB = = 1-U = 0.090M4 M4 = MDE - CEDMDC
0.191 * 0.291 [1 - (2 * 0.191) ]
M4
MB
= 0.090 [-0.138 - (-0.905 * -0.060)]L² = -0.017L² d. Value of MB when all spans are loaded = ( -0.119 - 0.057 - 0.028 - 0.017)L² = But L = 17.80m MB e
Section 0.0 0.1 0.2 0.3
=
-0.114 * 17.80²
=
-0.114L² -36.12KNm
Bending Moment at various sections due to the application of unit load. after calculating the bending moment at support B, the bending moment at various sections is now computed due to the application of unit load. This is as tabulate below: Calculations BM ordinates (KNm) 0.000 {(9/25) * (17.80²/8)} - 3.612 6.513 {(16/25) * (17.80²/8)} -7.224 10.776 {(21/25) * (17.80²/8)} - 10.836 12.789
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CALCULATIONS 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
OUTPUT
{(24/25) * (17.80²/8)} - 14.448 {(25/25) * (17.80²/8)} - 18.060 {(24/25) * (17.80²/8)} - 21.672 {(21/25) * (17.80²/8)} -25.284 {(16/25) * (17.80²/8)} -28.896 {(9/25) * (17.80²/8)} - 32.508 MB = -36.120 {(9/25) * (17.80²/8)} - 36.120 {(16/25) * (17.80²/8)} - 36.120 {(21/25) * (17.80²/8)} - 36.120 {(24/25) * (17.80²/8)} - 36.120 {(25/25) * (17.80²/8)} - 36.120 {(24/25) * (17.80²/8)} - 36.120 {(21/25) * (17.80²/8)} - 36.120 {(16/25) * (17.80²/8)} - 36.120 {(9/25) * (17.80²/8)} - 36.120
12.552 10.065 5.328 -1.659 -10.896 -22.383 -36.120 -25.995 -18.120 -12.495 -9.120 -7.995 -9.120 -12.495 -18.120 -25.995 0.000
BM Influence Line Diagram For udl 20
10
0 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
-10
-20
-30
-40
1.3.3 HA - live loads udl moments. from sections 1.1.3 and 1.1.4 of this report, the ultimate udl due to HA loading is 16.85KN/m . Using this influence ordinate table above, we now compute the various moments as below; a.
\
Support moments influence line ordinate design HA udl live load
= =
-0.657KNm 16.85KN/m
HA udl support moments
=
-0.657KNm * 16.85
20
21
22
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CALCULATIONS =
-11.07 KNm
b. Span moments maximum span moment occurs at 0.4L (1st span) and at 3.6L (4th span) influence line ordinate = 0.428KNm design HA udl live load = 16.85KN/m
\
HA udl span moments
= =
0.428KNm * 16.85 7.21 KNm
4.3.4 Dead load udl moments. from sections 3.1.1 and 3.1.4 of this report, the udl due to dead loading is 28.24KN/m per beam, while the factored udl per beam due to dead loads is 32.48KN/m Using this influence ordinate table above, we now compute the various moments as below; a.
\
Support moments influence line ordinate design dead load udl dead load udl support moments
= =
-0.657KNm 10.65KN/m
= =
-0.657KNm * 10.65 -7.00 KNm
b. Span moments maximum span moment occurs at 0.4L (1st span) and at 2.6L (3rd span) influence line ordinate = 0.428KNm design dead load udl = 10.65KN/m
\
dead load udl span moments
= =
0.428KNm * 10.65 4.56 KNm
4.2.1.3 HA - live loads udl moments. from sections 3.1.3 and 3.1.4 of this report, the udl due to HA loading is 22.40KN/m per beam, while the factored udl per beam due to HA loading is 33.60KN/m this is obtained from the HA udl across the bridge span and the foot path live loads. Using this influence ordinate table above, we now compute the various moments as below; a.
\
Support moments influence line ordinate design HA udl live load HA udl support moments
= =
-23.450KNm 33.60KN/m
= =
-23.45KNm * 33.60 -787.92 KNm
b. Span moments maximum span moment occurs at 0.4L (1st span) and at 2.6L (3rd span) influence line ordinate = -28.641KNm design HA udl live load = 33.60KN/m
\
HA udl span moments
= =
28.641KNm * 33.60 962.34 KNm
OUTPUT
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CALCULATIONS
4.2.1.4 Dead load udl moments. from sections 3.1.1 and 3.1.4 of this report, the udl due to dead loading is 28.24KN/m per beam, while the factored udl per beam due to dead loads is 32.48KN/m Using this influence ordinate table above, we now compute the various moments as below; a. Support moments influence line ordinate = -23.450KNm design dead load udl = 32.48KN/m
\
dead load udl support moments
= =
-23.45KNm * 32.48 -761.66 KNm
b. Span moments maximum span moment occurs at 0.4L (1st span) and at 2.6L (3rd span) influence line ordinate = -28.641KNm design dead load udl = 32.48KN/m
\
4.2.2
dead load udl span moments
= =
28.641KNm * 32.48 930.26 KNm
Influence Lines for Point Loads
The point loads are due primarily to either HA live loads or the HB live loads. The beam girder is designed to be continuous over three spans, and has a constant moment of inertia over all the spans. We can therfore, plot the influence lines using standard influence line tables for a three span continuous beam. The following assumptions are made in the analysis of the continuous bridge girders before using the standard influence tables: * The girder is simply supported at the supports and monolithic with the supports. * Rocker or roller bearings are provided at all supports. Find below the influence line tables and charts at sections 0.1L to 1.5L We prepared the influence charts only upto 1.5L as the loading is symmetrical over the three spans.
OUTPUT
Job No.
Era
Designed
Checked Page No.
OUTPUT
Job No.
Era
Designed
Checked Page No.
OUTPUT
Job No.
Era
Designed
Checked Page No.
OUTPUT
E
hc
Job No.
Era
Designed
Checked Page No.
OUTPUT
Job No.
Era
Designed
Checked Page No.
OUTPUT
Job No.
Era
Designed
Checked Page No.
OUTPUT
22
Job No.
Era
Designed
Checked Page No.
OUTPUT
Job No.
Era
Designed
Checked Page No.
OUTPUT
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Era
Designed
Checked Date___december '04
CALCULATIONS
OUTPUT
15.000 Lm Span Length = Bending Moment Influence Lines At First Internal Support, MB Influence Load Influence Line Posit Coefficients for Ordinate ion MB 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.0 -0.0257 -0.0584 -0.0739 -0.0874 -0.1000 -0.0994 -0.0928 -0.0742 -0.0408 0.0 -0.0754 -0.0614 -0.0746 -0.0774 -0.0750 -0.0664 -0.0484 -0.0316 -0.0156 0.0 0.0075 0.0150 0.0225 0.0250 0.0250 0.0220 0.0180 0.0120 0.0060 0.0
0.0 -0.3862 -0.8765 -1.1079 -1.3114 -1.5000 -1.4910 -1.3921 -1.1129 -0.6119 0.0 -1.1316 -0.9205 -1.1189 -1.1609 -1.1250 -0.9960 -0.7261 -0.4739 -0.2340 0.0 0.1125 0.2250 0.3375 0.3750 0.3750 0.3300 0.2700 0.1800 0.0900 0.0
BM Influence Line Ordinates for MB
0.5
0 1 -0.5 -1 -1.5
-2
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
REF. CALCULATIONS Influence Line ordinates for BM at Support C (Mc). Load Posit ion
Influence line coefficient
Influence line ordinates
0.0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L 1.1L 1.2L 1.3L 1.4L 1.5L 1.6L 1.7L 1.8L 1.9L 2.0L 2.1L 2.2L 2.3L 2.4L 2.5L 2.6L 2.7L 2.8L 2.9L 3.0L
0.0 0.0060 0.0120 0.0180 0.0220 0.0250 0.0250 0.0220 0.0150 0.0070 0.0 -0.0160 -0.0320 -0.0480 -0.0620 -0.0750 -0.0770 -0.0750 -0.0610 -0.0340 0.0 -0.0410 -0.0740 -0.0930 -0.0990 -0.1000 -0.0870 -0.0720 -0.0500 -0.0260 0.0
0.0 0.0900 0.1800 0.2700 0.3300 0.3750 0.3750 0.3300 0.2250 0.1050 0.0 -0.2400 -0.4800 -0.7200 -0.9300 -1.1250 -1.1550 -1.1250 -0.9150 -0.5100 0.0 -0.6150 -1.1100 -1.3950 -1.4850 -1.5000 -1.3050 -1.0800 -0.7500 -0.3900 0.0
0.5
OUTPUT
BM Influence Line Ordinates for MC
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5
-1
-1.5
-2
Bending Moment Influence Lines At 0.1L
REF. Load Posit ion
CALCULATIONS
m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0026 -0.0058 -0.0074 -0.0087 -0.0100 -0.0099 -0.0093 -0.0074 -0.0041 0.0 -0.0075 -0.0061 -0.0075 -0.0077 -0.0075 -0.0066 -0.0048 -0.0032 -0.0016 0.0 0.0008 0.0015 0.0023 0.0025 0.0025 0.0022 0.0018 0.0012 0.0006 0.0
0.0 0.0874 0.0742 0.0626 0.0513 0.0400 0.0301 0.0207 0.0126 0.0059 0.0 -0.0075 -0.0061 -0.0075 -0.0077 -0.0075 -0.0066 -0.0048 -0.0032 -0.0016 0.0 0.0008 0.0015 0.0023 0.0025 0.0025 0.0022 0.0018 0.0012 0.0006 0.0
0.0 1.3114 1.1124 0.9392 0.7689 0.6000 0.4509 0.3108 0.1887 0.0888 0.0000 -0.1132 -0.0920 -0.1119 -0.1161 -0.1125 -0.0996 -0.0726 -0.0474 -0.0234 0.0 0.0113 0.0225 0.0338 0.0375 0.0375 0.0330 0.0270 0.0180 0.0090 0.0
0.0 0.0900 0.0800 0.0700 0.0600 0.0500 0.0400 0.0300 0.0200 0.0100 0.0
0.0
0.0
OUTPUT
Influence Line Ordinate for Load @ 0.1L 1.4 1.2 1
0.8 0.6 0.4 0.2 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
-0.2
Bending Moment Influence Lines At 0.2L
REF. Load Posit ion
CALCULATIONS
m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
OUTPUT
Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0051 -0.0117 -0.0148 -0.0175 -0.0200 -0.0199 -0.0186 -0.0148 -0.0082 0.0 -0.0151 -0.0123 -0.0149 -0.0155 -0.0150 -0.0133 -0.0097 -0.0063 -0.0031 0.0 0.0015 0.0030 0.0045 0.0050 0.0050 0.0044 0.0036 0.0024 0.0012 0.0
