Simplified and Advanced Analysis of Membrane Action of Concrete Slabs

When comparing the simple method against the test results, Slabs M2, M11, and M12 were governed by compressive failure, whereas all the other tests were governed by tensile fracture. For the tensile mode of failure, the in-plane forces in the simple method are defined by the constant b given by Eq. (3). In deriving this equation, it is assumed that the in-plane forces are tensile across the full width of the slab with the compressive force being concentrated over a very small area near the edge of the slab (Fig. 9). For Slab M1, however, the advanced method shows that a greater proportion of the slab is in compression across the assumed fracture line (short span axis of symmetry in Fig. 17) suggesting that the assumption taken in the simple method needs to be addressed. To assess the impact of revising the assumption relating to the extent of the in-plane compressive force resisting the in-plane tensile force along the assumed fracture line, the derivation of the simple method will need extending and a sensitivity study conducted. This is currently being carried out by the authors.

For the compressive mode of failure, the in-plane forces in the simple method are defined by the constant b given by Eq. (5). In deriving this equation, it is assumed that the maximum compressive stress block through the depth of the slab is limited to 0.45d. To check this assumption against the advanced analysis, the principal stresses in the concrete at locations across the diagonal of the slab are shown in Fig. 19. It can be seen that limiting the depth of compressive stress, developed from bending and in-plane membrane forces, to 0.45d is a reasonable assumption. The same conclusion was reached considering the stress distribution in all the other slabs.

It should be noted that neither the simple nor the advanced method predicts failure accurately, with the test results diverging from the predictions during the latter stages of the test (Fig. 14 to 16). Further investigation into modeling actual failure, comprising of fracture of the reinforcement over a localized crack, is currently underway by the authors. This involves considering in more detail the ductility of the reinforcement, bond between the concrete and reinforcement, and the fracture energy of the concrete.

The previous method by Bailey,15 however, provided a very simplified prediction of the maximum vertical displacement, which at ambient temperature was given by

... (18)

The predicted maximum displacement is shown in Table 2, together with the predicted load capacity at this displacement. Comparison with the maximum test load shows that Eq. (18) is conservative and acceptable for design purposes until further research work is conducted.

CONCLUSIONS

A simple analytical method and an advanced analysis, using finite element software was used to model the 14 horizontally-unrestrained concrete slab tests carried out at The University of Manchester. Both the simple and advanced analysis incorporated membrane action, comprising compressive membrane action around the perimeter, and tensile membrane action in the central region. The simple method was based on rigid plastic behavior with the effects of change in geometry included. The load-displacement response from the simple method forms a failure envelope with the test results merging toward the predicted response when good correlation was observed. For the advanced analysis, the slab's response was predicted over the full load-displacement history of the test results.