ANALYSIS OF PRE-CAST WAFFLE SLABS USING YIELD LINE AND RANKINE GRASHOFF THEORIES

Abstract

Failure in pre-cast waffle slabs can be attributed to factors like analytical error, poor handling during transportation and placement which factors often lead to partial/total failure of slabs. The conventional method of analysing waffle slabs focuses on the ribs, while the slab portions at the top are avoided. This has led to under reinforcement and subsequent failure of the slab portions that are usually in direct contact with loads. In this study, a method that incorporates both the slab and rib portions in the analysis of pre-cast waffle slabs was therefore developed. Yield Line and Rankine Grashoff Theories (YLRGT) were combined for the analysis of pre-cast waffle slab. Six physical models of waffle slab were developed, each having five replicates, with the following dimensions: W1 (1353 x 430 x 58 mm), W2 (900 x 300 x 50 mm), W3 (1085 x 430 x 58 mm), W4 (407 x 364 x 50 mm), W5 (1312 x 300 x 58 mm) and W6 (860 x 360 x 50mm). Solid slabs of the same size and number designated S1, S2, S3, S4, S5 and S6 served as control. These models were validated using the slabs by testing for failure loads, deflections and crack width. Each slab was subjected to incremental load of 1.0 kN until failure occurred. Maximum bending moments were obtained for slab and rib portions using YLRGT, a finite element based method called ETABS was also used to analyse the slabs and results obtained were subjected to statistical analysis using ANOVA at p= 0.05. The YLRGT analysis of the various physical models (slab portion, transverse and longitudinal ribs) yielded the following bending moments: W1 (5526.0, 34.5, 918.3) Nm, W2 (1122.0, 279.2, 36.5) Nm, W3 (2880.0, 27.2, 619.9) Nm, W4 (590.0, 171.9, 160.9) Nm, W5 (947.0, 37.0, 4.4) Nm and W6 (1276.0, 90.4, 36.2) Nm respectively. The ETABS combined both slab and ribs giving W1 (4729.0) Nm, W2 (581.0) Nm, W3 (3338.0) Nm, W4 (733.0) Nm, W5 (851.0) Nm and W6 (686.0) Nm. Deflections at failure for waffle slab were smaller compared to solid slabs: (W1 = 1.19 and S1 =3.56) mm, (W2 = 3.64 and S2 =9.28) mm, (W3 = 3.90 and S3 =7.44) mm, (W5 = 8.17 and S5 =12.18) mm, (W6 = 3.29 and S6 =3.89) mm with the exception of W4 (6.60 mm) and S4 (6.44mm), where deflection of waffle slab was higher than that of solid slab. Mean deflection of S1 was significantly higher than W1, while S2 was significantly higher than W2. Average crack width for waffle (0.48 mm) and solid slabs (0.99 mm) were significantly different. High crack width in solid slab indicated lower shear strength. The Yield Line and Rankine Grashoff Theories have facilitated the accurate analysis of pre-cast waffle slabs by separating the slab and rib portions.