0.0 0.0749 0.1483 0.1252 0.1025 0.0800 0.0601 0.0414 0.0252 0.0118 0.0 -0.0151 -0.0123 -0.0149 -0.0155 -0.0150 -0.0133 -0.0097 -0.0063 -0.0031 0.0 0.0015 0.0030 0.0045 0.0050 0.0050 0.0044 0.0036 0.0024 0.0012 0.0
0.0 1.1228 2.2247 1.8784 1.5377 1.2000 0.9018 0.6216 0.3774 0.1776 0.0000 -0.2263 -0.1841 -0.2238 -0.2322 -0.2250 -0.1992 -0.1452 -0.0948 -0.0468 0.0 0.0225 0.0450 0.0675 0.0750 0.0750 0.0660 0.0540 0.0360 0.0180 0.0
0.0 0.0800 0.1600 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0
0.0
0.0
2.5 BM Influence Lines at 0.2L 2
1.5
1
0.5
0 1
3
5
7
9
-0.5 Bending Moment Influence Lines At 0.3L
11
13
15
17
19
21
23
25
27
29
31
REF. Load Posit ion
m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
CALCULATIONS
OUTPUT
Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0077 -0.0175 -0.0222 -0.0262 -0.0300 -0.0298 -0.0278 -0.0223 -0.0122 0.0 -0.0226 -0.0184 -0.0224 -0.0232 -0.0225 -0.0199 -0.0145 -0.0095 -0.0047 0.0 0.0023 0.0045 0.0068 0.0075 0.0075 0.0066 0.0054 0.0036 0.0018 0.0
0.0 0.0623 0.1225 0.1878 0.1538 0.1200 0.0902 0.0622 0.0377 0.0178 0.0 -0.0226 -0.0184 -0.0224 -0.0232 -0.0225 -0.0199 -0.0145 -0.0095 -0.0047 0.0 0.0023 0.0045 0.0068 0.0075 0.0075 0.0066 0.0054 0.0036 0.0018 0.0
0.0 0.9341 1.8371 2.8176 2.3066 1.8000 1.3527 0.9324 0.5661 0.2664 0.0000 -0.3395 -0.2761 -0.3357 -0.3483 -0.3375 -0.2988 -0.2178 -0.1422 -0.0702 0.0 0.0338 0.0675 0.1013 0.1125 0.1125 0.0990 0.0810 0.0540 0.0270 0.0
0.0 0.0700 0.1400 0.2100 0.1800 0.1500 0.1200 0.0900 0.0600 0.0300 0.0
0.0
0.0
BM Influence Line Ordinate For Load Position 0.3L
3 2.5 2 1.5 1 0.5 0 0
5
10
-0.5 -1
Bending Moment Influence Lines At 0.4L
15
20
25
30
35
REF. Load Posit ion
CALCULATIONS
m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
OUTPUT
Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0103 -0.0234 -0.0295 -0.0350 -0.0400 -0.0398 -0.0371 -0.0297 -0.0163 0.0 -0.0302 -0.0245 -0.0298 -0.0310 -0.0300 -0.0266 -0.0194 -0.0126 -0.0062 0.0 0.0030 0.0060 0.0090 0.0100 0.0100 0.0088 0.0072 0.0048 0.0024 0.0
0.0 0.0497 0.0966 0.1505 0.2050 0.1600 0.1202 0.0829 0.0503 0.0237 0.0 -0.0302 -0.0245 -0.0298 -0.0310 -0.0300 -0.0266 -0.0194 -0.0126 -0.0062 0.0 0.0030 0.0060 0.0090 0.0100 0.0100 0.0088 0.0072 0.0048 0.0024 0.0
0.0 0.7455 1.4494 2.2568 3.0754 2.4000 1.8036 1.2432 0.7548 0.3552 0.0 -0.4526 -0.3682 -0.4476 -0.4644 -0.4500 -0.3984 -0.2904 -0.1896 -0.0936 0.0 0.0450 0.0900 0.1350 0.1500 0.1500 0.1320 0.1080 0.0720 0.0360 0.0
0.0 0.0600 0.1200 0.1800 0.2400 0.2000 0.1600 0.1200 0.0800 0.0400 0.0
0.0
0.0
BM Influence Line Ordinate For Load Position At 0.4L 3.5 3 2.5 2 1.5 1 0.5 0
1
3
5
7
9
-0.5 -1 Bending Moment Influence Lines At 0.5L
11
13
15
17
19
21
23
25
27
29
31
REF. Load Posit ion
CALCULATIONS
m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
OUTPUT
Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0129 -0.0292 -0.0369 -0.0437 -0.0500 -0.0497 -0.0464 -0.0371 -0.0204 0.0 -0.0377 -0.0307 -0.0373 -0.0387 -0.0375 -0.0332 -0.0242 -0.0158 -0.0078 0.0 0.0038 0.0075 0.0113 0.0125 0.0125 0.0110 0.0090 0.0060 0.0030 0.0
0.0 0.0371 0.0708 0.1131 0.1563 0.2000 0.1503 0.1036 0.0629 0.0296 0.0 -0.0377 -0.0307 -0.0373 -0.0387 -0.0375 -0.0332 -0.0242 -0.0158 -0.0078 0.0 0.0038 0.0075 0.0113 0.0125 0.0125 0.0110 0.0090 0.0060 0.0030 0.0
0.0 0.5569 1.0618 1.6960 2.3443 3.0000 2.2545 1.5540 0.9435 0.4441 0.0 -0.5658 -0.4602 -0.5595 -0.5805 -0.5625 -0.4980 -0.3630 -0.2370 -0.1170 0.0 0.0563 0.1125 0.1688 0.1875 0.1875 0.1650 0.1350 0.0900 0.0450 0.0
0.0 0.0500 0.1000 0.1500 0.2000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0
0.0
0.0
BM Influence Line Ordinate For Load Position At 0.5L 3.5 3 2.5
2 1.5 1 0.5
0 1
3
5
7
9
-0.5 -1 Bending Moment Influence Lines At 0.6L
11
13
15
17
19
21
23
25
27
29
31
REF. Load Posit ion
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
m-Coefficients 0.0 0.0400 0.0800 0.1200 0.1600 0.2000 0.2400 0.1800 0.1200 0.0600 0.0
0.0
0.0
CALCULATIONS Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0154 -0.0351 -0.0443 -0.0525 -0.0600 -0.0596 -0.0557 -0.0445 -0.0245 0.0000 -0.0453 -0.0368 -0.0448 -0.0464 -0.0450 -0.0398 -0.0290 -0.0190 -0.0094 0.0000 0.0045 0.0090 0.0135 0.0150 0.0150 0.0132 0.0108 0.0072 0.0036 0.0
0.0 0.0246 0.0449 0.0757 0.1075 0.1400 0.1804 0.1243 0.0755 0.0355 0.0 -0.0453 -0.0368 -0.0448 -0.0464 -0.0450 -0.0398 -0.0290 -0.0190 -0.0094 0.0 0.0045 0.0090 0.0135 0.0150 0.0150 0.0132 0.0108 0.0072 0.0036 0.0
0.0 0.3683 0.6741 1.1352 1.6132 2.1000 2.7054 1.8648 1.1322 0.5329 0.0 -0.6789 -0.5523 -0.6714 -0.6966 -0.6750 -0.5976 -0.4356 -0.2844 -0.1404 0.0 0.0675 0.1350 0.2025 0.2250 0.2250 0.1980 0.1620 0.1080 0.0540 0.0
OUTPUT
BM Influence Line Ordinates For Load Position At 0.6L 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5 -1 Bending Moment Influence Lines At 0.7L
REF. Load Posit ion
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
m-Coefficients 0.0 0.0300 0.0600 0.0900 0.1200 0.1500 0.1800 0.2100 0.1400 0.0700 0.0
0.0
0.0
CALCULATIONS Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0180 -0.0409 -0.0517 -0.0612 -0.0700 -0.0696 -0.0650 -0.0519 -0.0286 0.0000 -0.0528 -0.0430 -0.0522 -0.0542 -0.0525 -0.0465 -0.0339 -0.0221 -0.0109 0.0000 0.0053 0.0105 0.0158 0.0175 0.0175 0.0154 0.0126 0.0084 0.0042 0.0
0.0 0.0120 0.0191 0.0383 0.0588 0.0800 0.1104 0.1450 0.0881 0.0414 0.0 -0.0528 -0.0430 -0.0522 -0.0542 -0.0525 -0.0465 -0.0339 -0.0221 -0.0109 0.0 0.0053 0.0105 0.0158 0.0175 0.0175 0.0154 0.0126 0.0084 0.0042 0.0
0.0 0.1796 0.2865 0.5745 0.8820 1.2000 1.6563 2.1756 1.3209 0.6217 0.0 -0.7921 -0.6443 -0.7832 -0.8126 -0.7875 -0.6972 -0.5082 -0.3318 -0.1638 0.0 0.0788 0.1575 0.2363 0.2625 0.2625 0.2310 0.1890 0.1260 0.0630 0.0
OUTPUT
BM Influence Line Ordinate For Load Position At 0.7L 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5 -1 Bending Moment Influence Lines At 0.8L
REF. Load Posit ion
m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.0 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.0800 0.0
0.0
0.0
CALCULATIONS Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0206 -0.0467 -0.0591 -0.0699 -0.0800 -0.0795 -0.0742 -0.0594 -0.0326 0.0000 -0.0604 -0.0491 -0.0597 -0.0619 -0.0600 -0.0531 -0.0387 -0.0253 -0.0125 0.0000 0.0060 0.0120 0.0180 0.0200 0.0200 0.0176 0.0144 0.0096 0.0048 0.0
0.0 -0.0006 -0.0067 0.0009 0.0101 0.0200 0.0405 0.0658 0.1006 0.0474 0.0 -0.0604 -0.0491 -0.0597 -0.0619 -0.0600 -0.0531 -0.0387 -0.0253 -0.0125 0.0 0.0060 0.0120 0.0180 0.0200 0.0200 0.0176 0.0144 0.0096 0.0048 0.0
0.0 -0.0090 -0.1012 0.0137 0.1509 0.3000 0.6072 0.9864 1.5096 0.7105 0.0 -0.9053 -0.7364 -0.8951 -0.9287 -0.9000 -0.7968 -0.5808 -0.3792 -0.1872 0.0 0.0900 0.1800 0.2700 0.3000 0.3000 0.2640 0.2160 0.1440 0.0720 0.0
OUTPUT
BM Influence Line Ordinate For Load Position At 0.8L 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5 -1 -1.5 Bending Moment Influence Lines At 0.9L
REF. Load Posit ion
CALCULATIONS
m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
OUTPUT
Influence Coefficients for MB
m+ MB
Influence Line Ordinate
0.0 -0.0232 -0.0526 -0.0665 -0.0787 -0.0900 -0.0895 -0.0835 -0.0668 -0.0367 0.0 -0.0679 -0.0552 -0.0671 -0.0697 -0.0675 -0.0598 -0.0436 -0.0284 -0.0140 0.0 0.0068 0.0135 0.0203 0.0225 0.0225 0.0198 0.0162 0.0108 0.0054 0.0
0.0 -0.0132 -0.0326 -0.0365 -0.0387 -0.0400 -0.0295 -0.0135 0.0132 0.0533 0.0 -0.0679 -0.0552 -0.0671 -0.0697 -0.0675 -0.0598 -0.0436 -0.0284 -0.0140 0.0 0.0068 0.0135 0.0203 0.0225 0.0225 0.0198 0.0162 0.0108 0.0054 0.0
0.0 -0.1976 -0.4888 -0.5471 -0.5802 -0.6000 -0.4419 -0.2029 0.1984 0.7993 0.0 -1.0184 -0.8284 -1.0070 -1.0448 -1.0125 -0.8964 -0.6534 -0.4266 -0.2106 0.0 0.1013 0.2025 0.3038 0.3375 0.3375 0.2970 0.2430 0.1620 0.0810 0.0
0.0 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.0
0.0
0.0
BM Influence Line Ordinate For Load Position At 0.9L 1
0.5
0 1
3
5
7
9
-0.5
-1
-1.5 Bending Moment Influence Lines At 1.1L
11
13
15
17
19
21
23
25
27
29
31
REF. m-Coefficients
Load Posit
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.0 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.0
0.0
Influence 0.0 0.0006 0.0012 0.0018 0.0022 0.0025 0.0025 0.0022 0.0015 0.0007 0.0000 -0.0016 -0.0032 -0.0048 -0.0062 -0.0075 -0.0077 -0.0075 -0.0061 -0.0034 0.0000 -0.0041 -0.0074 -0.0093 -0.0099 -0.0100 -0.0087 -0.0072 -0.0050 -0.0026 0.0000
CALCULATIONS Influence m+ MB + MC 0.0 -0.0257 -0.0584 -0.0739 -0.0874 -0.1000 -0.0994 -0.0928 -0.0742 -0.0408 0.0000 -0.0754 -0.0614 -0.0746 -0.0774 -0.0750 -0.0664 -0.0484 -0.0316 -0.0156 0.0000 0.0075 0.0150 0.0225 0.0250 0.0250 0.0220 0.0180 0.0120 0.0060 0.0000
0.0 -0.0251 -0.0572 -0.0721 -0.0852 -0.0975 -0.0969 -0.0906 -0.0727 -0.0401 0.0000 -0.0670 -0.0446 -0.0494 -0.0436 -0.0325 -0.0141 0.0141 0.0423 0.0710 0.0000 0.0034 0.0076 0.0132 0.0151 0.0150 0.0133 0.0108 0.0070 0.0034 0.0000
