154

Journal of Research in Engineering and Applied Sciences

JREAS, Vol. 04, Issue 04, Oct 2019

BEAHVIOURAL STUDY OF CONCRETEHOLLOW BRIDGE PIER

Abstract

Behaviour of hollow bridge pier is complex as compared to solid pier. But only a few studies have been reported in this area. In this paper, a numerical study is conducted on hollow bridge pier models with uniform and tapered sections for understanding the behaviour under lateral and torsional loads. It was found that tapered section has better performance over uniform section under the load cases studied.

Key Words : Hollow bridge pier, finite element analysis, tapered section, free vibration analysis, lateral load, torsion.

1. Introduction

ISSN (Print) : 2456-6411, ISSN (Online) : 2456-6403

With rapid developments in recent years, bridges with long piers are being built. But as the height increases, material requirement increases for solid pier, resulting in huge cost of construction. So solid sections become uneconomical and hence hollow sections are used, especially for bridge piers. This also helps in increased moment of inertia of section with lesser material. As the weight of the substructure decreases, the load on foundation is decreased, demanding a lesser size of the foundation which in turn leads to overall economy. Also when the strata is weak, the load is to be reduced which can be achieved by adopting

1. M.Tech Student, Department of Applied Mechanics, Visvesvaraya National Institute of Technology, Nagpur, India;

email: greatamariyamjessy@gmail.com.

2. M.Tech Student, Department of Applied Mechanics, Visvesvaraya National Institute of Technology, Nagpur, India;

email: mathewcs@gmail.com.

3. Professor, Department of Applied Mechanics, Visvesvaraya National Institute of Technology, Nagpur, India;

email: rkingle@apm.vnit.ac.in.

hollow section. But the behaviour of hollow bridge pier is complex as compared to solid pier and only few studies have been reported in this area. Several areas are yet to be explored for hollow bridge piers. So in this paper, a study on the behaviour of the hollow pier under lateral load and torsional load is done using numerical models.

1 2 3Greata Mariyam Jessy , Mathew C. S. and Ramakant K. Ingle

2. Modelling

Mathematical models were prepared for hollow pier of height 25m having uniform cross section of diameter 3m and 5m, tapered cross section of diameter varying from 3m at top to 5m at bottom. 0.5m wall thickness was considered in all models. The base was taken fixed. Thick shell element with six degrees of freedom at each node was selected for the mathematical model, as considered by Vishwakarma and Ingle[1]. Meshing is done with mesh size 0.25mx0.25m.

Three cases were considered for each model which is shown in Fig. 1. Fig. 1(a) shows model without diaphragm, Fig. 1(b) with diaphragm (thick shell element, 0.3m thick) and Fig. 1(c) with cut diaphragm (constant internal diameter 1.2m). The horizontal diaphragms are provided at 2m interval starting from 2m height and also at 25m.

Finite element analysis is done for uniform and tapered hollow bridge piers using SAP2000[2]. Each bridge model is analysed for lateral force as well as torsion and the results are compared. The results are then compared with analytical method and verified.

Fig. 1 : SAP model (a) without diaphragm, (b) withdiaphragm, and(c) with cut diaphragm

(a) (b) (c)

12Research Scholar, Department. of applied mechanics, VNIT, Nagpur3Professor, Department. of applied mechanics, VNIT, Nagpur

155 JREAS, Vol. 04, Issue 04, Oct 2019ISSN (Print) : 2456-6411, ISSN (Online) : 2456-6403

(a) (b) (c) (d) (e) (f) (g) (h) (i)

Fig. 2 : Mode shapes (a) 3m dia without diaphragm, (b) 3m dia with diaphragm, (c) 3m dia with cut diaphragm,(d) 5m dia without diaphragm, (e) 5m dia with diaphragm, (f) 5m dia with cut diaphragm,

(g) tapered without diaphragm, (h) tapered with diaphragm, and (i) tapered with cut diaphragm

3. Free Vibration Behaviour

The free vibration analysis was done for both uniform and tapered bridge piers. The predominant time period obtained are shown in Table 1 and mode shapes are shown in Fig. 2.

