Bridge Decks Design

716 International Journal of Earth Sciences and Engineering

ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp 716-719

#020410358 Copyright © 2011 CAFET-INNOVA TECHNICAL SOCIETY. All rights reserved

Investigations on simply supported concrete bridge deck slab for IRC vehicle

loadings using finite element analysis

Kanchan Sen Gupta Senior Lecturer, Civil Engineering Department, Malda Polytechnic, Govt. of West Bengal, Malda, WB, India– 732102,

Email – [email protected]

Somnath Karmakar

Assistant Professor, Civil Engineering Department, NIT Durgapur, WB, India- 713209,

Email – [email protected]

ABSTRACT : This paper presents the results related to finite element analysis (FEA) of simply supported reinforced

concrete bridge deck of different span lengths (3 m to 10 m) and constant width of 12 m, with and without footpath

under eleven possible Indian Road Congress (IRC) vehicle load cases. So, in total 88 no of cases were analyzed.

Dimension of deck slabs are taken from standard drawings of the Ministry of Road Transport & Highways-1991. Under

condition A (including footpath, carriageway-width 7.5 m), due to edge loading, maximum FEA bending moments are

similar to IRC bending moments for the span up to 4 m for few cases. However, for larger spans, the IRC bending

moments are less than FEA bending moments by 5 to 20%. Under condition B (without footpath, carriageway-width 9.6

m), due to edge loading, IRC bending moments are less than FEA bending moments by 4 to 30%. Under centered

loading, the IRC bending moments are similar to FEA bending moments for span up to 4 m under few cases and less

than FEA bending moments by 4 to 23% beyond 4 m. As per IRC, one lane of Class-70R or two lanes of Class-A and

one lane of class-70R with one lane of class-A or 3 lanes of class-A are to be considered as design live load for

condition A and B respectively. FEA result agrees with IRC for condition B but FEA design bending moment occurs

under IRC Class-AA Wheeled load or Tracked load for condition A.

KEY WORDS: Concrete bridge deck slabs; Finite element analysis; Vehicle loadings; Highway; Simply supported.

INTRODUCTION

In India, in the case of bridge deck slabs spanning in one

direction, the bending moment per unit width of slab

caused by the IRC vehicle loads can be calculated by

estimating the width of slab that may be taken as effective

in resisting the bending moment due to the loads and

accordingly the deck slab is designed for that bending

moment. The method of assessment of the effective width

is given in clause 305.16.2 (1) of IRC: 21 – 2000.

M. Mabsout et al. ( 2004 ) investigated the effect of

vehicle loads on simply supported deck slabs using FEA

based software ( SAP 2000 ) for different span lengths,

slab width with and without footpaths . Slabs are loaded

with highway design truck HS20 placed at critical

locations in the longitudinal direction of each lane. Two

possible transverse truck positions were considered: (i)

Centered loading condition where design trucks are

assumed to be traveling in the center of each lane and (ii)

edge loading condition where the design trucks are placed

close to one edge of the slab with the absolute minimum

spacing between adjacent trucks. For slabs without

shoulders, where the edge load condition is critical, and

for one-lane bridges, AASHTO (American Association of

State Highway and Transportation Officials ) moment

overestimates the FEA moments (30%) for short spans

(up to 7.5 m) and agrees with the FEA for longer spans.

For more than one lane, AASHTO agrees with the FEA

for short spans (less than 10.5 m) and underestimates FEA

(15 to 30%) for longer spans. Reinforced concrete slab

bridges with shoulders on both edges tend to increase in

load – carrying capacity. Therefore, the edge + truck load

condition was found to be critical for bridges with

shoulders on both free edges where AASHTO agrees with

the FEA for short spans ( up to 7.5 m ) and

underestimates the FEA by 25% for longer spans,

regardless of the number of lanes. Therefore, a suggested

20% reduction factor is applied to the FEA moments for

span lengths greater than 10.5 m, in combination with at

least two lanes, will tend to give results similar to those of

AASHTO moments. The AASHTO LRFD procedure

gives higher bending moments than AASHTO standard

specifications as well as the FEA results. The AASHTO

LRFD procedure gives design bending moments closer to

the FEA results subject to edge + truck load conditions.

Frederick (1997) presented the results of an experimental

and FEA investigation of load distribution in a concrete

slab bridge. A typical 8.5 m span, simply supported deck

slab with a 10.4 m width was considered. The design live-

load bending moments were calculated using AASHTO

standard specifications provisions. A one-fifteenth size

scale concrete model was constructed and tested in the

laboratory. Design trucks were positioned one at a time

along the center of each of the three lanes. The FEA

results correlated well with the test data and were less than

AASHTO empirical equation. Shekar et al. (1993)

performed extensive experimental and analytical

investigation to evaluate the load-carrying capacity of

existing reinforced concrete slab bridges. The

experimental phase of the investigation consisted of field

testing of six slab bridges. The test data compared

favorably with FEA results and verified that concrete slab

bridges have the strength necessary to resist highway

loading.