OUTPUT Influence Line 0.0 -0.3772 -0.8585 -1.0809 -1.2784 -1.4625 -1.4535 -1.3591 -1.0904 -0.6014 0.0 -1.0056 -0.6685 -0.7409 -0.6539 -0.4875 -0.2115 0.2114 0.6346 1.0650 0.0 0.0510 0.1140 0.1980 0.2265 0.2250 0.1995 0.1620 0.1050 0.0510 0.0
Influence Line Ordinate For Load Position At 1.1L 1.5
1
0.5
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5
-1
-1.5
-2 Bending Moment Influence Lines At 1.2L
REF. m-Coefficients
Load Posit
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.0 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.0800 0.0
0.0
Influence 0.0 0.0012 0.0024 0.0036 0.0044 0.0050 0.0050 0.0044 0.0030 0.0014 0.0000 -0.0032 -0.0064 -0.0096 -0.0124 -0.0150 -0.0154 -0.0150 -0.0122 -0.0068 0.0000 -0.0082 -0.0148 -0.0186 -0.0198 -0.0200 -0.0174 -0.0144 -0.0100 -0.0052 0.0000
CALCULATIONS Influence m+ MB + MC 0.0 -0.0257 -0.0584 -0.0739 -0.0874 -0.1000 -0.0994 -0.0928 -0.0742 -0.0408 0.0000 -0.0754 -0.0614 -0.0746 -0.0774 -0.0750 -0.0664 -0.0484 -0.0316 -0.0156 0.0000 0.0075 0.0150 0.0225 0.0250 0.0250 0.0220 0.0180 0.0120 0.0060 0.0000
0.0 -0.0245 -0.0560 -0.0703 -0.0830 -0.0950 -0.0944 -0.0884 -0.0712 -0.0394 0.0000 -0.0586 -0.0278 -0.0242 -0.0098 0.0100 0.0382 0.0766 0.1162 0.0576 0.0000 -0.0007 0.0002 0.0039 0.0052 0.0050 0.0046 0.0036 0.0020 0.0008 0.0000
OUTPUT Influence Line 0.0 -0.3682 -0.8405 -1.0539 -1.2454 -1.4250 -1.4160 -1.3261 -1.0679 -0.5909 0.0 -0.8796 -0.4165 -0.3629 -0.1469 0.1500 0.5730 1.1489 1.7431 0.8640 0.0 -0.0105 0.0030 0.0585 0.0780 0.0750 0.0690 0.0540 0.0300 0.0120 0.0
BM Influence Line Ordinates For Load Position At 1.2L 2
1.5
1
0.5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5
-1
-1.5
-2 Bending Moment Influence Lines At 1.3L
Load Posit
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
REF. m-Coefficients
0.0 0.0300 0.0600 0.0900 0.1200 0.1500 0.1800 0.2100 0.1400 0.0700 0.0
0.0
Influence 0.0 0.0018 0.0036 0.0054 0.0066 0.0075 0.0075 0.0066 0.0045 0.0021 0.0000 -0.0048 -0.0096 -0.0144 -0.0186 -0.0225 -0.0231 -0.0225 -0.0183 -0.0102 0.0000 -0.0123 -0.0222 -0.0279 -0.0297 -0.0300 -0.0261 -0.0216 -0.0150 -0.0078 0.0000
CALCULATIONS Influence m+ MB + MC 0.0 -0.0257 -0.0584 -0.0739 -0.0874 -0.1000 -0.0994 -0.0928 -0.0742 -0.0408 0.0000 -0.0754 -0.0614 -0.0746 -0.0774 -0.0750 -0.0664 -0.0484 -0.0316 -0.0156 0.0000 0.0075 0.0150 0.0225 0.0250 0.0250 0.0220 0.0180 0.0120 0.0060 0.0000
0.0 -0.0239 -0.0548 -0.0685 -0.0808 -0.0925 -0.0919 -0.0862 -0.0697 -0.0387 0.0000 -0.0502 -0.0110 0.0010 0.0240 0.0525 0.0905 0.1391 0.0901 0.0442 0.0000 -0.0048 -0.0072 -0.0054 -0.0047 -0.0050 -0.0041 -0.0036 -0.0030 -0.0018 0.0000
OUTPUT Influence Line 0.0 -0.3592 -0.8225 -1.0269 -1.2124 -1.3875 -1.3785 -1.2931 -1.0454 -0.5804 0.0 -0.7536 -0.1645 0.0151 0.3601 0.7875 1.3575 2.0864 1.3516 0.6630 0.0 -0.0720 -0.1080 -0.0810 -0.0705 -0.0750 -0.0615 -0.0540 -0.0450 -0.0270 0.0
Influence Line Ordinate For Load Position At 1.3L 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5 -1 -1.5 -2
REF.
CALCULATIONS
Bending Moment Influence Lines At 1.4L Load Influence Posit m-Coefficients 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.0 0.0400 0.0800 0.1200 0.1600 0.2000 0.2400 0.1800 0.1200 0.0600 0.0
0.0
0.0 0.0024 0.0048 0.0072 0.0088 0.0100 0.0100 0.0088 0.0060 0.0028 0.0000 -0.0064 -0.0128 -0.0192 -0.0248 -0.0300 -0.0308 -0.0300 -0.0244 -0.0136 0.0000 -0.0164 -0.0296 -0.0372 -0.0396 -0.0400 -0.0348 -0.0288 -0.0200 -0.0104 0.0000
OUTPUT
Influence
m+ MB + MC
Influence Line
0.0 -0.0257 -0.0584 -0.0739 -0.0874 -0.1000 -0.0994 -0.0928 -0.0742 -0.0408 0.0000 -0.0754 -0.0614 -0.0746 -0.0774 -0.0750 -0.0664 -0.0484 -0.0316 -0.0156 0.0000 0.0075 0.0150 0.0225 0.0250 0.0250 0.0220 0.0180 0.0120 0.0060 0.0000
0.0 -0.0233 -0.0536 -0.0667 -0.0786 -0.0900 -0.0894 -0.0840 -0.0682 -0.0380 0.0000 -0.0418 0.0058 0.0262 0.0578 0.0950 0.1428 0.1016 0.0640 0.0308 0.0000 -0.0089 -0.0146 -0.0147 -0.0146 -0.0150 -0.0128 -0.0108 -0.0080 -0.0044 0.0000
0.0 -0.3502 -0.8045 -0.9999 -1.1794 -1.3500 -1.3410 -1.2601 -1.0229 -0.5699 0.0 -0.6276 0.0875 0.3931 0.8671 1.4250 2.1420 1.5239 0.9601 0.4620 0.0 -0.1335 -0.2190 -0.2205 -0.2190 -0.2250 -0.1920 -0.1620 -0.1200 -0.0660 0.0
BM Influence Ordinate For Load Position At 1.4L 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -0.5 -1 -1.5 -2 Bending Moment Influence Lines At 1.5L
Load Posit
REF. m-Coefficients
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
CALCULATIONS Influence m+ MB + MC
Influence 0.0 0.0030 0.0060 0.0090 0.0110 0.0125 0.0125 0.0110 0.0075 0.0035 0.0000 -0.0080 -0.0160 -0.0240 -0.0310 -0.0375 -0.0385 -0.0375 -0.0305 -0.0170 0.0000 -0.0205 -0.0370 -0.0465 -0.0495 -0.0500 -0.0435 -0.0360 -0.0250 -0.0130 0.0000
0.0 0.0500 0.1000 0.1500 0.2000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0
0.0
0.0 -0.0257 -0.0584 -0.0739 -0.0874 -0.1000 -0.0994 -0.0928 -0.0742 -0.0408 0.0000 -0.0754 -0.0614 -0.0746 -0.0774 -0.0750 -0.0664 -0.0484 -0.0316 -0.0156 0.0000 0.0075 0.0150 0.0225 0.0250 0.0250 0.0220 0.0180 0.0120 0.0060 0.0000
OUTPUT Influence Line
0.0 -0.0227 -0.0524 -0.0649 -0.0764 -0.0875 -0.0869 -0.0818 -0.0667 -0.0373 0.0000 -0.0334 0.0226 0.0514 0.0916 0.1375 0.0951 0.0641 0.0379 0.0174 0.0000 -0.0130 -0.0220 -0.0240 -0.0245 -0.0250 -0.0215 -0.0180 -0.0130 -0.0070 0.0000
0.0 -0.3412 -0.7865 -0.9729 -1.1464 -1.3125 -1.3035 -1.2271 -1.0004 -0.5594 0.0 -0.5016 0.3395 0.7711 1.3741 2.0625 1.4265 0.9614 0.5686 0.2610 0.0 -0.1950 -0.3300 -0.3600 -0.3675 -0.3750 -0.3225 -0.2700 -0.1950 -0.1050 0.0
BM Influence Line Ordinates For Load Position At 1.5L 2.5 2 1.5
1 0.5 0 1 -0.5
-1 -1.5
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF.
Designed
Era
Checked
Bridge Beam/Girder
Page No.
Date___december '04
CALCULATIONS
OUTPUT
Since the structure is symmetrical, influence lines are only drawn for load positions upto 1.5L
4.2.2.1 Bending moments due to HA live loads (point loads) Sections 3.1.3 and 3.1.4 of this report
The point loads due to HA live loads is the HA Knife - Edge load (KEL). With reference to Clause 6.2.2 of BS 5400: Part II: 1978, 120KN of KEL is recommended per notional lane. Based on this, the KEL per beam per span is computed as 72.0KN; while the factored KEL per beam per span is108.0KN
a. Support moments i. ii. iii. iv.
when first span loaded; apply KEL at 0.4L: when second span loaded; apply KEL at 1.4L: when third span loaded; apply KEL at 2.6L: when all three spans are loaded where P = design KEL = 108.0KN Therefore M = -2.705 * 108.0KN
= = = =
-1.780P -1.370P +0.445P -2.705P
=
-292.14KNm
b. Span moments i. ii. iii. iv.
when first span loaded; apply KEL at 0.4L: when second span loaded; apply KEL at 1.4L: when third span loaded; apply KEL at 2.6L: when all three spans are loaded, M where P = design KEL = 108.0KN Therefore M = 10.3134 * 108.0KN
= = = =
3.6526P 3.0082P 3.6526P 10.3134P
=
1,113.85KNm
4.2.2.2 Total Bending moments due to HA live loads + Dead loads a. Support moments Sections 3.2.1.3 3.2.1.4 & 3.2.2.1 of this report
moments due to HA point loads moments due to HA udl loads moments due to dead loads Design HA + Dead loads
= = = =
-292.14KNm -787.92KNm -761.66KNm -1,841.72KNm
= = = =
1,113.85KNm 962.34KNm 930.26KNm 3,006.45KNm
design HA + Gk support mmts = -1,841.72KNm
b. Span moments moments due to HA point loads moments due to HA udl loads moments due to dead loads Design HA + Dead loads
design HA + Gk span mmts = 3,006.45KNm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF.
Designed
Bridge Beam/Girder
OUTPUT
4.3 HB Live loading This is done using a 45 - unit HB loading. A 45 - unit HB vehicle has 4 axles, carrying 4 wheels each. weight of each axle = 10KN Total axle weight = 10KN /axle * 4Axles = For a 45 - unit HB loading, wheel load = 45 * 40KN = 1,800KN Total No. of wheels supported = 16No. Therefore, load exerted by each wheel = 1,800/16 = 112.50KN Alternative method of calculating Load exerted by each wheel: 2,500j Newtons = (where j = no of units of HB load )
2,500 * 45 / 1,000
1,800
=
112.5KN
6,100 9,700
1,800
Fig 3: Dimensions of a HB vehicle 75
1,000 1,000 1,000
375
Table 9, R.C. H/Bk, Reynolds & Steedman. (10th ed)
DIRECTION OF TRAVEL
1,800
CAXLE
6,100
CAXLE
1,800
CAXLE
CAXLE
Fig 4 : A unit of HB - vehicle configuration
4.3.2 Sect. 1.17(11) Aswani, et al; Design of R.C. Bridges
DISPERSION OF WHEEL LOADS
Dispersion of wheel loads along the span lenghts through the wearing coat, and deck/slab is not considered. This is therefore not computed the bridge girders
4.3.3
Page No.
Date___december '04
CALCULATIONS
=
Era
Checked
MOMENTS DUE TO HB LIVE LOADS
40KN
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF.
