Advanced Structural Design
Problem 1: The concrete slab shown in Figure 1 is subjected to the ultimate uniformly distributed load of q(kN/m2 ). The positive moments per unit length of the slab in X and Y directions perpendicular to the reinforcement are assumed to be 20kNm/m and 12kNm/m, respectively. Moreover, the values of the negative moments in X and Y directions are 30kNm/m and 15kNm/m. Using yield line theory, determine the collapse load q.
Problem 2: It is often preferable to place the reinforcement parallel to the edges of the skew slab to avoid excessive cutting of bars to different lengths. Consequently, the limiting moments are considered perpendicular to slab edges. The skew slab OPQR shown in Figure 1 is subjected to the ultimate uniformly distributed load of 20kN/m2 . The positive moments per unit length of the slab in X and Y directions perpendicular to the reinforcement are assumed to be 1.0 m and 0.8m, respectively. Moreover, the values of the negative moments in X and Y directions are 1.33 times the corresponding values of the positive moments. Using yield line theory, determine the magnitude of m. Hint: You may need to research to find how the yield line theory can be employed for skew slabs. Research papers, textbooks, etc are recommended.