David et al. (2010) performed finite element analysis on a

reinforced concrete slab bridge. Only the concrete slab

717 Investigations on simply supported concrete bridge deck slab for IRC vehicle


International Journal of Earth Sciences and Engineering


was modeled and the reinforcing steel was ignored. The

slab moments from FEA agreed reasonably well with the

experimental moments.

Finite Element Method is used to investigate the effect of

IRC vehicle loads on simply supported concrete deck slab

for different span length and constant width of 12 m with

and without footpaths.

STANDARD DIMENSION OF DECK SLABS

Based on the Standard Drawings of MORT & H (1991),

dimensions of deck slabs are taken as follows:

Span

(m)

Avg. O/A Depth

(mm)

Thickness of Wearing coat

(mm)

3 375 56

4 425 56

5 475 56

6 525 56

7 575 56

8 675 56

9 745 56

10 825 56

IRC VEHICLE LOADS WITH THE MINIMUM

SPACING BETWEEN ADJASCENT TRUCKS

1. Vehicle Load Placed Close to One Edge of the Slab

with Footpath

a) One lane of IRC Class AA Tracked Load.

b) One lane of IRC Class 70R Tracked Load.

c) Two lanes of IRC Class A.

2. Vehicle Load Placed Close to One Edge of the Slab

without Footpath a) One lane of IRC Class AA Tracked Load. b) One lane of IRC Class 70R Tracked Load and one

lane of IRC Class A Load.

c) Three lanes of IRC Class A Load.

3. Vehicle Load Placed at the Centre of the Slab

a) One lane of IRC Class AA Tracked Load.

b) One lane of IRC Class 70R Tracked Load.

c) Two lanes of IRC Class A Load.

d) Three lanes of IRC Class A Load

e) One lane of IRC Class AA Wheeled Load.

Here two conditions are considered:

f) Condition A is for including footpath i. e.

carriage-way width of 7.5 m and consists of edge

loading [load cases 1(a), 1(b), 1(c)] and centered

loading [load cases 3(a), 3(b), 3(c) and 3(e)];

g) Condition B is for without footpath i. e. carriage-

way width of 9.6 m and consists of edge loading

[load cases 2(a), 2(b), 2(c)] and centered loading

[load cases 3(a), 3(b), 3(c), 3(d) and 3(e)]

Loading diagram for case 1(a) & 2(a) for span 6 m are

given below:

FINITE ELEMENT ANALYSIS

M. Mabsout et al. (2004) in his study considered all

elements to be linearly elastic, and the analysis assumed

small deformations and deflections. The concrete slabs

were modeled using quadrilateral shell elements (SHELL,

SAP 2000) with six degrees of freedom at each node.

Hinges were assigned at one bearing location and rollers

at the other to simulate simple support conditions. The

element size of 0.3 x 0.3 m was adopted.

Xiaoming S. H. et al. (2004) while investigating the

distribution factors of the live load moment in seven

bridges, modeled the deck slab using four-node shell

elements with six degrees of freedom per node (ANSYS

5.7). The shell elements accounted for both membrane

and bending stiffnesses, and considered in and out of

plane bending.

David V. J. et al. adopted quadrilateral shell elements

(SAP 2000) to model the deck slab for evaluating a

Reinforced Concrete Slab (RCS) bridge. Only the

concrete slab was modeled and the reinforcing steel was

ignored.

R. Michael Biggs (2000) adopted the quadrilateral shell

elements for modeling the reinforced-concrete slabs. In

this investigation, the general FEA programme ANSYS

rel. 10.0, developed by ANSYS. Inc. was used to analyze

each span of concrete deck slab for eleven no. of load

cases. All elements are considered as linearly elastic,

718 Kanchan Sen Gupta, Somnath Karmakar



isotropic. The standard element named SHELL93 (a 8

noded shell element having 6 DOF per node) of size 0.4 m

x 0.4 m is used for modeling the deck slab. Modulus of

elasticity and Poisson’s ratio are considered as 25 x 106

kN/m2 and 0.15 respectively. Hinges were assigned at one

support and rollers at the other to simulate simple support

condition.

ANALYSIS RESULTS

The maximum bending moments in kN-m/m for FEA and

IRC equation are given in Table 1.