Bridge Beam/Girder
Designed
OUTPUT
a. Supports The point loads are placed at critical positions to produce maximum effect.
when 1st span only is loaded The influence values are as tabulated below. Load Position BM ordinate BM 0.3L -1.2816P -144.18KNm 0.4L -1.5486P -174.22KNm 0.8L -1.3172P -148.19KNm 0.9L -0.7298P -82.10KNm -548.69KNm
ii.
iii.
But P = 112.5KNm
when only 3rd span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 2.3L 0.3916 P 44.06 KNm 2.4L 0.4450 P 50.06 KNm 2.8L 0.2136 P 24.03 KNm 2.9L 0.1068 P 12.02 KNm 130.16 KNm
iv.
But P = 112.5KNm
when only 2nd span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 1.3L -1.3350P -150.19KNm 1.4L -1.3706P -154.19KNm 1.8L -0.5696P -64.08KNm 1.9L -0.2848P -32.04KNm -400.50KNm
But P = 112.5KNm
When all 3 spans are loaded: Total moments due to HB load = -548.69KNm - 400.50KNm + 130.16KNm = -819.03KNm
a. Span moment The point loads are placed at critical positions to produce maximum effect. i.
when 1st span only is loaded The influence values are as tabulated below. Load Position BM ordinate BM 0.3L 3.3535 P 377.27 KNm 0.4L 3.6526 P 410.92 KNm 0.8L 1.7942 P 201.85 KNm 0.9L 0.9452 P 106.34 KNm 1,096.37 KNm
ii.
when only 2nd span is loaded The influence values are as tabulated below.
Page No.
Date___december '04
CALCULATIONS
i.
Era
Checked
But P = 112.5KNm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF.
Designed
Bridge Beam/Girder BM ordinate 2.5472 P 3.0082 P 0.4486 P 0.1050 P
iii.
BM 286.56 338.42 50.47 11.81 687.26
OUTPUT But P = 112.5KNm
KNm KNm KNm KNm KNm
when only 3rd span is loaded The influence values are as tabulated below. Load Position BM ordinate BM 2.3L 0.9452 P 106.34 KNm 2.4L 1.7942 P 201.85 KNm 2.8L 3.6526 P 410.92 KNm 2.9L 3.3535 P 377.27 KNm 1,096.37 KNm
iv.
Page No.
Date___december '04
CALCULATIONS Load Position 1.3L 1.4L 1.8L 1.9L
Era
Checked
But P = 112.5KNm
When all 3 spans are loaded: Total moments due to HB load = 1,096.37KNm + 687.26KNm + 1,096.37KNm = 2,880.00KNm
4.3.4 Total Bending moments due to HB live loads + Dead loads a. Support moments Sections 3.2.1.4 & 3.3.3
moments due to HB point loads moments due to dead loads
= =
-819.03KNm -761.66KNm
Design HB + Dead loads
=
-1,580.69KNm
moments due to HB point loads moments due to dead loads
= =
2,880.00KNm 930.26KNm
Design HA + Dead loads
=
3,810.26KNm
design HB + Gk support mmts = -1,580.69KNm
of this report
b. Span moments design HB + Gk span mmts = 3,810.26KNm
4.4 Design Moments The design moment is obtained by comparing the HA + Dead load moments with those of the HB + Dead load moments.
a.
Support Moments HA + Dead Load Moments HB + Dead Load Moments
= =
-1,841.72KNm -1,580.69KNm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF.
Designed
Bridge Beam/Girder b.
OUTPUT
Design moment is that due to HA + Dead load moment =
-1,841.72KNm
Span Moments HA + Dead Load Moments HB + Dead Load Moments
Page No.
Date___december '04
CALCULATIONS
Era
Checked
= =
3,006.45KNm 3,810.26KNm
Design moment is that due to HB + Dead load moment =
3,810.26KNm
DESIGN MOMENTS Design support moments
=
-1,841.72KNm (Hogging)
Design span mmts
=
3,810.26KNm
4.5
DESIGN FOR BENDING
Table 3.2
h = 1,000mm bw = (0.33 to 0.5) h Therefore 333.33 use bw = 450mm 410N/mm2 fy = 40N/mm2 fcu =
BS 8110:Part I: 1985
Conditions of exposure = Severe, and d = 1,000 - 40 - 32/2 - 12 =
R.C. Design,3rd ed, Mosley & Bungey
a.
500
Bar Diameter ie d' 930mm
=
32mm
=
40mm
SPAN DESIGNS Design moments
Clause 3.4.4.4 BS 8110:Part I: 1985
bw
=
3,810.26KNm
(Sagging)
Assuming moment redistribution less than or equal to10%, k' = 0.156 i.
k
=
M/bd2fcu
=
3,810.26 * 106 /(450 *9302 * 40)
250
=
0.245
1000
Ch. 17.3
(Sagging)
Since k is greater than k', Compression steel required. Eqn 2, Clause 5.3.2.3 BS 5400:Part IV: 1990
450
ii
Z/d
=
0.5 + (0.25 - k'/0.9)0.5 =
0.780
k is greater than k'. Compression
iii
As'
Required
=
( k - k')bd2fcu/ {0.87* fy(d - d')}
steel required
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF.
Designed
Bridge Beam/Girder
=
Eqn 1, Clause 5.3.2.3 BS 5400:Part IV:
iv.
=
k'bd2fcu
+
0.87 fy Z
1990
=
b.
As'
0.156 * 450 *9302 *40 + 0.87 * 410 * 0.78 * 930 12,198.26 mm2 (Bottom)
2,812.22mm2
SUPPORT DESIGNS Design moments
Clause 3.4.4.4 BS 8110:Part I: 1985
OUTPUT
(0.233 -0.156) * 30 * 450 *9302 0.87 * 425 * ( 930 - 40) 2,812.22mm2 (Top)
Required =
Page No.
Date___december '04
CALCULATIONS =
Era
Checked
=
1,841.72KNm
(Hogging)
Assuming moment redistribution less than or equal to10%, k' = 0.156 i.
k
=
M/bd2fcu
1,841.72 * 106 /(450 *9302 * 40) = Since k is less than k', Compression steel required.
=
0.118
Clause 5.3.2.3 BS 5400:Part IV: 1990
ii
Z/d
=
0.5 + (0.25 - k'/0.9)0.5
iii
As
= = =
M/0.87fyZ 1,841.72 *106/(0.87 * 410 * 0.845 * 930) 6,570.23mm² (Top)
=
0.845
REINFORCEMENT Apply 16 No. T32 Bars ( Bottom) in 3 rows 14,472 mm2 As provided = Apply
6 No. T32 Bars ( Top) 6 No. T20 Bars ( Top) As provided =
As = 4,824mm² As = 1,884mm² 6,708 mm2
DESIGN FOR SHEAR page 11 of this
Maximum shear , V = 740.07KN The shear stress is borne by a combination of bent-up bars and stirrups.
a.
BENT - UP BARS
6No.f32mm bars are bent - up in a double bent-up system. They are bent at45o and have spacing of 400mm. therefore,shear resistance of the bent up bars is
Reinforcement Bottom: Apply 16T32 Top: Apply 6T32 + 6T20
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF.
Designed
Bridge Beam/Girder V
=
1.34fyvAsb
=
Area of bent-up bars =
fyv = Therefore,
V
= =
Page No.
Date___december '04
CALCULATIONS Asb
Era
Checked
OUTPUT
6No. * 804
=
4,830mm²
410N/mm²
1.34 * 410 * 4,830 * 10 2653.6 KN
-3
As shown in the calculation above, the shear has already been borne by the bent up bars. The shear liks to be provided will now be nominal and to als prevent cracks on the beam sides.
SHEAR LINKS a
Design Shear Stress v = V/bd
= =
740.07 * 103/(450 * 930) 1.77N/mm2
CHECKS 0.8 * (fcu)0.5
0.5
= 0.8 * (30) 0.5 Since v is far less than 0.8 * (fcu)
=
4.38N/mm2
than 0.8 * (fcu)0.5
It implies that shear is okay Table 9
Depth factor, ξs
=
1.25
=
1.25 * 0.41
Since v is far less
shear
BS 5400:Part IV: 1990 Table 8
ξsvc
Therefore, vc
=
0.41
=
0.513N/mm2
( By interpolation)
BS 5400:Part IV: 1990
Clause 5.4.4
And Table 7 BS 5400:Part IV: 1990
=
1.25 * 0.41
0.513N/mm2
v < ξsvc It implies that shear reinforcement is required.
Asv/Sv
=
0.4 b/0.87fyv
= =
0.4 * 1000 / (0.87 * 425) 1.08
Provide T12 Bars at 200mm centres, reinforcement chairs, as shear reinforcement. (Asv/Sv provided = 1.13 ) Area of 4 - legs (Asv/Sv provided
452mm2 452mm2/200
= =
CHECKS FOR DEFLECTION Table 3.10 and Clause 3.4.6 BS 8110 :
=
since
BS 5400:Part IV: 1990 Clause 5.3.3.2
ξsvc
Therefore,
Basic
Span d
=
26.0
=
2.26
Provide a 4 - leg stirrup, T12 Bars at 200mm centres. as shear reinfor -
Job No.
KABIR & ASSOCIATES Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Member: REF. Part I :1985
Table 3.1
Designed
Bridge Beam/Girder =
Service stresss, fs
BS 8110 :
=
Page No.
Date___december '04
CALCULATIONS M b d²
Era
Checked
OUTPUT
3,810.26 * 106 450 * 9302
=
5 * fy * As Reqd 8 * As Prov.
*
9.79 1
Bb
Part I :1985
= =
5 * 410 * 12,198.26 8 * 14,472 239.99N/mm2
And Modification Factor, M.F.
=
Therefore,
1 0.9
*
( 477 - 239.99) 120 * (0.9 + 9.17) Limiting Span d
Actual Span d
=
( 477 - fs) + 120 * (0.9 + M/ b d2)
+
0.55
=
0.55
0.8
=
M.F. * 26
=
0.75 * 26
=
19.50
=
17,500 930
=
18.82
Since Actual
L
d is less than
Since
Actual Span d
<
Limiting Span d
Limiting L d
Excessive Deflection is remote.
It implies that the Design is okay w.r.t deflection
d
Era
d
Page No.
OUTPUT
design HA + Gk support mmts = -1,841.72KNm
design HA + Gk
= 3,006.45KNm
d
Era
d
Page No.
OUTPUT
d
Era
d
Page No.
OUTPUT
d
Era
d
Page No.
OUTPUT
design HB + Gk support mmts = -1,580.69KNm
design HB + Gk
= 3,810.26KNm
d
Era
d
Page No.
OUTPUT
450
k is greater than k'.
Compression
steel required
d
Era
d
Page No.
OUTPUT
Reinforcement
6T32 + 6T20
d
Era
d
Page No.
OUTPUT
beam sides.
e v is far less
de a 4 - leg p, T12 Bars 0mm centres. ear reinfor -
d
Era
d
Page No.
OUTPUT
is less than
t implies that the
Design is okay w.r.t
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
Page
Bridge Piers
Date___december '04
REF.
CALCULATIONS
OUTPUT
5.0 BRIDGE PIERS 5.1
MEMBER SIZING
T 169 & 170; Reynolds & Ste-
The pier are braced and restrained at both ends
edman : R.C
Effective length , Le
=
8,000mm
Designer's H/bk (10th ed)
The piers are designed as reinforced concrete walls 1,500mm wide Slenderness ratio
*
600mm thickness
Le/h
=
8,000/600
=
8.33 < 10
This implies that pier is a slender column.
5.2 i.
AXIAL LOADS Dead Loads a.
Self weights of piers: 2No. * 1.50m * 0.60m * 8.0 * 24KN/m3
b.
=
345.60 KN
=
87.12 KN
(740.07 * 6No ) + (6.79KN/m * 11.0m)
=
4515.11 KN
TOTAL DEAD LOADS
4,947.83 KN
Pier Cap (self weight) : 1.10m * 0.30m * 11.0m * 24KN/m3
c.
ii.
Deck and beam loads:
=
Live Loads a.
KEL
b.
Deck live loads =
c.
=
40KN/m * 11.0m
17.50m * 8.0m * 10.5KN/m2
=
440.00KN
=
1,470.00KN
=
210.00KN
Foot Path live loads =
2No. * 17.50m * 1.5m * 4.0KN/m2
TOTAL LIVE LOADS
iii. Design Axial Loads
=
2,120.00 KN
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
Page
Bridge Piers
Date___december '04
REF.