Table 1Predominant Time periods

Case Predominant Time Period (s)

3 m dia

Without Diaphragm 0.327

With Full Diaphragm 0.371

With Cut Diaphragm 0.364

5 m dia

Without Diaphragm 0.204

With Full Diaphragm 0.247

With Cut Diaphragm 0.245

Tapered

Without Diaphragm 0.188

With Full Diaphragm 0.215

With Cut Diaphragm 0.210

It can be seen that the tapered model shows rigid behaviour as compared with uniform (3m or 5m) diameter pier. The results also indicate that provision of diaphragm makes the pier section a little flexible. This behaviour is predominantly because of changed mass of pier. Only self

mass of pier is considered for modal analysis. The results may vary with point mass due to superstructure at the top of the pier.

4. Behaviour Under Lateral Load

As the height of the structure is more lateral forces, especially wind forces are predominant. So it is necessary that the behaviour under lateral load is studied. The models were analysed for lateral load by applying a horizontal load of 100kN at the top of the bridge pier. The tip displacements for all the models were obtained and are presented in Table 2.

Table 2Displacement due to lateral load – SAP results

Case Displacement (mm)

3 m dia

Without Diaphragm 3.635

With Full Diaphragm 3.618

With Cut Diaphragm 3.618

5 m dia

Without Diaphragm 1.096

With Full Diaphragm 0.925

With Cut Diaphragm 0.924

Tapered

Without Diaphragm 1.158

With Full Diaphragm 1.150

With Cut Diaphragm 1.150

156 JREAS, Vol. 04, Issue 04, Oct 2019ISSN (Print) : 2456-6411, ISSN (Online) : 2456-6403

The results indicate that the pier is rigid when 5m diameter section is used as compared to other models as shown in Fig.

3. Also with diaphragm (full or cut) cases indicate less deflection under static load.

Fig. 3 : Displacement due to lateral load

5. Behaviour Under Torsional Load

One of the main forces causing damages during earthquake is the torsional force developed[3]. Torsion mainly affects horizontally curved and skewed bridges. Hence it is important to study the effect of torsional load on the bridge pier. The models were analysed for torsional load in SAP 2000 by loading as shown in Fig. 4.

Fig. 4 : Torsional loading - Plan view

The rotations obtained are summarised in Table 3. A comparison between the results is given in Fig. 5. It can be seen that the rotation for the tapered model falls between the uniform models. Hence it can be concluded that the tapered section is economical considering torsion. Providing diaphragm contributes to the torsional stiffness of the structure

Fig. 5 : Displacement due to torsional load

Table 3Displacement due to torsional load – SAP results

CaseRotation (*10-3

radians)

3 m dia

Without Diaphragm 0.110

With Full Diaphragm 0.107

With Cut Diaphragm 0.106

5 m dia

Without Diaphragm 0.041

With Full Diaphragm 0.044

With Cut Diaphragm 0.040

Tapered

Without Diaphragm 0.054

With Full Diaphragm 0.052

With Cut Diaphragm 0.052

From the study, it can be concluded that tapered hollow section is preferable over uniform hollow section for bridge pier as it provide adequate stiffness along with economy. Also, tapered section is found to provide higher torsional stiffness compared to lower diameter uniform sections. Hence tapered section is superior to the uniform sections.

6. Conclusions

Based on the finite element analysis conducted on the uniform and tapered hollow bridge pier models, the following conclusions can be made:

l Tapered section provides higher lateral and torsional stiffness compared to the uniform section of lower diameter.

l Tapered section can be preferred over uniform sections considering both effectiveness and economy.

l Providing diaphragm increases the lateral and torsional stiffness of the hollow pier. Cut diaphragms are more effective than full diaphraghms.

157 JREAS, Vol. 04, Issue 04, Oct 2019ISSN (Print) : 2456-6411, ISSN (Online) : 2456-6403

References

[1] Vishwakarma R. J. and Ingle, R. K., “Simplified approach for the evaluation of critical stresses in concrete pavement”, Structural Engineering and Mechanics, 61(3), 2017, 389-396.

[2] CSI Analysis Reference Manual for SAP2000, ETABS, SAFE and CSiBridge (California: Computers and Structures, Inc., 2010).

[3] Mondal T. G. and Prakash S. S., “Nonlinear Finite-Element Analysis of RC Bridge Columns under Torsion with and without Axial Compression”, Journal of Bridge Engineering, 21(2), 2015, 04015037-1-13.