Question

The following figure 1(a) shows a part of a reinforced concrete building in a school. The structure consists of precast concrete hollow slabs that rests on the 10.8m long two reinforced concrete beams. The beams are supported on reinforced concrete columns. It is given that, on the top surface of the hollow slab, there will be a concrete screed with 50 mm thickness (assume density of concrete screed is 25 kN/m). In addition, there will be tiles that weigh 0.05 kN/m. It is given that self-weight of reinforced concrete hollow slab is 367 kg/m. a) Calculate the characteristic permanent load and variable load on the precast concrete hollow slab per m². b) Calculate the characteristic permanent load and characteristic variable load on beam AB Consider the weight of beam AB. c) Calculate the partial factor of safety using e. 6.10a and e.q 6.10b for beam AB at the Ultimate Limit State. d) Calculate and draw design bending moment and shear diagrams for all possible load arrangements on beam AB. Precast Concrete hollow slab Precast Concrete hollow slab Column Beam AB beam 2.8m Figure 1: (a) Front and end elevations of the part of a concrete building in a school

Answer 1

Given length of beam = 10.8m. density of Concrete screed - 25KN/m3 Concrete screed thickness = somm -0.05 m weight of tiles = 0.05kN/m2 Self weight of RC hollow slab is 367 kg/en? k 8m - k 2.8m (a) Calculate the characteristic permanent land and variable load on the precast Concrete hallaw slab per m² characteristic permanent laad due to self weight and weight of tiles 367x9.81 N/m2 + 0.05x10²N/m² 4.1 kN/m²

Variable laad due to concrete screed. - 0.05 x 25x103 N/m2 2 1250N/m² = 1.25 kN/m² (6) self weight of beam 350mm Soomm 0:35*0.5210-8 * 25 KN assuming density of Concrete = 47.25 KN 125kN/m3 S Total weight on Beam AB - 4.14103 / 1018 10 m 2 (There are two beam). + 47.25x 103N = 268.65 KN Permanent load = 268.65KN. Variable load a 1.25x 10x10.8 KN = 135KN.

(C) Partial factor of safety for eat beam AB is 1.5 because it must be designed for Persistent and transient situations. a deal diagram for Beam AB 2.8m Total land on beam = 268.65 + 135 KN = 403.65 EN laad per unit length - 403.65/100 KN/m - 37.375 kN/m 10.8 w = 37.375 kN/m 8m 12.8m A4 By Ay+ By = 403.65 Byx 8 = 403.65 x 514 By = 272.46 KN

By = 272.46 KN Ay = 403.65-272.46 Kn = 131119 KN olx=8m V = 131.19 – wa Ve=131-19 - 37,375 % Mx = 131.19x - 37.375 e² &nk x 3 10. 8m x = 131-19 +272.46 - 37.3750 x = 403.65-37.3752

Mx = 131198 + 272.46 (x-8) – 37.315x² 2 Mar 403.65x – 18.6875x² – 2179.68 Man a 230.23 kNm 146.51 KNM [131.19 KN 104,65 KN 1.51m 167.81 KN