CALCULATIONS
OUTPUT
Table 2.1 BS 8110:Part I:
Total Axial load, N
1997
=
(1.4 * 4,947.83) + (1.6 * 2,120.0)
=
No of piers
10,318.96 KN
=
2
Design Axial load
Therefore, Design Axial load per pier: =
5.3 Clause 6.6 BS 5400: Part II
A.
10,318.96KN/2
=
per pier: 5,159.48 KN
= 5,159.48KN
HORIZONTAL LOADS Longitudinal Force Lf Longitudinal loads resulting from traction or breaking of vehicles shall be taken as the more severe of nominal loads for type HA and nominal loads for type HB, applied at the road surface, and parallel to it in one nominal lane.
Clause 6.6.1
i.
BS 5400: Part II
type HA loading The nominal load for HA shall be 8KN/m of loaded length plus 200KN, subject to a maximum of 700KN.
Clause 6.6.1
ii.
BS 5400: Part II
Loaded length
=
8.0m
Longitudinal force
=
( 8 * 8.0m) + 200
=
264.0KN
type HB loading The nominal load for HB shall be 25% of the total nominal HB load adopted. 45 units of HB load was adopted Longitudinal force
iii.
=
0.25 * 1,800
1,800KN =
450KN
From above calculations, design longitudinal loading comes from HB loading
iv.
=
Moments due to Lf:
=
450KN
Moments due
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
Page
Bridge Piers
Date___december '04
REF.
CALCULATIONS mmt at the base of the pier due to Lf,
to Lf:
Ml
=
=
Le. Lf
=
450 *8.0m
=
B.
OUTPUT 3,600.0KNm
3600.00 KNm
Wind Loads, W Exposed heiht of the structure =
Depth of
+
Height of
girders
=
+
Height of
kerbs
railing
1.0m
+
0.45m
+
1.05m
Loaded lengt
=
17.50m ( Bridge span)
=
2.50m
Exposed height contributing to wind pressure per pier =
span * height
=
17.50m * 2.50m
=
=
Table 1.1
Height of piers
Aswami, et al:
By interpolation, wind pressure
43.75m2
5.0m =
1.4KN/m2
Design of con crete Bridges
Therefore, wind force on exposed surface, W =
1.4KN/m2
Wind on HB live load
*
43.75m2
=
=
Vehicle length *
61.25KN
3KN/m
(3KN/m being the lateral wind load, acting 1.5m above the roadway). Length of HB vehicle
=
Wind load on HB live load
Total wind foce
9.75m =
9.75m * 3.0KN/m
=
29.25KN
=
61.25
=
90.60KN
the design wind load
+
=
29.25KN
105.0KN
wind load =
This force is assumed to be acting at the mid- point of the exposed height:
=
2.5/2
=
1.25m
105.0KN
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
Page
Bridge Piers
Date___december '04
REF.
CALCULATIONS
OUTPUT
Therefore, Moment at the base of the pier about the y - y axis, due to wind force is Mw
C. Bureau of Public
mmt due to wind
=
wind load * (pier ht + pier cap ht + mid ht)
force, Mw
=
105.0 * (8.0m + 0.8 +1.25m )
740.25KNm
=
1,055.25 KNm
Water Force Currents The pressure due to water currents is computed from the equations:
Roads, Washington, D.C.
Pw
=
K r w A V2 2g
where,
Pw
=
Total force on surface in KN
rw =
unit weight of water in KN/m3
A
=
Area of wetted surface in m2
=
10 * 0.60m
=
velocity of the water current in m/s ( due to the high
V
=
=
9.81 KN/m3
6.0 m2
velocity of rivers in this area, V is assumed to be 3.2 m/s) =
9.81 m/s2
g
=
acceleration due to gravity
k
=
1.8 for rectangular piers, is a function of the pier shape
Pw
2
Pw = 55.30KN Therefore,
=
1.0 * 9.81 * 6.0 * 3.2
=
55.30KN
2 * 9.81 This force is assumed to act at two - thirds the highest water level. =
5.0 * 2/3
=
3.33m
Moment at the base due to water current, Mp
D
=
55.30KN * 3.33m
=
184.15 KNm
Mp =
184.15KNm
Design Moments, M
pp 22 & 23 of
Total mmt at the base of pier, M
this work.
=
3,600.00 + =
1,055.25 +
=
Ml + Mw + Mp
184.15
4,839.40 KNm Design mmt per
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
Page
Bridge Piers
Date___december '04
REF.
CALCULATIONS Design moments per pier
=
4,839.40 /2
=
OUTPUT 2,419.70 KNm
pier
=
2,419.70KNm
5.4 a.
STRUCTURAL DESIGNS Longitudinal Bars (vertical)
Page 21 of this
M
=
2,419.70 KNm
report
N
=
5,159.48 KN
h
=
wall thickness
d
=
600 - {40 + 0.5*(25) }
=
600mm
=
548mm
Clause 5.5.3.3
The design charts that form BS 8110: Part III may be used for the design
BS 5400:Part IV
of rectangular and circular column sections having a symmetrical arran gement of reinforcements. The same charts are used in Reynolds & Steed-
Table 154; Reynolds & Ste-
man's R.C. Designer's Handbook. d/h
=
548/600
=
0.90
edman : R.C Designer's H/bk
M/bh2fcu
10th ed
=
2,419.70 * 106/1,500 * 6002 * 30
=
N/bhfcu
=
0.149 5,159.48 * 103/1,500 * 600 * 30
= By interpolation, ef fcu/fy
ef
0.191 =
0.20
=
0.20 *30/410
= Asc
Reqd
0.01
=
ef
*
Ac
=
ef
*
1,500 * 600
=
9,000 mm2
Reinforcement required on either face of the wall =
9,000 mm2 2.00
CHECKS
=
4,500 mm2
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
Page
Bridge Piers
Date___december '04
REF.
CALCULATIONS a.
100 * Asc
Minimum steel area
OUTPUT >
1.00
Ac
Asc
1.0 * Ac
=
minimum
=
1.0 *1,000 * 600
100.00
Asc
b
6,000 mm2
=
minimum
100.00
per m run of pier
100 * Asc
Maximum steel area
<
6.00
Ac
Asc
maximum
6.0 * Ac
=
=
6.0 *1,000 * 600
100.00
Asc
maximum
100.00
36,000 mm2
=
per m run of pier
Provide 16 T25 at 100mm c - c
1 Provide T25 at 100mm c - c on each face of wall Asc
provided
=
on each face of wall
4,910mm² Provide T2 5 at
2 Provide T2 5 at 150mm c - c on each face of wall as distribution bars Asy
provided
=
3, 437 mm
2
150mm c - c on each face of wall as distribution bars
5.5
LINKS
Ch. 9.3 R.C. Design,3rd ed, Mosley &
Minimum size
=
0.25 * Largest compression bar
=
0.25 * 32
=
8.0mm
Bungey Maximum spacing
=
12 * 32mm
=
384mm
Apply T12 bars as wall clips at 300mm c - c ( either ways)
Job No.
Era
Designed
Checked
Page
OUTPUT
Job No.
Era
Designed
Checked
Page
OUTPUT
Design Axial load
= 5,159.48KN
Moments due
Job No.
Era
Designed
Checked
Page
OUTPUT 3,600.0KNm
105.0KN
Job No.
Era
Designed
Checked
Page
OUTPUT mmt due to wind =
Pw = 55.30KN
184.15KNm
Design mmt per
Job No.
Era
Designed
Checked
Page
OUTPUT 2,419.70KNm
Job No.
Era
Designed
Checked
Page
OUTPUT
Provide 16 T25 at 100mm c - c on each face of wall
Provide T2 5 at 150mm c - c on each face of wall as distribution bars
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
PRECAST CONCRETE PIER CAP
REF.
Page
Date:december '04
CALCULATIONS
OUTPUT
6.0 DESIGN OF PRECAST CONCRETE CAP BEAM This is designed to support its own self weight & loads from the precast longitudinal beam girders. For structural rigidity and continuity, it is cast integral with the transverse/cross (or diaphragm) beams. This implies that deflection and shear of this beam is not a serious design criteria for this member. Deflection was not checked for this member, but will be checked for the transverse beams. Shear could be checked for the integral element (i.e. cap beam + the cross beam). Even though chances of excessive shear is very remote in the integral structure, it was checked to allow fo the shear reinforcement to be used as the starter bars for the cross beams.
6.1
LOADING
R
R
R
1.55
R
R
6.50
1.55
9.60
Ra
Rb
R
=
Reaction from beam girders
i.
Load from beam girders
=
5R
= ii.
Self weight of pier cap
=
iii.
=
1.50 * 7.92
=
0.5( F
1.10m * 0.30m * 24KN/m3
=
Rb
=
6.2
=
11.88 KN/m
+
( 11.88 * 9.6 ))
3,757.37 KN
DESIGN MOMENTS
Maximum moments occur at the midspan Mmax
=
- ( 2 * 740.07 ) * ( 2.4 + 4.8 ) - (31.68 * 4.82 *0.50) +
= ii.
7.92 KN/m
Rxns Ra
i.
5 * (2* 740.07)
7400.7 KN
= Design udl
=
(3,757.37 * 6.5 * 0.5 )
1,189.49 KNm
Cantilever mmts = =
6.3
( 1.55 * 2 *740.07) + ( 11.88 * 1.552 * 0.50) 2,308.13 KNm
DESIGN FOR BENDING (MID-SPAN)
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
PRECAST CONCRETE PIER CAP
REF.
CALCULATIONS
OUTPUT
Design as a rectangular - beam
\
Design Moment
=
1,189.490 KNm
Span Length
=
6,500 mm
Depth of slab/deck
=
250 mm
beam depth, h
=
300 mm
width of beam web, bw
=
1100 mm
Flange depth, hf
=
0 mm
fire resistance
=
2.0 hrs
cover to reinforcement, d'
=
30.0 mm
reinforcement size, f
=
16.0 mm
stirrup diameter, t
=
12.0 mm
effective depth, d
1100
h - (d' + f/2 + t)
= =
effective width, b
mm
CALCULATION OF EFFECTIVE DEPTH, d
300
a.
250 mm
=
bw+(0.7L/5) 1,100 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
k
=
M/bd²fcu
therefore, k
1997
since k'
fcu
=
0.433
=
0.156
=
40 N/mm²
it implies that compression steel required. use z c.
=
0.775 d
TENSILE REINFORCEMENT fy
=
As'
= Apply
410 N/mm² ((k-k')fcu.bd2) /(0.87fy.(d-d')) 11
T 32
(As prov. As
=
=
8,528 mm2
TOP
=
8,847 mm2
(k'fcu.bd2) /(0.87fy.z) + As'
=
14,736 mm2
Table A.7 Mosley, Bungay
Apply
19
T 32 (As prov.
Hulse: r.c. design, 5th ed.
6.4 DESIGN FOR SHEAR
BOTTOM =
Page
Date:december '04
15,281 mm2
mm
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
PRECAST CONCRETE PIER CAP
REF.
CALCULATIONS i.
OUTPUT
Design shear Force Design Shear Force ,V
ii.
=
0.8(fcu)
V/bd
3,757 KN
=
=
13.663 N/mm²
5.060 N/mm²
fcu =
design okay with respect to shear
(should be 3.00)
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc
(should not be < 1.00)
=
5.358
=
1.600
0.79(100As/(bvd))1/3(400/d)0.25/1.25
Use 400/d =
=
1
1.106 N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
13.663 N/mm²
vc
=
1.106 N/mm²
vc + 0.4
ie (vc +0.4) < v < 0.8(fcu)
Asv/Sv = bv(v - vc)/(0.87fyv)
and Asv/Sv reqd
=
Apply a
fyv
=
410 N/mm²
38.724
30 Leg stirrup T 16
and Asv/Sv provided =
6.5
40
Obtaining the design concrete shear stress, vc
= iv.
=
Design Shear Stress, v Checks:
iii.
Page
Date:december '04
@
150 mm centres 40.212
DESIGN FOR BENDING (CANTILEVER)
=
1.506
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
PRECAST CONCRETE PIER CAP
REF.
