Simplified and Advanced Analysis of Membrane Action of Concrete Slabs

Comparison with the test results showed that the simple method was as accurate as the advanced method for predicting the load-displacement response as the maximum test load is approached. The detail stress distributions obtainable from carrying out an advanced analysis allowed some of the assumptions embodied in the simple analysis to be investigated. It was found, from the advanced analysis, that the formation of compressive membrane action around the perimeter and tensile membrane action in the central region is reasonably represented in the simple approach. It was also found that the assumption in the simple approach of the in-plane compressive forces in the concrete being limited to a depth of 0.45d in the compressive membrane region is reasonable. However, the advanced analysis indicated that assuming a tensile force across the whole slab at the location where fracture of the reinforcement occurs is questionable. The derivation of the simple method is currently being extended and a sensitive study will be presented to quantify the effect of including a defined compressive region at the edges of the slab, in-line with the fracture plane.

The finite-element modeling presented in this paper generally produces good correlation with the measured load-displacement response for each slab up to the test failure load. The prediction of the actual failure load, however, is poor and clearly requires further work. For the case where fracture occurs, this will involve investigating the localized fracture of the reinforcement over a full-depth crack. The authors are currently investigating localized fracture looking at the effects of reinforcement durability, bond between the concrete and reinforcement, and the fracture energy of the concrete. In addition, once the bond is accurately represented, the advanced model can be extended to investigate slabs reinforced with individual bars. In the case of compression failure, the biaxial modeling of the concrete will be further investigated to obtain better estimates of the failure load.

The tests presented in this paper, together with the simple and advanced analysis, did not take long-term effects into account such as creep and shrinkage, which may reduce the membrane capacity of the slab when catastrophic loads occur. Further work is required to quantify the effects of long-term effects on membrane action of slabs.

NOTATION

a = aspect ratio (L/l)

b = parameter defining magnitude of membrane force

d = average effective depth of reinforcement

d^sup 1^, d^sup 2^ = effective depth of reinforcement

E = elastic modulus of reinforcement

e = enhancement of yield-line load due to membrane action

e^sup 1b^, e^sup 2b^ = enhancement due to bending action for Element 1 and 2

e^sup 1m^, e^sup 2m^ = enhancement due to membrane forces for Element 1 and 2

f^sup ck^ = compressive cylinder strength of concrete

f^sup cu^ = compressive cube strength of concrete

f^sup t^ = tensile strength of concrete

f^sup y^ = yield strength of reinforcement