Simplified and Advanced Analysis of Membrane Action of Concrete Slabs

Although the advanced model predicts the load-displacement response well during the early stages of Slabs M1 (Fig. 14) and M2 (Fig. 15), the comparison is not so good toward the end of the test.

In the case of Slabs M3 and M4 (Fig. 16(a)), where the mesh size was 0.059 in. (1.51 mm) in diameter at 1.0 in. (25.4 mm) spacing, both the simple and advance methods merge together with an increase in displacement, but are both overpredicting the load capacity compared with the test. For Slabs M5 and M6 (Fig. 16(b)), where the mesh size was 0.058 in. (1.48 mm) in diameter at 0.5 in. (12.7 mm) spacing, both the simple and advanced methods provide excellent predictions compared with the test results. For Slabs M7 and M8 (Fig. 16(c)), where the mesh size was 0.033 in. (0.84 mm) in diameter at 0.5 in. (12.7 mm) spacing, the simple method provides excellent results. For Slab M7, the advanced prediction produces good correlation with the tests results, whereas for Slab M8, the correlation was not so good. For Slabs M9 and M10 (Fig. 16(d)), where the mesh size was 0.026 in. (0.67 mm) in diameter at 0.25 in. (6.35 mm) spacing, both the simple and advanced methods produce poor correlation to the test results, although for Slab M9, both methods produce similar predictions in load capacity between 1.969 and 2.756 in. (50 and 70 mm) displacement. For Slabs M11 and M12 (Fig. 16(e)), where the mesh size was 0.095 in. (2.42 mm) in diameter at 2 in. (50.8 mm) spacing with an increased cover of 0.354 in. (9 mm) (Table 1), the simple method provides good correlation to the test results, whereas the advanced method overpredicts the load carrying capacity. For Slabs M13 and M14 (Fig. 16(f)), where the mesh size was 0.095 in. (2.42 mm) in diameter at 2.0 in. (50.8 mm) spacing with an increased cover of 0.354 in. (9 mm) and increased overall thickness (Table 1), the simple and advanced methods merge and provide excellent correlation against Slab M13, but overpredict the load capacity for Slab M14.

When comparing Slabs M13 and M14 with Slabs M1 and M2, where the difference is due to the slab's thickness and cover to the mesh reinforcement (Table 1), it can be seen that the thicker slabs (M13 and M14) have a higher failure load but a lower enhancement (maximum test load/yield-line load) value. This suggests that as the slab gets thicker, the mobilization of membrane action becomes lower.

Considering the comparison between the test results, simple method and advanced method, for the 14 tests (Fig. 14 to 16), it can be seen that the simple method predicts the load displacement response as well as, or better than, the advanced analyses, within the limitations imposed by assuming rigid-plastic behavior with a change of geometry. The advanced method, however, has the advantage of predicting the response over the full load-displacement history of the test.

There are a few assumptions relating to stress patterns within the simple model that can be checked using the advanced analyses. In the first instance, the distribution of inplane stresses (Fig. 8) is assumed to comprise compression around the perimeter and tension in the center. The tractions from the advanced model, defined as the resultant force over the depth of the slab (based on principal stress), are shown in Fig. 17 for the rectangular Slab M1 and in Fig. 18 for the square Slab M2. These tractions correspond to a load of 391.69 lbf/ft^sup 2^ (18.75 kN/m^sup 2^) for Slab M1 and 563.19 lbf/ft^sup 2^ (26.96 kN/m^sup 2^) for Slab M2, and confirm the basic assumed in-plane stress pattern adopted for the simple method.