CALCULATIONS
OUTPUT
Design as a rectangular - beam
\
Design Moment
=
2,308.130 KNm
Span Length
=
1,550 mm
Depth of slab/deck
=
250 mm
beam depth, h
=
300 mm
width of beam web, bw
=
1100 mm
Flange depth, hf
=
0 mm
fire resistance
=
2.0 hrs
cover to reinforcement, d'
=
30.0 mm
reinforcement size, f
=
16.0 mm
stirrup diameter, t
=
12.0 mm
effective depth, d
1100
h - (d' + f/2 + t)
= =
effective width, b
mm
CALCULATION OF EFFECTIVE DEPTH, d
300
a.
250 mm
=
bw+(0.7L/5) 1,100 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
k
=
M/bd²fcu
therefore, k
1997
since k'
fcu
=
0.839
=
0.156
=
40 N/mm²
it implies that compression steel required. use z c.
=
0.775 d
TENSILE REINFORCEMENT fy
=
As'
= Apply
410 N/mm² ((k-k')fcu.bd2) /(0.87fy.(d-d')) 27
T 32
(As prov. As
=
=
21,072 mm2
BOTTOM
=
21,715 mm2
(k'fcu.bd2) /(0.87fy.z) + As'
=
27,280 mm2
Table A.7 Mosley, Bungay
Apply
34
T 32 (As prov.
Hulse: r.c. design, 5th ed.
6.6 DESIGN FOR SHEAR
TOP =
Page
Date:december '04
27,344 mm2
mm
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
PRECAST CONCRETE PIER CAP
REF.
CALCULATIONS i.
OUTPUT
Design shear Force Design Shear Force ,V
ii.
=
0.8(fcu)
V/bd
3,757 KN
=
=
13.663 N/mm²
5.060 N/mm²
fcu =
40
design okay with respect to shear
Obtaining the design concrete shear stress, vc (should be 3.00)
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc =
iv.
=
Design Shear Stress, v Checks:
iii.
Page
Date:december '04
(should not be < 1.00)
=
9.920
=
1.600
0.79(100As/(bvd))1/3(400/d)0.25/1.25
Use 400/d =
=
1
1.358 N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
13.663 N/mm²
vc
=
1.358 N/mm²
vc + 0.4
ie (vc +0.4) < v < 0.8(fcu)
Asv/Sv = bv(v - vc)/(0.87fyv)
and Asv/Sv reqd
=
Apply a
37.947
30 Leg stirrup T 16
and Asv/Sv provided =
@
150 mm centres 40.212
fyv
=
410 N/mm²
=
1.758
Job No.
Era
Designed
Checked
Page
OUTPUT
. Deflection was not
ote in the integral
Job No.
Era
Designed
Checked
Page
OUTPUT
Job No.
Era
Designed
Checked
Page
OUTPUT
Job No.
Era
Designed
Checked
Page
OUTPUT
Job No.
Era
Designed
Checked
Page
OUTPUT
Job No.
KABIR & ASSOCIATES
Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
BRIDGE ABUTMENT
REF.
Date:december
CALCULATIONS
7.0
Page
'04
OUTPUT
BRIDGE ABUTMENT
The design of the bridge abutment takes care of only the frontal wall and excludes the wing walls. Stability conditions ( over-turning and sliding) are met even though the foundation bears on end - bearing piles. The walls are designed as retaining structures with the traffic load as surcharge. The back faces of the abutment wall will be subjected to hydrostatic forces from ground water. A 300mm thick layer of French drain is provided at the face of the wall. Drainage pipes (weep holes) are then provided, to dissipate the hydrostatic pressure. The weep holes are f150mm pvc pipes placed from the back to the front of the walls.
7.1
FORCES AND MOMENTS
The backfill material will be a granular material of saturated density 2,000Kg/m3 = 19.60KN/m3 = o
Table 10; Reynolds & Ste-
Angle of internal friction = A = 3 Bulk Weight , dry = 17.30KN/m Height of abutment = 8.00m w = Weight of abutment wall W = Weight of soil h = H/2 = 10.50/2 Ha Surcharge load on retaining walls 10.0KN/m2 qs =
edman : R.C Designer's H/bk
Ka
=
1 1
- Sin A + Sin A
=
1 1
- Sin 30 + Sin 30
30 o
=
5.25m
=
0.3
7.1.1 HORIZONTAL FORCES AND MOMENTS i.
Active earth pressure, Pa
=
0.5 * Ka * rsat * H2
0.5 * 0.33 * 19.60 * 8.02
=
Taking mmts about the toe, Lever arm
and mmt
=
= = =
206.98KN * 3.50m
Surcharge load per unit length of wall Qs = = Ka * H * qs = 0.33 * 8.0 * 10 = Mmts about the toe = 26.40 * H/2
206.98 KNm
h1 = h1 3 3 2.067m 724.43 KNm ( Overturning)
ii.
w
e
26.40 KN = 105.60 KNm ( Overturning)
W
Surcharge load is 26.40KN
KABIR & ASSOCIATES
Job No.
Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
BRIDGE ABUTMENT
REF.
CALCULATIONS
w
OUTPUT
W
e
Page
'04
q Ground Level
Surcharge Pressure
H = 8.0m
Qs
h1= 10.50m
Member
Date:december
y =h1/2
Fs
Pa
Active Earth Pressure
1.25m
h1/3
1,225mm
4,275mm
850mm t =750mm
P1
7.1.2 a.
P3
3,900mm
Bearing Pressures
P2
VERTICAL LOADS
Stem weight per unit length, w
Stem wt per m
Job No.
KABIR & ASSOCIATES
Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
BRIDGE ABUTMENT
REF.
Date:december
CALCULATIONS w
= =
b.
=
=
144.00 KN
144.0 * ( 0.85 + t/2)
=
176.40 KNm Base weight / m
rconc * t b* B
=
24 * 2.50 * 5.50m
mmt about toe
=
= =
Soil weight/m = 611.52KN =
611.52 KN
Lever arm = 0.85 + 0.75 + 3.90/2 = 3.55 m 611.52 * 3.55 = 2,170.90 KNm
Loads from beams (total rxns) per Lm of wall = {(740.07 * 6No. ) + (6.79 *11.0)} / 9
=
419.50 KN
mmts about toe, M = 419.50 * (0.85 +0.75/2)
=
513.89 KNm
7.2
330.00KN
330.00 KN
330.00 * 5.5 * 0.5 907.50 KNm
Soil weight per unit length, W = width * height * rsoil = 3.90 * 8.0 * 19.60
mmts about toe: mmt = d.
= 144.0KN
24 * 0.75 * 8.0
Base weight per unit length, Bw = =
c.
OUTPUT
rconc * t * H
mmt about the toe, M
Page
'04
CHECKS FOR STABILITY
The critical conditions for stability are when a maximum horizontal force acts with a minimal vertical load.
7.2.1 OVERTURNING 1.6 * Overturning mmts < 0.9 Restraining mmts Overturning mmts
=
= 724.43 and 1.6 * Overturning mmts Restraining mmts = 176.40 + =
=
Sum of horizontal mmts (mmts from Pa & Qs ) + 105.60 = = 1,328.05 KNm
Sum of vertical mmts 907.50 + 2,170.90 +
830.03 KNm
513.89
3,768.69 KNm
0.9 of restraining mmts
=
3,391.82 KNm
Since 0.9 * Restraining mmts >> 1.6 * Overturning mmts, It implies that the design is safe against overturning.
7.2.2
SLIDING
For no heel beam,
Design is safe against over turning.
Job No.
KABIR & ASSOCIATES
Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
BRIDGE ABUTMENT
REF.
Date:december
CALCULATIONS
OUTPUT
u ( 0.9 Gk + 0.9Vk ) > rf * Hk (Vk + Gk ) = Sum of vertical forces = 144.00 + 330.00 + 611.52 = 1,505.02 KN m
=
coefficient of friction
Frictional resisting force
Hk
= =
= =
=
= =
+
419.50
0.50 ( assumed)
0.5 * 0.9 * 1,505.02KN 677.26 KN
Sum of horizontal forces 206.98 + 26.40
Sliding force
Page
'04
=
233.38 KN
1.6 * 233.38 373.41 KN
Design is safe against sliding
Since frictional resisting force exceeds sliding force, it implies that design is safe against sliding
7.3
DESIGN FOR BENDING ( WALLS)
The stem (wall) is designed to resist maximum moments caused by horizontal forces. Like for all cantilever retaining walls, this is designed as a slab. Design horizontontal force Maximum overturning mmts Clause 3.4.4.4 BS 8110: Part 1
Design moments
= = =
373.41 KN 1,328.05 KNm
Design mmt =333.39KNm
1,328.05 KNm (Sagging)
Assuming moment redistribution less than or equal to10%, k' = 0.156 i.
k
=
M/bd2fcu
= =
1,328.05 * 106 /(1,000 *7002 * 30) 0.090
Since k is greater than k', Compression steel required. ii Clause 5.3.2.3 BS 5400:Part IV: Asx 1990
=
Tables A7 & A8,
Asv
R.C. Designs; Mosley,Bungey & Hulse;( 5th ed.)
Asv
Z/d
M/(0.87fyZ)
min
max
=
0.5 + (0.25 - k /0.9)0.5
= =
=
0.887
1,328.05 * 106/(0.87 * 410 * 0.887 * 700 ) 5,996.38 mm²
=
0.4 * A col / 100
=
0.4 * 1,000 * 750 / 100
=
4.0 * A col / 100
=
3,000mm2
KABIR & ASSOCIATES
Job No.
Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
BRIDGE ABUTMENT
REF.
Date:december
CALCULATIONS =
OUTPUT
4.0 * 1000 * 750 / 100
=
30,000mm
2
thus area of steel required on either face of wall = 2,998.19mm² Apply
T 25 (As prov.
=
@
150
Page
'04
Provide T20 at 100mm centre - centre on either face of wall.
mm On each face of wall
3,272 mm2
LINKS Chapter 9.3 R.c. Designs; Mosley & Bungey ( 3rd ed.)
Minimum size
=
0.25* 20
=
5.0mm
Maximum spacing
=
12 *20
=
240.0mm
Apply T12 as wall clips at 200mm c/c either ways.
Apply T12 as wall clips at 200mm c/c either ways.
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
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Era
Checked
Member
PILED FOUNDATION DESIGNS
REF.
Date:december '04
CALCULATIONS
8.0 PILE FOUNDATION DESIGN 8.1
INTRODUCTION
Piles are relatively long and slender members used in transmitting foundation loads through soil strata of low bearing capacity of low bearing capacity to deeper soil or rock strata having a higher bearing capacity. The piles must extend to a firmer soil so that the load is borne by (i). end bearing, (ii). friction and (iii). Combination of (i) and (ii).
8.2
PURPOSES OF PILES
*
Used in normal ground conditions to resist uplift pressure or in poor soil conditions to resist horizontal loads; ** To transfer loads through water and soft soils to a suitable bearing stratum by means of end bearing of these piles; *** To carry the foundation loads through the depth of scour and to provide safety in the event that the soil is eroded away; **** The combined mass and bending resistance of the pile group serves as protection against ship and boat collision.
8.3
DEEP SOIL INVESTIGATION
Sub-soil survey was carried out inorder to determine the depth to firm soil and the properties of the soil. This information will provide a guide to the length of pile required; and the probable safe load capacity of piles. From the deep soil investigation reports, it is indicated that piles will reach refusal at depths between 5.50m and 13.65m.
8.4
REASONS FOR CHOICE OF PILE TYPE
Piles to be used are steel cased reinforced concrete end-bearing piles , driven into the ground until it reaches the bearing stratum. The steel shell casing are of a uniform cross-section. - These piles have a relatively large bearing capacity (upto 75Tons per pile) - They are permanent - They can be treated for sea water installation. - It is easy to alter the pile lengths. - Damages due to handling or driving are eliminated.
8.5
Page
LOAD BEARING CAPACITY OF PILES & GROUP ACTION
When a single end-bearing pile is acted upon by an axial load,Q, the soil above the tip is stressed. If a group of piles arranged at ordinary pile spacing and each is acted upon by an axial load, Q, the stress at any given point is equal to the sum of stresses introduced by each of these piles. The total stress may be several times greater than, or may even be considerably less than
OUTPUT
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member
PILED FOUNDATION DESIGNS
REF.
