Collings R&DMaking the complex simple

A Review of Arching and Compressive Membrane Action (CMA) in Concrete Bridges

Summary presentation of a paper published in ICE Proceedings; Bridge Engineering; December 2016.

The full paper can be read at http://www.icevirtuallibrary.com/doi/10.1680/bren.14.00039 

Authors

David Collings BSc CEng FICE

Juan Sagaseta Eur Ing, PhD, DIC, CEng, MICE,

MCICCP,  

Collings R&DMaking the complex simple

Abstract

This presentation contains a summary of the recent Compressive Membrane Action review paper by Collings and Sagaseta (Ref 1). It also summarises some of the test data outlined in a recent conference paper (Ref 2). The author has recently used CMA in the assessment of major box girder decks (Ref 3), some data on this is also presented.

The presentation is produced as part of a research project by Collings R&D and University of Surrey with support ICE R&D fund entitled ‘Arching action in structures, visualisation, simplification, extension and developments of practical methods for design’.

Introduction

It is over a century ago that testing of reinforced concrete slabs by pioneers of the material such as Robert Maillart showed that restrained slabs could carry significant loads. Since that time the interest in and knowledge of arching action or compressive membrane action (CMA) has waxed and waned.

An early load test on an RC slab by Maillart.

DefinitionArching Action; where loads are transmitted by compression within the structure. Depending on the shape and form of the structure this arching action may be from geometric arching action, compressive membrane action, or both.

In 1956 McDowell, et al. outlined a theory for the strength enhancement of masonry due to CMA. It assumed the slab or jammed between end restraints.

Theory

In 1963 Christiansen outlined the relative capacity due to arching (see equation), allowing the arching (PA) and bending (PB) components to be compared. Comparison of restrained and unrestrained tests clearly show the arching component.

PA = Pmax – PB

In the 1940’s, 1950’s and 1960’s various tests on bridge decks were carried out. In 1971 a series of papers on CMA were published in a special edition of ACI journal. Further tests led to the incorporation of rules for the use of CMA in bridge decks in a Canadian Code (OMTC 1979).

Testing

Over the years many tests have been carried out. Most exceeding the theoretical bending strength.

If the data is sorted by the reported failure type some separation between the flexural-CMA failure and punching shear failure is evident.

If the data is normalised against the concrete capacity the separation of failure types is clearer, the flexural-CMA failure tending to be above the line and the punching below. The equation for the line is:

P/Pc = (1 - δ / h )2

There is a similar split if the data is sorted by the loading type:

Slabs loaded with a heavy wheel tend to fail by punching.

Slabs loaded with UDL tend to fail in CMA-flexure.

There is less data on the axial internal arch thrust, however measurements confirm that the data is within the theoretical limits. Again there is some separation with those tests failing in punching shear achieving lower membrane forces.

Finite Element analysis (FEA) of restrained slabs was started in the 1970’s. Fujii (1981) and Lahlouh and Waldron (1992) used FEA to visualise the principal compressive stress distribution and directions of the CMA in their tests.

Stress trajectory plots from NL-FEA (above) give a good insight into the behaviour of restrained slabs with CMA.

Finite Element Analysis

It is important to verify NL-FEA with test data, the strip tests of Taylor, et al. provide a good range of tests for verification.

Modern layered shell NL-FEA with simple bi-linear materials similar to Eurocode 2 give reasonable estimates of behaviour.

Punching shear is a common failure mechanism, normal code methods (AASHTO and EC2) give very conservative predictions. The BD81 and FIP methods give better results compared with tests.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.050.1

0 5 10 15 20 25 30 35 40 45

The FEA method is an important tool, however, their complex formulation can cause difficulties in practice.

The methods included in design and assessment codes adopt simplifications, one example is the strut-and-tie method.

Polytechnic University of Valencia has developed a method to analyze strut and tie systems. Extended to CMA the method gives a good indication of the load-deflection profile and a good visualization of the internal arching.

In real structures such as box girders the behaviour is more complex than in the simple slab tests. The membrane forces are complicated by frame action and the arching from the haunched shape.

Modeling the true arched geometry as recommended by SETRA (2007) and El-Mezaini, et al. (1991) using a frame strip or 3D model will give a good estimation of these other membrane forces.

Box Girders

Tests by Choi and Oh (2013) showed membrane effects in box girders enhanced their load capacity. Re-analysis indicates that the frame action and geometric arching dominate at serviceability with CMA increasing as rotations increase near ultimate load.

Box girder test at MARA University of Technology, Malaysia.

Codes using CMA are generally empirical, giving geometric limits for CMA.

Requirement AASHTO BD81 Test Data

Min depth h 175 mm 160 mm 50 mm

Max span L 4.1 m 3.7 m 5.75mMax Span to depth ratio L/h 18 15 60

Min total reinforcement 950 mm2/m 750 mm2/m

Min concrete strength 28 MPa Varies with L/h 18 MPa

Max concrete strength 70 MPa 100 MPaRequirement for global analysis

Only for torsionaly stiff cross sections For all situations

Eurocode 2 does not specifically mention CMA!

The span to depth ratio limits of 15-18 in current codes are conservative, significant CMA occurs in structures with L/h =30

Recent tests show some CMA in structures with L/h of 50

In modern codes the serviceability limit state is often a governing criteria. Tests confirm CMA reduces crack widths and reduces deflections

Summary• Extensive testing shows the type of load has a

big effect on failure type;

• CMA is useful in structures with greater slenderness than currently defined in codes;

• Modern NL-FEA using EC2 concrete material models can give a good estimate of CMA at SLS and ULS.

Collings R&DMaking the complex simple

References 1. Collings D and Sagaseta J, A Review of Arching and Compressive Membrane Action in Concrete Bridges, Proc ICE BE 169, Dec 2016, http://www.icevirtuallibrary.com/doi/10.1680/bren.14.00039

2. Collings D and Sagaseta J, Analysis of a test Database for RC Structures and CMA, European Bridge Conference, Edinburgh 2015.

3. Zaid A, Collings D, Transverse assessment of a concrete box girder bridge, Proc ICE BE 169, Dec 2016, http://www.icevirtuallibrary.com/doi/abs/10.1680/jbren.15.00018