Table 1 Maximum Bending Moment (kN-m/m) along span

Span

(m)

Type Load Case

1(a) 1(b) 1(c) 2(a) 2(b) 2(c) 3(a) 3(b) 3(c) 3(d) 3(e)

3.0

FEA 41.88 32.91 31.76 43.17 46.41 33.47 41.84 32.88 31.85 33.30 46.03

IRC 41.57 32.73 26.30 41.57 36.87 28.11 41.57 32.73 26.30 27.23 40.00

R.F. 0.993 0.995 0.828 0.963 0.794 0.840 0.994 0.995 0.836 0.818 0.869

4.0

FEA 63.70 50.94 44.16 68.25 69.21 49.31 62.92 50.33 43.92 48.71 57.83

IRC 58.22 50.94 36.87 58.22 53.06 42.03 58.22 50.33 36.87 39.81 52.42

R.F. 0.914 1.000 0.835 0.853 0.767 0.852 0.925 1.000 0.840 0.817 0.906

5.0

FEA 81.41 68.33 55.01 90.36 93.03 65.51 80.02 67.61 54.41 63.33 66.64

IRC 69.07 64.70 45.19 71.55 67.84 54.38 69.07 64.70 45.19 53.35 61.72

R.F. 0.849 0.947 0.822 0.792 0.729 0.830 0.863 0.957 0.831 0.842 0.927

6.0

FEA 96.65 84.16 65.00 111.58 116.04 81.77 94.68 82.78 64.00 77.54 75.15

IRC 84.31 73.00 52.29 91.72 80.84 65.97 84.31 73.00 52.29 66.90 68.44

R.F. 0.872 0.867 0.805 0.822 0.697 0.807 0.891 0.882 0.817 0.863 0.911

7.0

FEA 111.20 99.13 74.83 130.76 139.41 98.03 108.45 96.71 73.45 91.97 82.22

IRC 98.32 87.89 61.74 110.80 104.20 79.61 98.32 87.89 61.74 79.61 75.10

R.F. 0.884 0.867 0.825 0.847 0.748 0.812 0.907 0.909 0.817 0.866 0.914

8.0

FEA 125.60 113.60 85.51 149.22 163.19 115.80 121.96 110.26 83.68 107.53 89.83

IRC 110.12 100.44 69.08 127.71 149.14 92.71 110.12 100.44 64.78 89.71 80.78

R.F. 0.877 0.884 0.808 0.856 0.914 0.801 0.903 0.911 0.774 0.834 0.899

9.0

FEA 139.87 127.93 94.26 166.51 184.92 130.43 135.98 123.86 92.34 120.90 97.50

IRC 121.84 112.60 88.26 144.55 168.00 117.25 121.84 112.60 84.90 117.95 86.68

R.F. 0.871 0.880 0.936 0.868 0.909 0.899 0.896 0.909 0.919 0.976 0.889

10.0

FEA 154.05 142.14 104.74 182.98 208.39 152.12 149.17 137.49 105.36 140.78 105.38

IRC 133.25 124.41 92.51 161.00 188.24 127.36 133.25 124.41 88.36 127.21 92.63

R.F. 0.865 0.875 0.883 0.880 0.903 0.837 0.893 0.905 0.839 0.904 0.879

Bending stress contour diagrams for 6 m span under load cases 1(a) and 2(a) are given below:

Fig 4. Bending Stress contour diagrams for 6 m span under load cases 1(a) and 2(a)

719 Investigations on simply supported concrete bridge deck slab for IRC vehicle




CONCLUSION

The paper presented the results of an investigation of

concrete bridge deck slabs using finite-element analysis.

Simply supported deck slabs were considered for various

span lengths & load cases. Total 88 load cases were

analyzed and maximum bending moments along span

were compared with those obtained from Cl. 305.16.2.(1)

of IRC : 21 – 2000.

Based on the results of this investigation, the following

conclusions can be drawn:

(i) Under condition A, as per Table 2 of IRC 6: 2000, load

case 1(b) or 1(c) or 3(c) is to be considered as design live

load. But FEA results showed that:

(a) for 3 m span, the design i. e. maximum bending

moment occurs under load case 3(e),

(b) for spans beyond 3 m, the design bending moment

occurs under load case 1(a).

Again calculations based on IRC equation showed that

design bending moment occurs under load case 1(a) or

3(a), both giving the same value.

(ii) Under condition B, as per Table 2 of IRC 6 : 2000,

load case 2(b) or 2(c) or 3(d) is to be considered as design

live load.

FEA results showed that the design i. e. maximum

bending moment occurs under load case 2(b), which

means that the FEA results agree with IRC.

Again IRC based calculations showed that the design

bending moment occurs under load case 2(a) or 3(a) up to

span of 7 m and under load case 2(b) beyond 7 m. So, the

IRC equation based results agree with Table 2 of IRC 6:

2000 beyond 7 m span.

Therefore, design bending moment should be checked for

(i) one lane of IRC Class AA Tracked load placed close

to one edge & at the centre of the slab and one lane of

IRC Class AA Wheeled load at the centre of the slab

under condition A and

(ii) one lane of IRC Class AA Tracked load placed close

to one edge and at the centre of the slab for span up to

7 m under condition B.

Also the suggested reduction factors (R. F.), given in

Table 1, can be applied to the FEA bending moments to

give results similar to IRC bending moments.

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Documents

Bridge Decks Design