Page
Date:december '04
CALCULATIONS
OUTPUT
that under a single pile load. The load capacity for a group of end-bearing piles on a thick stratum of rock or compact gravel is substantially the sum total of the resistance of each individual pile.
8.6 QUANTITY OF PILE REQUIRED & ARRANGEMENT 8.6.1 Section 5.2 (iii) of this report
PILES FOR BRIDGE PIERS
i. Total axial load from bridge pier
=
10,318.96 KN
ii. Weight of pier pile cap = 24.0KN/m3 * 3.30m * 12.90m * 1.25m
=
1,277.10 KN
TOTAL AXIAL LOAD PER PIER, N
=
11,596.06 KN
Bearing Capacity Per Unit Pile, P = 75Tons * 9.81m/s2
=
735.75 KN
Since piles are end bearing, it is assumed that the total axial load from the piers is borne equally by all the piles. Therefore, Number of piles required = N/P
=
15.76 No.
Use 17 No. Piles 8.6.2 Section 7.2.2 of this report
PILES FOR BRIDGE ABUTMENTS
A. LOAD COMPUTATION i. Total axial loads from bridge abutment (factored) Total length of abutment Total load from abutment
= = =
2,257.53 KN/m 12.90 m 29,122.14 KN
ii. Total axial load from wingwalls fo each abutment (factored). = 2No. *0.75m(thick) * 7.50m (ht) * 7.0m * 24KN/m3 * 1.5
=
2,835.00 KN
iii. Loads from abutment pile cap (factored) = 9.0m * 12.90m * 1.25m * 24KN/m3 * 1.5
=
5,224.50 KN
=
37,181.64 KN
Bearing Capacity Per Unit Pile, P = 75Tons * 9.81m/s2
=
735.75 KN
Therefore, Number of piles required = N/P
=
50.54 No.
TOTAL AXIAL LOAD PER ABUTMENT N
Use 51 No. Piles
Job No.
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PILED FOUNDATION DESIGNS
REF.
Date:december '04
CALCULATIONS
8.6.3
Page
OUTPUT
PILE SPACING
The British Standard Code of Practice, BS 8004: Foundations recommends that for piles, a minimum spacing centre - to - centre of not less than three times the pile diameter must be provided. The edge distance should not be less than the pile diameter
M.J Tomlinson Section 7.14.2 Fdn Design & Construction (6th edn)
Pile diameter,f Pile Spacing, S = Use edge distance
8.6.3
3 *f
=
400.00 mm
= =
1,200.00 mm 450.00 mm
PILE LAYOUT
It is impossible to ensure that piles are driven or bored to be trully vertical or exactly to the prescribed rake. The piles are therefore arranged so that the centroid of the pile group coincides with the line of action of the load. This is to ensure that all the piles carry equal loads. Based on the above information and all computations above, we now produce the layout of piles for both the piers and abutments as below. 0.45
1. 3,300
1.20 1.20 0.45 450 1,200
1,200
1,200
1,200
1,200
1,200
1,200
1,200
1,200
1,200 450
12, 900 mm fig. 8.1: Pile Arrangement for The Bridge Piers. 12, 900 mm 450 1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
450
450
5,500
1,150
C.G
1,150 1,150 1,150
2,300
1,150 1,150 500 2,2000
1,3000
5,9000
1,3000
2,2000
fig 8.2: Pile Arrangement for The Bridge Abutment. 1. impacts on the way any applied bending moment is shared among The layout 1. the pile with respect to I and y. No of Pile = 51 for abutments = 17 for Piers
y
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
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Member
PILED FOUNDATION DESIGNS
REF.
Page
Date:december '04
CALCULATIONS
OUTPUT
8.7 STRUCTURAL DESIGN OF PILE A pile is designed as a short column unless if it is slender and the surrounding soil is too weak to provide adequate restraint. We start by distributing the axial load on the respective member piles using the equation:
Pn
=
Pn
where
N
exx & eyy
Nexx Neyy N yn ± ± Ixx Iyy n = axial load on individual pile = vertical load on the pile group =
xn
eccentricities of the load N about the centroidal axes XX and YY of the pile group.
Ixx & Iyy xn & yn
=
second mmt of area of the pile group about axes XX and YY
=
distance of the individual pile from the XX and YY axes.
8.7.1 LOADS IN THE ABUTMENT PILE GROUP Iy
=
{11 * 2 * 2.42} + {5 * 2 * 1.22}
Ix
= =
141.12 m4 = mmt of inertia about the y - axis {3 * 2 (62 +3.62 + 1.22)} + {4 * 2 (4.82 +2.42)}
=
532.8 m4
=
mmt of inertia about the x - axis
with N = (Axial load +pile cap load -displaced soil) *1.5 sum of Axial load N
= =
=(23.1 + 126 + 73.8 + 9.6 + 343) *10 + 4515.11 = 10,270.11 KN (10270.11 + 1226.02 - 817.34) KN *1.5 16,018.19 KN
M
=
10, 060.57 KNm (moment about CG)
H
=
2,280.38 KN (frictional resisting force)
Axial load on each Pile is : Np = 16,018.19 10, 060.57 * y2 + 38 141.12 y2 is the distance along the y - y direction, of pile from C.G of pile group. y2
=
-2
For pile at boundary (11 No.at bridge approach unraked) Therefore, Np
= 421.53 - ( 71.29 * 2.40 ) = 250.43 KN Since Np > 0, It implies design Ok against pile upliftment, and no pile tension
For piles at the other boundary, 11 No. at water side raked y2 = 2.4 Np
= 421.53 + ( 71.29 * 2.40 ) = 592.63 KN at top of pile. Using West's shell pile with nominal working load of 800 - 1,000KN
Since Np > 0, It implies des ign Ok against pile upliftment, and no pile tension
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
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Member
PILED FOUNDATION DESIGNS
REF.
Date:december '04
CALCULATIONS Npb =
Npb =
OUTPUT
592.63 + pile wt 3.142 * ( D2 - d2 ) * 15 * 7.5 4 2 + 3.142 * d * 24 * 15 4 655.17KN at the bottom of pile.
Pile weight
=
8.7.2 PRINCIPAL FORCES AT PILE TOE Abutment Piles
N H M
= = =
655.17KN (Service) 60.01 KN (Service) 179.5KNm (service)
Pier Piles
N H M
= = =
659.54KN (Service) 0 0
PILE STRENGTH Pile Specifications: Casing = Wall thickness =
400mm outer diameter 12mm
12
376mm
12
Assume 0.1mm/year corrossion in weathered rock. Also, assume a 60 year design period. Therefore , total corrossion = 60 * 0.1
=
Hence, design with a wall thickness of 12 - 6 =
6.0mm
outer diameter, D
=
=
6
376mm + (2 * 6)
376mm
6
Page
6.0mm
388mm.
Job No.
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PILED FOUNDATION DESIGNS
REF.
Date:december '04
CALCULATIONS 8.7.3 REINFORCEMENT DETAILS design axial load on pile, N therefore Load at ultimate limit state
but ,
N
\ Asc
fcu
=
30N/mm²
fy
=
410N/mm²
= = =
OUTPUT
659.54KN (Service) 1.60 * 659.54KN 1,055.26 KN
= 0.4fcuAc + Asc(0.8fy - 0.4fcu) =
N - 0.4fcuAc (0.8fy - 0.4fcu) Ac
=
=
0.25pD²
=
0.25 * 3.142 * 376²
(1,055.26 * 103) - (0.4 * 30 * 111,050.85) {(0.8*410) - (0.4*30)}
= =
111,050.85 mm²
-877.69
mm²
Since Asc cannot be negative, apply minimum reinforcement for columns. Minimum reinforcement for columns
=
0.4% of Ac
=
444.20 mm²
Maximum reinforcement for columns
=
6.0% of Ac
=
6,663.05 mm²
Provide 9No. T16 bars round the circumference of the pile (Asc prov. = 1,810mm²)
Links minimum bar size
=
¼ * size of largest compression bar minimum allowable
= =
¼ * 16 6mm
=
4.0mm
maximum spacing
=
12 * size of smallest compression bar
=
12 * 16
=
192 mm
Use a spiral link T10mm of 150mm pitch.
Page
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
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Member
PILED FOUNDATION DESIGNS
REF.
Page
Date:december '04
CALCULATIONS
OUTPUT
8.8 STRUCTURAL ANALYSIS & DESIGN OF PILE CAP 8.8.1 INTRODUCTION The pile cap is designed to be sufficiently rigid and capable of transmitting the pier and abutment loads through the piles to the bearing strata. The anchorage lengths of the dowel bars for the pier and pile cap reinforcements were taken into consideration in choosing the cap thickness of 1.250m. The pile cap is designed using the beam theory, in which case, the pile cap is treated as an inverted beam with a udl, and is designed for the usual conditions of bending and shear.
8.8.2 DESIGN OF PIER PILE CAP Section 8.6.1 of this report
A. i.
LOADING Total axial load from piers including self weight of pile cap, W
=
ii.
Total Length of pile cap, L
=
12.90 m
iii.
Design Moment The pile cap is considered to be simply supported, therefore Design Moment, M = WL/8
=
18,698.65 KNm
Design Moment
=
18698.650 KNm
Span Length
=
12,900 mm
Depth of slab/deck
=
150 mm
B.
11,596.06 KN
DESIGN FOR BENDING
Design as a rectangular - beam
\
CALCULATION OF EFFECTIVE DEPTH, d beam depth, h
=
1250 mm
width of beam web, bw
=
3300 mm
Flange depth, hf
=
0 mm
fire resistance
=
2.0 hrs
cover to reinforcement, d' reinforcement size, f
=
30.0 mm
=
16.0 mm
stirrup diameter, t
=
12.0 mm
effective depth, d
=
h - (d' + f/2 + t)
= effective width, b
=
1,200 mm bw+(0.7L/5) 3,300 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
1997
k = therefore, k since k'
M/bd²fcu
fcu
=
0.131
=
0.156
=
30 N/mm²
it implies that compression steel not required.
ii.
z use z
=
d(0.5 + (0.25 - k/0.9)0.5) =
0.823 d
=
0.823 d
1250 mm
a.
3300
mm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
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Member
PILED FOUNDATION DESIGNS
REF. fy
=
410 N/mm²
As
=
M/(0.87fy.Z)
Checks for minimum steel:
Mosley, Bungay
As min
=
T 25
0.13Ac/100
Apply
Hulse: r.c. design, 5th ed.
=
110
Table A.7
Table 3.10
OUTPUT
TENSILE REINFORCEMENT
Apply
=
25
T 20
53,086 mm²
Bottom
(As prov.
=
53,996 mm²)
5,362.50 mm² Top
(A's prov. =
7,853.98 mm² )
C.
CHECKS FOR DEFLECTION
a.
Basic span - effective depth ratio
=
20.00
To avoid damages to finishes, modified ratio
=
16.67
BS8110:PART1: 1997
b.
Tensile reinforcement modification factor:
Table 3.11
i.
M/bd²
=
BS8110:PART1:
ii.
service stress, fs = 5fyAsreq./8Asprov.)*1/bb By interpolation, Modification Factor, MF
=
=
=
1997
Date:december '04
CALCULATIONS c.
iii.
Note: MF should not
0.55 + (477 - fs)/(120(0.9+(M/bd²)) Use MF
be greater than 2
3.93 279.92 N/mm²
0.89
=
0.89
c.
Modified span - effective depth ratio = MF * Basic span - effective ratio
=
14.83
d.
Actual span - effective depth ratio
=
10.75
D.
Design okay w.r.t deflection. DESIGN FOR SHEAR
=
L/d
Since Modified L/d > Actual L/d,
i.
Design shear Force Design Shear Force ,V
ii.
Design Shear Stress, v = Checks: 0.8(fcu)
iii.
iv.
= V/bd
11,596 KN
=
=
2.928 N/mm²
4.382 N/mm²
fcu
=
30 N/mm²
design okay with respect to shear
Obtaining the design concrete shear stress, vc (should be 3.00)=
1.364
=
0.333
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc 0.79(100As/(bvd))1/3(400/d)0.25/1.25 = =
(should not be < 1.00)
Use 400/d
=
1.00
0.701 N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
2.928 N/mm²
vc
=
0.701 N/mm²
vc + 0.4
ie (vc +0.4) < v < 0.8(fcu)
Asv/Sv = bv(v - vc)/(0.87fyv)
and Asv/Sv reqd
=
Apply a
20.607 22 Leg stirrup
T 16 and Asv/Sv provided =
@
200 mm centres 22.117
fyv
=
Page
410 N/mm²
=
1.101 N/mm²
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
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Member
PILED FOUNDATION DESIGNS
REF.
