Reinforced Concrete Slab

2029EXQ/4 page 1 August 2020 Coventry University Faculty of Engineering, Environment and Computing 2029EXQ Structural Design Instructions to candidates Time allowed: 2 Hours Answer: All q uestions on this paper. The total number of questions in this paper: 4 All questions carry equal marks. Start each question on a new page and carefully identify your answers with the correct question number This is an open book exam. There is no restriction on the extent of books or notes that st udents may use in the examination. page 2 2029EXQ/4 Question 1 : A new mezzanine floor is to be constructed in an existing building. The new floor will be used as an Reading room with no book storage . It will be constructed with a steel frame. A plan of the beam and column layout is shown in Figure Q1 -2: on the next page, and a 3D elevation, shown in Figure Q1 -3: also on the next page. The floor will be constructed with a 140 mm thick reinforced concrete slab , which will be finished with floor tiles to the top surface (assume loading from tiles = 0. 80 kN/m 2). Below t he slab will be a suspended ceiling, and between the underside of the slab and the suspended ceiling will be services (assume a loading of 0.5 kN/m 2 for the total load from the suspended ceiling including services) . A section through the floor construction is shown in Figure Q1 -1: below. Assume the RC slab is one way spanning in the shorter direction as shown on the plan. NOTE: - All Calculations are to be in accordance with BS EN 1990:, BS EN 1991 -1-1: & BS EN 19 93 -1-1: FIGURE Q1 -1: - Section through Floor Construction: a) Calculate the Ultimate Limit State Design Floor Loading. (10 marks) b) Calculate the ULS Design Loads to be supported by Beam A (as labelled on the Figures Q1A -2 & 3:) (5 marks) c) For Beam A calc ulate the ULS Design Shear Forces & Bending Moments, and draw the Shear Force & Bending Moment Diagrams. (10 marks) Total marks: 25 Question 1 continues overleaf… continued… page 3 2029EXQ/4 Question 1 continued… FIGURE Q1 -2: - Beam & Column Plan: (Not to scale). FIGURE Q1 -3: - 3D Elevation of frame. continued… page 4 2029EXQ/4 Question 2: a) A simply supported beam spans 8.0m and supports the Design Loads as shown in Figure Q 2-1: below. The resulting Bending Moments and shear Forces are as shown in Figure Q 2-2: on the following page. Lateral torsional restraints are provided at the pinned supports A & D, and at the point loads (B & C) only , and the beam is Unrestrained between these points. From the Bending Moment Diagram, and using Table 3.2.of NCCI Document SN003b , determine C1 for the section of beam between the point loads B & C. (5 marks) Figure Q 2-1: Question 2 continue d over page … continued… page 5 2029EXQ/4 Question 2 continued… Figure Q 2-2: b) It is proposed that a 406 x 178 x 54kg UB section with a steel grade of S355 will be used to support the Loads. Calculate the Elastic Critical Moment M cr for the beam proposed between points B & C . Note: - All calculations are to be in accordance with Clause 6.3.2.3, for rolled sections, of BS EN 1993. The beam can be assumed to be Class 1, and satisfactory in shear, and web buckling is satisfactory. (10 mar ks) c) With the aid of annotated sketches and in your own words, describe the phenomenon of lateral torsional buckling in steel beams, and outline how this can be prevented or partially prevented from occurring. (10 marks) (Total marks 25) continued… page 6 2029EXQ/4 Question 3: A braced frame as shown in Figure Q3 supports first order design moments, 125 kN.m (positive) at the top and 60 kN.m (negative) at the base. The column is fixed at the base. Additional design axial load of 2500 kN is applicable. Material properties are: fyk = 500 N/mm 2, fck = 32 N/mm 2. Determine the following, stating all necessary assumptions: a) Classify the column 450 mm x 450 mm in cross -section as either short or slender. Comment on your calculation output. Use the relevant tabl e to assess the column end conditions. (8 marks) b) Determine the nominal cover to all sides of the column, assuming the diameters of the shear links and main steel are 8 mm and 25 mm, respectively. The columns are classed under condition XC3/XF1. Fire resistance requirement is to be 2 hours. (5 marks) c) Determine the value of the design moment, MED , and use this in conjunction with the design axial load to calculate the reinforcement required. (12 marks) (Total: 25 marks) FIGURE Q3 Continued page 7 2029EXQ/4 Question 4 Figure Q4 shows a simply supported singly reinforced concrete beam of rectangular cross -section, which is subject to two design point loads, P. The dimensions of the beam are b = 120 mm, and d = 200 mm (all other dimensions are in mm). Steel reinforcement provided to resist bending in the tension zone is As = 402 mm 2. Material properties are: f yk = 500 N/mm 2, fck = 40 N/mm 2. Ignoring the self -weight of the beam and by assuming that only bending reinforcement is present, work from first principles using the stress diagrams in (b) above to establish the following: i) Show that the beam is under -reinforced, by determining the depth of the neutral axis, x, within the beam cross -section. (8 marks) ii) Calculate the lever arm, z, and the maximum bending moment that can be applied to the beam (nothing that it is a singly -reinforced section). (8 marks) iii) Calculate the value of the design loads, P, that can be applied to the beam. (3 marks) iv) Determine the shear capacity of the beam given that the links are 10 mm bars with two legs and are spaced at 200 mm centres. Take θ = 22º. (6 marks) (Total: 25 marks) FIGURE Q4 END