Page
Date:december '04
CALCULATIONS
OUTPUT
8.8.3 DESIGN OF ABUTMENT PILE CAP This is analysed and designed as a purely rectangular section of width 5.50m A. i.
LOADING Total axial load from piers including self weight of pile cap, W and the weight of wingwalls.
=
ii.
Total Length of pile cap, L
=
12.90 m
iii.
Design Moment The pile cap is considered to be simply supported, therefore Design Moment, M = WL/8
=
59,955.39 KNm
Design Moment
=
59,955.390 KNm
Span Length
=
12,900 mm
Depth of slab/deck
=
0 mm
Section 8.6.1 of this report
B.
37,181.64 KN
DESIGN FOR BENDING
Design as a rectangular - beam
\
CALCULATION OF EFFECTIVE DEPTH, d beam depth, h
=
1250 mm
width of beam web, bw
=
5500 mm
Flange depth, hf
=
0 mm
fire resistance
=
2.0 hrs
cover to reinforcement, d' reinforcement size, f
=
30.0 mm
=
16.0 mm
stirrup diameter, t
=
12.0 mm
effective depth, d
= =
5500
h - (d' + f/2 + t)
= effective width, b
1250 mm
a.
1,200 mm bw+(0.7L/5) 5,500 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
1997
k = therefore, k
M/bd²fcu
since k'
fcu
=
0.252
=
0.156
=
30 N/mm²
it implies that compression steel required. ii. use z c.
=
0.775 d
TENSILE REINFORCEMENT fy
=
As'
=
410 N/mm² ((k-k')fcu.bd2) /(0.87fy.(d-d'))
Apply As
=
115
T 25
TOP
(As prov.
(k'fcu.bd2) /(0.87fy.z) + As'
Apply
140
T 32
BOTTOM
(As prov.
=
54,847 mm²
=
56,450 mm²)
=
111,734 mm²
=
112,595 mm²)
mm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
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Member
PILED FOUNDATION DESIGNS
REF. Table 3.10
C. a.
Basic span - effective depth ratio
=
20.00
To avoid damages to finishes, modified ratio
=
16.67
b.
OUTPUT
Tensile reinforcement modification factor:
Table 3.11
i.
M/bd²
=
BS8110:PART1:
ii.
service stress, fs = 5fyAsreq./8Asprov.)*1/bb By interpolation, Modification Factor, MF
=
=
=
1997
Date:december '04
CALCULATIONS CHECKS FOR DEFLECTION
BS8110:PART1: 1997
iii.
Note: MF should not
0.55 + (477 - fs)/(120(0.9+(M/bd²)) Use MF
be greater than 2
7.57 282.55 N/mm²
0.74
=
0.74
c.
Modified span - effective depth ratio = MF * Basic span - effective ratio
=
12.36
d.
Actual span - effective depth ratio
=
10.75
D.
Design okay w.r.t deflection. DESIGN FOR SHEAR
=
L/d
Since Modified L/d > Actual L/d,
i.
Design shear Force Design Shear Force ,V
ii.
Design Shear Stress, v = Checks: 0.8(fcu)
iii.
iv.
= V/bd
37,182 KN
=
=
5.634 N/mm²
4.382 N/mm²
fcu
=
30 N/mm²
design okay with respect to shear
Obtaining the design concrete shear stress, vc (should be 3.00)=
0.855
=
0.333
a.
Compute 100As/(bvd)
b.
compute 400/d
c.
By interpolation, obtain the design concrete shear stress, vc 0.79(100As/(bvd))1/3(400/d)0.25/1.25 = =
(should not be < 1.00)
Use 400/d
=
1.00
0.600 N/mm²
Obtain the form and area of shear reinforcement a.
if v < 0.5vc
provide nominal links
b.
if 0.5vc +v < (vc + 0.4)
then Asv/Sv = 0.4*bv/(0.87fyv)
c.
if (vc +0.4) < v < 0.8(fcu)
then Asv/Sv = bv(v - vc)/(0.87fyv)
for this design
v
=
5.634 N/mm²
vc
=
0.600 N/mm²
vc + 0.4
=
1.000 N/mm²
ie (vc +0.4) < v < 0.8(fcu)
Asv/Sv = bv(v - vc)/(0.87fyv)
and Asv/Sv reqd
=
Apply a
fyv
=
410 N/mm²
77.615 80 Leg stirrup
T 16 and Asv/Sv provided =
@
200 mm centres 80.425
8.8.4 DESIGN FOR PUNCHING SHEAR As pile spacing is at three times the pile diameter, check for punching shear is not necessary. This is only necessary when the spacing of piles is greater than three times the pile diameter.
8.8.5 SHEAR AT THE FACE OF THE PIER Total Shear Force per Pier, N No. of piles, n depth of pile cap, d Dimension of 1No. Pier
Page
= = = =
5,798 17 1,250.00 1500 *
KN No. m 600 mm
Job No.
KABIR & ASSOCIATES Project: Bridge No. 3,4 &4a; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Era
Checked
Member
PILED FOUNDATION DESIGNS
REF. Shear at the face of pier where
Checks:
n
=
0.8(fcu)
=
CALCULATIONS n =N/md = m = pier perimeter
4.382 N/mm²
Date:december '04
OUTPUT =
1.10439 N/mm2
Design okay with respect to shear.
Page
4200 mm
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
Designed
Era
Checked
Page
OUTPUT
GEMENT
Job No.
Designed
Era
Checked
Page
OUTPUT
escribed rake.
x
Job No.
Designed
Era
Checked
Page
OUTPUT
Since Np > 0, It implies des ign Ok against pile upliftment, and no pile
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
Designed
Era
Checked
Page
OUTPUT
Job No.
KABIR & ASSOCIATES Era
Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD
Designed
Checked
Member
DIRECT FOUNDATION DESIGNS
Date: march '05
CALCULATIONS
REF.
OUTPUT
9.0 DIRECT FOUNDATION DESIGN 9.1
INTRODUCTION
Based on the deep soil investigation carried out at the bridge foundation location, the depth to bearing rock strata for the piers and abutments is between 0.75m to 2.65m. It will thus be more economical for the footings to bear directly on the rock strata. The design is made with the provision that 'micro - piles' will be drilled atleast 1.0m into the rock and tied into the footing. Micro - Piles' are to be constructed using f32mm high tensile reinforcement bars, which will be placed at 1No. Per square metre of either of the footing area. They will provide resistance against slippage, and allow for a monolithic action between the footing and the bearing strata. The 'micro - piles are to be drilled into the rock strata, and grouted using a cement - sand slurry.
9.2 9.2.1
PIER FOUNDATION General
The pier foundation is designed as a combined footing of a rectangle shape and cross-section. It is designed to have a uniform thickness. * The footing is designed with a grade 30 concrete ** It is recommended that a 100mm thick blinding be laid before starting the construction of the base. A grade 10 concrete should be used for the blinding. *** The 'micro - piles' should be drilled and grouted into the rock strata before casting the blinding. The dimensions of the footing are chosen with care for the following reasons: a. A footing that is too long will have large longitudinal moments on the lengths projecting beyond the piers. b. A footing that is short will have large span moments between the piers. c. Larger widths will cause large transverse moments; and d. A very thick footing will have excessive shear stress.
9.2.2 a. Section 5.2 of this report b.
Page
Analysis & Design Of Pier Footing
LOADING The piers carry a combined axial load and an imposed load
= =
4,947.83 KN dead load, 2,120.00 KN
BASE AREA Allow for self weight of footing
=
1,500.00 KN
Based on the deep soil investigation report, conservative value for safe bearing pressure of bearing rock strata = 250.00 KN Total Load at Serviceability`Limit State
=
8,567.83 KN
Area of Base
=
34.27 m2
Length of base Based on the geometry of the bridge, the piers are spaced 6,500mm apart. Considering the total width of the pier being 1,500mm, outer distance from one pier to the other is 9,500mm. Allowing an edge distance of 1,000mm on either side of the pier, the total pier foundation length = 11.50 m minimum width required
=
2.98 m
Use a base width
=
3.00 m
c.
RESULTANT LOADS CENTROID OF BASE The axial loads are equally distributed between the 2No. Piers, and the piers are symetrically located within the pier base, the resultant load will be acting at the centroid of the pier base.
d.
BEARING PRESSURE AT THE ULTIMATE LIMIT STATE Pier Loads at the ultimate limit state = 12,418.96 KN Therefore earth pressure = load @ uls/footing area =
e.
359.97 KN/m2
LONGITUDINAL MOMENTS & SHEAR FORCE 6,209.48
6,209.48
2.10
8.00
w = earth pressure * width
=
2.10
1,079.91 KN/m
i. Moment at midspan between the piers = 19,385.73 KNm Design For Bending Design as a rectangular - beam
\
=
Span Length
=
19,385.730 KNm 8,000 mm
CALCULATION OF EFFECTIVE DEPTH, d base depth, h
=
1,750.00 mm
width of base, bw
=
3,000.00 mm
Nature of Exposure
=
cover to reinforcement, d'
=
50.0 mm
reinforcement size, f
=
20.0 mm
stirrup diameter, t
=
12.0 mm
=
h - (d' + f/2 + t)
effective depth, d
Very Severe
= effective width, b
=
1,678 mm bw 3,000 mm
b.
LEVER ARM CALCULATIONS, Z
1750 mm
a.
Design Moment
3,000.00 mm
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
1997
k = therefore, k
M/bd²fcu
since k' ii.
z
=
0.076
=
0.156
d(0.5 + (0.25 - k/0.9)0.5)
use z c.
fcu
=
=
=
30 N/mm²
it implies that compression not steel required.
=
0.906 d
0.906 d
TENSILE REINFORCEMENT fy
=
410 N/mm²
As
=
M/(0.87fy.Z)
=
Apply
35,741 mm² 75
T 25
(As prov. =
Bottom
@
107
mm centres
36,816 mm²)
Checks for minimum steel: As min
Table A.7
=
0.13Ac/100
=
22
T 20
Apply
Mosley, Bungay
6,825.00 mm² Top
(A's prov.
Hulse: r.c. design, 5th ed.
@
136
mm centres
6,911.50 mm² )
ii. Transverse Bending Moment = 809.93 KNm Design For Bending Design as a rectangular - beam
\
=
809.932 KNm
Span Length
=
3,000 mm
CALCULATION OF EFFECTIVE DEPTH, d base depth, h
=
1,750.00 mm
width of base, bw
=
3,000.00 mm
Nature of Exposure
=
cover to reinforcement, d'
=
50.0 mm
reinforcement size, f
=
20.0 mm
stirrup diameter, t
=
12.0 mm
=
h - (d' + f/2 + t)
effective depth, d
Very Severe
= effective width, b
1750 mm
a.
Design Moment
3,000.00 mm
1,678 mm
=
bw 3,000 mm
b.
LEVER ARM CALCULATIONS, Z
clause 3.4.4.4
assume moment redistribution < 10%. This implies that k' = 0.156
BS8110:PART1:
i.
1997
k = therefore, k
M/bd²fcu
since k' ii.
z use z
c.
=
fcu
=
0.003
=
0.156
d(0.5 + (0.25 - k/0.9)0.5) =
=
=
30 N/mm²
it implies that compression not steel required. 0.996 d
0.950 d
TENSILE REINFORCEMENT fy
=
410 N/mm²
As
=
M/(0.87fy.Z)
=
1,424 mm²
Checks for minimum steel: Table A.7 Mosley, Bungay Hulse: r.c. design, 5th ed.
As min
= Apply
0.13Ac/100
=
22
T 20
(A's prov.
6,825.00 mm² Bottom & Top @
136
6,911.50 mm² )
9.3 Checks For Punching Shear
mm centres in the transverse direction
Shear Stress,uc
0.8 * √fcu
=
Axial Load/pier perimeter * d
=
0.88108 N/mm²
=
4.38178 N/mm²
Since uc
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